LMFDB - Embedded newform 324.3.f.p.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, not 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.207360000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.2
Root			$1.14412 + 1.98168i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.p.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58114 + 1.22474i) q^{2} +(1.00000 - 3.87298i) q^{4} +(-0.540182 - 0.935622i) q^{5} +(-5.20820 - 3.00696i) q^{7} +(3.16228 + 7.34847i) q^{8} +O(q^{10})$	\(q+(-1.58114 + 1.22474i) q^{2} +(1.00000 - 3.87298i) q^{4} +(-0.540182 - 0.935622i) q^{5} +(-5.20820 - 3.00696i) q^{7} +(3.16228 + 7.34847i) q^{8} +(2.00000 + 0.817763i) q^{10} +(15.3500 + 8.86234i) q^{11} +(-6.20820 - 10.7529i) q^{13} +(11.9176 - 1.62430i) q^{14} +(-14.0000 - 7.74597i) q^{16} -26.3786 q^{17} +5.19615i q^{19} +(-4.16383 + 1.15649i) q^{20} +(-35.1246 + 4.78727i) q^{22} +(-25.8384 + 14.9178i) q^{23} +(11.9164 - 20.6398i) q^{25} +(22.9856 + 9.39840i) q^{26} +(-16.8541 + 17.1643i) q^{28} +(-2.16073 + 3.74249i) q^{29} +(-38.8328 + 22.4201i) q^{31} +(31.6228 - 4.89898i) q^{32} +(41.7082 - 32.3070i) q^{34} +6.49721i q^{35} -20.4164 q^{37} +(-6.36396 - 8.21584i) q^{38} +(5.16718 - 6.92820i) q^{40} +(-29.6197 - 51.3028i) q^{41} +(-16.5836 - 9.57454i) q^{43} +(49.6737 - 50.5880i) q^{44} +(22.5836 - 55.2326i) q^{46} +(-35.5617 - 20.5315i) q^{47} +(-6.41641 - 11.1135i) q^{49} +(6.43702 + 47.2290i) q^{50} +(-47.8541 + 13.2913i) q^{52} -70.0430 q^{53} -19.1491i q^{55} +(5.62675 - 47.7812i) q^{56} +(-1.16718 - 8.56373i) q^{58} +(25.0733 - 14.4761i) q^{59} +(-9.20820 + 15.9491i) q^{61} +(33.9411 - 83.0096i) q^{62} +(-44.0000 + 46.4758i) q^{64} +(-6.70711 + 11.6171i) q^{65} +(82.1656 - 47.4383i) q^{67} +(-26.3786 + 102.164i) q^{68} +(-7.95743 - 10.2730i) q^{70} +83.8931i q^{71} +55.8328 q^{73} +(32.2812 - 25.0049i) q^{74} +(20.1246 + 5.19615i) q^{76} +(-53.2974 - 92.3137i) q^{77} +(35.5426 + 20.5205i) q^{79} +(0.315246 + 17.2829i) q^{80} +(109.666 + 44.8403i) q^{82} +(-30.7000 - 17.7247i) q^{83} +(14.2492 + 24.6804i) q^{85} +(37.9473 - 5.17199i) q^{86} +(-16.5836 + 140.824i) q^{88} -26.3786 q^{89} +74.6712i q^{91} +(31.9380 + 114.990i) q^{92} +(81.3738 - 11.0908i) q^{94} +(4.86163 - 2.80687i) q^{95} +(-38.1656 + 66.1048i) q^{97} +(23.7565 + 9.71359i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 12 q^{7}+O(q^{10}) $ 8 * q + 8 * q^4 + 12 * q^7	$ 8 q + 8 q^{4} + 12 q^{7} + 16 q^{10} + 4 q^{13} - 112 q^{16} - 120 q^{22} - 12 q^{25} - 108 q^{28} - 96 q^{31} + 280 q^{34} - 56 q^{37} + 256 q^{40} - 240 q^{43} + 288 q^{46} + 56 q^{49} - 356 q^{52} - 224 q^{58} - 20 q^{61} - 352 q^{64} + 228 q^{67} + 312 q^{70} + 232 q^{73} + 660 q^{79} + 448 q^{82} - 208 q^{85} - 240 q^{88} + 168 q^{94} + 124 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 + 12 * q^7 + 16 * q^10 + 4 * q^13 - 112 * q^16 - 120 * q^22 - 12 * q^25 - 108 * q^28 - 96 * q^31 + 280 * q^34 - 56 * q^37 + 256 * q^40 - 240 * q^43 + 288 * q^46 + 56 * q^49 - 356 * q^52 - 224 * q^58 - 20 * q^61 - 352 * q^64 + 228 * q^67 + 312 * q^70 + 232 * q^73 + 660 * q^79 + 448 * q^82 - 208 * q^85 - 240 * q^88 + 168 * q^94 + 124 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.58114	+	1.22474i	−0.790569	+	0.612372i
$2$	−1.58114	+	1.22474i	−0.790569	+	0.612372i
$3$		0			0
$3$		0			0
$4$	1.00000	−	3.87298i	0.250000	−	0.968246i
$5$	−0.540182	−	0.935622i	−0.108036	−	0.187124i	0.806938	−	0.590636i	$-0.201123\pi$
$5$	−0.540182	−	0.935622i	−0.108036	−	0.187124i	−0.914975	+	0.403511i	$0.867790\pi$
$6$		0			0
$7$	−5.20820	−	3.00696i	−0.744029	−	0.429565i	0.0795033	−	0.996835i	$-0.474667\pi$
$7$	−5.20820	−	3.00696i	−0.744029	−	0.429565i	−0.823532	+	0.567269i	$0.808000\pi$
$8$	3.16228	+	7.34847i	0.395285	+	0.918559i
$9$		0			0
$10$	2.00000	+	0.817763i	0.200000	+	0.0817763i
$11$	15.3500	+	8.86234i	1.39546	+	0.805667i	0.993912	−	0.110173i	$-0.0351404\pi$
$11$	15.3500	+	8.86234i	1.39546	+	0.805667i	0.401544	+	0.915840i	$0.368474\pi$
$12$		0			0
$13$	−6.20820	−	10.7529i	−0.477554	−	0.827148i	0.522115	−	0.852875i	$-0.325143\pi$
$13$	−6.20820	−	10.7529i	−0.477554	−	0.827148i	−0.999669	+	0.0257271i	$0.991810\pi$
$14$	11.9176	−	1.62430i	0.851261	−	0.116022i
$15$		0			0
$16$	−14.0000	−	7.74597i	−0.875000	−	0.484123i
$17$	−26.3786			−1.55168			−0.775841	−	0.630929i	$-0.782674\pi$
$17$	−26.3786			−1.55168			−0.775841	+	0.630929i	$0.782674\pi$
$18$		0			0
$19$			5.19615i			0.273482i	0.990607	+	0.136741i	$0.0436628\pi$
$19$			5.19615i			0.273482i	−0.990607	+	0.136741i	$0.956337\pi$
$20$	−4.16383	+	1.15649i	−0.208191	+	0.0578246i
$21$		0			0
$22$	−35.1246	+	4.78727i	−1.59657	+	0.217603i
$23$	−25.8384	+	14.9178i	−1.12341	+	0.648600i	−0.942269	−	0.334857i	$-0.891312\pi$
$23$	−25.8384	+	14.9178i	−1.12341	+	0.648600i	−0.181140	+	0.983457i	$0.557979\pi$
$24$		0			0
$25$	11.9164	−	20.6398i	0.476656	−	0.825593i
$26$	22.9856	+	9.39840i	0.884062	+	0.361477i
$27$		0			0
$28$	−16.8541	+	17.1643i	−0.601932	+	0.613012i
$29$	−2.16073	+	3.74249i	−0.0745078	+	0.129051i	−0.900872	−	0.434085i	$-0.857072\pi$
$29$	−2.16073	+	3.74249i	−0.0745078	+	0.129051i	0.826364	+	0.563136i	$0.190405\pi$
$30$		0			0
$31$	−38.8328	+	22.4201i	−1.25267	+	0.723230i	−0.971639	−	0.236468i	$-0.924010\pi$
$31$	−38.8328	+	22.4201i	−1.25267	+	0.723230i	−0.281032	+	0.959698i	$0.590677\pi$
$32$	31.6228	−	4.89898i	0.988212	−	0.153093i
$33$		0			0
$34$	41.7082	−	32.3070i	1.22671	−	0.950207i
$35$			6.49721i			0.185635i
$36$		0			0
$37$	−20.4164			−0.551795			−0.275897	−	0.961187i	$-0.588975\pi$
$37$	−20.4164			−0.551795			−0.275897	+	0.961187i	$0.588975\pi$
$38$	−6.36396	−	8.21584i	−0.167473	−	0.216206i
$39$		0			0
$40$	5.16718	−	6.92820i	0.129180	−	0.173205i
$41$	−29.6197	−	51.3028i	−0.722431	−	1.25129i	−0.960023	−	0.279922i	$-0.909691\pi$
$41$	−29.6197	−	51.3028i	−0.722431	−	1.25129i	0.237592	−	0.971365i	$-0.423642\pi$
$42$		0			0
$43$	−16.5836	−	9.57454i	−0.385665	−	0.222664i	0.294615	−	0.955616i	$-0.404809\pi$
$43$	−16.5836	−	9.57454i	−0.385665	−	0.222664i	−0.680280	+	0.732952i	$0.738142\pi$
$44$	49.6737	−	50.5880i	1.12895	−	1.14973i
$45$		0			0
$46$	22.5836	−	55.2326i	0.490948	−	1.20071i
$47$	−35.5617	−	20.5315i	−0.756631	−	0.436841i	0.0714537	−	0.997444i	$-0.477236\pi$
$47$	−35.5617	−	20.5315i	−0.756631	−	0.436841i	−0.828085	+	0.560603i	$0.810570\pi$
$48$		0			0
$49$	−6.41641	−	11.1135i	−0.130947	−	0.226807i
$50$	6.43702	+	47.2290i	0.128740	+	0.944580i
$51$		0			0
$52$	−47.8541	+	13.2913i	−0.920271	+	0.255603i
$53$	−70.0430			−1.32157			−0.660783	−	0.750577i	$-0.729776\pi$
$53$	−70.0430			−1.32157			−0.660783	+	0.750577i	$0.729776\pi$
$54$		0			0
$55$		−	19.1491i		−	0.348165i
$56$	5.62675	−	47.7812i	0.100478	−	0.853235i
$57$		0			0
$58$	−1.16718	−	8.56373i	−0.0201239	−	0.147651i
$59$	25.0733	−	14.4761i	0.424971	−	0.245357i	−0.272231	−	0.962232i	$-0.587761\pi$
$59$	25.0733	−	14.4761i	0.424971	−	0.245357i	0.697202	+	0.716875i	$0.254428\pi$
$60$		0			0
$61$	−9.20820	+	15.9491i	−0.150954	+	0.261460i	−0.931578	−	0.363540i	$-0.881568\pi$
$61$	−9.20820	+	15.9491i	−0.150954	+	0.261460i	0.780624	+	0.625001i	$0.214901\pi$
$62$	33.9411	−	83.0096i	0.547438	−	1.33887i
$63$		0			0
$64$	−44.0000	+	46.4758i	−0.687500	+	0.726184i
$65$	−6.70711	+	11.6171i	−0.103186	+	0.178724i
$66$		0			0
$67$	82.1656	−	47.4383i	1.22635	−	0.708035i	0.260088	−	0.965585i	$-0.416249\pi$
$67$	82.1656	−	47.4383i	1.22635	−	0.708035i	0.966265	+	0.257550i	$0.0829152\pi$
$68$	−26.3786	+	102.164i	−0.387920	+	1.50241i
$69$		0			0
$70$	−7.95743	−	10.2730i	−0.113678	−	0.146757i
$71$			83.8931i			1.18159i	0.806821	+	0.590797i	$0.201186\pi$
$71$			83.8931i			1.18159i	−0.806821	+	0.590797i	$0.798814\pi$
$72$		0			0
$73$	55.8328			0.764833			0.382417	−	0.923990i	$-0.375092\pi$
$73$	55.8328			0.764833			0.382417	+	0.923990i	$0.375092\pi$
$74$	32.2812	−	25.0049i	0.436232	−	0.337904i
$75$		0			0
$76$	20.1246	+	5.19615i	0.264798	+	0.0683704i
$77$	−53.2974	−	92.3137i	−0.692173	−	1.19888i
$78$		0			0
$79$	35.5426	+	20.5205i	0.449906	+	0.259753i	0.707790	−	0.706422i	$-0.249692\pi$
$79$	35.5426	+	20.5205i	0.449906	+	0.259753i	−0.257885	+	0.966176i	$0.583025\pi$
$80$	0.315246	+	17.2829i	0.00394057	+	0.216037i
$81$		0			0
$82$	109.666	+	44.8403i	1.33739	+	0.546833i
$83$	−30.7000	−	17.7247i	−0.369880	−	0.213550i	0.303526	−	0.952823i	$-0.401836\pi$
$83$	−30.7000	−	17.7247i	−0.369880	−	0.213550i	−0.673406	+	0.739273i	$0.735169\pi$
$84$		0			0
$85$	14.2492	+	24.6804i	0.167638	+	0.290357i
$86$	37.9473	−	5.17199i	0.441248	−	0.0601394i
$87$		0			0
$88$	−16.5836	+	140.824i	−0.188450	+	1.60028i
$89$	−26.3786			−0.296389			−0.148194	−	0.988958i	$-0.547346\pi$
$89$	−26.3786			−0.296389			−0.148194	+	0.988958i	$0.547346\pi$
$90$		0			0
$91$			74.6712i			0.820563i
$92$	31.9380	+	114.990i	0.347152	+	1.24989i
$93$		0			0
$94$	81.3738	−	11.0908i	0.865679	−	0.117987i
$95$	4.86163	−	2.80687i	0.0511751	−	0.0295460i
$96$		0			0
$97$	−38.1656	+	66.1048i	−0.393460	+	0.681493i	−0.992903	−	0.118924i	$-0.962055\pi$
$97$	−38.1656	+	66.1048i	−0.393460	+	0.681493i	0.599443	+	0.800417i	$0.295389\pi$
$98$	23.7565	+	9.71359i	0.242413	+	0.0991183i
$99$		0			0
$100$	−68.0213	−	66.7919i	−0.680213	−	0.667919i
$101$	−36.1019	+	62.5302i	−0.357444	+	0.619111i	−0.987533	−	0.157412i	$-0.949685\pi$
$101$	−36.1019	+	62.5302i	−0.357444	+	0.619111i	0.630089	+	0.776523i	$0.283018\pi$
$102$		0			0
$103$	−50.2082	+	28.9877i	−0.487458	+	0.281434i	−0.723519	−	0.690304i	$-0.757477\pi$
$103$	−50.2082	+	28.9877i	−0.487458	+	0.281434i	0.236061	+	0.971738i	$0.424143\pi$
$104$	59.3855	−	79.6245i	0.571014	−	0.765620i
$105$		0			0
$106$	110.748	−	85.7848i	1.04479	−	0.809290i
$107$			64.4015i			0.601883i	0.953643	+	0.300942i	$0.0973009\pi$
$107$			64.4015i			0.601883i	−0.953643	+	0.300942i	$0.902699\pi$
$108$		0			0
$109$	−43.1672			−0.396029			−0.198015	−	0.980199i	$-0.563449\pi$
$109$	−43.1672			−0.396029			−0.198015	+	0.980199i	$0.563449\pi$
$110$	23.4527	+	30.2774i	0.213207	+	0.275249i
$111$		0			0
$112$	49.6231	+	82.4400i	0.443063	+	0.736071i
$113$	40.6482	+	70.4048i	0.359719	+	0.623051i	0.987914	−	0.155005i	$-0.0495392\pi$
$113$	40.6482	+	70.4048i	0.359719	+	0.623051i	−0.628195	+	0.778056i	$0.716206\pi$
$114$		0			0
$115$	27.9149	+	16.1166i	0.242738	+	0.140145i
$116$	12.3339	+	12.1109i	0.106326	+	0.104405i
$117$		0			0
$118$	−21.9149	+	53.5971i	−0.185719	+	0.454212i
$119$	137.385	+	79.3193i	1.15450	+	0.666549i
$120$		0			0
$121$	96.5820	+	167.285i	0.798199	+	1.38252i
$122$	−4.97410	−	36.4954i	−0.0407713	−	0.299143i
$123$		0			0
$124$	48.0000	+	172.819i	0.387097	+	1.39370i
$125$	−52.7572			−0.422057
$126$		0			0
$127$		−	191.968i		−	1.51156i	−0.654826	−	0.755780i	$-0.727258\pi$
$127$		−	191.968i		−	1.51156i	0.654826	−	0.755780i	$-0.272742\pi$
$128$	12.6491	−	127.373i	0.0988212	−	0.995105i
$129$		0			0
$130$	−3.62306	−	26.5827i	−0.0278697	−	0.204482i
$131$	−122.800	+	70.8987i	−0.937406	+	0.541211i	−0.889146	−	0.457623i	$-0.848701\pi$
$131$	−122.800	+	70.8987i	−0.937406	+	0.541211i	−0.0482596	+	0.998835i	$0.515367\pi$
$132$		0			0
$133$	15.6246	−	27.0626i	0.117478	−	0.203478i
$134$	−71.8154	+	175.639i	−0.535936	+	1.31074i
$135$		0			0
$136$	−83.4164	−	193.842i	−0.613356	−	1.42531i
$137$	43.8893	−	76.0185i	0.320360	−	0.554880i	−0.660202	−	0.751088i	$-0.729529\pi$
$137$	43.8893	−	76.0185i	0.320360	−	0.554880i	0.980562	+	0.196208i	$0.0628628\pi$
$138$		0			0
$139$	158.916	−	91.7504i	1.14328	−	0.660075i	0.196042	−	0.980596i	$-0.437191\pi$
$139$	158.916	−	91.7504i	1.14328	−	0.660075i	0.947242	+	0.320520i	$0.103858\pi$
$140$	25.1636	+	6.49721i	0.179740	+	0.0464087i
$141$		0			0
$142$	−102.748	−	132.647i	−0.723575	−	0.934131i
$143$		−	220.077i		−	1.53900i
$144$		0			0
$145$	4.66874			0.0321982
$146$	−88.2794	+	68.3810i	−0.604654	+	0.468363i
$147$		0			0
$148$	−20.4164	+	79.0724i	−0.137949	+	0.534273i
$149$	76.9750	+	133.325i	0.516611	+	0.894796i	0.999814	+	0.0192880i	$0.00613996\pi$
$149$	76.9750	+	133.325i	0.516611	+	0.894796i	−0.483203	+	0.875508i	$0.660527\pi$
$150$		0			0
$151$	160.539	+	92.6875i	1.06318	+	0.613825i	0.926309	−	0.376765i	$-0.122964\pi$
$151$	160.539	+	92.6875i	1.06318	+	0.613825i	0.136866	+	0.990590i	$0.456297\pi$
$152$	−38.1838	+	16.4317i	−0.251209	+	0.108103i
$153$		0			0
$154$	197.331	+	80.6851i	1.28137	+	0.523930i
$155$	41.9535	+	24.2219i	0.270668	+	0.156270i
$156$		0			0
$157$	−98.0820	−	169.883i	−0.624726	−	1.08206i	−0.988594	−	0.150607i	$-0.951877\pi$
$157$	−98.0820	−	169.883i	−0.624726	−	1.08206i	0.363867	−	0.931451i	$-0.381456\pi$
$158$	−81.3301	+	11.0848i	−0.514748	+	0.0701570i
$159$		0			0
$160$	−21.6656	−	26.9406i	−0.135410	−	0.168379i
$161$	179.429			1.11447
$162$		0			0
$163$			129.325i			0.793403i	0.917948	+	0.396701i	$0.129845\pi$
$163$			129.325i			0.793403i	−0.917948	+	0.396701i	$0.870155\pi$
$164$	−228.314	+	63.4137i	−1.39216	+	0.386669i
$165$		0			0
$166$	70.2492	−	9.57454i	0.423188	−	0.0576780i
$167$	119.469	−	68.9753i	0.715382	−	0.413026i	−0.0976688	−	0.995219i	$-0.531139\pi$
$167$	119.469	−	68.9753i	0.715382	−	0.413026i	0.813051	+	0.582193i	$0.197805\pi$
$168$		0			0
$169$	7.41641	−	12.8456i	0.0438841	−	0.0760094i
$170$	−52.7572	−	21.5714i	−0.310336	−	0.126891i
$171$		0			0
$172$	−53.6656	+	54.6534i	−0.312009	+	0.317753i
$173$	80.2161	−	138.938i	0.463677	−	0.803112i	−0.535464	−	0.844558i	$-0.679863\pi$
$173$	80.2161	−	138.938i	0.463677	−	0.803112i	0.999141	+	0.0414461i	$0.0131965\pi$
$174$		0			0
$175$	−124.126	+	71.6643i	−0.709292	+	0.409510i
$176$	−146.253	−	242.973i	−0.830982	−	1.38053i
$177$		0			0
$178$	41.7082	−	32.3070i	0.234316	−	0.181500i
$179$		−	201.469i		−	1.12552i	−0.826619	−	0.562762i	$-0.809739\pi$
$179$		−	201.469i		−	1.12552i	0.826619	−	0.562762i	$-0.190261\pi$
$180$		0			0
$181$	−48.2523			−0.266587			−0.133294	−	0.991077i	$-0.542555\pi$
$181$	−48.2523			−0.266587			−0.133294	+	0.991077i	$0.542555\pi$
$182$	−91.4532	−	118.066i	−0.502490	−	0.648712i
$183$		0			0
$184$	−191.331	−	142.698i	−1.03984	−	0.775535i
$185$	11.0286	+	19.1020i	0.0596139	+	0.103254i
$186$		0			0
$187$	−404.912	−	233.776i	−2.16530	−	1.25014i
$188$	−115.080	+	117.198i	−0.612128	+	0.623395i
$189$		0			0
$190$	−4.24922	+	10.3923i	−0.0223643	+	0.0546963i
$191$	−127.662	−	73.7056i	−0.668386	−	0.385893i	0.127079	−	0.991893i	$-0.459440\pi$
$191$	−127.662	−	73.7056i	−0.668386	−	0.385893i	−0.795465	+	0.606000i	$0.792773\pi$
$192$		0			0
$193$	−12.5820	−	21.7927i	−0.0651919	−	0.112916i	0.831587	−	0.555394i	$-0.187433\pi$
$193$	−12.5820	−	21.7927i	−0.0651919	−	0.112916i	−0.896779	+	0.442479i	$0.854099\pi$
$194$	−20.6164	−	151.264i	−0.106270	−	0.779712i
$195$		0			0
$196$	−49.4590	+	13.7371i	−0.252342	+	0.0700872i
$197$	385.506			1.95688			0.978441	−	0.206528i	$-0.0662165\pi$
$197$	385.506			1.95688			0.978441	+	0.206528i	$0.0662165\pi$
$198$		0			0
$199$			121.386i			0.609978i	0.952356	+	0.304989i	$0.0986528\pi$
$199$			121.386i			0.609978i	−0.952356	+	0.304989i	$0.901347\pi$
$200$	189.354	+	22.2985i	0.946771	+	0.111493i
$201$		0			0
$202$	−19.5016	−	143.085i	−0.0965423	−	0.708339i
$203$	22.5070	−	12.9944i	0.110872	−	0.0640119i
$204$		0			0
$205$	−32.0000	+	55.4256i	−0.156098	+	0.270369i
$206$	43.8836	−	107.326i	0.213027	−	0.520999i
$207$		0			0
$208$	3.62306	+	198.629i	0.0174186	+	0.954949i
$209$	−46.0501	+	79.7610i	−0.220335	+	0.381632i
$210$		0			0
$211$	−226.579	+	130.815i	−1.07383	+	0.619978i	−0.929226	−	0.369511i	$-0.879525\pi$
$211$	−226.579	+	130.815i	−1.07383	+	0.619978i	−0.144607	+	0.989489i	$0.546192\pi$
$212$	−70.0430	+	271.275i	−0.330391	+	1.27960i
$213$		0			0
$214$	−78.8754	−	101.828i	−0.368577	−	0.475830i
$215$			20.6880i			0.0962231i
$216$		0			0
$217$	269.666			1.24270
$218$	68.2533	−	52.8688i	0.313089	−	0.242517i
$219$		0			0
$220$	−74.1641	−	19.1491i	−0.337109	−	0.0870413i
$221$	163.764	+	283.647i	0.741012	+	1.28347i
$222$		0			0
$223$	60.6687	+	35.0271i	0.272057	+	0.157072i	0.629822	−	0.776739i	$-0.283128\pi$
$223$	60.6687	+	35.0271i	0.272057	+	0.157072i	−0.357765	+	0.933812i	$0.616461\pi$
$224$	−179.429	−	69.5735i	−0.801022	−	0.310596i
$225$		0			0
$226$	−150.498	−	61.5361i	−0.665922	−	0.272283i
$227$	−258.384	−	149.178i	−1.13826	−	0.657172i	−0.192258	−	0.981344i	$-0.561581\pi$
$227$	−258.384	−	149.178i	−1.13826	−	0.657172i	−0.945998	+	0.324172i	$0.894914\pi$
$228$		0			0
$229$	−129.833	−	224.877i	−0.566956	−	0.981996i	−0.996865	−	0.0791237i	$-0.974788\pi$
$229$	−129.833	−	224.877i	−0.566956	−	0.981996i	0.429909	−	0.902872i	$-0.358546\pi$
$230$	−63.8760	+	8.70592i	−0.277722	+	0.0378518i
$231$		0			0
$232$	−34.3344	−	4.04324i	−0.147993	−	0.0174278i
$233$	7.38192			0.0316821			0.0158410	−	0.999875i	$-0.494957\pi$
$233$	7.38192			0.0316821			0.0158410	+	0.999875i	$0.494957\pi$
$234$		0			0
$235$			44.3630i			0.188779i
$236$	−30.9923	−	111.584i	−0.131323	−	0.472816i
$237$		0			0
$238$	−314.371	+	42.8468i	−1.32089	+	0.180029i
$239$	71.1233	−	41.0631i	0.297587	−	0.171812i	−0.343771	−	0.939053i	$-0.611704\pi$
$239$	71.1233	−	41.0631i	0.297587	−	0.171812i	0.641358	+	0.767241i	$0.278371\pi$
$240$		0			0
$241$	207.913	−	360.116i	0.862711	−	1.49426i	−0.00659158	−	0.999978i	$-0.502098\pi$
$241$	207.913	−	360.116i	0.862711	−	1.49426i	0.869302	−	0.494281i	$-0.164568\pi$
$242$	−357.591	−	146.212i	−1.47765	−	0.604184i
$243$		0			0
$244$	52.5623	+	51.6123i	0.215419	+	0.211526i
$245$	−6.93205	+	12.0067i	−0.0282941	+	0.0490068i
$246$		0			0
$247$	55.8738	−	32.2588i	0.226210	−	0.130602i
$248$	−287.554	−	214.463i	−1.15949	−	0.864770i
$249$		0			0
$250$	83.4164	−	64.6141i	0.333666	−	0.258456i
$251$			140.030i			0.557890i	0.960307	+	0.278945i	$0.0899847\pi$
$251$			140.030i			0.557890i	−0.960307	+	0.278945i	$0.910015\pi$
$252$		0			0
$253$	−528.827			−2.09022
$254$	235.112	+	303.528i	0.925637	+	1.19499i
$255$		0			0
$256$	136.000	+	216.887i	0.531250	+	0.847215i
$257$	33.4913	+	58.0086i	0.130316	+	0.225714i	0.923798	−	0.382879i	$-0.125067\pi$
$257$	33.4913	+	58.0086i	0.130316	+	0.225714i	−0.793482	+	0.608593i	$0.791734\pi$
$258$		0			0
$259$	106.333	+	61.3913i	0.410551	+	0.237032i
$260$	38.2856	+	37.5936i	0.147252	+	0.144591i
$261$		0			0
$262$	107.331	−	262.500i	0.409661	−	1.00191i
$263$	32.2303	+	18.6082i	0.122549	+	0.0707534i	0.560021	−	0.828478i	$-0.310793\pi$
$263$	32.2303	+	18.6082i	0.122549	+	0.0707534i	−0.437473	+	0.899232i	$0.644126\pi$
$264$		0			0
$265$	37.8359	+	65.5337i	0.142777	+	0.247297i
$266$	8.44013	+	61.9259i	0.0317298	+	0.232804i
$267$		0			0
$268$	−101.562	−	365.664i	−0.378964	−	1.36442i
$269$	279.092			1.03752			0.518758	−	0.854921i	$-0.326395\pi$
$269$	279.092			1.03752			0.518758	+	0.854921i	$0.326395\pi$
$270$		0			0
$271$		−	406.305i		−	1.49928i	−0.661845	−	0.749641i	$-0.730226\pi$
$271$		−	406.305i		−	1.49928i	0.661845	−	0.749641i	$-0.269774\pi$
$272$	369.300	+	204.328i	1.35772	+	0.751205i
$273$		0			0
$274$	23.7082	+	173.949i	0.0865263	+	0.634851i
$275$	365.834	−	211.214i	1.33031	−	0.768053i
$276$		0			0
$277$	−2.41641	+	4.18534i	−0.00872349	+	0.0151095i	−0.870354	−	0.492426i	$-0.836110\pi$
$277$	−2.41641	+	4.18534i	−0.00872349	+	0.0151095i	0.861631	+	0.507536i	$0.169443\pi$
$278$	−138.898	+	339.702i	−0.499633	+	1.22195i
$279$		0			0
$280$	−47.7446	+	20.5460i	−0.170516	+	0.0733785i
$281$	−2.16073	+	3.74249i	−0.00768942	+	0.0133185i	−0.869845	−	0.493326i	$-0.835781\pi$
$281$	−2.16073	+	3.74249i	−0.00768942	+	0.0133185i	0.862155	+	0.506644i	$0.169114\pi$
$282$		0			0
$283$	38.4195	−	22.1815i	0.135758	−	0.0783799i	−0.430583	−	0.902551i	$-0.641692\pi$
$283$	38.4195	−	22.1815i	0.135758	−	0.0783799i	0.566341	+	0.824171i	$0.308359\pi$
$284$	324.917	+	83.8931i	1.14407	+	0.295398i
$285$		0			0
$286$	269.538	+	347.972i	0.942440	+	1.21669i
$287$			356.260i			1.24133i
$288$		0			0
$289$	406.830			1.40772
$290$	−7.38192	+	5.71801i	−0.0254549	+	0.0197173i
$291$		0			0
$292$	55.8328	−	216.240i	0.191208	−	0.740546i
$293$	−194.464	−	336.821i	−0.663699	−	1.14956i	−0.979636	−	0.200780i	$-0.935652\pi$
$293$	−194.464	−	336.821i	−0.663699	−	1.14956i	0.315938	−	0.948780i	$-0.397681\pi$
$294$		0			0
$295$	−27.0883	−	15.6394i	−0.0918246	−	0.0530149i
$296$	−64.5624	−	150.029i	−0.218116	−	0.506856i
$297$		0			0
$298$	−284.997	−	116.530i	−0.956365	−	0.391040i
$299$	320.820	+	185.226i	1.07298	+	0.619484i
$300$		0			0
$301$	57.5805	+	99.7323i	0.191297	+	0.331337i
$302$	−367.354	+	50.0681i	−1.21640	+	0.165788i
$303$		0			0
$304$	40.2492	−	72.7461i	0.132399	−	0.239296i
$305$	19.8964			0.0652341
$306$		0			0
$307$			96.6999i			0.314983i	0.987520	+	0.157492i	$0.0503407\pi$
$307$			96.6999i			0.314983i	−0.987520	+	0.157492i	$0.949659\pi$
$308$	−410.827	+	114.106i	−1.33385	+	0.370474i
$309$		0			0
$310$	−96.0000	+	13.0842i	−0.309677	+	0.0422071i
$311$	−117.939	+	68.0918i	−0.379224	+	0.218945i	−0.677480	−	0.735541i	$-0.736928\pi$
$311$	−117.939	+	68.0918i	−0.379224	+	0.218945i	0.298257	+	0.954486i	$0.403595\pi$
$312$		0			0
$313$	−141.080	+	244.359i	−0.450736	+	0.780698i	−0.998432	−	0.0559794i	$-0.982172\pi$
$313$	−141.080	+	244.359i	−0.450736	+	0.780698i	0.547696	+	0.836678i	$0.315505\pi$
$314$	363.145	+	148.483i	1.15651	+	0.472877i
$315$		0			0
$316$	115.018	−	117.135i	0.363982	−	0.370681i
$317$	−137.745	+	238.581i	−0.434526	+	0.752620i	−0.997257	−	0.0740196i	$-0.976417\pi$
$317$	−137.745	+	238.581i	−0.434526	+	0.752620i	0.562731	+	0.826640i	$0.309751\pi$
$318$		0			0
$319$	−66.3344	+	38.2982i	−0.207945	+	0.120057i
$320$	67.2518	+	16.0620i	0.210162	+	0.0501937i
$321$		0			0
$322$	−283.702	+	219.755i	−0.881062	+	0.682468i
$323$		−	137.067i		−	0.424356i
$324$		0			0
$325$	−295.918			−0.910517
$326$	−158.390	−	204.480i	−0.485858	−	0.627240i
$327$		0			0
$328$	283.331	−	379.893i	0.863815	−	1.15821i
$329$	123.475	+	213.865i	0.375304	+	0.650045i
$330$		0			0
$331$	−48.0836	−	27.7611i	−0.145268	−	0.0838703i	0.425605	−	0.904909i	$-0.360061\pi$
$331$	−48.0836	−	27.7611i	−0.145268	−	0.0838703i	−0.570872	+	0.821039i	$0.693395\pi$
$332$	−99.3474	+	101.176i	−0.299239	+	0.304747i
$333$		0			0
$334$	−104.420	+	255.378i	−0.312633	+	0.764606i
$335$	−88.7687	−	51.2506i	−0.264981	−	0.152987i
$336$		0			0
$337$	215.330	+	372.962i	0.638961	+	1.10671i	0.985661	+	0.168736i	$0.0539686\pi$
$337$	215.330	+	372.962i	0.638961	+	1.10671i	−0.346701	+	0.937976i	$0.612698\pi$
$338$	4.00621	+	29.3939i	0.0118527	+	0.0869641i
$339$		0			0
$340$	109.836	−	30.5066i	0.323047	−	0.0897254i
$341$	−794.779			−2.33073
$342$		0			0
$343$			371.857i			1.08413i
$344$	17.9163	−	152.141i	0.0520823	−	0.442271i
$345$		0			0
$346$	43.3313	+	317.925i	0.125235	+	0.918859i
$347$	−117.668	+	67.9354i	−0.339100	+	0.195779i	−0.659874	−	0.751376i	$-0.729390\pi$
$347$	−117.668	+	67.9354i	−0.339100	+	0.195779i	0.320774	+	0.947156i	$0.396057\pi$
$348$		0			0
$349$	−144.041	+	249.486i	−0.412725	+	0.714861i	−0.995187	−	0.0979975i	$-0.968756\pi$
$349$	−144.041	+	249.486i	−0.412725	+	0.714861i	0.582462	+	0.812858i	$0.302090\pi$
$350$	108.490	−	265.334i	0.309972	−	0.758097i
$351$		0			0
$352$	528.827	+	205.052i	1.50235	+	0.582535i
$353$	99.4820	−	172.308i	0.281819	−	0.488124i	−0.690014	−	0.723796i	$-0.742396\pi$
$353$	99.4820	−	172.308i	0.281819	−	0.488124i	0.971833	+	0.235672i	$0.0757290\pi$
$354$		0			0
$355$	78.4922	−	45.3175i	0.221105	−	0.127655i
$356$	−26.3786	+	102.164i	−0.0740971	+	0.286977i
$357$		0			0
$358$	246.748	+	318.550i	0.689239	+	0.889804i
$359$		−	324.658i		−	0.904339i	−0.891932	−	0.452170i	$-0.850650\pi$
$359$		−	324.658i		−	0.904339i	0.891932	−	0.452170i	$-0.149350\pi$
$360$		0			0
$361$	334.000			0.925208
$362$	76.2936	−	59.0968i	0.210756	−	0.163251i
$363$		0			0
$364$	289.200	+	74.6712i	0.794507	+	0.205141i
$365$	−30.1599	−	52.2384i	−0.0826297	−	0.143119i
$366$		0			0
$367$	152.543	+	88.0705i	0.415647	+	0.239974i	0.693213	−	0.720732i	$-0.256194\pi$
$367$	152.543	+	88.0705i	0.415647	+	0.239974i	−0.277566	+	0.960707i	$0.589528\pi$
$368$	477.290	−	8.70592i	1.29699	−	0.0236574i
$369$		0			0
$370$	−40.8328	−	16.6958i	−0.110359	−	0.0451238i
$371$	364.798	+	210.616i	0.983283	+	0.567699i
$372$		0			0
$373$	−298.290	−	516.654i	−0.799706	−	1.38513i	−0.919808	−	0.392369i	$-0.871655\pi$
$373$	−298.290	−	516.654i	−0.799706	−	1.38513i	0.120102	−	0.992762i	$-0.461678\pi$
$374$	926.538	−	126.281i	2.47737	−	0.337651i
$375$		0			0
$376$	38.4195	−	326.250i	0.102180	−	0.867687i
$377$	53.6569			0.142326
$378$		0			0
$379$		−	30.3082i		−	0.0799689i	−0.999200	−	0.0399844i	$-0.987269\pi$
$379$		−	30.3082i		−	0.0799689i	0.999200	−	0.0399844i	$-0.0127308\pi$
$380$	−6.00931	−	21.6359i	−0.0158140	−	0.0569366i
$381$		0			0
$382$	292.122	−	39.8144i	0.764716	−	0.104226i
$383$	−612.470	+	353.610i	−1.59914	+	0.923264i	−0.607486	+	0.794330i	$0.707822\pi$
$383$	−612.470	+	353.610i	−1.59914	+	0.923264i	−0.991653	+	0.128934i	$0.958845\pi$
$384$		0			0
$385$	−57.5805	+	99.7323i	−0.149560	+	0.259045i
$386$	46.5845	+	19.0475i	0.120685	+	0.0493460i
$387$		0			0
$388$	217.857	+	213.920i	0.561488	+	0.551339i
$389$	288.544	−	499.773i	0.741758	−	1.28476i	−0.209936	−	0.977715i	$-0.567326\pi$
$389$	288.544	−	499.773i	0.741758	−	1.28476i	0.951694	−	0.307048i	$-0.0993411\pi$
$390$		0			0
$391$	681.580	−	393.511i	1.74317	−	1.00642i
$392$	61.3771	−	82.2949i	0.156574	−	0.209936i
$393$		0			0
$394$	−609.538	+	472.146i	−1.54705	+	1.19834i
$395$		−	44.3392i		−	0.112251i
$396$		0			0
$397$	26.8266			0.0675733			0.0337867	−	0.999429i	$-0.489243\pi$
$397$	26.8266			0.0675733			0.0337867	+	0.999429i	$0.489243\pi$
$398$	−148.666	−	191.928i	−0.373534	−	0.482230i
$399$		0			0
$400$	−326.705	+	196.653i	−0.816763	+	0.491634i
$401$	−252.532	−	437.399i	−0.629756	−	1.09077i	−0.987600	−	0.156989i	$-0.949821\pi$
$401$	−252.532	−	437.399i	−0.629756	−	1.09077i	0.357844	−	0.933781i	$-0.383512\pi$
$402$		0			0
$403$	482.164	+	278.378i	1.19644	+	0.690763i
$404$	206.077	+	202.352i	0.510091	+	0.500872i
$405$		0			0
$406$	−19.6718	+	48.1113i	−0.0484528	+	0.118501i
$407$	−313.392	−	180.937i	−0.770005	−	0.444563i
$408$		0			0
$409$	341.664	+	591.780i	0.835364	+	1.44689i	0.893733	+	0.448599i	$0.148077\pi$
$409$	341.664	+	591.780i	0.835364	+	1.44689i	−0.0583688	+	0.998295i	$0.518590\pi$
$410$	−17.2858	−	126.827i	−0.0421605	−	0.309335i
$411$		0			0
$412$	62.0608	+	223.443i	0.150633	+	0.542338i
$413$	−174.116			−0.421588
$414$		0			0
$415$			38.2982i			0.0922847i
$416$	−248.999	−	309.623i	−0.598555	−	0.744287i
$417$		0			0
$418$	−24.8754	−	182.513i	−0.0595105	−	0.436634i
$419$	−265.541	+	153.310i	−0.633749	+	0.365895i	−0.782203	−	0.623024i	$-0.785904\pi$
$419$	−265.541	+	153.310i	−0.633749	+	0.365895i	0.148453	+	0.988919i	$0.452571\pi$
$420$		0			0
$421$	9.29335	−	16.0966i	0.0220745	−	0.0382341i	−0.854777	−	0.518995i	$-0.826306\pi$
$421$	9.29335	−	16.0966i	0.0220745	−	0.0382341i	0.876852	+	0.480761i	$0.159640\pi$
$422$	198.037	−	484.339i	0.469283	−	1.14772i
$423$		0			0
$424$	−221.495	−	514.709i	−0.522395	−	1.21394i
$425$	−314.338	+	544.449i	−0.739619	+	1.28106i
$426$		0			0
$427$	95.9164	−	55.3774i	0.224629	−	0.129689i
$428$	249.426	+	64.4015i	0.582771	+	0.150471i
$429$		0			0
$430$	−25.3375	−	32.7105i	−0.0589244	−	0.0760710i
$431$		−	308.130i		−	0.714918i	−0.933929	−	0.357459i	$-0.883643\pi$
$431$		−	308.130i		−	0.714918i	0.933929	−	0.357459i	$-0.116357\pi$
$432$		0			0
$433$	174.839			0.403785			0.201893	−	0.979408i	$-0.435291\pi$
$433$	174.839			0.403785			0.201893	+	0.979408i	$0.435291\pi$
$434$	−426.379	+	330.272i	−0.982440	+	0.760994i
$435$		0			0
$436$	−43.1672	+	167.186i	−0.0990073	+	0.383454i
$437$	−77.5152	−	134.260i	−0.177380	−	0.307232i
$438$		0			0
$439$	−415.830	−	240.079i	−0.947220	−	0.546878i	−0.0550040	−	0.998486i	$-0.517517\pi$
$439$	−415.830	−	240.079i	−0.947220	−	0.546878i	−0.892216	+	0.451608i	$0.850850\pi$
$440$	140.716	−	60.5547i	0.319810	−	0.137624i
$441$		0			0
$442$	−606.328	−	247.917i	−1.37178	−	0.560897i
$443$	−481.477	−	277.981i	−1.08686	−	0.627497i	−0.154119	−	0.988052i	$-0.549254\pi$
$443$	−481.477	−	277.981i	−1.08686	−	0.627497i	−0.932738	+	0.360556i	$0.882587\pi$
$444$		0			0
$445$	14.2492	+	24.6804i	0.0320207	+	0.0554615i
$446$	−138.825	+	18.9210i	−0.311267	+	0.0424238i
$447$		0			0
$448$	368.912	−	109.749i	0.823464	−	0.244976i
$449$	−801.711			−1.78555			−0.892774	−	0.450504i	$-0.851244\pi$
$449$	−801.711			−1.78555			−0.892774	+	0.450504i	$0.851244\pi$
$450$		0			0
$451$		−	1050.00i		−	2.32816i
$452$	313.325	−	87.0251i	0.693197	−	0.192533i
$453$		0			0
$454$	591.246	−	80.5832i	1.30230	−	0.177496i
$455$	69.8640	−	40.3360i	0.153547	−	0.0886506i
$456$		0			0
$457$	68.9149	−	119.364i	0.150798	−	0.261190i	−0.780723	−	0.624877i	$-0.785149\pi$
$457$	68.9149	−	119.364i	0.150798	−	0.261190i	0.931521	+	0.363687i	$0.118482\pi$
$458$	480.701	+	196.550i	1.04956	+	0.429148i
$459$		0			0
$460$	90.3344	−	91.9971i	0.196379	−	0.199994i
$461$	−94.1705	+	163.108i	−0.204274	+	0.353814i	−0.949901	−	0.312550i	$-0.898817\pi$
$461$	−94.1705	+	163.108i	−0.204274	+	0.353814i	0.745627	+	0.666364i	$0.232150\pi$
$462$		0			0
$463$	−474.950	+	274.212i	−1.02581	+	0.592251i	−0.915781	−	0.401677i	$-0.868427\pi$
$463$	−474.950	+	274.212i	−1.02581	+	0.592251i	−0.110028	+	0.993928i	$0.535094\pi$
$464$	59.2393	−	35.6579i	0.127671	−	0.0768489i
$465$		0			0
$466$	−11.6718	+	9.04097i	−0.0250469	+	0.0194012i
$467$			618.597i			1.32462i	0.749231	+	0.662309i	$0.230423\pi$
$467$			618.597i			1.32462i	−0.749231	+	0.662309i	$0.769577\pi$
$468$		0			0
$469$	−570.580			−1.21659
$470$	−54.3334	−	70.1441i	−0.115603	−	0.149243i
$471$		0			0
$472$	185.666	+	138.473i	0.393359	+	0.293375i
$473$	−169.706	−	293.939i	−0.358786	−	0.621435i
$474$		0			0
$475$	107.248	+	61.9195i	0.225785	+	0.130357i
$476$	444.587	−	452.771i	0.934007	−	0.951199i
$477$		0			0
$478$	−62.1641	+	152.034i	−0.130050	+	0.318064i
$479$	667.208	+	385.213i	1.39292	+	0.804202i	0.993637	−	0.112627i	$-0.0359265\pi$
$479$	667.208	+	385.213i	1.39292	+	0.804202i	0.399281	+	0.916829i	$0.369260\pi$
$480$		0			0
$481$	126.749	+	219.536i	0.263512	+	0.456416i
$482$	112.311	+	824.035i	0.233010	+	1.70962i
$483$		0			0
$484$	744.474	−	206.776i	1.53817	−	0.427222i
$485$	82.4655			0.170032
$486$		0			0
$487$			549.208i			1.12774i	0.825865	+	0.563868i	$0.190687\pi$
$487$			549.208i			1.12774i	−0.825865	+	0.563868i	$0.809313\pi$
$488$	−146.320	−	17.2308i	−0.299836	−	0.0353090i
$489$		0			0
$490$	−3.74457	−	27.4742i	−0.00764197	−	0.0560698i
$491$	19.9407	−	11.5128i	0.0406125	−	0.0234476i	−0.479556	−	0.877511i	$-0.659202\pi$
$491$	19.9407	−	11.5128i	0.0406125	−	0.0234476i	0.520169	+	0.854063i	$0.325869\pi$
$492$		0			0
$493$	56.9969	−	98.7215i	0.115612	−	0.200246i
$494$	−48.8355	+	119.437i	−0.0988573	+	0.241775i
$495$		0			0
$496$	717.325	−	13.0842i	1.44622	−	0.0263795i
$497$	252.263	−	436.932i	0.507572	−	0.879140i
$498$		0			0
$499$	−542.833	+	313.405i	−1.08784	+	0.628065i	−0.933001	−	0.359874i	$-0.882820\pi$
$499$	−542.833	+	313.405i	−1.08784	+	0.628065i	−0.154840	+	0.987939i	$0.549486\pi$
$500$	−52.7572	+	204.328i	−0.105514	+	0.408655i
$501$		0			0
$502$	−171.502	−	221.408i	−0.341637	−	0.441051i
$503$			732.896i			1.45705i	0.685019	+	0.728525i	$0.259794\pi$
$503$			732.896i			1.45705i	−0.685019	+	0.728525i	$0.740206\pi$
$504$		0			0
$505$	78.0062			0.154468
$506$	836.148	−	647.678i	1.65247	−	1.28000i
$507$		0			0
$508$	−743.489	−	191.968i	−1.46356	−	0.377890i
$509$	−218.682	−	378.768i	−0.429630	−	0.744140i	0.567211	−	0.823573i	$-0.308023\pi$
$509$	−218.682	−	378.768i	−0.429630	−	0.744140i	−0.996840	+	0.0794323i	$0.974689\pi$
$510$		0			0
$511$	−290.789	−	167.887i	−0.569058	−	0.328546i
$512$	−480.666	−	176.363i	−0.938801	−	0.344459i
$513$		0			0
$514$	−124.000	−	50.7013i	−0.241245	−	0.0986407i
$515$	54.2431	+	31.3173i	0.105326	+	0.0608102i
$516$		0			0
$517$	−363.915	−	630.319i	−0.703897	−	1.21919i
$518$	−243.316	+	33.1624i	−0.469721	+	0.0640201i
$519$		0			0
$520$	−106.577	−	12.5506i	−0.204957	−	0.0241359i
$521$	−385.236			−0.739417			−0.369709	−	0.929148i	$-0.620542\pi$
$521$	−385.236			−0.739417			−0.369709	+	0.929148i	$0.620542\pi$
$522$		0			0
$523$			418.572i			0.800328i	0.916443	+	0.400164i	$0.131047\pi$
$523$			418.572i			0.800328i	−0.916443	+	0.400164i	$0.868953\pi$
$524$	151.789	+	546.502i	0.289674	+	1.04294i
$525$		0			0
$526$	−73.7508	+	10.0518i	−0.140211	+	0.0191099i
$527$	1024.35	−	591.411i	1.94375	−	1.12222i
$528$		0			0
$529$	180.582	−	312.777i	0.341365	−	0.591261i
$530$	−140.086	−	57.2786i	−0.264313	−	0.108073i
$531$		0			0
$532$	−89.1885	−	87.5765i	−0.167648	−	0.164617i
$533$	−367.770	+	636.996i	−0.690000	+	1.19511i
$534$		0			0
$535$	60.2554	−	34.7885i	0.112627	−	0.0650252i
$536$	608.430	+	453.778i	1.13513	+	0.846601i
$537$		0			0
$538$	−441.282	+	341.816i	−0.820228	+	0.635346i
$539$		−	227.457i		−	0.421999i
$540$		0			0
$541$	−23.4257			−0.0433008			−0.0216504	−	0.999766i	$-0.506892\pi$
$541$	−23.4257			−0.0433008			−0.0216504	+	0.999766i	$0.506892\pi$
$542$	497.620	+	642.425i	0.918119	+	1.18529i
$543$		0			0
$544$	−834.164	+	129.228i	−1.53339	+	0.237552i
$545$	23.3181	+	40.3882i	0.0427855	+	0.0741067i
$546$		0			0
$547$	625.412	+	361.082i	1.14335	+	0.660113i	0.947258	−	0.320473i	$-0.103842\pi$
$547$	625.412	+	361.082i	1.14335	+	0.660113i	0.196091	+	0.980586i	$0.437175\pi$
$548$	−250.529	−	246.001i	−0.457170	−	0.448907i
$549$		0			0
$550$	−319.751	+	782.013i	−0.581365	+	1.42184i
$551$	−19.4465	−	11.2275i	−0.0352932	−	0.0203765i
$552$		0			0
$553$	−123.409	−	213.750i	−0.223162	−	0.386528i
$554$	−1.30530	−	9.57709i	−0.00235614	−	0.0172872i
$555$		0			0
$556$	−196.431	−	707.231i	−0.353294	−	1.27200i
$557$	−2.34135			−0.00420349			−0.00210175	−	0.999998i	$-0.500669\pi$
$557$	−2.34135			−0.00420349			−0.00210175	+	0.999998i	$0.500669\pi$
$558$		0			0
$559$			237.763i			0.425336i
$560$	50.3272	−	90.9610i	0.0898700	−	0.162430i
$561$		0			0
$562$	−1.16718	−	8.56373i	−0.00207684	−	0.0152380i
$563$	−311.591	+	179.897i	−0.553448	+	0.319533i	−0.750511	−	0.660857i	$-0.770193\pi$
$563$	−311.591	+	179.897i	−0.553448	+	0.319533i	0.197064	+	0.980391i	$0.436859\pi$
$564$		0			0
$565$	43.9149	−	76.0628i	0.0777254	−	0.134624i
$566$	−33.5799	+	82.1262i	−0.0593284	+	0.145099i
$567$		0			0
$568$	−616.486	+	265.293i	−1.08536	+	0.467066i
$569$	−9.31771	+	16.1388i	−0.0163756	+	0.0283634i	−0.874097	−	0.485751i	$-0.838546\pi$
$569$	−9.31771	+	16.1388i	−0.0163756	+	0.0283634i	0.857721	+	0.514115i	$0.171879\pi$
$570$		0			0
$571$	246.409	−	142.264i	0.431539	−	0.249149i	−0.268463	−	0.963290i	$-0.586516\pi$
$571$	246.409	−	142.264i	0.431539	−	0.249149i	0.700002	+	0.714141i	$0.253182\pi$
$572$	−852.354	−	220.077i	−1.49013	−	0.384750i
$573$		0			0
$574$	−436.328	−	563.297i	−0.760154	−	0.981354i
$575$			711.067i			1.23664i
$576$		0			0
$577$	664.823			1.15221			0.576104	−	0.817377i	$-0.304572\pi$
$577$	664.823			1.15221			0.576104	+	0.817377i	$0.304572\pi$
$578$	−643.254	+	498.263i	−1.11290	+	0.862046i
$579$		0			0
$580$	4.66874	−	18.0819i	0.00804955	−	0.0311758i
$581$	106.595	+	184.627i	0.183468	+	0.317775i
$582$		0			0
$583$	−1075.16	−	620.744i	−1.84419	−	1.06474i
$584$	176.559	+	410.286i	0.302327	+	0.702544i
$585$		0			0
$586$	719.994	+	294.392i	1.22866	+	0.502376i
$587$	−653.388	−	377.234i	−1.11310	−	0.642647i	−0.173467	−	0.984840i	$-0.555497\pi$
$587$	−653.388	−	377.234i	−1.11310	−	0.642647i	−0.939630	+	0.342193i	$0.888830\pi$
$588$		0			0
$589$	−116.498	−	201.781i	−0.197790	−	0.342583i
$590$	61.9846	−	8.44812i	0.105059	−	0.0143188i
$591$		0			0
$592$	285.830	+	158.145i	0.482820	+	0.267137i
$593$	550.801			0.928838			0.464419	−	0.885615i	$-0.346263\pi$
$593$	550.801			0.928838			0.464419	+	0.885615i	$0.346263\pi$
$594$		0			0
$595$		−	171.387i		−	0.288046i
$596$	593.339	−	164.798i	0.995536	−	0.276507i
$597$		0			0
$598$	−734.115	+	100.055i	−1.22762	+	0.167317i
$599$	22.5070	−	12.9944i	0.0375743	−	0.0216935i	−0.481095	−	0.876668i	$-0.659761\pi$
$599$	22.5070	−	12.9944i	0.0375743	−	0.0216935i	0.518669	+	0.854975i	$0.326428\pi$
$600$		0			0
$601$	−93.0851	+	161.228i	−0.154884	+	0.268267i	−0.933017	−	0.359833i	$-0.882834\pi$
$601$	−93.0851	+	161.228i	−0.154884	+	0.268267i	0.778133	+	0.628100i	$0.216167\pi$
$602$	−213.189	−	87.1693i	−0.354135	−	0.144799i
$603$		0			0
$604$	519.517	−	529.079i	0.860127	−	0.875959i
$605$	104.344	−	180.729i	0.172469	−	0.298725i
$606$		0			0
$607$	−86.2082	+	49.7723i	−0.142023	+	0.0819972i	−0.569328	−	0.822110i	$-0.692797\pi$
$607$	−86.2082	+	49.7723i	−0.142023	+	0.0819972i	0.427305	+	0.904108i	$0.359463\pi$
$608$	25.4558	+	164.317i	0.0418682	+	0.270258i
$609$		0			0
$610$	−31.4590	+	24.3680i	−0.0515721	+	0.0399476i
$611$			509.856i			0.834461i
$612$		0			0
$613$	−960.234			−1.56645			−0.783225	−	0.621739i	$-0.786427\pi$
$613$	−960.234			−1.56645			−0.783225	+	0.621739i	$0.786427\pi$
$614$	−118.433	−	152.896i	−0.192887	−	0.249016i
$615$		0			0
$616$	509.823	−	683.576i	0.827636	−	1.10970i
$617$	−177.312	−	307.114i	−0.287378	−	0.497754i	0.685805	−	0.727786i	$-0.259450\pi$
$617$	−177.312	−	307.114i	−0.287378	−	0.497754i	−0.973183	+	0.230032i	$0.926117\pi$
$618$		0			0
$619$	−312.330	−	180.324i	−0.504571	−	0.291314i	0.226028	−	0.974121i	$-0.427426\pi$
$619$	−312.330	−	180.324i	−0.504571	−	0.291314i	−0.730599	+	0.682806i	$0.760759\pi$
$620$	135.765	−	138.263i	0.218975	−	0.223006i
$621$		0			0
$622$	103.082	−	252.107i	0.165727	−	0.405317i
$623$	137.385	+	79.3193i	0.220522	+	0.127318i
$624$		0			0
$625$	−269.412	−	466.635i	−0.431059	−	0.746616i
$626$	−76.2091	−	559.152i	−0.121740	−	0.893215i
$627$		0			0
$628$	−756.036	+	209.987i	−1.20388	+	0.334374i
$629$	538.556			0.856210
$630$		0			0
$631$			82.7121i			0.131081i	0.997850	+	0.0655405i	$0.0208772\pi$
$631$			82.7121i			0.131081i	−0.997850	+	0.0655405i	$0.979123\pi$
$632$	−38.3989	+	326.075i	−0.0607577	+	0.515942i
$633$		0			0
$634$	−74.4071	−	545.931i	−0.117361	−	0.861090i
$635$	−179.610	+	103.698i	−0.282850	+	0.163303i
$636$		0			0
$637$	−79.6687	+	137.990i	−0.125069	+	0.216625i
$638$	57.9784	−	141.797i	0.0908752	−	0.222253i
$639$		0			0
$640$	−126.006	+	56.9700i	−0.196885	+	0.0890156i
$641$	−380.284	+	658.672i	−0.593267	+	1.02757i	0.400521	+	0.916287i	$0.368829\pi$
$641$	−380.284	+	658.672i	−0.593267	+	1.02757i	−0.993789	+	0.111282i	$0.964504\pi$
$642$		0			0
$643$	−681.580	+	393.511i	−1.06000	+	0.611992i	−0.925432	−	0.378913i	$-0.876298\pi$
$643$	−681.580	+	393.511i	−1.06000	+	0.611992i	−0.134568	+	0.990904i	$0.542965\pi$
$644$	179.429	−	694.925i	0.278616	−	1.07908i
$645$		0			0
$646$	167.872	+	216.722i	0.259864	+	0.335483i
$647$		−	978.962i		−	1.51308i	−0.653948	−	0.756539i	$-0.726889\pi$
$647$		−	978.962i		−	1.51308i	0.653948	−	0.756539i	$-0.273111\pi$
$648$		0			0
$649$	513.167			0.790704
$650$	467.887	−	362.424i	0.719827	−	0.557575i
$651$		0			0
$652$	500.872	+	129.325i	0.768209	+	0.198351i
$653$	469.774	+	813.672i	0.719409	+	1.24605i	0.961234	+	0.275733i	$0.0889205\pi$
$653$	469.774	+	813.672i	0.719409	+	1.24605i	−0.241826	+	0.970320i	$0.577746\pi$
$654$		0			0
$655$	132.669	+	76.5963i	0.202548	+	0.116941i
$656$	17.2858	+	947.672i	0.0263503	+	1.44462i
$657$		0			0
$658$	−457.161	−	186.925i	−0.694774	−	0.284080i
$659$	129.463	+	74.7455i	0.196454	+	0.113423i	0.595000	−	0.803726i	$-0.297152\pi$
$659$	129.463	+	74.7455i	0.196454	+	0.113423i	−0.398547	+	0.917148i	$0.630485\pi$
$660$		0			0
$661$	−168.710	−	292.214i	−0.255234	−	0.442078i	0.709725	−	0.704479i	$-0.248819\pi$
$661$	−168.710	−	292.214i	−0.255234	−	0.442078i	−0.964959	+	0.262400i	$0.915486\pi$
$662$	110.027	−	14.9960i	0.166204	−	0.0226526i
$663$		0			0
$664$	33.1672	−	281.649i	0.0499506	−	0.424170i
$665$	−33.7605			−0.0507677
$666$		0			0
$667$		−	128.933i		−	0.193303i
$668$	−147.671	−	531.676i	−0.221065	−	0.795922i
$669$		0			0
$670$	203.125	−	27.6846i	0.303171	−	0.0413204i
$671$	−282.692	+	163.212i	−0.421300	+	0.243238i
$672$		0			0
$673$	160.670	−	278.289i	0.238737	−	0.413505i	−0.721615	−	0.692295i	$-0.756600\pi$
$673$	160.670	−	278.289i	0.238737	−	0.413505i	0.960352	+	0.278789i	$0.0899331\pi$
$674$	−797.249	−	325.981i	−1.18286	−	0.483651i
$675$		0			0
$676$	−42.3344	−	41.5692i	−0.0626248	−	0.0614929i
$677$	370.921	−	642.454i	0.547889	−	0.948971i	−0.450530	−	0.892761i	$-0.648765\pi$
$677$	370.921	−	642.454i	0.547889	−	0.948971i	0.998419	−	0.0562100i	$-0.0179016\pi$
$678$		0			0
$679$	397.549	−	229.525i	0.585492	−	0.338034i
$680$	−136.303	+	182.756i	−0.200446	+	0.268759i
$681$		0			0
$682$	1256.66	−	973.402i	1.84260	−	1.42728i
$683$		−	1259.02i		−	1.84337i	−0.387938	−	0.921686i	$-0.626812\pi$
$683$		−	1259.02i		−	1.84337i	0.387938	−	0.921686i	$-0.373188\pi$
$684$		0			0
$685$	−94.8328			−0.138442
$686$	−455.430	−	587.958i	−0.663893	−	0.857082i
$687$		0			0
$688$	158.006	+	262.500i	0.229660	+	0.381540i
$689$	434.841	+	753.167i	0.631119	+	1.09313i
$690$		0			0
$691$	192.924	+	111.385i	0.279196	+	0.161194i	0.633059	−	0.774103i	$-0.281799\pi$
$691$	192.924	+	111.385i	0.279196	+	0.161194i	−0.353864	+	0.935297i	$0.615132\pi$
$692$	−457.890	−	449.614i	−0.661691	−	0.649731i
$693$		0			0
$694$	102.845	−	251.528i	0.148192	−	0.362432i
$695$	−171.687	−	99.1238i	−0.247032	−	0.142624i
$696$		0			0
$697$	781.325	+	1353.29i	1.12098	+	1.94160i
$698$	−77.8083	−	570.886i	−0.111473	−	0.817888i
$699$		0			0
$700$	153.428	+	552.403i	0.219183	+	0.789147i
$701$	−2.34135			−0.00334001			−0.00167000	−	0.999999i	$-0.500532\pi$
$701$	−2.34135			−0.00334001			−0.00167000	+	0.999999i	$0.500532\pi$
$702$		0			0
$703$		−	106.087i		−	0.150906i
$704$	−1087.29	+	323.462i	−1.54444	+	0.459462i
$705$		0			0
$706$	53.7384	+	394.283i	0.0761166	+	0.558474i
$707$	376.052	−	217.113i	0.531898	−	0.307091i
$708$		0			0
$709$	247.543	−	428.756i	0.349143	−	0.604734i	−0.636954	−	0.770902i	$-0.719806\pi$
$709$	247.543	−	428.756i	0.349143	−	0.604734i	0.986098	+	0.166168i	$0.0531393\pi$
$710$	−68.6047	+	167.786i	−0.0966264	+	0.236319i
$711$		0			0
$712$	−83.4164	−	193.842i	−0.117158	−	0.272250i
$713$	668.919	−	1158.60i	0.938175	−	1.62497i
$714$		0			0
$715$	−205.909	+	118.881i	−0.287984	+	0.166268i
$716$	−780.285	−	201.469i	−1.08978	−	0.281381i
$717$		0			0
$718$	397.623	+	513.329i	0.553793	+	0.714943i
$719$		−	962.433i		−	1.33857i	−0.743005	−	0.669286i	$-0.766600\pi$
$719$		−	962.433i		−	1.33857i	0.743005	−	0.669286i	$-0.233400\pi$
$720$		0			0
$721$	348.659			0.483578
$722$	−528.100	+	409.065i	−0.731441	+	0.566572i
$723$		0			0
$724$	−48.2523	+	186.880i	−0.0666469	+	0.258122i
$725$	51.4962	+	89.1940i	0.0710292	+	0.123026i
$726$		0			0
$727$	471.659	+	272.313i	0.648775	+	0.374570i	0.787987	−	0.615692i	$-0.211124\pi$
$727$	471.659	+	272.313i	0.648775	+	0.374570i	−0.139212	+	0.990263i	$0.544457\pi$
$728$	−548.719	+	236.131i	−0.753735	+	0.324356i
$729$		0			0
$730$	111.666	+	45.6580i	0.152967	+	0.0625453i
$731$	437.452	+	252.563i	0.598429	+	0.345503i
$732$		0			0
$733$	73.0851	+	126.587i	0.0997069	+	0.172697i	0.911563	−	0.411160i	$-0.134876\pi$
$733$	73.0851	+	126.587i	0.0997069	+	0.172697i	−0.811856	+	0.583857i	$0.801543\pi$
$734$	−349.055	+	47.5741i	−0.475552	+	0.0648148i
$735$		0			0
$736$	−744.000	+	598.324i	−1.01087	+	0.812941i
$737$	1681.66			2.28176
$738$		0			0
$739$		−	1172.87i		−	1.58710i	−0.608505	−	0.793550i	$-0.708231\pi$
$739$		−	1172.87i		−	1.58710i	0.608505	−	0.793550i	$-0.291769\pi$
$740$	85.0104	−	23.6114i	0.114879	−	0.0319073i
$741$		0			0
$742$	−834.748	+	113.771i	−1.12500	+	0.153330i
$743$	−428.541	+	247.418i	−0.576771	+	0.332999i	−0.759849	−	0.650099i	$-0.774727\pi$
$743$	−428.541	+	247.418i	−0.576771	+	0.332999i	0.183078	+	0.983098i	$0.441394\pi$
$744$		0			0
$745$	83.1610	−	144.039i	0.111625	−	0.193341i
$746$	1104.41	+	451.572i	1.48044	+	0.605324i
$747$		0			0
$748$	−1310.32	+	1334.44i	−1.75177	+	1.78401i
$749$	193.653	−	335.416i	0.258548	−	0.447819i
$750$		0			0
$751$	803.022	−	463.625i	1.06927	−	0.617344i	0.141289	−	0.989968i	$-0.454875\pi$
$751$	803.022	−	463.625i	1.06927	−	0.617344i	0.927982	+	0.372625i	$0.121542\pi$
$752$	338.827	+	562.901i	0.450567	+	0.748539i
$753$		0			0
$754$	−84.8390	+	65.7160i	−0.112519	+	0.0871565i
$755$		−	200.272i		−	0.265261i
$756$		0			0
$757$	−757.748			−1.00099			−0.500494	−	0.865740i	$-0.666848\pi$
$757$	−757.748			−1.00099			−0.500494	+	0.865740i	$0.666848\pi$
$758$	37.1198	+	47.9215i	0.0489707	+	0.0632209i
$759$		0			0
$760$	36.0000	+	26.8495i	0.0473684	+	0.0353283i
$761$	476.570	+	825.443i	0.626241	+	1.08468i	0.988299	+	0.152526i	$0.0487409\pi$
$761$	476.570	+	825.443i	0.626241	+	1.08468i	−0.362058	+	0.932156i	$0.617926\pi$
$762$		0			0
$763$	224.823	+	129.802i	0.294657	+	0.170120i
$764$	−413.122	+	420.726i	−0.540736	+	0.550689i
$765$		0			0
$766$	535.319	−	1309.23i	0.698850	−	1.70917i
$767$	−311.320	−	179.741i	−0.405893	−	0.234343i
$768$		0			0
$769$	−72.8375	−	126.158i	−0.0947171	−	0.164055i	0.814773	−	0.579780i	$-0.196861\pi$
$769$	−72.8375	−	126.158i	−0.0947171	−	0.164055i	−0.909491	+	0.415725i	$0.863528\pi$
$770$	−31.1039	−	228.212i	−0.0403947	−	0.296379i
$771$		0			0
$772$	−96.9849	+	26.9373i	−0.125628	+	0.0348929i
$773$	−60.1391			−0.0777996			−0.0388998	−	0.999243i	$-0.512385\pi$
$773$	−60.1391			−0.0777996			−0.0388998	+	0.999243i	$0.512385\pi$
$774$		0			0
$775$			1068.67i			1.37893i
$776$	−606.460	−	71.4172i	−0.781520	−	0.0920325i
$777$		0			0
$778$	155.866	+	1143.60i	0.200342	+	1.46993i
$779$	266.577	−	153.908i	0.342204	−	0.197572i
$780$		0			0
$781$	−743.489	+	1287.76i	−0.951971	+	1.64886i
$782$	−595.723	+	1456.96i	−0.761794	+	1.86312i
$783$		0			0
$784$	3.74457	+	205.291i	0.00477623	+	0.261851i
$785$	−105.964	+	183.535i	−0.134986	+	0.233803i
$786$		0			0
$787$	−284.327	+	164.156i	−0.361279	+	0.208585i	−0.669642	−	0.742684i	$-0.733552\pi$
$787$	−284.327	+	164.156i	−0.361279	+	0.208585i	0.308363	+	0.951269i	$0.400219\pi$
$788$	385.506	−	1493.06i	0.489220	−	1.89474i
$789$		0			0
$790$	54.3042	+	70.1064i	0.0687395	+	0.0887423i
$791$		−	488.910i		−	0.618091i
$792$		0			0
$793$	228.666			0.288355
$794$	−42.4166	+	32.8557i	−0.0534214	+	0.0413800i
$795$		0			0
$796$	470.125	+	121.386i	0.590609	+	0.152495i
$797$	−223.363	−	386.875i	−0.280254	−	0.485414i	0.691193	−	0.722670i	$-0.257085\pi$
$797$	−223.363	−	386.875i	−0.280254	−	0.485414i	−0.971447	+	0.237256i	$0.923752\pi$
$798$		0			0
$799$	938.067	+	541.593i	1.17405	+	0.677838i
$800$	275.716	−	711.067i	0.344645	−	0.888833i
$801$		0			0
$802$	934.991	+	382.301i	1.16582	+	0.476684i
$803$	857.035	+	494.809i	1.06729	+	0.616201i
$804$		0			0
$805$	−96.9242	−	167.878i	−0.120403	−	0.208544i
$806$	−1103.31	+	150.374i	−1.36887	+	0.186569i
$807$		0			0
$808$	−573.666	−	67.5554i	−0.709982	−	0.0836081i
$809$	793.341			0.980644			0.490322	−	0.871541i	$-0.336879\pi$
$809$	793.341			0.980644			0.490322	+	0.871541i	$0.336879\pi$
$810$		0			0
$811$			788.930i			0.972787i	0.873740	+	0.486394i	$0.161688\pi$
$811$			788.930i			0.972787i	−0.873740	+	0.486394i	$0.838312\pi$
$812$	−27.8202	−	100.164i	−0.0342613	−	0.123354i
$813$		0			0
$814$	717.118	−	97.7389i	0.880981	−	0.120072i
$815$	120.999	−	69.8588i	0.148465	−	0.0857163i
$816$		0			0
$817$	49.7508	−	86.1709i	0.0608945	−	0.105472i
$818$	−1265.00	−	517.234i	−1.54645	−	0.632316i
$819$		0			0
$820$	182.663	+	179.361i	0.222759	+	0.218733i
$821$	−724.377	+	1254.66i	−0.882310	+	1.52821i	−0.0335444	+	0.999437i	$0.510680\pi$
$821$	−724.377	+	1254.66i	−0.882310	+	1.52821i	−0.848766	+	0.528769i	$0.822654\pi$
$822$		0			0
$823$	112.530	−	64.9693i	0.136732	−	0.0789421i	−0.430074	−	0.902794i	$-0.641512\pi$
$823$	112.530	−	64.9693i	0.136732	−	0.0789421i	0.566805	+	0.823852i	$0.308179\pi$
$824$	−371.788	−	277.286i	−0.451199	−	0.336512i
$825$		0			0
$826$	275.301	−	213.247i	0.333294	−	0.258169i
$827$			350.389i			0.423687i	0.977304	+	0.211843i	$0.0679467\pi$
$827$			350.389i			0.423687i	−0.977304	+	0.211843i	$0.932053\pi$
$828$		0			0
$829$	167.748			0.202349			0.101175	−	0.994869i	$-0.467740\pi$
$829$	167.748			0.202349			0.101175	+	0.994869i	$0.467740\pi$
$830$	−46.9055	−	60.5547i	−0.0565126	−	0.0729575i
$831$		0			0
$832$	772.912	+	184.597i	0.928980	+	0.221872i
$833$	169.256	+	293.160i	0.203188	+	0.351932i
$834$		0			0
$835$	−129.070	−	74.5184i	−0.154574	−	0.0892436i
$836$	262.863	+	258.112i	0.314430	+	0.308747i
$837$		0			0
$838$	232.091	−	567.625i	0.276959	−	0.677356i
$839$	−573.036	−	330.842i	−0.682998	−	0.394329i	0.117985	−	0.993015i	$-0.462356\pi$
$839$	−573.036	−	330.842i	−0.682998	−	0.394329i	−0.800984	+	0.598686i	$0.795690\pi$
$840$		0			0
$841$	411.163	+	712.154i	0.488897	+	0.846795i
$842$	5.02010	+	36.8329i	0.00596211	+	0.0437445i
$843$		0			0
$844$	280.067	+	1008.35i	0.331833	+	1.19473i
$845$	−16.0248			−0.0189643
$846$		0			0
$847$		−	1161.67i		−	1.37151i
$848$	980.602	+	542.551i	1.15637	+	0.639800i
$849$		0			0
$850$	−169.800	−	1245.83i	−0.199764	−	1.46569i
$851$	527.527	−	304.568i	0.619891	−	0.357894i
$852$		0			0
$853$	−8.53947	+	14.7908i	−0.0100111	+	0.0173397i	−0.870988	−	0.491305i	$-0.836520\pi$
$853$	−8.53947	+	14.7908i	−0.0100111	+	0.0173397i	0.860976	+	0.508645i	$0.169853\pi$
$854$	−83.8340	+	205.032i	−0.0981663	+	0.240085i
$855$		0			0
$856$	−473.252	+	203.655i	−0.552865	+	0.237915i
$857$	211.209	−	365.825i	0.246452	−	0.426867i	−0.716087	−	0.698011i	$-0.754069\pi$
$857$	211.209	−	365.825i	0.246452	−	0.426867i	0.962539	+	0.271144i	$0.0874019\pi$
$858$		0			0
$859$	1145.91	−	661.590i	1.33400	−	0.770186i	0.348091	−	0.937461i	$-0.386830\pi$
$859$	1145.91	−	661.590i	1.33400	−	0.770186i	0.985910	+	0.167275i	$0.0534967\pi$
$860$	80.1241	+	20.6880i	0.0931676	+	0.0240558i
$861$		0			0
$862$	377.380	+	487.196i	0.437796	+	0.565192i
$863$			1455.50i			1.68656i	0.537473	+	0.843281i	$0.319379\pi$
$863$			1455.50i			1.68656i	−0.537473	+	0.843281i	$0.680621\pi$
$864$		0			0
$865$	−173.325			−0.200376
$866$	−276.445	+	214.133i	−0.319220	+	0.247267i
$867$		0			0
$868$	269.666	−	1044.41i	0.310675	−	1.20324i
$869$	363.719	+	629.981i	0.418549	+	0.724949i
$870$		0			0
$871$	−1020.20	−	589.014i	−1.17130	−	0.676250i
$872$	−136.507	−	317.213i	−0.156544	−	0.363776i
$873$		0			0
$874$	286.997	+	117.348i	0.328372	+	0.134265i
$875$	274.770	+	158.639i	0.314023	+	0.181301i
$876$		0			0
$877$	376.543	+	652.191i	0.429353	+	0.743661i	0.996816	−	0.0797378i	$-0.0254083\pi$
$877$	376.543	+	652.191i	0.429353	+	0.743661i	−0.567463	+	0.823399i	$0.692075\pi$
$878$	951.521	−	129.686i	1.08374	−	0.147707i
$879$		0			0
$880$	−148.328	+	268.087i	−0.168555	+	0.304644i
$881$	−996.177			−1.13073			−0.565367	−	0.824839i	$-0.691265\pi$
$881$	−996.177			−1.13073			−0.565367	+	0.824839i	$0.691265\pi$
$882$		0			0
$883$			950.011i			1.07589i	0.842980	+	0.537945i	$0.180799\pi$
$883$			950.011i			1.07589i	−0.842980	+	0.537945i	$0.819201\pi$
$884$	1262.32	−	350.607i	1.42797	−	0.396614i
$885$		0			0
$886$	1101.74	−	150.160i	1.24350	−	0.169481i
$887$	−375.063	+	216.543i	−0.422845	+	0.244129i	−0.696294	−	0.717757i	$-0.745169\pi$
$887$	−375.063	+	216.543i	−0.422845	+	0.244129i	0.273449	+	0.961887i	$0.411836\pi$
$888$		0			0
$889$	−577.240	+	999.809i	−0.649314	+	1.12464i
$890$	−52.7572	−	21.5714i	−0.0592777	−	0.0242376i
$891$		0			0
$892$	196.328	−	199.942i	0.220099	−	0.224150i
$893$	106.685	−	184.784i	0.119468	−	0.206925i
$894$		0			0
$895$	−188.498	+	108.830i	−0.210613	+	0.121597i
$896$	−448.886	+	625.352i	−0.500989	+	0.697937i
$897$		0			0
$898$	1267.62	−	981.892i	1.41160	−	1.09342i
$899$		−	193.775i		−	0.215545i
$900$		0			0
$901$	1847.63			2.05065
$902$	1285.98	+	1660.19i	1.42570	+	1.84057i
$903$		0			0
$904$	−388.827	+	521.342i	−0.430118	+	0.576706i
$905$	26.0650	+	45.1459i	0.0288011	+	0.0498850i
$906$		0			0
$907$	−593.837	−	342.852i	−0.654727	−	0.378007i	0.135538	−	0.990772i	$-0.456724\pi$
$907$	−593.837	−	342.852i	−0.654727	−	0.378007i	−0.790265	+	0.612765i	$0.790057\pi$
$908$	−836.148	+	851.539i	−0.920868	+	0.937818i
$909$		0			0
$910$	−61.0634	+	149.342i	−0.0671026	+	0.164113i
$911$	−31.2419	−	18.0375i	−0.0342941	−	0.0197997i	0.482755	−	0.875755i	$-0.339636\pi$
$911$	−31.2419	−	18.0375i	−0.0342941	−	0.0197997i	−0.517049	+	0.855956i	$0.672970\pi$
$912$		0			0
$913$	−314.164	−	544.148i	−0.344101	−	0.596000i
$914$	37.2265	+	273.134i	0.0407292	+	0.298834i
$915$		0			0
$916$	−1000.78	+	277.963i	−1.09255	+	0.303453i
$917$	852.758			0.929943
$918$		0			0
$919$		−	953.775i		−	1.03784i	−0.854823	−	0.518920i	$-0.826334\pi$
$919$		−	953.775i		−	1.03784i	0.854823	−	0.518920i	$-0.173666\pi$
$920$	−30.1582	+	256.097i	−0.0327806	+	0.278366i
$921$		0			0
$922$	−50.8692	−	373.231i	−0.0551726	−	0.404806i
$923$	902.096	−	520.826i	0.977353	−	0.564275i
$924$		0			0
$925$	−243.290	+	421.391i	−0.263016	+	0.455558i
$926$	415.121	−	1015.26i	0.448295	−	1.09639i
$927$		0			0
$928$	−49.9938	+	128.933i	−0.0538726	+	0.138937i
$929$	−74.8143	+	129.582i	−0.0805321	+	0.139486i	−0.903479	−	0.428633i	$-0.858995\pi$
$929$	−74.8143	+	129.582i	−0.0805321	+	0.139486i	0.822947	+	0.568119i	$0.192329\pi$
$930$		0			0
$931$	57.7477	−	33.3406i	0.0620276	−	0.0358116i
$932$	7.38192	−	28.5901i	0.00792052	−	0.0306760i
$933$		0			0
$934$	−757.623	−	978.087i	−0.811160	−	1.04720i
$935$			505.126i			0.540241i
$936$		0			0
$937$	−661.158			−0.705611			−0.352806	−	0.935697i	$-0.614772\pi$
$937$	−661.158			−0.705611			−0.352806	+	0.935697i	$0.614772\pi$
$938$	902.167	−	698.816i	0.961798	−	0.745006i
$939$		0			0
$940$	171.817	+	44.3630i	0.182784	+	0.0471947i
$941$	−233.357	−	404.186i	−0.247988	−	0.429528i	0.714979	−	0.699145i	$-0.246436\pi$
$941$	−233.357	−	404.186i	−0.247988	−	0.429528i	−0.962967	+	0.269618i	$0.913103\pi$
$942$		0			0
$943$	1530.65	+	883.721i	1.62317	+	0.937138i
$944$	−463.157	+	8.44812i	−0.490633	+	0.00894928i
$945$		0			0
$946$	628.328	+	256.912i	0.664195	+	0.271577i
$947$	−1128.20	−	651.368i	−1.19134	−	0.687823i	−0.232732	−	0.972541i	$-0.574767\pi$
$947$	−1128.20	−	651.368i	−1.19134	−	0.687823i	−0.958611	+	0.284718i	$0.908100\pi$
$948$		0			0
$949$	−346.622	−	600.366i	−0.365249	−	0.632630i
$950$	−245.409	+	33.4478i	−0.258325	+	0.0352082i
$951$		0			0
$952$	−148.426	+	1260.40i	−0.155909	+	1.32395i
$953$	21.6959			0.0227659			0.0113829	−	0.999935i	$-0.496377\pi$
$953$	21.6959			0.0227659			0.0113829	+	0.999935i	$0.496377\pi$
$954$		0			0
$955$			159.258i			0.166762i
$956$	−87.9133	−	316.523i	−0.0919595	−	0.331091i
$957$		0			0
$958$	−1526.74	+	208.085i	−1.59367	+	0.217207i
$959$	−457.169	+	263.947i	−0.476714	+	0.275231i
$960$		0			0
$961$	524.825	−	909.024i	0.546124	−	0.945914i
$962$	−469.284	−	191.882i	−0.487821	−	0.199461i
$963$		0			0
$964$	−1186.81	−	1165.36i	−1.23113	−	1.20888i
$965$	−13.5932	+	23.5441i	−0.0140862	+	0.0243980i
$966$		0			0
$967$	555.035	−	320.449i	0.573976	−	0.331385i	−0.184760	−	0.982784i	$-0.559151\pi$
$967$	555.035	−	320.449i	0.573976	−	0.331385i	0.758736	+	0.651399i	$0.225817\pi$
$968$	−923.869	+	1238.73i	−0.954411	+	1.27968i
$969$		0			0
$970$	−130.389	+	100.999i	−0.134422	+	0.104123i
$971$			1396.09i			1.43779i	0.695121	+	0.718893i	$0.255351\pi$
$971$			1396.09i			1.43779i	−0.695121	+	0.718893i	$0.744649\pi$
$972$		0			0
$973$	−1103.56			−1.13418
$974$	−672.639	−	868.373i	−0.690595	−	0.891554i
$975$		0			0
$976$	252.456	−	151.961i	0.258664	−	0.155697i
$977$	−504.976	−	874.644i	−0.516864	−	0.895235i	−0.999808	−	0.0195835i	$-0.993766\pi$
$977$	−504.976	−	874.644i	−0.516864	−	0.895235i	0.482944	−	0.875651i	$-0.339567\pi$
$978$		0			0
$979$	−404.912	−	233.776i	−0.413597	−	0.238791i
$980$	39.5696	+	38.8544i	0.0403771	+	0.0396473i
$981$		0			0
$982$	−17.4288	+	42.6256i	−0.0177483	+	0.0434069i
$983$	420.348	+	242.688i	0.427618	+	0.246885i	0.698331	−	0.715775i	$-0.253926\pi$
$983$	420.348	+	242.688i	0.427618	+	0.246885i	−0.270714	+	0.962660i	$0.587260\pi$
$984$		0			0
$985$	−208.243	−	360.687i	−0.211414	−	0.366180i
$986$	30.7887	+	225.899i	0.0312258	+	0.229107i
$987$		0			0
$988$	−69.0639	−	248.657i	−0.0699027	−	0.251677i
$989$	571.325			0.577679
$990$		0			0
$991$			265.720i			0.268133i	0.990972	+	0.134066i	$0.0428035\pi$
$991$			265.720i			0.268133i	−0.990972	+	0.134066i	$0.957196\pi$
$992$	−1118.17	+	899.228i	−1.12718	+	0.906480i
$993$		0			0
$994$	136.268	+	999.809i	0.137090	+	1.00584i
$995$	113.571	−	65.5703i	0.114142	−	0.0658998i
$996$		0			0
$997$	857.906	−	1485.94i	0.860487	−	1.49041i	−0.0109725	−	0.999940i	$-0.503493\pi$
$997$	857.906	−	1485.94i	0.860487	−	1.49041i	0.871460	−	0.490467i	$-0.163174\pi$
$998$	474.453	−	1160.37i	0.475404	−	1.16269i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.p.55.2		8
3.2	odd	2	inner	324.3.f.p.55.3		8
4.3	odd	2		324.3.f.o.55.2		8
9.2	odd	6		108.3.d.d.55.1	✓	8
9.4	even	3		324.3.f.o.271.2		8
9.5	odd	6		324.3.f.o.271.3		8
9.7	even	3		108.3.d.d.55.8	yes	8
12.11	even	2		324.3.f.o.55.3		8
36.7	odd	6		108.3.d.d.55.7	yes	8
36.11	even	6		108.3.d.d.55.2	yes	8
36.23	even	6	inner	324.3.f.p.271.4		8
36.31	odd	6	inner	324.3.f.p.271.1		8
72.11	even	6		1728.3.g.l.703.5		8
72.29	odd	6		1728.3.g.l.703.6		8
72.43	odd	6		1728.3.g.l.703.3		8
72.61	even	6		1728.3.g.l.703.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.d.d.55.1	✓	8	9.2	odd	6
108.3.d.d.55.2	yes	8	36.11	even	6
108.3.d.d.55.7	yes	8	36.7	odd	6
108.3.d.d.55.8	yes	8	9.7	even	3
324.3.f.o.55.2		8	4.3	odd	2
324.3.f.o.55.3		8	12.11	even	2
324.3.f.o.271.2		8	9.4	even	3
324.3.f.o.271.3		8	9.5	odd	6
324.3.f.p.55.2		8	1.1	even	1	trivial
324.3.f.p.55.3		8	3.2	odd	2	inner
324.3.f.p.271.1		8	36.31	odd	6	inner
324.3.f.p.271.4		8	36.23	even	6	inner
1728.3.g.l.703.3		8	72.43	odd	6
1728.3.g.l.703.4		8	72.61	even	6
1728.3.g.l.703.5		8	72.11	even	6
1728.3.g.l.703.6		8	72.29	odd	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.58114 + 1.22474i) q^{2} +(1.00000 - 3.87298i) q^{4} +(-0.540182 - 0.935622i) q^{5} +(-5.20820 - 3.00696i) q^{7} +(3.16228 + 7.34847i) q^{8} +O(q^{10})\)	\(q+(-1.58114 + 1.22474i) q^{2} +(1.00000 - 3.87298i) q^{4} +(-0.540182 - 0.935622i) q^{5} +(-5.20820 - 3.00696i) q^{7} +(3.16228 + 7.34847i) q^{8} +(2.00000 + 0.817763i) q^{10} +(15.3500 + 8.86234i) q^{11} +(-6.20820 - 10.7529i) q^{13} +(11.9176 - 1.62430i) q^{14} +(-14.0000 - 7.74597i) q^{16} -26.3786 q^{17} +5.19615i q^{19} +(-4.16383 + 1.15649i) q^{20} +(-35.1246 + 4.78727i) q^{22} +(-25.8384 + 14.9178i) q^{23} +(11.9164 - 20.6398i) q^{25} +(22.9856 + 9.39840i) q^{26} +(-16.8541 + 17.1643i) q^{28} +(-2.16073 + 3.74249i) q^{29} +(-38.8328 + 22.4201i) q^{31} +(31.6228 - 4.89898i) q^{32} +(41.7082 - 32.3070i) q^{34} +6.49721i q^{35} -20.4164 q^{37} +(-6.36396 - 8.21584i) q^{38} +(5.16718 - 6.92820i) q^{40} +(-29.6197 - 51.3028i) q^{41} +(-16.5836 - 9.57454i) q^{43} +(49.6737 - 50.5880i) q^{44} +(22.5836 - 55.2326i) q^{46} +(-35.5617 - 20.5315i) q^{47} +(-6.41641 - 11.1135i) q^{49} +(6.43702 + 47.2290i) q^{50} +(-47.8541 + 13.2913i) q^{52} -70.0430 q^{53} -19.1491i q^{55} +(5.62675 - 47.7812i) q^{56} +(-1.16718 - 8.56373i) q^{58} +(25.0733 - 14.4761i) q^{59} +(-9.20820 + 15.9491i) q^{61} +(33.9411 - 83.0096i) q^{62} +(-44.0000 + 46.4758i) q^{64} +(-6.70711 + 11.6171i) q^{65} +(82.1656 - 47.4383i) q^{67} +(-26.3786 + 102.164i) q^{68} +(-7.95743 - 10.2730i) q^{70} +83.8931i q^{71} +55.8328 q^{73} +(32.2812 - 25.0049i) q^{74} +(20.1246 + 5.19615i) q^{76} +(-53.2974 - 92.3137i) q^{77} +(35.5426 + 20.5205i) q^{79} +(0.315246 + 17.2829i) q^{80} +(109.666 + 44.8403i) q^{82} +(-30.7000 - 17.7247i) q^{83} +(14.2492 + 24.6804i) q^{85} +(37.9473 - 5.17199i) q^{86} +(-16.5836 + 140.824i) q^{88} -26.3786 q^{89} +74.6712i q^{91} +(31.9380 + 114.990i) q^{92} +(81.3738 - 11.0908i) q^{94} +(4.86163 - 2.80687i) q^{95} +(-38.1656 + 66.1048i) q^{97} +(23.7565 + 9.71359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 12 q^{7}+O(q^{10}) \) 8 * q + 8 * q^4 + 12 * q^7	\( 8 q + 8 q^{4} + 12 q^{7} + 16 q^{10} + 4 q^{13} - 112 q^{16} - 120 q^{22} - 12 q^{25} - 108 q^{28} - 96 q^{31} + 280 q^{34} - 56 q^{37} + 256 q^{40} - 240 q^{43} + 288 q^{46} + 56 q^{49} - 356 q^{52} - 224 q^{58} - 20 q^{61} - 352 q^{64} + 228 q^{67} + 312 q^{70} + 232 q^{73} + 660 q^{79} + 448 q^{82} - 208 q^{85} - 240 q^{88} + 168 q^{94} + 124 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 + 12 * q^7 + 16 * q^10 + 4 * q^13 - 112 * q^16 - 120 * q^22 - 12 * q^25 - 108 * q^28 - 96 * q^31 + 280 * q^34 - 56 * q^37 + 256 * q^40 - 240 * q^43 + 288 * q^46 + 56 * q^49 - 356 * q^52 - 224 * q^58 - 20 * q^61 - 352 * q^64 + 228 * q^67 + 312 * q^70 + 232 * q^73 + 660 * q^79 + 448 * q^82 - 208 * q^85 - 240 * q^88 + 168 * q^94 + 124 * q^97

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