LMFDB - Embedded newform 459.3.i.a.152.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,3,Mod(152,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.152"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	459.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.5068441341$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			152.4
Character	$\chi$	$=$	459.152
Dual form			459.3.i.a.305.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.92590 + 1.68927i) q^{2} +(3.70725 - 6.42114i) q^{4} +(-1.55065 + 2.68581i) q^{5} +(5.43225 - 3.13631i) q^{7} +11.5360i q^{8} -10.4779i q^{10} +(1.87833 + 3.25336i) q^{11} +(1.73808 - 3.01044i) q^{13} +(-10.5961 + 18.3530i) q^{14} +(-4.65840 - 8.06858i) q^{16} +(-0.217614 - 16.9986i) q^{17} -18.1729 q^{19} +(11.4973 + 19.9139i) q^{20} +(-10.9916 - 6.34600i) q^{22} +(0.563797 - 0.976526i) q^{23} +(7.69097 + 13.3211i) q^{25} +11.7443i q^{26} -46.5083i q^{28} +(-22.3389 - 38.6921i) q^{29} +(-13.2930 - 7.67472i) q^{31} +(-12.7019 - 7.33345i) q^{32} +(29.3519 + 49.3686i) q^{34} +19.4533i q^{35} -18.6072i q^{37} +(53.1720 - 30.6989i) q^{38} +(-30.9835 - 17.8883i) q^{40} +(29.8151 - 51.6413i) q^{41} +(-16.0790 - 27.8497i) q^{43} +27.8537 q^{44} +3.80962i q^{46} +(38.0772 - 21.9839i) q^{47} +(-4.82711 + 8.36080i) q^{49} +(-45.0059 - 25.9842i) q^{50} +(-12.8870 - 22.3209i) q^{52} +89.1367i q^{53} -11.6505 q^{55} +(36.1805 + 62.6664i) q^{56} +(130.723 + 75.4728i) q^{58} +(-48.3462 - 27.9127i) q^{59} +(84.9883 - 49.0680i) q^{61} +51.8586 q^{62} +86.8198 q^{64} +(5.39030 + 9.33627i) q^{65} +(17.8439 - 30.9065i) q^{67} +(-109.957 - 61.6207i) q^{68} +(-32.8618 - 56.9183i) q^{70} +121.996 q^{71} +34.4286i q^{73} +(31.4325 + 54.4427i) q^{74} +(-67.3714 + 116.691i) q^{76} +(20.4071 + 11.7820i) q^{77} +(91.8612 - 53.0361i) q^{79} +28.8942 q^{80} +201.463i q^{82} +(85.2416 - 49.2143i) q^{83} +(45.9924 + 25.7744i) q^{85} +(94.0911 + 54.3235i) q^{86} +(-37.5308 + 21.6684i) q^{88} +59.2783i q^{89} -21.8046i q^{91} +(-4.18027 - 7.24045i) q^{92} +(-74.2733 + 128.645i) q^{94} +(28.1798 - 48.8088i) q^{95} +(-8.23298 + 4.75331i) q^{97} -32.6171i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.92590	+	1.68927i	−1.46295	+	0.844634i	−0.999147	−	0.0413052i	$-0.986848\pi$
$2$	−2.92590	+	1.68927i	−1.46295	+	0.844634i	−0.463802	+	0.885939i	$0.653515\pi$
$3$		0			0
$3$		0			0
$4$	3.70725	−	6.42114i	0.926812	−	1.60529i
$5$	−1.55065	+	2.68581i	−0.310130	+	0.537161i	−0.978390	−	0.206767i	$-0.933706\pi$
$5$	−1.55065	+	2.68581i	−0.310130	+	0.537161i	0.668260	+	0.743928i	$0.267039\pi$
$6$		0			0
$7$	5.43225	−	3.13631i	0.776036	−	0.448044i	−0.0589878	−	0.998259i	$-0.518787\pi$
$7$	5.43225	−	3.13631i	0.776036	−	0.448044i	0.835023	+	0.550214i	$0.185454\pi$
$8$			11.5360i			1.44200i
$9$		0			0
$10$		−	10.4779i		−	1.04779i
$11$	1.87833	+	3.25336i	0.170757	+	0.295760i	0.938685	−	0.344777i	$-0.112045\pi$
$11$	1.87833	+	3.25336i	0.170757	+	0.295760i	−0.767928	+	0.640537i	$0.778712\pi$
$12$		0			0
$13$	1.73808	−	3.01044i	0.133698	−	0.231572i	−0.791401	−	0.611297i	$-0.790648\pi$
$13$	1.73808	−	3.01044i	0.133698	−	0.231572i	0.925099	+	0.379725i	$0.123981\pi$
$14$	−10.5961	+	18.3530i	−0.756867	+	1.31093i
$15$		0			0
$16$	−4.65840	−	8.06858i	−0.291150	−	0.504286i
$17$	−0.217614	−	16.9986i	−0.0128008	−	0.999918i
$17$	−0.217614	−	16.9986i	−0.0128008	−	0.999918i
$18$		0			0
$19$	−18.1729			−0.956467			−0.478234	−	0.878233i	$-0.658723\pi$
$19$	−18.1729			−0.956467			−0.478234	+	0.878233i	$0.658723\pi$
$20$	11.4973	+	19.9139i	0.574865	+	0.995695i
$21$		0			0
$22$	−10.9916	−	6.34600i	−0.499618	−	0.288454i
$23$	0.563797	−	0.976526i	0.0245129	−	0.0424576i	−0.853509	−	0.521079i	$-0.825530\pi$
$23$	0.563797	−	0.976526i	0.0245129	−	0.0424576i	0.878022	+	0.478621i	$0.158863\pi$
$24$		0			0
$25$	7.69097	+	13.3211i	0.307639	+	0.532846i
$26$			11.7443i			0.451704i
$27$		0			0
$28$		−	46.5083i		−	1.66101i
$29$	−22.3389	−	38.6921i	−0.770307	−	1.33421i	−0.937394	−	0.348269i	$-0.886769\pi$
$29$	−22.3389	−	38.6921i	−0.770307	−	1.33421i	0.167087	−	0.985942i	$-0.446564\pi$
$30$		0			0
$31$	−13.2930	−	7.67472i	−0.428807	−	0.247572i	0.270031	−	0.962852i	$-0.412966\pi$
$31$	−13.2930	−	7.67472i	−0.428807	−	0.247572i	−0.698838	+	0.715280i	$0.746299\pi$
$32$	−12.7019	−	7.33345i	−0.396934	−	0.229170i
$33$		0			0
$34$	29.3519	+	49.3686i	0.863292	+	1.45202i
$35$			19.4533i			0.555808i
$36$		0			0
$37$		−	18.6072i		−	0.502897i	−0.967871	−	0.251448i	$-0.919093\pi$
$37$		−	18.6072i		−	0.502897i	0.967871	−	0.251448i	$-0.0809069\pi$
$38$	53.1720	−	30.6989i	1.39926	−	0.807865i
$39$		0			0
$40$	−30.9835	−	17.8883i	−0.774586	−	0.447208i
$41$	29.8151	−	51.6413i	0.727198	−	1.25954i	−0.230865	−	0.972986i	$-0.574156\pi$
$41$	29.8151	−	51.6413i	0.727198	−	1.25954i	0.958063	−	0.286558i	$-0.0925110\pi$
$42$		0			0
$43$	−16.0790	−	27.8497i	−0.373931	−	0.647667i	0.616236	−	0.787562i	$-0.288657\pi$
$43$	−16.0790	−	27.8497i	−0.373931	−	0.647667i	−0.990166	+	0.139895i	$0.955324\pi$
$44$	27.8537			0.633039
$45$		0			0
$46$			3.80962i			0.0828178i
$47$	38.0772	−	21.9839i	0.810153	−	0.467742i	−0.0368561	−	0.999321i	$-0.511734\pi$
$47$	38.0772	−	21.9839i	0.810153	−	0.467742i	0.847009	+	0.531579i	$0.178401\pi$
$48$		0			0
$49$	−4.82711	+	8.36080i	−0.0985125	+	0.170629i
$50$	−45.0059	−	25.9842i	−0.900119	−	0.519684i
$51$		0			0
$52$	−12.8870	−	22.3209i	−0.247826	−	0.429248i
$53$			89.1367i			1.68183i	0.541171	+	0.840913i	$0.317981\pi$
$53$			89.1367i			1.68183i	−0.541171	+	0.840913i	$0.682019\pi$
$54$		0			0
$55$	−11.6505			−0.211828
$56$	36.1805	+	62.6664i	0.646080	+	1.11904i
$57$		0			0
$58$	130.723	+	75.4728i	2.25384	+	1.30126i
$59$	−48.3462	−	27.9127i	−0.819427	−	0.473097i	0.0307916	−	0.999526i	$-0.490197\pi$
$59$	−48.3462	−	27.9127i	−0.819427	−	0.473097i	−0.850219	+	0.526429i	$0.823531\pi$
$60$		0			0
$61$	84.9883	−	49.0680i	1.39325	−	0.804394i	0.399577	−	0.916699i	$-0.369157\pi$
$61$	84.9883	−	49.0680i	1.39325	−	0.804394i	0.993674	+	0.112306i	$0.0358236\pi$
$62$	51.8586			0.836429
$63$		0			0
$64$	86.8198			1.35656
$65$	5.39030	+	9.33627i	0.0829277	+	0.143635i
$66$		0			0
$67$	17.8439	−	30.9065i	0.266326	−	0.461291i	−0.701584	−	0.712587i	$-0.747523\pi$
$67$	17.8439	−	30.9065i	0.266326	−	0.461291i	0.967910	+	0.251296i	$0.0808567\pi$
$68$	−109.957	−	61.6207i	−1.61702	−	0.906187i
$69$		0			0
$70$	−32.8618	−	56.9183i	−0.469454	−	0.813119i
$71$	121.996			1.71825			0.859124	−	0.511767i	$-0.171009\pi$
$71$	121.996			1.71825			0.859124	+	0.511767i	$0.171009\pi$
$72$		0			0
$73$			34.4286i			0.471625i	0.971799	+	0.235812i	$0.0757751\pi$
$73$			34.4286i			0.471625i	−0.971799	+	0.235812i	$0.924225\pi$
$74$	31.4325	+	54.4427i	0.424764	+	0.735712i
$75$		0			0
$76$	−67.3714	+	116.691i	−0.886466	+	1.53540i
$77$	20.4071	+	11.7820i	0.265027	+	0.153014i
$78$		0			0
$79$	91.8612	−	53.0361i	1.16280	−	0.671343i	0.210827	−	0.977523i	$-0.432384\pi$
$79$	91.8612	−	53.0361i	1.16280	−	0.671343i	0.951974	+	0.306180i	$0.0990510\pi$
$80$	28.8942			0.361177
$81$		0			0
$82$			201.463i			2.45686i
$83$	85.2416	−	49.2143i	1.02701	−	0.592943i	0.110881	−	0.993834i	$-0.464633\pi$
$83$	85.2416	−	49.2143i	1.02701	−	0.592943i	0.916126	+	0.400891i	$0.131299\pi$
$84$		0			0
$85$	45.9924	+	25.7744i	0.541087	+	0.303229i
$86$	94.0911	+	54.3235i	1.09408	+	0.631669i
$87$		0			0
$88$	−37.5308	+	21.6684i	−0.426486	+	0.246232i
$89$			59.2783i			0.666048i	0.942918	+	0.333024i	$0.108069\pi$
$89$			59.2783i			0.666048i	−0.942918	+	0.333024i	$0.891931\pi$
$90$		0			0
$91$		−	21.8046i		−	0.239611i
$92$	−4.18027	−	7.24045i	−0.0454378	−	0.0787005i
$93$		0			0
$94$	−74.2733	+	128.645i	−0.790141	+	1.36856i
$95$	28.1798	−	48.8088i	0.296629	−	0.513777i
$96$		0			0
$97$	−8.23298	+	4.75331i	−0.0848761	+	0.0490032i	−0.541837	−	0.840483i	$-0.682271\pi$
$97$	−8.23298	+	4.75331i	−0.0848761	+	0.0490032i	0.456961	+	0.889487i	$0.348938\pi$
$98$		−	32.6171i		−	0.332828i
$99$		0			0
$100$	114.049			1.14049
$101$	−40.1218	+	23.1644i	−0.397246	+	0.229350i	−0.685295	−	0.728266i	$-0.740327\pi$
$101$	−40.1218	+	23.1644i	−0.397246	+	0.229350i	0.288049	+	0.957616i	$0.406993\pi$
$102$		0			0
$103$	−24.2875	+	42.0672i	−0.235801	+	0.408419i	−0.959505	−	0.281691i	$-0.909105\pi$
$103$	−24.2875	+	42.0672i	−0.235801	+	0.408419i	0.723704	+	0.690110i	$0.242438\pi$
$104$	34.7284	+	20.0505i	0.333927	+	0.192793i
$105$		0			0
$106$	−150.576	−	260.805i	−1.42053	−	2.46042i
$107$	−35.7990			−0.334570			−0.167285	−	0.985909i	$-0.553500\pi$
$107$	−35.7990			−0.334570			−0.167285	+	0.985909i	$0.553500\pi$
$108$		0			0
$109$		−	127.370i		−	1.16853i	−0.811561	−	0.584267i	$-0.801382\pi$
$109$		−	127.370i		−	1.16853i	0.811561	−	0.584267i	$-0.198618\pi$
$110$	34.0882	−	19.6808i	0.309893	−	0.178917i
$111$		0			0
$112$	−50.6112	−	29.2204i	−0.451885	−	0.260896i
$113$	94.1325	−	163.042i	0.833031	−	1.44285i	−0.0625918	−	0.998039i	$-0.519937\pi$
$113$	94.1325	−	163.042i	0.833031	−	1.44285i	0.895623	−	0.444814i	$-0.146730\pi$
$114$		0			0
$115$	1.74851	+	3.02850i	0.0152044	+	0.0263348i
$116$	−331.264			−2.85572
$117$		0			0
$118$	188.608			1.59837
$119$	−54.4950	−	91.6582i	−0.457942	−	0.770237i
$120$		0			0
$121$	53.4438	−	92.5673i	0.441684	−	0.765019i
$122$	−165.778	+	287.136i	−1.35884	+	2.35357i
$123$		0			0
$124$	−98.5610	+	56.9042i	−0.794847	+	0.458905i
$125$	−125.237			−1.00189
$126$		0			0
$127$	−64.3461			−0.506662			−0.253331	−	0.967380i	$-0.581526\pi$
$127$	−64.3461			−0.506662			−0.253331	+	0.967380i	$0.581526\pi$
$128$	−203.218	+	117.328i	−1.58764	+	0.916626i
$129$		0			0
$130$	−31.5429	−	18.2113i	−0.242638	−	0.140087i
$131$	108.920	−	188.655i	0.831452	−	1.44012i	−0.0654350	−	0.997857i	$-0.520843\pi$
$131$	108.920	−	188.655i	0.831452	−	1.44012i	0.896887	−	0.442260i	$-0.145823\pi$
$132$		0			0
$133$	−98.7196	+	56.9958i	−0.742253	+	0.428540i
$134$			120.572i			0.899793i
$135$		0			0
$136$	196.096	−	2.51040i	1.44188	−	0.0184588i
$137$	−26.0269	+	15.0267i	−0.189978	+	0.109684i	−0.591972	−	0.805958i	$-0.701650\pi$
$137$	−26.0269	+	15.0267i	−0.189978	+	0.109684i	0.401995	+	0.915642i	$0.368317\pi$
$138$		0			0
$139$	−162.976	−	94.0945i	−1.17249	−	0.676939i	−0.218227	−	0.975898i	$-0.570027\pi$
$139$	−162.976	−	94.0945i	−1.17249	−	0.676939i	−0.954266	+	0.298959i	$0.903361\pi$
$140$	124.912	+	72.1182i	0.892231	+	0.515130i
$141$		0			0
$142$	−356.947	+	206.083i	−2.51371	+	1.45129i
$143$	13.0587			0.0913197
$144$		0			0
$145$	138.559			0.955582
$146$	−58.1591	−	100.735i	−0.398350	−	0.689963i
$147$		0			0
$148$	−119.479	−	68.9815i	−0.807293	−	0.466091i
$149$	−132.226	−	76.3405i	−0.887420	−	0.512352i	−0.0143224	−	0.999897i	$-0.504559\pi$
$149$	−132.226	−	76.3405i	−0.887420	−	0.512352i	−0.873098	+	0.487545i	$0.837892\pi$
$150$		0			0
$151$	−81.9727	−	141.981i	−0.542866	−	0.940271i	−0.998738	−	0.0502257i	$-0.984006\pi$
$151$	−81.9727	−	141.981i	−0.542866	−	0.940271i	0.455872	−	0.890045i	$-0.349327\pi$
$152$		−	209.642i		−	1.37923i
$153$		0			0
$154$	−79.6121			−0.516962
$155$	41.2256	−	23.8016i	0.265972	−	0.153559i
$156$		0			0
$157$	−67.7624	+	117.368i	−0.431608	+	0.747567i	−0.997012	−	0.0772472i	$-0.975387\pi$
$157$	−67.7624	+	117.368i	−0.431608	+	0.747567i	0.565404	+	0.824814i	$0.308720\pi$
$158$	−179.184	+	310.356i	−1.13408	+	1.96428i
$159$		0			0
$160$	39.3924	−	22.7432i	0.246203	−	0.142145i
$161$		−	7.07297i		−	0.0439315i
$162$		0			0
$163$			27.3494i			0.167788i	0.996475	+	0.0838939i	$0.0267357\pi$
$163$			27.3494i			0.167788i	−0.996475	+	0.0838939i	$0.973264\pi$
$164$	−221.064	−	382.894i	−1.34795	−	2.33472i
$165$		0			0
$166$	−166.272	+	287.992i	−1.00164	+	1.73489i
$167$	−129.894	+	224.983i	−0.777810	+	1.34721i	0.155392	+	0.987853i	$0.450336\pi$
$167$	−129.894	+	224.983i	−0.777810	+	1.34721i	−0.933202	+	0.359353i	$0.882997\pi$
$168$		0			0
$169$	78.4582	+	135.894i	0.464250	+	0.804104i
$170$	−178.109	+	2.28013i	−1.04770	+	0.0134125i
$171$		0			0
$172$	−238.436			−1.38625
$173$	36.9180	+	63.9438i	0.213399	+	0.369617i	0.952776	−	0.303674i	$-0.0982133\pi$
$173$	36.9180	+	63.9438i	0.213399	+	0.369617i	−0.739377	+	0.673291i	$0.764880\pi$
$174$		0			0
$175$	83.5585	+	48.2425i	0.477477	+	0.275672i
$176$	17.5000	−	30.3109i	0.0994318	−	0.172221i
$177$		0			0
$178$	−100.137	−	173.442i	−0.562567	−	0.974394i
$179$		−	45.6082i		−	0.254795i	−0.991852	−	0.127397i	$-0.959338\pi$
$179$		−	45.6082i		−	0.254795i	0.991852	−	0.127397i	$-0.0406623\pi$
$180$		0			0
$181$		−	160.242i		−	0.885315i	−0.896691	−	0.442657i	$-0.854036\pi$
$181$		−	160.242i		−	0.885315i	0.896691	−	0.442657i	$-0.145964\pi$
$182$	36.8338	+	63.7980i	0.202383	+	0.350538i
$183$		0			0
$184$	11.2652	+	6.50397i	0.0612239	+	0.0353476i
$185$	49.9753	+	28.8532i	0.270137	+	0.155963i
$186$		0			0
$187$	54.8938	−	32.6369i	0.293550	−	0.174529i
$188$		−	325.999i		−	1.73404i
$189$		0			0
$190$			190.413i			1.00217i
$191$	198.771	−	114.761i	1.04069	−	0.600842i	0.120660	−	0.992694i	$-0.461499\pi$
$191$	198.771	−	114.761i	1.04069	−	0.600842i	0.920028	+	0.391852i	$0.128166\pi$
$192$		0			0
$193$	−195.454	−	112.845i	−1.01271	−	0.584690i	−0.100728	−	0.994914i	$-0.532117\pi$
$193$	−195.454	−	112.845i	−1.01271	−	0.584690i	−0.911985	+	0.410224i	$0.865450\pi$
$194$	16.0592	−	27.8154i	0.0827796	−	0.143378i
$195$		0			0
$196$	35.7906	+	61.9911i	0.182605	+	0.316281i
$197$	−21.3390			−0.108320			−0.0541598	−	0.998532i	$-0.517248\pi$
$197$	−21.3390			−0.108320			−0.0541598	+	0.998532i	$0.517248\pi$
$198$		0			0
$199$		−	226.404i		−	1.13771i	−0.822438	−	0.568855i	$-0.807387\pi$
$199$		−	226.404i		−	1.13771i	0.822438	−	0.568855i	$-0.192613\pi$
$200$	−153.673	+	88.7230i	−0.768364	+	0.443615i
$201$		0			0
$202$	78.2616	−	135.553i	0.387434	−	0.671055i
$203$	−242.701	−	140.124i	−1.19557	−	0.690264i
$204$		0			0
$205$	92.4656	+	160.155i	0.451052	+	0.781245i
$206$		−	164.112i		−	0.796662i
$207$		0			0
$208$	−32.3866			−0.155705
$209$	−34.1346	−	59.1229i	−0.163324	−	0.282885i
$210$		0			0
$211$	278.389	+	160.728i	1.31938	+	0.761744i	0.983629	−	0.180206i	$-0.0576766\pi$
$211$	278.389	+	160.728i	1.31938	+	0.761744i	0.335751	+	0.941951i	$0.391010\pi$
$212$	572.360	+	330.452i	2.69981	+	1.55874i
$213$		0			0
$214$	104.744	−	60.4740i	0.489458	−	0.282589i
$215$	99.7317			0.463869
$216$		0			0
$217$	−96.2812			−0.443692
$218$	215.162	+	372.672i	0.986983	+	1.70951i
$219$		0			0
$220$	−43.1914	+	74.8097i	−0.196325	+	0.340044i
$221$	−51.5515	−	28.8898i	−0.233265	−	0.130723i
$222$		0			0
$223$	214.036	+	370.721i	0.959803	+	1.66243i	0.722973	+	0.690877i	$0.242775\pi$
$223$	214.036	+	370.721i	0.959803	+	1.66243i	0.236831	+	0.971551i	$0.423891\pi$
$224$	−91.9999			−0.410714
$225$		0			0
$226$			636.060i			2.81443i
$227$	97.0001	+	168.009i	0.427313	+	0.740128i	0.996633	−	0.0819880i	$-0.0261269\pi$
$227$	97.0001	+	168.009i	0.427313	+	0.740128i	−0.569320	+	0.822116i	$0.692794\pi$
$228$		0			0
$229$	190.008	−	329.103i	0.829728	−	1.43713i	−0.0685233	−	0.997650i	$-0.521829\pi$
$229$	190.008	−	329.103i	0.829728	−	1.43713i	0.898251	−	0.439482i	$-0.144838\pi$
$230$	−10.2319	−	5.90739i	−0.0444865	−	0.0256843i
$231$		0			0
$232$	446.353	−	257.702i	1.92393	−	1.11078i
$233$	320.365			1.37496			0.687478	−	0.726205i	$-0.258718\pi$
$233$	320.365			1.37496			0.687478	+	0.726205i	$0.258718\pi$
$234$		0			0
$235$			136.357i			0.580243i
$236$	−358.463	+	206.959i	−1.51891	+	0.876944i
$237$		0			0
$238$	314.282	+	176.126i	1.32051	+	0.740024i
$239$	274.338	+	158.389i	1.14786	+	0.662716i	0.948364	−	0.317183i	$-0.102737\pi$
$239$	274.338	+	158.389i	1.14786	+	0.662716i	0.199494	+	0.979899i	$0.436070\pi$
$240$		0			0
$241$	−343.500	+	198.320i	−1.42531	+	0.822903i	−0.996746	−	0.0806081i	$-0.974314\pi$
$241$	−343.500	+	198.320i	−1.42531	+	0.822903i	−0.428564	+	0.903511i	$0.640980\pi$
$242$			361.123i			1.49224i
$243$		0			0
$244$		−	727.630i		−	2.98209i
$245$	−14.9703	−	25.9294i	−0.0611034	−	0.105834i
$246$		0			0
$247$	−31.5859	+	54.7083i	−0.127878	+	0.221491i
$248$	88.5356	−	153.348i	0.356998	−	0.618339i
$249$		0			0
$250$	366.429	−	211.558i	1.46572	−	0.846232i
$251$			34.8071i			0.138674i	0.997593	+	0.0693369i	$0.0220883\pi$
$251$			34.8071i			0.138674i	−0.997593	+	0.0693369i	$0.977912\pi$
$252$		0			0
$253$	4.23599			0.0167430
$254$	188.270	−	108.698i	0.741221	−	0.427944i
$255$		0			0
$256$	222.757	−	385.827i	0.870146	−	1.50714i
$257$	−186.465	−	107.655i	−0.725544	−	0.418893i	0.0912460	−	0.995828i	$-0.470915\pi$
$257$	−186.465	−	107.655i	−0.725544	−	0.418893i	−0.816790	+	0.576936i	$0.804248\pi$
$258$		0			0
$259$	−58.3579	−	101.079i	−0.225320	−	0.390266i
$260$	79.9327			0.307434
$261$		0			0
$262$			735.981i			2.80909i
$263$	−93.8398	+	54.1785i	−0.356806	+	0.206002i	−0.667679	−	0.744450i	$-0.732712\pi$
$263$	−93.8398	+	54.1785i	−0.356806	+	0.206002i	0.310873	+	0.950451i	$0.399379\pi$
$264$		0			0
$265$	−239.404	−	138.220i	−0.903411	−	0.521585i
$266$	192.562	−	333.528i	0.723918	−	1.25386i
$267$		0			0
$268$	−132.303	−	229.156i	−0.493669	−	0.855060i
$269$	−16.9331			−0.0629482			−0.0314741	−	0.999505i	$-0.510020\pi$
$269$	−16.9331			−0.0629482			−0.0314741	+	0.999505i	$0.510020\pi$
$270$		0			0
$271$	99.3182			0.366488			0.183244	−	0.983067i	$-0.441340\pi$
$271$	99.3182			0.366488			0.183244	+	0.983067i	$0.441340\pi$
$272$	−136.141	+	80.9421i	−0.500518	+	0.297581i
$273$		0			0
$274$	50.7681	−	87.9329i	0.185285	−	0.320923i
$275$	−28.8923	+	50.0430i	−0.105063	+	0.181974i
$276$		0			0
$277$	−113.792	+	65.6978i	−0.410801	+	0.237176i	−0.691134	−	0.722727i	$-0.742888\pi$
$277$	−113.792	+	65.6978i	−0.410801	+	0.237176i	0.280333	+	0.959903i	$0.409555\pi$
$278$	635.803			2.28706
$279$		0			0
$280$	−224.413			−0.801476
$281$	−225.418	+	130.145i	−0.802201	+	0.463151i	−0.844240	−	0.535965i	$-0.819948\pi$
$281$	−225.418	+	130.145i	−0.802201	+	0.463151i	0.0420394	+	0.999116i	$0.486614\pi$
$282$		0			0
$283$	−133.186	−	76.8948i	−0.470621	−	0.271713i	0.245879	−	0.969301i	$-0.420923\pi$
$283$	−133.186	−	76.8948i	−0.470621	−	0.271713i	−0.716500	+	0.697588i	$0.754257\pi$
$284$	452.268	−	783.352i	1.59249	−	2.75828i
$285$		0			0
$286$	−38.2085	+	22.0597i	−0.133596	+	0.0771317i
$287$		−	374.038i		−	1.30327i
$288$		0			0
$289$	−288.905	+	7.39828i	−0.999672	+	0.0255996i
$290$	−405.411	+	234.064i	−1.39797	+	0.807117i
$291$		0			0
$292$	221.071	+	127.635i	0.757093	+	0.437108i
$293$	−82.2824	−	47.5058i	−0.280827	−	0.162136i	0.352971	−	0.935634i	$-0.385172\pi$
$293$	−82.2824	−	47.5058i	−0.280827	−	0.162136i	−0.633798	+	0.773499i	$0.718505\pi$
$294$		0			0
$295$	149.936	−	86.5657i	0.508258	−	0.293443i
$296$	214.653			0.725177
$297$		0			0
$298$	515.838			1.73100
$299$	−1.95985	−	3.39455i	−0.00655467	−	0.0113530i
$300$		0			0
$301$	−174.690	−	100.858i	−0.580367	−	0.335075i
$302$	479.687	+	276.948i	1.58837	+	0.917045i
$303$		0			0
$304$	84.6565	+	146.629i	0.278475	+	0.482333i
$305$			304.349i			0.997867i
$306$		0			0
$307$	−471.076			−1.53445			−0.767224	−	0.641379i	$-0.778363\pi$
$307$	−471.076			−1.53445			−0.767224	+	0.641379i	$0.778363\pi$
$308$	151.308	−	87.3579i	0.491261	−	0.283630i
$309$		0			0
$310$	−80.4146	+	139.282i	−0.259402	+	0.449297i
$311$	−190.810	+	330.493i	−0.613539	+	1.06268i	0.377101	+	0.926172i	$0.376921\pi$
$311$	−190.810	+	330.493i	−0.613539	+	1.06268i	−0.990639	+	0.136508i	$0.956412\pi$
$312$		0			0
$313$	−10.4278	+	6.02047i	−0.0333155	+	0.0192347i	−0.516565	−	0.856248i	$-0.672790\pi$
$313$	−10.4278	+	6.02047i	−0.0333155	+	0.0192347i	0.483250	+	0.875483i	$0.339456\pi$
$314$		−	457.876i		−	1.45820i
$315$		0			0
$316$		−	786.472i		−	2.48884i
$317$	−137.067	−	237.407i	−0.432388	−	0.748919i	0.564690	−	0.825303i	$-0.308996\pi$
$317$	−137.067	−	237.407i	−0.432388	−	0.748919i	−0.997078	+	0.0763844i	$0.975662\pi$
$318$		0			0
$319$	83.9196	−	145.353i	0.263071	−	0.455652i
$320$	−134.627	+	233.181i	−0.420710	+	0.728691i
$321$		0			0
$322$	11.9481	+	20.6948i	0.0371060	+	0.0642695i
$323$	3.95468	+	308.914i	0.0122436	+	0.956389i
$324$		0			0
$325$	53.4700			0.164523
$326$	−46.2005	−	80.0216i	−0.141719	−	0.245465i
$327$		0			0
$328$	595.734	+	343.947i	1.81626	+	1.04862i
$329$	137.897	−	238.844i	0.419138	−	0.725969i
$330$		0			0
$331$	57.1777	+	99.0347i	0.172742	+	0.299199i	0.939378	−	0.342884i	$-0.111404\pi$
$331$	57.1777	+	99.0347i	0.172742	+	0.299199i	−0.766635	+	0.642083i	$0.778071\pi$
$332$		−	729.798i		−	2.19819i
$333$		0			0
$334$		−	877.704i		−	2.62786i
$335$	55.3392	+	95.8503i	0.165192	+	0.286120i
$336$		0			0
$337$	242.067	+	139.758i	0.718301	+	0.414711i	0.814127	−	0.580687i	$-0.197216\pi$
$337$	242.067	+	139.758i	0.718301	+	0.414711i	−0.0958260	+	0.995398i	$0.530549\pi$
$338$	−459.121	−	265.074i	−1.35835	−	0.784242i
$339$		0			0
$340$	336.007	−	199.772i	0.988255	−	0.587563i
$341$		−	57.6626i		−	0.169098i
$342$		0			0
$343$			367.916i			1.07264i
$344$	321.274	−	185.488i	0.933936	−	0.539208i
$345$		0			0
$346$	−216.036	−	124.729i	−0.624383	−	0.360488i
$347$	−162.231	+	280.992i	−0.467523	+	0.809774i	−0.999311	−	0.0371034i	$-0.988187\pi$
$347$	−162.231	+	280.992i	−0.467523	+	0.809774i	0.531788	+	0.846877i	$0.321520\pi$
$348$		0			0
$349$	−139.028	−	240.803i	−0.398360	−	0.689980i	0.595164	−	0.803604i	$-0.297087\pi$
$349$	−139.028	−	240.803i	−0.398360	−	0.689980i	−0.993524	+	0.113625i	$0.963754\pi$
$350$	−325.978			−0.931366
$351$		0			0
$352$		−	55.0985i		−	0.156530i
$353$	410.603	−	237.062i	1.16318	−	0.671563i	0.211117	−	0.977461i	$-0.432290\pi$
$353$	410.603	−	237.062i	1.16318	−	0.671563i	0.952065	+	0.305897i	$0.0989564\pi$
$354$		0			0
$355$	−189.173	+	327.657i	−0.532881	+	0.922976i
$356$	380.635	+	219.759i	1.06920	+	0.617302i
$357$		0			0
$358$	77.0445	+	133.445i	0.215208	+	0.372751i
$359$			486.308i			1.35462i	0.735699	+	0.677309i	$0.236854\pi$
$359$			486.308i			1.35462i	−0.735699	+	0.677309i	$0.763146\pi$
$360$		0			0
$361$	−30.7465			−0.0851704
$362$	270.692	+	468.851i	0.747767	+	1.29517i
$363$		0			0
$364$	−140.010	−	80.8351i	−0.384644	−	0.222074i
$365$	−92.4686	−	53.3868i	−0.253339	−	0.146265i
$366$		0			0
$367$	−282.323	+	162.999i	−0.769271	+	0.444139i	−0.832615	−	0.553853i	$-0.813157\pi$
$367$	−282.323	+	162.999i	−0.769271	+	0.444139i	0.0633433	+	0.997992i	$0.479824\pi$
$368$	−10.5056			−0.0285477
$369$		0			0
$370$	−194.963			−0.526928
$371$	279.560	+	484.213i	0.753532	+	1.30516i
$372$		0			0
$373$	167.244	−	289.676i	0.448377	−	0.776611i	−0.549904	−	0.835228i	$-0.685336\pi$
$373$	167.244	−	289.676i	0.448377	−	0.776611i	0.998281	+	0.0586169i	$0.0186690\pi$
$374$	−105.481	+	188.223i	−0.282035	+	0.503269i
$375$		0			0
$376$	253.606	+	439.259i	0.674484	+	1.16824i
$377$	−155.307			−0.411955
$378$		0			0
$379$		−	56.3312i		−	0.148631i	−0.997235	−	0.0743155i	$-0.976323\pi$
$379$		−	56.3312i		−	0.148631i	0.997235	−	0.0743155i	$-0.0236772\pi$
$380$	−208.939	−	361.893i	−0.549839	−	0.952350i
$381$		0			0
$382$	−387.723	+	671.556i	−1.01498	+	1.75800i
$383$	41.7301	+	24.0929i	0.108956	+	0.0629057i	0.553488	−	0.832857i	$-0.313297\pi$
$383$	41.7301	+	24.0929i	0.108956	+	0.0629057i	−0.444532	+	0.895763i	$0.646630\pi$
$384$		0			0
$385$	−63.2885	+	36.5397i	−0.164386	+	0.0949082i
$386$	762.502			1.97539
$387$		0			0
$388$			70.4869i			0.181667i
$389$	30.8371	−	17.8038i	0.0792728	−	0.0457682i	−0.459840	−	0.888002i	$-0.652093\pi$
$389$	30.8371	−	17.8038i	0.0792728	−	0.0457682i	0.539112	+	0.842234i	$0.318760\pi$
$390$		0			0
$391$	−16.7223	−	9.37126i	−0.0427679	−	0.0239674i
$392$	−96.4502	−	55.6856i	−0.246046	−	0.142055i
$393$		0			0
$394$	62.4356	−	36.0472i	0.158466	−	0.0914904i
$395$			328.962i			0.832815i
$396$		0			0
$397$		−	151.892i		−	0.382601i	−0.981532	−	0.191300i	$-0.938730\pi$
$397$		−	151.892i		−	0.382601i	0.981532	−	0.191300i	$-0.0612704\pi$
$398$	382.457	+	662.435i	0.960948	+	1.66441i
$399$		0			0
$400$	71.6551	−	124.110i	0.179138	−	0.310276i
$401$	−132.184	+	228.950i	−0.329636	+	0.570947i	−0.982440	−	0.186580i	$-0.940259\pi$
$401$	−132.184	+	228.950i	−0.329636	+	0.570947i	0.652803	+	0.757527i	$0.273593\pi$
$402$		0			0
$403$	−46.2085	+	26.6785i	−0.114661	+	0.0661998i
$404$			343.504i			0.850258i
$405$		0			0
$406$	946.825			2.33208
$407$	60.5359	−	34.9504i	0.148737	−	0.0858732i
$408$		0			0
$409$	17.3829	−	30.1081i	0.0425011	−	0.0736140i	−0.843992	−	0.536355i	$-0.819801\pi$
$409$	17.3829	−	30.1081i	0.0425011	−	0.0736140i	0.886493	+	0.462741i	$0.153134\pi$
$410$	−541.090	−	312.398i	−1.31973	−	0.761947i
$411$		0			0
$412$	180.080	+	311.907i	0.437086	+	0.757056i
$413$	−350.172			−0.847873
$414$		0			0
$415$			305.256i			0.735558i
$416$	−44.1538	+	25.4922i	−0.106139	+	0.0612793i
$417$		0			0
$418$	199.749	+	115.325i	0.477868	+	0.275897i
$419$	−45.5169	+	78.8375i	−0.108632	+	0.188156i	−0.915216	−	0.402963i	$-0.867980\pi$
$419$	−45.5169	+	78.8375i	−0.108632	+	0.188156i	0.806584	+	0.591119i	$0.201314\pi$
$420$		0			0
$421$	−270.867	−	469.156i	−0.643390	−	1.11438i	−0.984671	−	0.174423i	$-0.944194\pi$
$421$	−270.867	−	469.156i	−0.643390	−	1.11438i	0.341281	−	0.939961i	$-0.389139\pi$
$422$	−1086.05			−2.57358
$423$		0			0
$424$	−1028.28			−2.42519
$425$	224.767	−	133.635i	0.528864	−	0.314434i
$426$		0			0
$427$	307.785	−	533.100i	0.720808	−	1.24848i
$428$	−132.716	+	229.870i	−0.310083	+	0.537080i
$429$		0			0
$430$	−291.805	+	168.474i	−0.678616	+	0.391799i
$431$	16.8736			0.0391498			0.0195749	−	0.999808i	$-0.493769\pi$
$431$	16.8736			0.0391498			0.0195749	+	0.999808i	$0.493769\pi$
$432$		0			0
$433$	254.232			0.587141			0.293571	−	0.955937i	$-0.405156\pi$
$433$	254.232			0.587141			0.293571	+	0.955937i	$0.405156\pi$
$434$	281.709	−	162.645i	0.649099	−	0.374758i
$435$		0			0
$436$	−817.863	−	472.193i	−1.87583	−	1.08301i
$437$	−10.2458	+	17.7463i	−0.0234458	+	0.0406093i
$438$		0			0
$439$	628.864	−	363.075i	1.43249	−	0.827049i	0.435181	−	0.900343i	$-0.356684\pi$
$439$	628.864	−	363.075i	1.43249	−	0.827049i	0.997310	+	0.0732936i	$0.0233510\pi$
$440$		−	134.400i		−	0.305456i
$441$		0			0
$442$	199.637	−	2.55573i	0.451667	−	0.00578220i
$443$	288.481	−	166.555i	0.651199	−	0.375970i	−0.137716	−	0.990472i	$-0.543976\pi$
$443$	288.481	−	166.555i	0.651199	−	0.375970i	0.788916	+	0.614502i	$0.210643\pi$
$444$		0			0
$445$	−159.210	−	91.9199i	−0.357775	−	0.206562i
$446$	−1252.50	−	723.128i	−2.80829	−	1.62136i
$447$		0			0
$448$	471.627	−	272.294i	1.05274	−	0.607799i
$449$	−229.219			−0.510509			−0.255254	−	0.966874i	$-0.582159\pi$
$449$	−229.219			−0.510509			−0.255254	+	0.966874i	$0.582159\pi$
$450$		0			0
$451$	224.010			0.496697
$452$	−697.946	−	1208.88i	−1.54413	−	2.67451i
$453$		0			0
$454$	−567.624	−	327.718i	−1.25027	−	0.721846i
$455$	58.5629	+	33.8113i	0.128710	+	0.0743106i
$456$		0			0
$457$	284.894	+	493.451i	0.623401	+	1.07976i	0.988848	+	0.148930i	$0.0475828\pi$
$457$	284.894	+	493.451i	0.623401	+	1.07976i	−0.365447	+	0.930832i	$0.619084\pi$
$458$			1283.90i			2.80327i
$459$		0			0
$460$	25.9286			0.0563665
$461$	−53.8225	+	31.0745i	−0.116752	+	0.0674066i	−0.557239	−	0.830352i	$-0.688139\pi$
$461$	−53.8225	+	31.0745i	−0.116752	+	0.0674066i	0.440487	+	0.897759i	$0.354806\pi$
$462$		0			0
$463$	−217.615	+	376.921i	−0.470011	+	0.814084i	−0.999412	−	0.0342882i	$-0.989084\pi$
$463$	−217.615	+	376.921i	−0.470011	+	0.814084i	0.529400	+	0.848372i	$0.322417\pi$
$464$	−208.127	+	360.487i	−0.448550	+	0.776911i
$465$		0			0
$466$	−937.354	+	541.182i	−2.01149	+	1.16133i
$467$		−	63.8071i		−	0.136632i	−0.997664	−	0.0683159i	$-0.978237\pi$
$467$		−	63.8071i		−	0.136632i	0.997664	−	0.0683159i	$-0.0217626\pi$
$468$		0			0
$469$		−	223.856i		−	0.477304i
$470$	−230.344	−	398.967i	−0.490093	−	0.848866i
$471$		0			0
$472$	322.001	−	557.722i	0.682205	−	1.18161i
$473$	60.4033	−	104.622i	0.127703	−	0.221187i
$474$		0			0
$475$	−139.767	−	242.084i	−0.294246	−	0.509650i
$476$	−790.577	+	10.1209i	−1.66088	+	0.0212624i
$477$		0			0
$478$	−1070.25			−2.23901
$479$	−320.143	−	554.503i	−0.668356	−	1.15763i	−0.978364	−	0.206893i	$-0.933665\pi$
$479$	−320.143	−	554.503i	−0.668356	−	1.15763i	0.310007	−	0.950734i	$-0.399669\pi$
$480$		0			0
$481$	−56.0158	−	32.3407i	−0.116457	−	0.0672364i
$482$	670.030	−	1160.53i	1.39010	−	2.40773i
$483$		0			0
$484$	−396.259	−	686.340i	−0.818716	−	1.41806i
$485$		−	29.4829i		−	0.0607895i
$486$		0			0
$487$			140.676i			0.288863i	0.989515	+	0.144432i	$0.0461354\pi$
$487$			140.676i			0.288863i	−0.989515	+	0.144432i	$0.953865\pi$
$488$	566.049	+	980.425i	1.15994	+	2.00907i
$489$		0			0
$490$	87.6033	+	50.5778i	0.178782	+	0.103220i
$491$	145.858	+	84.2113i	0.297064	+	0.171510i	0.641123	−	0.767438i	$-0.278469\pi$
$491$	145.858	+	84.2113i	0.297064	+	0.171510i	−0.344059	+	0.938948i	$0.611802\pi$
$492$		0			0
$493$	−652.851	+	388.150i	−1.32424	+	0.787323i
$494$		−	213.428i		−	0.432040i
$495$		0			0
$496$			143.008i			0.288322i
$497$	662.711	−	382.616i	1.33342	−	0.769852i
$498$		0			0
$499$	−101.189	−	58.4214i	−0.202783	−	0.117077i	0.395170	−	0.918608i	$-0.370686\pi$
$499$	−101.189	−	58.4214i	−0.202783	−	0.117077i	−0.597953	+	0.801531i	$0.704019\pi$
$500$	−464.283	+	804.162i	−0.928566	+	1.60832i
$501$		0			0
$502$	−58.7986	−	101.842i	−0.117129	−	0.202873i
$503$	572.958			1.13908			0.569541	−	0.821963i	$-0.307121\pi$
$503$	572.958			1.13908			0.569541	+	0.821963i	$0.307121\pi$
$504$		0			0
$505$		−	143.679i		−	0.284513i
$506$	−12.3941	+	7.15571i	−0.0244942	+	0.0141417i
$507$		0			0
$508$	−238.547	+	413.176i	−0.469581	+	0.813338i
$509$	−385.460	−	222.546i	−0.757290	−	0.437221i	0.0710321	−	0.997474i	$-0.477371\pi$
$509$	−385.460	−	222.546i	−0.757290	−	0.437221i	−0.828322	+	0.560253i	$0.810704\pi$
$510$		0			0
$511$	107.979	+	187.025i	0.211309	+	0.365998i
$512$			566.563i			1.10657i
$513$		0			0
$514$	727.435			1.41524
$515$	−75.3228	−	130.463i	−0.146258	−	0.253326i
$516$		0			0
$517$	143.043	+	82.5859i	0.276679	+	0.159741i
$518$	341.498	+	197.164i	0.659263	+	0.380626i
$519$		0			0
$520$	−107.703	+	62.1825i	−0.207122	+	0.119582i
$521$	−353.566			−0.678630			−0.339315	−	0.940673i	$-0.610195\pi$
$521$	−353.566			−0.678630			−0.339315	+	0.940673i	$0.610195\pi$
$522$		0			0
$523$	−606.215			−1.15911			−0.579556	−	0.814933i	$-0.696774\pi$
$523$	−606.215			−1.15911			−0.579556	+	0.814933i	$0.696774\pi$
$524$	−807.589	−	1398.78i	−1.54120	−	2.66944i
$525$		0			0
$526$	183.044	−	317.041i	0.347992	−	0.602740i
$527$	−127.567	+	227.633i	−0.242062	+	0.431941i
$528$		0			0
$529$	263.864	+	457.026i	0.498798	+	0.863944i
$530$	933.962			1.76219
$531$		0			0
$532$			845.190i			1.58870i
$533$	−103.642	−	179.513i	−0.194450	−	0.336797i
$534$		0			0
$535$	55.5117	−	96.1491i	0.103760	−	0.179718i
$536$	356.537	+	205.847i	0.665182	+	0.384043i
$537$		0			0
$538$	49.5444	−	28.6045i	0.0920899	−	0.0531682i
$539$	−36.2676			−0.0672868
$540$		0			0
$541$			973.359i			1.79918i	0.436731	+	0.899592i	$0.356136\pi$
$541$			973.359i			1.79918i	−0.436731	+	0.899592i	$0.643864\pi$
$542$	−290.595	+	167.775i	−0.536153	+	0.309548i
$543$		0			0
$544$	−121.894	+	217.511i	−0.224070	+	0.399836i
$545$	342.092	+	197.507i	0.627691	+	0.362398i
$546$		0			0
$547$	939.697	−	542.534i	1.71791	−	0.991836i	0.795197	−	0.606351i	$-0.207368\pi$
$547$	939.697	−	542.534i	1.71791	−	0.991836i	0.922714	−	0.385485i	$-0.125966\pi$
$548$			222.830i			0.406624i
$549$		0			0
$550$		−	195.227i		−	0.354959i
$551$	405.962	+	703.147i	0.736774	+	1.27613i
$552$		0			0
$553$	332.675	−	576.211i	0.601583	−	1.04197i
$554$	221.962	−	384.450i	0.400654	−	0.693953i
$555$		0			0
$556$	−1208.39	+	697.663i	−2.17336	+	1.25479i
$557$		−	266.109i		−	0.477755i	−0.971050	−	0.238877i	$-0.923221\pi$
$557$		−	266.109i		−	0.477755i	0.971050	−	0.238877i	$-0.0767794\pi$
$558$		0			0
$559$	−111.786			−0.199975
$560$	156.960	−	90.6211i	0.280286	−	0.161823i
$561$		0			0
$562$	439.701	−	761.584i	0.782386	−	1.35513i
$563$	−95.8869	−	55.3603i	−0.170314	−	0.0983310i	0.412420	−	0.910994i	$-0.364684\pi$
$563$	−95.8869	−	55.3603i	−0.170314	−	0.0983310i	−0.582734	+	0.812663i	$0.698017\pi$
$564$		0			0
$565$	291.933	+	505.643i	0.516696	+	0.894944i
$566$	519.583			0.917992
$567$		0			0
$568$			1407.34i			2.47771i
$569$	−820.458	+	473.692i	−1.44193	+	0.832499i	−0.997979	−	0.0635520i	$-0.979757\pi$
$569$	−820.458	+	473.692i	−1.44193	+	0.832499i	−0.443952	+	0.896051i	$0.646424\pi$
$570$		0			0
$571$	781.546	+	451.226i	1.36873	+	0.790238i	0.990766	−	0.135582i	$-0.0432903\pi$
$571$	781.546	+	451.226i	1.36873	+	0.790238i	0.377966	+	0.925819i	$0.376624\pi$
$572$	48.4119	−	83.8519i	0.0846362	−	0.146594i
$573$		0			0
$574$	631.850	+	1094.40i	1.10078	+	1.90661i
$575$	17.3446			0.0301645
$576$		0			0
$577$	−770.496			−1.33535			−0.667674	−	0.744453i	$-0.732710\pi$
$577$	−770.496			−1.33535			−0.667674	+	0.744453i	$0.732710\pi$
$578$	832.809	−	509.685i	1.44085	−	0.881808i
$579$		0			0
$580$	513.674	−	889.710i	0.885645	−	1.53398i
$581$	308.702	−	534.688i	0.531329	−	0.920290i
$582$		0			0
$583$	−289.994	+	167.428i	−0.497417	+	0.287184i
$584$	−397.169			−0.680083
$585$		0			0
$586$	321.000			0.547781
$587$	−749.343	+	432.633i	−1.27656	+	0.737024i	−0.976215	−	0.216805i	$-0.930436\pi$
$587$	−749.343	+	432.633i	−1.27656	+	0.737024i	−0.300349	+	0.953829i	$0.597103\pi$
$588$		0			0
$589$	241.572	+	139.472i	0.410140	+	0.236794i
$590$	−292.465	+	506.565i	−0.495704	+	0.858584i
$591$		0			0
$592$	−150.134	+	86.6797i	−0.253604	+	0.146418i
$593$		−	197.080i		−	0.332344i	−0.986097	−	0.166172i	$-0.946859\pi$
$593$		−	197.080i		−	0.332344i	0.986097	−	0.166172i	$-0.0531406\pi$
$594$		0			0
$595$	330.679	−	4.23332i	0.555763	−	0.00711482i
$596$	−980.387	+	566.026i	−1.64494	+	0.949709i
$597$		0			0
$598$	11.4686	+	6.62141i	0.0191783	+	0.0110726i
$599$	−498.466	−	287.789i	−0.832164	−	0.480450i	0.0224293	−	0.999748i	$-0.492860\pi$
$599$	−498.466	−	287.789i	−0.832164	−	0.480450i	−0.854593	+	0.519299i	$0.826193\pi$
$600$		0			0
$601$	603.473	−	348.416i	1.00412	−	0.579726i	0.0946521	−	0.995510i	$-0.469826\pi$
$601$	603.473	−	348.416i	1.00412	−	0.579726i	0.909463	+	0.415784i	$0.136493\pi$
$602$	681.502			1.13206
$603$		0			0
$604$	−1215.57			−2.01254
$605$	165.745	+	287.079i	0.273959	+	0.474511i
$606$		0			0
$607$	383.777	+	221.574i	0.632252	+	0.365031i	0.781624	−	0.623750i	$-0.214392\pi$
$607$	383.777	+	221.574i	0.632252	+	0.365031i	−0.149372	+	0.988781i	$0.547725\pi$
$608$	230.830	+	133.270i	0.379655	+	0.219194i
$609$		0			0
$610$	−514.128	−	890.495i	−0.842832	−	1.45983i
$611$		−	152.839i		−	0.250145i
$612$		0			0
$613$	−718.550			−1.17219			−0.586093	−	0.810244i	$-0.699335\pi$
$613$	−718.550			−1.17219			−0.586093	+	0.810244i	$0.699335\pi$
$614$	1378.32	−	795.773i	2.24482	−	1.29605i
$615$		0			0
$616$	−135.918	+	235.416i	−0.220646	+	0.382169i
$617$	382.705	−	662.864i	0.620267	−	1.07433i	−0.369169	−	0.929362i	$-0.620358\pi$
$617$	382.705	−	662.864i	0.620267	−	1.07433i	0.989436	−	0.144971i	$-0.0463090\pi$
$618$		0			0
$619$	74.0367	−	42.7451i	0.119607	−	0.0690551i	−0.439003	−	0.898486i	$-0.644668\pi$
$619$	74.0367	−	42.7451i	0.119607	−	0.0690551i	0.558610	+	0.829430i	$0.311335\pi$
$620$		−	352.954i		−	0.569281i
$621$		0			0
$622$		−	1289.32i		−	2.07286i
$623$	185.915	+	322.015i	0.298419	+	0.516877i
$624$		0			0
$625$	1.92394	−	3.33236i	0.00307830	−	0.00533177i
$626$	20.3404	−	35.2305i	0.0324926	−	0.0562788i
$627$		0			0
$628$	502.425	+	870.225i	0.800039	+	1.38571i
$629$	−316.296	+	4.04919i	−0.502856	+	0.00643751i
$630$		0			0
$631$	151.653			0.240338			0.120169	−	0.992753i	$-0.461656\pi$
$631$	151.653			0.240338			0.120169	+	0.992753i	$0.461656\pi$
$632$	611.825	+	1059.71i	0.968077	+	1.67676i
$633$		0			0
$634$	802.089	+	463.086i	1.26512	+	0.730420i
$635$	99.7783	−	172.821i	0.157131	−	0.272159i
$636$		0			0
$637$	16.7798	+	29.0634i	0.0263419	+	0.0456255i
$638$			567.051i			0.888794i
$639$		0			0
$640$		−	727.739i		−	1.13709i
$641$	−367.170	−	635.958i	−0.572809	−	0.992134i	−0.996276	−	0.0862224i	$-0.972520\pi$
$641$	−367.170	−	635.958i	−0.572809	−	0.992134i	0.423467	−	0.905911i	$-0.360813\pi$
$642$		0			0
$643$	1094.69	+	632.019i	1.70247	+	0.982922i	0.943246	+	0.332094i	$0.107755\pi$
$643$	1094.69	+	632.019i	1.70247	+	0.982922i	0.759225	+	0.650828i	$0.225578\pi$
$644$	−45.4166	−	26.2213i	−0.0705226	−	0.0407163i
$645$		0			0
$646$	−533.409	−	897.169i	−0.825710	−	1.38881i
$647$		−	654.568i		−	1.01170i	−0.862622	−	0.505849i	$-0.831179\pi$
$647$		−	654.568i		−	1.01170i	0.862622	−	0.505849i	$-0.168821\pi$
$648$		0			0
$649$		−	209.717i		−	0.323138i
$650$	−156.448	+	90.3251i	−0.240689	+	0.138962i
$651$		0			0
$652$	175.615	+	101.391i	0.269348	+	0.155508i
$653$	−351.643	+	609.064i	−0.538504	+	0.932716i	0.460481	+	0.887670i	$0.347677\pi$
$653$	−351.643	+	609.064i	−0.538504	+	0.932716i	−0.998985	+	0.0450465i	$0.985656\pi$
$654$		0			0
$655$	337.794	+	585.077i	0.515717	+	0.893247i
$656$	−555.562			−0.846894
$657$		0			0
$658$			931.776i			1.41607i
$659$	−394.144	+	227.559i	−0.598094	+	0.345310i	−0.768292	−	0.640100i	$-0.778893\pi$
$659$	−394.144	+	227.559i	−0.598094	+	0.345310i	0.170197	+	0.985410i	$0.445560\pi$
$660$		0			0
$661$	−134.035	+	232.155i	−0.202776	+	0.351218i	−0.949422	−	0.314004i	$-0.898330\pi$
$661$	−134.035	+	232.155i	−0.202776	+	0.351218i	0.746646	+	0.665222i	$0.231663\pi$
$662$	−334.592	−	193.177i	−0.505426	−	0.291808i
$663$		0			0
$664$	567.736	+	983.347i	0.855024	+	1.48094i
$665$		−	353.522i		−	0.531612i
$666$		0			0
$667$	−50.3785			−0.0755300
$668$	963.100	+	1668.14i	1.44177	+	2.49721i
$669$		0			0
$670$	−323.834	−	186.965i	−0.483334	−	0.279053i
$671$	319.272	+	184.332i	0.475815	+	0.274712i
$672$		0			0
$673$	572.251	−	330.389i	0.850299	−	0.490920i	−0.0104531	−	0.999945i	$-0.503327\pi$
$673$	572.251	−	330.389i	0.850299	−	0.490920i	0.860752	+	0.509025i	$0.169994\pi$
$674$	−944.353			−1.40112
$675$		0			0
$676$	1163.46			1.72109
$677$	−367.380	−	636.321i	−0.542659	−	0.939913i	−0.998750	−	0.0499797i	$-0.984084\pi$
$677$	−367.380	−	636.321i	−0.542659	−	0.939913i	0.456091	−	0.889933i	$-0.349249\pi$
$678$		0			0
$679$	−29.8157	+	51.6424i	−0.0439113	+	0.0760565i
$680$	−297.334	+	530.568i	−0.437256	+	0.780248i
$681$		0			0
$682$	97.4075	+	168.715i	0.142826	+	0.247382i
$683$	290.069			0.424699			0.212349	−	0.977194i	$-0.431889\pi$
$683$	290.069			0.424699			0.212349	+	0.977194i	$0.431889\pi$
$684$		0			0
$685$		−	93.2043i		−	0.136065i
$686$	−621.508	−	1076.48i	−0.905988	−	1.56922i
$687$		0			0
$688$	−149.805	+	259.470i	−0.217740	+	0.377136i
$689$	268.341	+	154.926i	0.389464	+	0.224857i
$690$		0			0
$691$	−141.683	+	81.8008i	−0.205041	+	0.118380i	−0.599004	−	0.800746i	$-0.704437\pi$
$691$	−141.683	+	81.8008i	−0.205041	+	0.118380i	0.393964	+	0.919126i	$0.371104\pi$
$692$	547.457			0.791122
$693$		0			0
$694$		−	1096.20i		−	1.57954i
$695$	505.439	−	291.815i	0.727250	−	0.419878i
$696$		0			0
$697$	−884.318	−	495.577i	−1.26875	−	0.711015i
$698$	813.561	+	469.710i	1.16556	+	0.672936i
$699$		0			0
$700$	619.544	−	357.694i	0.885063	−	0.510992i
$701$			447.750i			0.638730i	0.947632	+	0.319365i	$0.103470\pi$
$701$			447.750i			0.638730i	−0.947632	+	0.319365i	$0.896530\pi$
$702$		0			0
$703$			338.146i			0.481004i
$704$	163.076	+	282.456i	0.231642	+	0.401216i
$705$		0			0
$706$	−800.922	+	1387.24i	−1.13445	+	1.96493i
$707$	−145.301	+	251.669i	−0.205518	+	0.355968i
$708$		0			0
$709$	−1029.74	+	594.519i	−1.45238	+	0.838532i	−0.998616	−	0.0525907i	$-0.983252\pi$
$709$	−1029.74	+	594.519i	−1.45238	+	0.838532i	−0.453763	+	0.891122i	$0.649919\pi$
$710$		−	1278.25i		−	1.80036i
$711$		0			0
$712$	−683.835			−0.960442
$713$	−14.9891	+	8.65397i	−0.0210226	+	0.0121374i
$714$		0			0
$715$	−20.2495	+	35.0732i	−0.0283210	+	0.0490534i
$716$	−292.857	−	169.081i	−0.409018	−	0.236147i
$717$		0			0
$718$	−821.504	−	1422.89i	−1.14416	−	1.98174i
$719$	−746.256			−1.03791			−0.518954	−	0.854802i	$-0.673678\pi$
$719$	−746.256			−1.03791			−0.518954	+	0.854802i	$0.673678\pi$
$720$		0			0
$721$			304.692i			0.422597i
$722$	89.9611	−	51.9391i	0.124600	−	0.0719378i
$723$		0			0
$724$	−1028.94	−	594.057i	−1.42118	−	0.820521i
$725$	343.616	−	595.160i	0.473953	−	0.820910i
$726$		0			0
$727$	195.358	+	338.371i	0.268719	+	0.465434i	0.968531	−	0.248892i	$-0.0800665\pi$
$727$	195.358	+	338.371i	0.268719	+	0.465434i	−0.699813	+	0.714327i	$0.746733\pi$
$728$	251.538			0.345519
$729$		0			0
$730$	360.738			0.494162
$731$	−469.907	+	279.381i	−0.642827	+	0.382191i
$732$		0			0
$733$	−4.87965	+	8.45179i	−0.00665709	+	0.0115304i	−0.869335	−	0.494224i	$-0.835452\pi$
$733$	−4.87965	+	8.45179i	−0.00665709	+	0.0115304i	0.862678	+	0.505754i	$0.168786\pi$
$734$	550.698	−	953.837i	0.750270	−	1.29951i
$735$		0			0
$736$	−14.3226	+	8.26916i	−0.0194601	+	0.0112353i
$737$	134.067			0.181909
$738$		0			0
$739$	1168.07			1.58060			0.790302	−	0.612717i	$-0.209924\pi$
$739$	1168.07			1.58060			0.790302	+	0.612717i	$0.209924\pi$
$740$	370.542	−	213.932i	0.500732	−	0.289098i
$741$		0			0
$742$	−1635.93	−	944.505i	−2.20476	−	1.27292i
$743$	−113.536	+	196.649i	−0.152807	+	0.264670i	−0.932258	−	0.361793i	$-0.882165\pi$
$743$	−113.536	+	196.649i	−0.152807	+	0.264670i	0.779451	+	0.626463i	$0.215498\pi$
$744$		0			0
$745$	410.071	−	236.755i	0.550431	−	0.317792i
$746$			1130.08i			1.51486i
$747$		0			0
$748$	−6.06137	−	473.475i	−0.00810344	−	0.632987i
$749$	−194.469	+	112.277i	−0.259638	+	0.149902i
$750$		0			0
$751$	123.140	+	71.0950i	0.163968	+	0.0946670i	0.579739	−	0.814803i	$-0.303155\pi$
$751$	123.140	+	71.0950i	0.163968	+	0.0946670i	−0.415770	+	0.909470i	$0.636488\pi$
$752$	−354.757	−	204.819i	−0.471752	−	0.272366i
$753$		0			0
$754$	454.412	−	262.355i	0.602669	−	0.347951i
$755$	508.444			0.673436
$756$		0			0
$757$	−479.636			−0.633601			−0.316800	−	0.948492i	$-0.602609\pi$
$757$	−479.636			−0.633601			−0.316800	+	0.948492i	$0.602609\pi$
$758$	95.1584	+	164.819i	0.125539	+	0.217440i
$759$		0			0
$760$	563.059	+	325.082i	0.740867	+	0.427740i
$761$	37.8559	+	21.8561i	0.0497449	+	0.0287202i	0.524666	−	0.851308i	$-0.324190\pi$
$761$	37.8559	+	21.8561i	0.0497449	+	0.0287202i	−0.474921	+	0.880028i	$0.657523\pi$
$762$		0			0
$763$	−399.473	−	691.907i	−0.523555	−	0.906824i
$764$		−	1701.79i		−	2.22747i
$765$		0			0
$766$	−162.797			−0.212529
$767$	−168.059	+	97.0288i	−0.219112	+	0.126504i
$768$		0			0
$769$	475.251	−	823.159i	0.618012	−	1.07043i	−0.371836	−	0.928298i	$-0.621272\pi$
$769$	475.251	−	823.159i	0.618012	−	1.07043i	0.989848	−	0.142129i	$-0.0453949\pi$
$770$	123.451	−	213.823i	0.160325	−	0.277692i
$771$		0			0
$772$	−1449.19	+	836.690i	−1.87719	+	1.08380i
$773$			416.660i			0.539017i	0.962998	+	0.269509i	$0.0868613\pi$
$773$			416.660i			0.539017i	−0.962998	+	0.269509i	$0.913139\pi$
$774$		0			0
$775$		−	236.104i		−	0.304650i
$776$	−54.8342	−	94.9757i	−0.0706627	−	0.122391i
$777$		0			0
$778$	−60.1508	+	104.184i	−0.0773147	+	0.133913i
$779$	−541.826	+	938.471i	−0.695541	+	1.20471i
$780$		0			0
$781$	229.148	+	396.896i	0.293403	+	0.508189i
$782$	64.7582	−	0.829028i	0.0828110	−	0.00106014i
$783$		0			0
$784$	89.9464			0.114728
$785$	−210.152	−	363.993i	−0.267709	−	0.463686i
$786$		0			0
$787$	−783.381	−	452.285i	−0.995401	−	0.574695i	−0.0885166	−	0.996075i	$-0.528213\pi$
$787$	−783.381	−	452.285i	−0.995401	−	0.574695i	−0.906884	+	0.421380i	$0.861546\pi$
$788$	−79.1088	+	137.021i	−0.100392	+	0.173884i
$789$		0			0
$790$	−555.705	−	962.509i	−0.703424	−	1.21837i
$791$		−	1180.92i		−	1.49294i
$792$		0			0
$793$		−	341.136i		−	0.430184i
$794$	256.587	+	444.422i	0.323157	+	0.559725i
$795$		0			0
$796$	−1453.77	−	839.337i	−1.82635	−	1.05444i
$797$	1150.83	+	664.429i	1.44395	+	0.833663i	0.998110	−	0.0614514i	$-0.0195729\pi$
$797$	1150.83	+	664.429i	1.44395	+	0.833663i	0.445837	+	0.895114i	$0.352906\pi$
$798$		0			0
$799$	−381.981	−	642.475i	−0.478074	−	0.804099i
$800$		−	225.605i		−	0.282006i
$801$		0			0
$802$		−	893.178i		−	1.11369i
$803$	−112.009	+	64.6682i	−0.139488	+	0.0805333i
$804$		0			0
$805$	18.9966	+	10.9677i	0.0235983	+	0.0136245i
$806$	90.1343	−	156.117i	0.111829	−	0.193694i
$807$		0			0
$808$	−267.224	−	462.846i	−0.330723	−	0.572829i
$809$	−807.379			−0.997996			−0.498998	−	0.866603i	$-0.666299\pi$
$809$	−807.379			−0.997996			−0.498998	+	0.866603i	$0.666299\pi$
$810$		0			0
$811$		−	108.693i		−	0.134024i	−0.997752	−	0.0670118i	$-0.978654\pi$
$811$		−	108.693i		−	0.134024i	0.997752	−	0.0670118i	$-0.0213465\pi$
$812$	−1799.51	+	1038.95i	−2.21614	+	1.27949i
$813$		0			0
$814$	−118.081	+	204.523i	−0.145063	+	0.251256i
$815$	−73.4552	−	42.4094i	−0.0901291	−	0.0520361i
$816$		0			0
$817$	292.202	+	506.109i	0.357652	+	0.619472i
$818$			117.458i			0.143591i
$819$		0			0
$820$	1371.17			1.67216
$821$	−465.360	−	806.027i	−0.566821	−	0.981762i	−0.996878	−	0.0789605i	$-0.974840\pi$
$821$	−465.360	−	806.027i	−0.566821	−	0.981762i	0.430057	−	0.902802i	$-0.358493\pi$
$822$		0			0
$823$	804.670	+	464.576i	0.977727	+	0.564491i	0.901583	−	0.432606i	$-0.142406\pi$
$823$	804.670	+	464.576i	0.977727	+	0.564491i	0.0761441	+	0.997097i	$0.475739\pi$
$824$	−485.287	−	280.181i	−0.588940	−	0.340025i
$825$		0			0
$826$	1024.57	−	591.533i	1.24039	−	0.716142i
$827$	−309.018			−0.373661			−0.186830	−	0.982392i	$-0.559821\pi$
$827$	−309.018			−0.373661			−0.186830	+	0.982392i	$0.559821\pi$
$828$		0			0
$829$	−356.784			−0.430378			−0.215189	−	0.976572i	$-0.569037\pi$
$829$	−356.784			−0.430378			−0.215189	+	0.976572i	$0.569037\pi$
$830$	−515.660	−	893.149i	−0.621277	−	1.07608i
$831$		0			0
$832$	150.899	−	261.366i	0.181370	−	0.314141i
$833$	143.172	+	80.2347i	0.171876	+	0.0963202i
$834$		0			0
$835$	−402.841	−	697.741i	−0.482444	−	0.835618i
$836$	−506.182			−0.605481
$837$		0			0
$838$		−	307.561i		−	0.367017i
$839$	201.748	+	349.438i	0.240462	+	0.416493i	0.960846	−	0.277083i	$-0.0893676\pi$
$839$	201.748	+	349.438i	0.240462	+	0.416493i	−0.720384	+	0.693576i	$0.756034\pi$
$840$		0			0
$841$	−577.554	+	1000.35i	−0.686747	+	1.18948i
$842$	1585.06	+	915.134i	1.88249	+	1.08686i
$843$		0			0
$844$	2064.12	−	1191.72i	2.44563	−	1.41199i
$845$	−486.645			−0.575911
$846$		0			0
$847$		−	670.465i		−	0.791576i
$848$	719.207	−	415.234i	0.848121	−	0.489663i
$849$		0			0
$850$	−431.901	+	770.693i	−0.508119	+	0.906698i
$851$	−18.1704	−	10.4907i	−0.0213518	−	0.0123275i
$852$		0			0
$853$	−159.462	+	92.0654i	−0.186943	+	0.107931i	−0.590550	−	0.807001i	$-0.701089\pi$
$853$	−159.462	+	92.0654i	−0.186943	+	0.107931i	0.403608	+	0.914932i	$0.367756\pi$
$854$			2079.73i			2.43528i
$855$		0			0
$856$		−	412.977i		−	0.482450i
$857$	488.567	+	846.222i	0.570090	+	0.987424i	0.996556	+	0.0829208i	$0.0264249\pi$
$857$	488.567	+	846.222i	0.570090	+	0.987424i	−0.426467	+	0.904503i	$0.640242\pi$
$858$		0			0
$859$	598.778	−	1037.11i	0.697064	−	1.20735i	−0.272416	−	0.962180i	$-0.587823\pi$
$859$	598.778	−	1037.11i	0.697064	−	1.20735i	0.969480	−	0.245171i	$-0.0788440\pi$
$860$	369.730	−	640.392i	0.429919	−	0.744642i
$861$		0			0
$862$	−49.3703	+	28.5039i	−0.0572741	+	0.0330672i
$863$			20.1789i			0.0233823i	0.999932	+	0.0116912i	$0.00372149\pi$
$863$			20.1789i			0.0233823i	−0.999932	+	0.0116912i	$0.996279\pi$
$864$		0			0
$865$	−228.988			−0.264725
$866$	−743.857	+	429.466i	−0.858958	+	0.495919i
$867$		0			0
$868$	−356.939	+	618.236i	−0.411220	+	0.712253i
$869$	345.091	+	199.238i	0.397113	+	0.229273i
$870$		0			0
$871$	−62.0280	−	107.436i	−0.0712147	−	0.123348i
$872$	1469.34			1.68503
$873$		0			0
$874$		−	69.2317i		−	0.0792125i
$875$	−680.316	+	392.781i	−0.777504	+	0.448892i
$876$		0			0
$877$	−600.576	−	346.742i	−0.684807	−	0.395373i	0.116857	−	0.993149i	$-0.462718\pi$
$877$	−600.576	−	346.742i	−0.684807	−	0.395373i	−0.801664	+	0.597775i	$0.796051\pi$
$878$	−1226.66	+	2124.64i	−1.39711	+	2.41986i
$879$		0			0
$880$	54.2728	+	94.0032i	0.0616736	+	0.106822i
$881$	1461.79			1.65925			0.829623	−	0.558325i	$-0.188556\pi$
$881$	1461.79			1.65925			0.829623	+	0.558325i	$0.188556\pi$
$882$		0			0
$883$	1331.57			1.50801			0.754006	−	0.656868i	$-0.228119\pi$
$883$	1331.57			1.50801			0.754006	+	0.656868i	$0.228119\pi$
$884$	−376.620	+	223.918i	−0.426040	+	0.253301i
$885$		0			0
$886$	−562.711	+	974.644i	−0.635114	+	1.10005i
$887$	159.590	−	276.418i	0.179921	−	0.311632i	−0.761932	−	0.647657i	$-0.775749\pi$
$887$	159.590	−	276.418i	0.179921	−	0.311632i	0.941853	+	0.336025i	$0.109083\pi$
$888$		0			0
$889$	−349.544	+	201.809i	−0.393188	+	0.227007i
$890$	621.109			0.697876
$891$		0			0
$892$	3173.94			3.55823
$893$	−691.972	+	399.510i	−0.774885	+	0.447380i
$894$		0			0
$895$	122.495	+	70.7224i	0.136866	+	0.0790194i
$896$	−735.955	+	1274.71i	−0.821378	+	1.42267i
$897$		0			0
$898$	670.670	−	387.211i	0.746848	−	0.431193i
$899$			685.780i			0.762825i
$900$		0			0
$901$	1515.20	−	19.3974i	1.68169	−	0.0215288i
$902$	−655.431	+	378.413i	−0.726642	+	0.419527i
$903$		0			0
$904$	1880.86	+	1085.91i	2.08059	+	1.20123i
$905$	430.379	+	248.479i	0.475557	+	0.274563i
$906$		0			0
$907$	−97.7878	+	56.4578i	−0.107815	+	0.0622468i	−0.552938	−	0.833223i	$-0.686493\pi$
$907$	−97.7878	+	56.4578i	−0.107815	+	0.0622468i	0.445123	+	0.895469i	$0.353160\pi$
$908$	1438.41			1.58416
$909$		0			0
$910$	−228.465			−0.251061
$911$	0.456798	+	0.791197i	0.000501424	+	0.000868493i	0.866276	−	0.499566i	$-0.166507\pi$
$911$	0.456798	+	0.791197i	0.000501424	+	0.000868493i	−0.865775	+	0.500434i	$0.833174\pi$
$912$		0			0
$913$	320.223	+	184.881i	0.350738	+	0.202498i
$914$	−1667.14	−	962.525i	−1.82401	−	1.05309i
$915$		0			0
$916$	−1408.81	−	2440.13i	−1.53800	−	2.66390i
$917$		−	1366.43i		−	1.49011i
$918$		0			0
$919$	−211.594			−0.230244			−0.115122	−	0.993351i	$-0.536726\pi$
$919$	−211.594			−0.230244			−0.115122	+	0.993351i	$0.536726\pi$
$920$	−34.9368	+	20.1708i	−0.0379748	+	0.0219247i
$921$		0			0
$922$	104.986	−	181.841i	0.113868	−	0.197225i
$923$	212.038	−	367.260i	0.229727	−	0.397898i
$924$		0			0
$925$	247.869	−	143.107i	0.267966	−	0.154711i
$926$		−	1470.44i		−	1.58795i
$927$		0			0
$928$			655.285i			0.706126i
$929$	205.464	+	355.873i	0.221166	+	0.383071i	0.955162	−	0.296082i	$-0.0956803\pi$
$929$	205.464	+	355.873i	0.221166	+	0.383071i	−0.733996	+	0.679154i	$0.762347\pi$
$930$		0			0
$931$	87.7225	−	151.940i	0.0942239	−	0.163201i
$932$	1187.67	−	2057.11i	1.27433	−	2.20720i
$933$		0			0
$934$	107.787	+	186.693i	0.115404	+	0.199885i
$935$	2.53532	+	198.043i	0.00271157	+	0.211810i
$936$		0			0
$937$	−1139.43			−1.21604			−0.608018	−	0.793923i	$-0.708035\pi$
$937$	−1139.43			−1.21604			−0.608018	+	0.793923i	$0.708035\pi$
$938$	378.152	+	654.979i	0.403147	+	0.698272i
$939$		0			0
$940$	875.569	+	505.510i	0.931457	+	0.537777i
$941$	−201.972	+	349.826i	−0.214636	+	0.371760i	−0.953160	−	0.302467i	$-0.902190\pi$
$941$	−201.972	+	349.826i	−0.214636	+	0.371760i	0.738524	+	0.674227i	$0.235523\pi$
$942$		0			0
$943$	−33.6194	−	58.2304i	−0.0356515	−	0.0617502i
$944$			520.114i			0.550968i
$945$		0			0
$946$			408.150i			0.431448i
$947$	869.969	+	1506.83i	0.918658	+	1.59116i	0.801456	+	0.598054i	$0.204059\pi$
$947$	869.969	+	1506.83i	0.918658	+	1.59116i	0.117201	+	0.993108i	$0.462608\pi$
$948$		0			0
$949$	103.645	+	59.8396i	0.109215	+	0.0630554i
$950$	817.888	+	472.208i	0.860934	+	0.497061i
$951$		0			0
$952$	1057.37	−	628.655i	1.11068	−	0.660352i
$953$		−	1741.50i		−	1.82739i	−0.406406	−	0.913693i	$-0.633218\pi$
$953$		−	1741.50i		−	1.82739i	0.406406	−	0.913693i	$-0.366782\pi$
$954$		0			0
$955$			711.815i			0.745356i
$956$	2034.08	−	1174.38i	2.12770	−	1.22843i
$957$		0			0
$958$	1873.41	+	1081.61i	1.95554	+	1.12903i
$959$	−94.2565	+	163.257i	−0.0982862	+	0.170237i
$960$		0			0
$961$	−362.697	−	628.210i	−0.377417	−	0.653705i
$962$	218.528			0.227161
$963$		0			0
$964$			2940.88i			3.05071i
$965$	606.160	−	349.967i	0.628145	−	0.362660i
$966$		0			0
$967$	−914.968	+	1584.77i	−0.946192	+	1.63885i	−0.192845	+	0.981229i	$0.561771\pi$
$967$	−914.968	+	1584.77i	−0.946192	+	1.63885i	−0.753347	+	0.657623i	$0.771562\pi$
$968$	1067.86	+	616.527i	1.10316	+	0.636908i
$969$		0			0
$970$	49.8045	+	86.2640i	0.0513449	+	0.0889319i
$971$			799.025i			0.822889i	0.911435	+	0.411445i	$0.134976\pi$
$971$			799.025i			0.822889i	−0.911435	+	0.411445i	$0.865024\pi$
$972$		0			0
$973$	−1180.44			−1.21319
$974$	−237.640	−	411.605i	−0.243984	−	0.422592i
$975$		0			0
$976$	−791.819	−	457.157i	−0.811290	−	0.468398i
$977$	−51.3985	−	29.6749i	−0.0526085	−	0.0303735i	0.473465	−	0.880813i	$-0.343003\pi$
$977$	−51.3985	−	29.6749i	−0.0526085	−	0.0303735i	−0.526074	+	0.850439i	$0.676336\pi$
$978$		0			0
$979$	−192.854	+	111.344i	−0.196990	+	0.113732i
$980$	−221.995			−0.226525
$981$		0			0
$982$	−569.022			−0.579452
$983$	586.501	+	1015.85i	0.596644	+	1.03342i	0.993313	+	0.115456i	$0.0368330\pi$
$983$	586.501	+	1015.85i	0.596644	+	1.03342i	−0.396668	+	0.917962i	$0.629834\pi$
$984$		0			0
$985$	33.0893	−	57.3123i	0.0335932	−	0.0581851i
$986$	1254.49	−	2238.53i	1.27230	−	2.27031i
$987$		0			0
$988$	234.193	+	405.635i	0.237038	+	0.410561i
$989$	−36.2612			−0.0366645
$990$		0			0
$991$			46.3789i			0.0468001i	0.999726	+	0.0234000i	$0.00744914\pi$
$991$			46.3789i			0.0468001i	−0.999726	+	0.0234000i	$0.992551\pi$
$992$	112.564	+	194.967i	0.113472	+	0.196539i
$993$		0			0
$994$	−1292.68	+	2238.99i	−1.30049	+	2.25251i
$995$	608.078	+	351.074i	0.611133	+	0.352838i
$996$		0			0
$997$	−1421.66	+	820.797i	−1.42594	+	0.823267i	−0.996797	−	0.0799703i	$-0.974517\pi$
$997$	−1421.66	+	820.797i	−1.42594	+	0.823267i	−0.429142	+	0.903237i	$0.641184\pi$
$998$	394.758			0.395549
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.3.i.a.152.4		68
3.2	odd	2		153.3.i.a.50.31	✓	68
9.2	odd	6	inner	459.3.i.a.305.3		68
9.7	even	3		153.3.i.a.101.32	yes	68
17.16	even	2	inner	459.3.i.a.152.3		68
51.50	odd	2		153.3.i.a.50.32	yes	68
153.16	even	6		153.3.i.a.101.31	yes	68
153.101	odd	6	inner	459.3.i.a.305.4		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.31	✓	68	3.2	odd	2
153.3.i.a.50.32	yes	68	51.50	odd	2
153.3.i.a.101.31	yes	68	153.16	even	6
153.3.i.a.101.32	yes	68	9.7	even	3
459.3.i.a.152.3		68	17.16	even	2	inner
459.3.i.a.152.4		68	1.1	even	1	trivial
459.3.i.a.305.3		68	9.2	odd	6	inner
459.3.i.a.305.4		68	153.101	odd	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	459.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.92590 + 1.68927i) q^{2} +(3.70725 - 6.42114i) q^{4} +(-1.55065 + 2.68581i) q^{5} +(5.43225 - 3.13631i) q^{7} +11.5360i q^{8} -10.4779i q^{10} +(1.87833 + 3.25336i) q^{11} +(1.73808 - 3.01044i) q^{13} +(-10.5961 + 18.3530i) q^{14} +(-4.65840 - 8.06858i) q^{16} +(-0.217614 - 16.9986i) q^{17} -18.1729 q^{19} +(11.4973 + 19.9139i) q^{20} +(-10.9916 - 6.34600i) q^{22} +(0.563797 - 0.976526i) q^{23} +(7.69097 + 13.3211i) q^{25} +11.7443i q^{26} -46.5083i q^{28} +(-22.3389 - 38.6921i) q^{29} +(-13.2930 - 7.67472i) q^{31} +(-12.7019 - 7.33345i) q^{32} +(29.3519 + 49.3686i) q^{34} +19.4533i q^{35} -18.6072i q^{37} +(53.1720 - 30.6989i) q^{38} +(-30.9835 - 17.8883i) q^{40} +(29.8151 - 51.6413i) q^{41} +(-16.0790 - 27.8497i) q^{43} +27.8537 q^{44} +3.80962i q^{46} +(38.0772 - 21.9839i) q^{47} +(-4.82711 + 8.36080i) q^{49} +(-45.0059 - 25.9842i) q^{50} +(-12.8870 - 22.3209i) q^{52} +89.1367i q^{53} -11.6505 q^{55} +(36.1805 + 62.6664i) q^{56} +(130.723 + 75.4728i) q^{58} +(-48.3462 - 27.9127i) q^{59} +(84.9883 - 49.0680i) q^{61} +51.8586 q^{62} +86.8198 q^{64} +(5.39030 + 9.33627i) q^{65} +(17.8439 - 30.9065i) q^{67} +(-109.957 - 61.6207i) q^{68} +(-32.8618 - 56.9183i) q^{70} +121.996 q^{71} +34.4286i q^{73} +(31.4325 + 54.4427i) q^{74} +(-67.3714 + 116.691i) q^{76} +(20.4071 + 11.7820i) q^{77} +(91.8612 - 53.0361i) q^{79} +28.8942 q^{80} +201.463i q^{82} +(85.2416 - 49.2143i) q^{83} +(45.9924 + 25.7744i) q^{85} +(94.0911 + 54.3235i) q^{86} +(-37.5308 + 21.6684i) q^{88} +59.2783i q^{89} -21.8046i q^{91} +(-4.18027 - 7.24045i) q^{92} +(-74.2733 + 128.645i) q^{94} +(28.1798 - 48.8088i) q^{95} +(-8.23298 + 4.75331i) q^{97} -32.6171i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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