LMFDB - Embedded newform 378.3.q.a.71.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(71,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.71"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.q (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:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.12
Character	$\chi$	$=$	378.71
Dual form			378.3.q.a.197.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50944 + 2.60353i) q^{5} +(1.32288 + 2.29129i) q^{7} -2.82843i q^{8} +7.36389 q^{10} +(11.4711 - 6.62282i) q^{11} +(-4.01343 + 6.95146i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} +8.82428i q^{17} -3.48936 q^{19} +(9.01889 - 5.20706i) q^{20} +(9.36608 - 16.2225i) q^{22} +(32.7769 + 18.9238i) q^{23} +(1.05672 + 1.83030i) q^{25} +11.3517i q^{26} +5.29150 q^{28} +(13.4482 - 7.76433i) q^{29} +(11.9168 - 20.6405i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(6.23971 + 10.8075i) q^{34} +13.7766i q^{35} +19.2212 q^{37} +(-4.27358 + 2.46735i) q^{38} +(7.36389 - 12.7546i) q^{40} +(-29.2689 - 16.8984i) q^{41} +(-22.7888 - 39.4714i) q^{43} -26.4913i q^{44} +53.5245 q^{46} +(-52.1392 + 30.1026i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(2.58843 + 1.49443i) q^{50} +(8.02685 + 13.9029i) q^{52} -63.7924i q^{53} +68.9708 q^{55} +(6.48074 - 3.74166i) q^{56} +(10.9804 - 19.0187i) q^{58} +(94.5815 + 54.6066i) q^{59} +(-39.6043 - 68.5967i) q^{61} -33.7057i q^{62} -8.00000 q^{64} +(-36.1966 + 20.8981i) q^{65} +(-53.3828 + 92.4617i) q^{67} +(15.2841 + 8.82428i) q^{68} +(9.74151 + 16.8728i) q^{70} +94.1409i q^{71} -3.40818 q^{73} +(23.5411 - 13.5915i) q^{74} +(-3.48936 + 6.04375i) q^{76} +(30.3496 + 17.5223i) q^{77} +(-78.0889 - 135.254i) q^{79} -20.8282i q^{80} -47.7959 q^{82} +(-130.062 + 75.0915i) q^{83} +(-22.9743 + 39.7926i) q^{85} +(-55.8210 - 32.2283i) q^{86} +(-18.7322 - 32.4450i) q^{88} -29.5689i q^{89} -21.2371 q^{91} +(65.5539 - 37.8476i) q^{92} +(-42.5715 + 73.7360i) q^{94} +(-15.7351 - 9.08466i) q^{95} +(40.7964 + 70.6614i) q^{97} +9.89949i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	4.50944	+	2.60353i	0.901889	+	0.520706i	0.877812	−	0.479004i	$-0.159002\pi$
$5$	4.50944	+	2.60353i	0.901889	+	0.520706i	0.0240762	+	0.999710i	$0.492336\pi$
$6$		0			0
$7$	1.32288	+	2.29129i	0.188982	+	0.327327i
$7$	1.32288	+	2.29129i	0.188982	+	0.327327i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	7.36389			0.736389
$11$	11.4711	−	6.62282i	1.04282	−	0.602074i	0.122191	−	0.992507i	$-0.461008\pi$
$11$	11.4711	−	6.62282i	1.04282	−	0.602074i	0.920632	+	0.390432i	$0.127674\pi$
$12$		0			0
$13$	−4.01343	+	6.95146i	−0.308725	+	0.534728i	−0.978084	−	0.208212i	$-0.933236\pi$
$13$	−4.01343	+	6.95146i	−0.308725	+	0.534728i	0.669359	+	0.742939i	$0.266569\pi$
$14$	3.24037	+	1.87083i	0.231455	+	0.133631i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			8.82428i			0.519075i	0.965733	+	0.259538i	$0.0835702\pi$
$17$			8.82428i			0.519075i	−0.965733	+	0.259538i	$0.916430\pi$
$18$		0			0
$19$	−3.48936			−0.183651			−0.0918253	−	0.995775i	$-0.529270\pi$
$19$	−3.48936			−0.183651			−0.0918253	+	0.995775i	$0.529270\pi$
$20$	9.01889	−	5.20706i	0.450944	−	0.260353i
$21$		0			0
$22$	9.36608	−	16.2225i	0.425731	−	0.737387i
$23$	32.7769	+	18.9238i	1.42508	+	0.822773i	0.996727	−	0.0808365i	$-0.0257592\pi$
$23$	32.7769	+	18.9238i	1.42508	+	0.822773i	0.428357	+	0.903609i	$0.359093\pi$
$24$		0			0
$25$	1.05672	+	1.83030i	0.0422689	+	0.0732118i
$26$			11.3517i			0.436603i
$27$		0			0
$28$	5.29150			0.188982
$29$	13.4482	−	7.76433i	0.463732	−	0.267736i	−0.249880	−	0.968277i	$-0.580391\pi$
$29$	13.4482	−	7.76433i	0.463732	−	0.267736i	0.713612	+	0.700541i	$0.247058\pi$
$30$		0			0
$31$	11.9168	−	20.6405i	0.384412	−	0.665821i	−0.607275	−	0.794491i	$-0.707738\pi$
$31$	11.9168	−	20.6405i	0.384412	−	0.665821i	0.991687	+	0.128670i	$0.0410708\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	6.23971	+	10.8075i	0.183521	+	0.317867i
$35$			13.7766i			0.393617i
$36$		0			0
$37$	19.2212			0.519492			0.259746	−	0.965677i	$-0.416361\pi$
$37$	19.2212			0.519492			0.259746	+	0.965677i	$0.416361\pi$
$38$	−4.27358	+	2.46735i	−0.112463	+	0.0649303i
$39$		0			0
$40$	7.36389	−	12.7546i	0.184097	−	0.318866i
$41$	−29.2689	−	16.8984i	−0.713875	−	0.412156i	0.0986192	−	0.995125i	$-0.468557\pi$
$41$	−29.2689	−	16.8984i	−0.713875	−	0.412156i	−0.812494	+	0.582969i	$0.801891\pi$
$42$		0			0
$43$	−22.7888	−	39.4714i	−0.529973	−	0.917940i	−0.999389	−	0.0349628i	$-0.988869\pi$
$43$	−22.7888	−	39.4714i	−0.529973	−	0.917940i	0.469416	−	0.882977i	$-0.344465\pi$
$44$		−	26.4913i		−	0.602074i
$45$		0			0
$46$	53.5245			1.16358
$47$	−52.1392	+	30.1026i	−1.10935	+	0.640481i	−0.938660	−	0.344845i	$-0.887932\pi$
$47$	−52.1392	+	30.1026i	−1.10935	+	0.640481i	−0.170685	+	0.985326i	$0.554598\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	2.58843	+	1.49443i	0.0517686	+	0.0298886i
$51$		0			0
$52$	8.02685	+	13.9029i	0.154363	+	0.267364i
$53$		−	63.7924i		−	1.20363i	−0.798636	−	0.601815i	$-0.794445\pi$
$53$		−	63.7924i		−	1.20363i	0.798636	−	0.601815i	$-0.205555\pi$
$54$		0			0
$55$	68.9708			1.25401
$56$	6.48074	−	3.74166i	0.115728	−	0.0668153i
$57$		0			0
$58$	10.9804	−	19.0187i	0.189318	−	0.327908i
$59$	94.5815	+	54.6066i	1.60308	+	0.925536i	0.990867	+	0.134840i	$0.0430519\pi$
$59$	94.5815	+	54.6066i	1.60308	+	0.925536i	0.612208	+	0.790697i	$0.290281\pi$
$60$		0			0
$61$	−39.6043	−	68.5967i	−0.649251	−	1.12454i	−0.983302	−	0.181981i	$-0.941749\pi$
$61$	−39.6043	−	68.5967i	−0.649251	−	1.12454i	0.334051	−	0.942555i	$-0.391584\pi$
$62$		−	33.7057i		−	0.543641i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−36.1966	+	20.8981i	−0.556872	+	0.321510i
$66$		0			0
$67$	−53.3828	+	92.4617i	−0.796758	+	1.38003i	0.124958	+	0.992162i	$0.460120\pi$
$67$	−53.3828	+	92.4617i	−0.796758	+	1.38003i	−0.921717	+	0.387864i	$0.873213\pi$
$68$	15.2841	+	8.82428i	0.224766	+	0.129769i
$69$		0			0
$70$	9.74151	+	16.8728i	0.139164	+	0.241040i
$71$			94.1409i			1.32593i	0.748651	+	0.662964i	$0.230702\pi$
$71$			94.1409i			1.32593i	−0.748651	+	0.662964i	$0.769298\pi$
$72$		0			0
$73$	−3.40818			−0.0466874			−0.0233437	−	0.999727i	$-0.507431\pi$
$73$	−3.40818			−0.0466874			−0.0233437	+	0.999727i	$0.507431\pi$
$74$	23.5411	−	13.5915i	0.318123	−	0.183668i
$75$		0			0
$76$	−3.48936	+	6.04375i	−0.0459127	+	0.0795231i
$77$	30.3496	+	17.5223i	0.394150	+	0.227563i
$78$		0			0
$79$	−78.0889	−	135.254i	−0.988467	−	1.71208i	−0.625381	−	0.780320i	$-0.715056\pi$
$79$	−78.0889	−	135.254i	−0.988467	−	1.71208i	−0.363087	−	0.931755i	$-0.618277\pi$
$80$		−	20.8282i		−	0.260353i
$81$		0			0
$82$	−47.7959			−0.582876
$83$	−130.062	+	75.0915i	−1.56702	+	0.904717i	−0.570502	+	0.821296i	$0.693251\pi$
$83$	−130.062	+	75.0915i	−1.56702	+	0.904717i	−0.996514	+	0.0834211i	$0.973415\pi$
$84$		0			0
$85$	−22.9743	+	39.7926i	−0.270286	+	0.468148i
$86$	−55.8210	−	32.2283i	−0.649082	−	0.374747i
$87$		0			0
$88$	−18.7322	−	32.4450i	−0.212865	−	0.368694i
$89$		−	29.5689i		−	0.332235i	−0.986106	−	0.166117i	$-0.946877\pi$
$89$		−	29.5689i		−	0.332235i	0.986106	−	0.166117i	$-0.0531230\pi$
$90$		0			0
$91$	−21.2371			−0.233374
$92$	65.5539	−	37.8476i	0.712542	−	0.411386i
$93$		0			0
$94$	−42.5715	+	73.7360i	−0.452888	+	0.784425i
$95$	−15.7351	−	9.08466i	−0.165632	−	0.0956280i
$96$		0			0
$97$	40.7964	+	70.6614i	0.420581	+	0.728468i	0.995996	−	0.0893933i	$-0.0284928\pi$
$97$	40.7964	+	70.6614i	0.420581	+	0.728468i	−0.575415	+	0.817862i	$0.695159\pi$
$98$			9.89949i			0.101015i
$99$		0			0
$100$	4.22689			0.0422689
$101$	0.619620	−	0.357738i	0.00613485	−	0.00354196i	−0.496929	−	0.867791i	$-0.665539\pi$
$101$	0.619620	−	0.357738i	0.00613485	−	0.00354196i	0.503064	+	0.864249i	$0.332206\pi$
$102$		0			0
$103$	−89.9236	+	155.752i	−0.873044	+	1.51216i	−0.0142130	+	0.999899i	$0.504524\pi$
$103$	−89.9236	+	155.752i	−0.873044	+	1.51216i	−0.858831	+	0.512258i	$0.828809\pi$
$104$	19.6617	+	11.3517i	0.189055	+	0.109151i
$105$		0			0
$106$	−45.1080	−	78.1294i	−0.425547	−	0.737070i
$107$		−	63.7076i		−	0.595398i	−0.954660	−	0.297699i	$-0.903781\pi$
$107$		−	63.7076i		−	0.595398i	0.954660	−	0.297699i	$-0.0962191\pi$
$108$		0			0
$109$	−184.582			−1.69341			−0.846705	−	0.532063i	$-0.821417\pi$
$109$	−184.582			−1.69341			−0.846705	+	0.532063i	$0.821417\pi$
$110$	84.4716	−	48.7697i	0.767923	−	0.443361i
$111$		0			0
$112$	5.29150	−	9.16515i	0.0472456	−	0.0818317i
$113$	−108.448	−	62.6124i	−0.959715	−	0.554092i	−0.0636298	−	0.997974i	$-0.520268\pi$
$113$	−108.448	−	62.6124i	−0.959715	−	0.554092i	−0.896085	+	0.443882i	$0.853601\pi$
$114$		0			0
$115$	98.5372	+	170.671i	0.856845	+	1.48410i
$116$		−	31.0573i		−	0.267736i
$117$		0			0
$118$	154.451			1.30891
$119$	−20.2190	+	11.6734i	−0.169907	+	0.0980960i
$120$		0			0
$121$	27.2234	−	47.1523i	0.224987	−	0.389688i
$122$	−97.0103	−	56.0090i	−0.795167	−	0.459090i
$123$		0			0
$124$	−23.8336	−	41.2809i	−0.192206	−	0.332911i
$125$		−	119.172i		−	0.953373i
$126$		0			0
$127$	186.865			1.47138			0.735688	−	0.677320i	$-0.236859\pi$
$127$	186.865			1.47138			0.735688	+	0.677320i	$0.236859\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−29.5544	+	51.1898i	−0.227342	+	0.393768i
$131$	−12.5131	−	7.22447i	−0.0955202	−	0.0551486i	0.451479	−	0.892282i	$-0.350897\pi$
$131$	−12.5131	−	7.22447i	−0.0955202	−	0.0551486i	−0.546999	+	0.837133i	$0.684230\pi$
$132$		0			0
$133$	−4.61599	−	7.99514i	−0.0347067	−	0.0601138i
$134$			150.989i			1.12679i
$135$		0			0
$136$	24.9588			0.183521
$137$	−31.0324	+	17.9166i	−0.226514	+	0.130778i	−0.608963	−	0.793199i	$-0.708414\pi$
$137$	−31.0324	+	17.9166i	−0.226514	+	0.130778i	0.382449	+	0.923977i	$0.375081\pi$
$138$		0			0
$139$	−17.5299	+	30.3627i	−0.126115	+	0.218437i	−0.922168	−	0.386789i	$-0.873584\pi$
$139$	−17.5299	+	30.3627i	−0.126115	+	0.218437i	0.796053	+	0.605226i	$0.206917\pi$
$140$	23.8617	+	13.7766i	0.170441	+	0.0984041i
$141$		0			0
$142$	66.5677	+	115.299i	0.468786	+	0.811962i
$143$			106.321i			0.743502i
$144$		0			0
$145$	80.8586			0.557646
$146$	−4.17415	+	2.40995i	−0.0285901	+	0.0165065i
$147$		0			0
$148$	19.2212	−	33.2921i	0.129873	−	0.224947i
$149$	−145.432	−	83.9654i	−0.976056	−	0.563526i	−0.0749788	−	0.997185i	$-0.523889\pi$
$149$	−145.432	−	83.9654i	−0.976056	−	0.563526i	−0.901077	+	0.433659i	$0.857222\pi$
$150$		0			0
$151$	−97.0005	−	168.010i	−0.642387	−	1.11265i	−0.984898	−	0.173133i	$-0.944611\pi$
$151$	−97.0005	−	168.010i	−0.642387	−	1.11265i	0.342511	−	0.939514i	$-0.388723\pi$
$152$			9.86941i			0.0649303i
$153$		0			0
$154$	49.5606			0.321822
$155$	107.476	−	62.0513i	0.693394	−	0.400331i
$156$		0			0
$157$	−8.25239	+	14.2936i	−0.0525630	+	0.0910417i	−0.891110	−	0.453788i	$-0.850072\pi$
$157$	−8.25239	+	14.2936i	−0.0525630	+	0.0910417i	0.838547	+	0.544830i	$0.183406\pi$
$158$	−191.278	−	110.434i	−1.21062	−	0.698952i
$159$		0			0
$160$	−14.7278	−	25.5093i	−0.0920486	−	0.159433i
$161$			100.135i			0.621958i
$162$		0			0
$163$	−174.369			−1.06975			−0.534873	−	0.844933i	$-0.679641\pi$
$163$	−174.369			−1.06975			−0.534873	+	0.844933i	$0.679641\pi$
$164$	−58.5377	+	33.7968i	−0.356937	+	0.206078i
$165$		0			0
$166$	−106.195	+	183.936i	−0.639732	+	1.10805i
$167$	126.279	+	72.9072i	0.756162	+	0.436570i	0.827916	−	0.560852i	$-0.189526\pi$
$167$	126.279	+	72.9072i	0.756162	+	0.436570i	−0.0717543	+	0.997422i	$0.522860\pi$
$168$		0			0
$169$	52.2848	+	90.5599i	0.309378	+	0.535858i
$170$			64.9810i			0.382241i
$171$		0			0
$172$	−91.1553			−0.529973
$173$	50.3479	−	29.0684i	0.291028	−	0.168025i	−0.347377	−	0.937725i	$-0.612928\pi$
$173$	50.3479	−	29.0684i	0.291028	−	0.168025i	0.638406	+	0.769700i	$0.279594\pi$
$174$		0			0
$175$	−2.79582	+	4.84251i	−0.0159761	+	0.0276715i
$176$	−45.8842	−	26.4913i	−0.260706	−	0.150519i
$177$		0			0
$178$	−20.9084	−	36.2143i	−0.117463	−	0.203451i
$179$		−	177.566i		−	0.991989i	−0.868326	−	0.495995i	$-0.834804\pi$
$179$		−	177.566i		−	0.991989i	0.868326	−	0.495995i	$-0.165196\pi$
$180$		0			0
$181$	42.0375			0.232251			0.116126	−	0.993235i	$-0.462952\pi$
$181$	42.0375			0.232251			0.116126	+	0.993235i	$0.462952\pi$
$182$	−26.0100	+	15.0169i	−0.142912	+	0.0825103i
$183$		0			0
$184$	53.5245	−	92.7072i	0.290894	−	0.503843i
$185$	86.6770	+	50.0430i	0.468524	+	0.270503i
$186$		0			0
$187$	58.4416	+	101.224i	0.312522	+	0.541304i
$188$			120.410i			0.640481i
$189$		0			0
$190$	−25.6953			−0.135238
$191$	74.7660	−	43.1662i	0.391445	−	0.226001i	−0.291341	−	0.956619i	$-0.594101\pi$
$191$	74.7660	−	43.1662i	0.391445	−	0.226001i	0.682786	+	0.730618i	$0.260768\pi$
$192$		0			0
$193$	69.3030	−	120.036i	0.359083	−	0.621950i	−0.628725	−	0.777628i	$-0.716423\pi$
$193$	69.3030	−	120.036i	0.359083	−	0.621950i	0.987808	+	0.155678i	$0.0497562\pi$
$194$	99.9303	+	57.6948i	0.515105	+	0.297396i
$195$		0			0
$196$	7.00000	+	12.1244i	0.0357143	+	0.0618590i
$197$			39.4308i			0.200156i	0.994980	+	0.100078i	$0.0319093\pi$
$197$			39.4308i			0.200156i	−0.994980	+	0.100078i	$0.968091\pi$
$198$		0			0
$199$	88.0429			0.442427			0.221213	−	0.975225i	$-0.428998\pi$
$199$	88.0429			0.442427			0.221213	+	0.975225i	$0.428998\pi$
$200$	5.17686	−	2.98886i	0.0258843	−	0.0149443i
$201$		0			0
$202$	0.505918	−	0.876275i	0.00250454	−	0.00433800i
$203$	35.5806	+	20.5425i	0.175274	+	0.101195i
$204$		0			0
$205$	−87.9909	−	152.405i	−0.429224	−	0.743437i
$206$			254.342i			1.23467i
$207$		0			0
$208$	32.1074			0.154363
$209$	−40.0267	+	23.1094i	−0.191515	+	0.110571i
$210$		0			0
$211$	−96.3691	+	166.916i	−0.456726	+	0.791072i	−0.998786	−	0.0492677i	$-0.984311\pi$
$211$	−96.3691	+	166.916i	−0.456726	+	0.791072i	0.542060	+	0.840340i	$0.317645\pi$
$212$	−110.492	−	63.7924i	−0.521187	−	0.300907i
$213$		0			0
$214$	−45.0480	−	78.0255i	−0.210505	−	0.364605i
$215$		−	237.326i		−	1.10384i
$216$		0			0
$217$	63.0577			0.290588
$218$	−226.065	+	130.519i	−1.03700	+	0.598711i
$219$		0			0
$220$	68.9708	−	119.461i	0.313503	−	0.543004i
$221$	−61.3416	−	35.4156i	−0.277564	−	0.160252i
$222$		0			0
$223$	−89.9715	−	155.835i	−0.403459	−	0.698812i	0.590681	−	0.806905i	$-0.298859\pi$
$223$	−89.9715	−	155.835i	−0.403459	−	0.698812i	−0.994141	+	0.108093i	$0.965526\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−177.095			−0.783604
$227$	82.1961	−	47.4559i	0.362097	−	0.209057i	−0.307903	−	0.951418i	$-0.599627\pi$
$227$	82.1961	−	47.4559i	0.362097	−	0.209057i	0.670000	+	0.742361i	$0.266294\pi$
$228$		0			0
$229$	177.233	−	306.977i	0.773945	−	1.34051i	−0.161441	−	0.986882i	$-0.551614\pi$
$229$	177.233	−	306.977i	0.773945	−	1.34051i	0.935386	−	0.353629i	$-0.115052\pi$
$230$	241.366	+	139.353i	1.04942	+	0.605881i
$231$		0			0
$232$	−21.9608	−	38.0373i	−0.0946588	−	0.163954i
$233$		−	192.278i		−	0.825226i	−0.910907	−	0.412613i	$-0.864616\pi$
$233$		−	192.278i		−	0.825226i	0.910907	−	0.412613i	$-0.135384\pi$
$234$		0			0
$235$	−313.492			−1.33401
$236$	189.163	−	109.213i	0.801538	−	0.462768i
$237$		0			0
$238$	−16.5087	+	28.5939i	−0.0693644	+	0.120143i
$239$	251.206	+	145.034i	1.05107	+	0.606836i	0.922949	−	0.384922i	$-0.125772\pi$
$239$	251.206	+	145.034i	1.05107	+	0.606836i	0.128122	+	0.991758i	$0.459105\pi$
$240$		0			0
$241$	55.9605	+	96.9265i	0.232201	+	0.402184i	0.958456	−	0.285242i	$-0.0920739\pi$
$241$	55.9605	+	96.9265i	0.232201	+	0.402184i	−0.726254	+	0.687426i	$0.758741\pi$
$242$		−	76.9993i		−	0.318179i
$243$		0			0
$244$	−158.417			−0.649251
$245$	−31.5661	+	18.2247i	−0.128841	+	0.0743865i
$246$		0			0
$247$	14.0043	−	24.2562i	0.0566976	−	0.0982031i
$248$	−58.3800	−	33.7057i	−0.235403	−	0.135910i
$249$		0			0
$250$	−84.2671	−	145.955i	−0.337068	−	0.583819i
$251$			203.517i			0.810826i	0.914134	+	0.405413i	$0.132872\pi$
$251$			203.517i			0.810826i	−0.914134	+	0.405413i	$0.867128\pi$
$252$		0			0
$253$	501.315			1.98148
$254$	228.862	−	132.133i	0.901030	−	0.520210i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−259.814	−	150.004i	−1.01095	−	0.583673i	−0.0994809	−	0.995039i	$-0.531718\pi$
$257$	−259.814	−	150.004i	−1.01095	−	0.583673i	−0.911470	+	0.411367i	$0.865052\pi$
$258$		0			0
$259$	25.4273	+	44.0413i	0.0981748	+	0.170044i
$260$			83.5926i			0.321510i
$261$		0			0
$262$	−20.4339			−0.0779919
$263$	163.477	−	94.3833i	0.621584	−	0.358872i	−0.155901	−	0.987773i	$-0.549828\pi$
$263$	163.477	−	94.3833i	0.621584	−	0.358872i	0.777486	+	0.628901i	$0.216495\pi$
$264$		0			0
$265$	166.085	−	287.668i	0.626737	−	1.08554i
$266$	−11.3068	−	6.52800i	−0.0425069	−	0.0245414i
$267$		0			0
$268$	106.766	+	184.923i	0.398379	+	0.690013i
$269$			260.462i			0.968261i	0.874996	+	0.484131i	$0.160864\pi$
$269$			260.462i			0.968261i	−0.874996	+	0.484131i	$0.839136\pi$
$270$		0			0
$271$	−142.144			−0.524518			−0.262259	−	0.964998i	$-0.584467\pi$
$271$	−142.144			−0.524518			−0.262259	+	0.964998i	$0.584467\pi$
$272$	30.5682	−	17.6486i	0.112383	−	0.0648844i
$273$		0			0
$274$	−25.3378	+	43.8864i	−0.0924739	+	0.160169i
$275$	24.2434	+	13.9969i	0.0881579	+	0.0508980i
$276$		0			0
$277$	5.33049	+	9.23268i	0.0192436	+	0.0333310i	0.875487	−	0.483242i	$-0.160541\pi$
$277$	5.33049	+	9.23268i	0.0192436	+	0.0333310i	−0.856243	+	0.516573i	$0.827208\pi$
$278$			49.5822i			0.178353i
$279$		0			0
$280$	38.9660			0.139164
$281$	153.223	−	88.4636i	0.545279	−	0.314817i	−0.201937	−	0.979399i	$-0.564724\pi$
$281$	153.223	−	88.4636i	0.545279	−	0.314817i	0.747216	+	0.664582i	$0.231390\pi$
$282$		0			0
$283$	151.466	−	262.347i	0.535216	−	0.927022i	−0.463936	−	0.885869i	$-0.653563\pi$
$283$	151.466	−	262.347i	0.535216	−	0.927022i	0.999153	−	0.0411536i	$-0.0131033\pi$
$284$	163.057	+	94.1409i	0.574144	+	0.331482i
$285$		0			0
$286$	75.1801	+	130.216i	0.262868	+	0.455300i
$287$		−	89.4179i		−	0.311561i
$288$		0			0
$289$	211.132			0.730561
$290$	99.0312	−	57.1757i	0.341487	−	0.197158i
$291$		0			0
$292$	−3.40818	+	5.90314i	−0.0116719	+	0.0202162i
$293$	465.106	+	268.529i	1.58739	+	0.916481i	0.993735	+	0.111763i	$0.0356499\pi$
$293$	465.106	+	268.529i	1.58739	+	0.916481i	0.593657	+	0.804718i	$0.297683\pi$
$294$		0			0
$295$	284.340	+	492.491i	0.963864	+	1.66946i
$296$		−	54.3658i		−	0.183668i
$297$		0			0
$298$	−237.490			−0.796946
$299$	−263.096	+	151.898i	−0.879919	+	0.508021i
$300$		0			0
$301$	60.2936	−	104.432i	0.200311	−	0.346949i
$302$	−237.602	−	137.179i	−0.786760	−	0.454236i
$303$		0			0
$304$	6.97873	+	12.0875i	0.0229563	+	0.0397615i
$305$		−	412.444i		−	1.35227i
$306$		0			0
$307$	509.581			1.65987			0.829937	−	0.557858i	$-0.188376\pi$
$307$	509.581			1.65987			0.829937	+	0.557858i	$0.188376\pi$
$308$	60.6991	−	35.0446i	0.197075	−	0.113781i
$309$		0			0
$310$	87.7538	−	151.994i	0.283077	−	0.490304i
$311$	270.660	+	156.265i	0.870289	+	0.502461i	0.867444	−	0.497535i	$-0.165761\pi$
$311$	270.660	+	156.265i	0.870289	+	0.502461i	0.00284453	+	0.999996i	$0.499095\pi$
$312$		0			0
$313$	−282.583	−	489.447i	−0.902820	−	1.56373i	−0.823817	−	0.566855i	$-0.808160\pi$
$313$	−282.583	−	489.447i	−0.902820	−	1.56373i	−0.0790023	−	0.996874i	$-0.525173\pi$
$314$			23.3413i			0.0743353i
$315$		0			0
$316$	−312.356			−0.988467
$317$	−118.015	+	68.1358i	−0.372286	+	0.214939i	−0.674457	−	0.738314i	$-0.735622\pi$
$317$	−118.015	+	68.1358i	−0.372286	+	0.214939i	0.302171	+	0.953254i	$0.402289\pi$
$318$		0			0
$319$	102.843	−	178.130i	0.322393	−	0.558402i
$320$	−36.0755	−	20.8282i	−0.112736	−	0.0650882i
$321$		0			0
$322$	70.8063	+	122.640i	0.219895	+	0.380870i
$323$		−	30.7911i		−	0.0953286i
$324$		0			0
$325$	−16.9643			−0.0521978
$326$	−213.557	+	123.297i	−0.655083	+	0.378212i
$327$		0			0
$328$	−47.7959	+	82.7849i	−0.145719	+	0.252393i
$329$	−137.947	−	79.6440i	−0.419293	−	0.242079i
$330$		0			0
$331$	243.423	+	421.621i	0.735416	+	1.27378i	0.954540	+	0.298081i	$0.0963467\pi$
$331$	243.423	+	421.621i	0.735416	+	1.27378i	−0.219124	+	0.975697i	$0.570320\pi$
$332$			300.366i			0.904717i
$333$		0			0
$334$	206.213			0.617403
$335$	−481.454	+	277.967i	−1.43717	+	0.829753i
$336$		0			0
$337$	29.0085	−	50.2442i	0.0860786	−	0.149093i	−0.819772	−	0.572690i	$-0.805900\pi$
$337$	29.0085	−	50.2442i	0.0860786	−	0.149093i	0.905850	+	0.423598i	$0.139233\pi$
$338$	128.071	+	73.9419i	0.378909	+	0.218763i
$339$		0			0
$340$	45.9485	+	79.5852i	0.135143	+	0.234074i
$341$		−	315.690i		−	0.925778i
$342$		0			0
$343$	−18.5203			−0.0539949
$344$	−111.642	+	64.4566i	−0.324541	+	0.187374i
$345$		0			0
$346$	41.1089	−	71.2027i	0.118812	−	0.205788i
$347$	216.133	+	124.784i	0.622861	+	0.359609i	0.777982	−	0.628287i	$-0.216243\pi$
$347$	216.133	+	124.784i	0.622861	+	0.359609i	−0.155121	+	0.987895i	$0.549577\pi$
$348$		0			0
$349$	−112.209	−	194.351i	−0.321515	−	0.556880i	0.659286	−	0.751892i	$-0.270859\pi$
$349$	−112.209	−	194.351i	−0.321515	−	0.556880i	−0.980801	+	0.195012i	$0.937525\pi$
$350$			7.90778i			0.0225937i
$351$		0			0
$352$	−74.9286			−0.212865
$353$	−192.298	+	111.023i	−0.544753	+	0.314513i	−0.747003	−	0.664821i	$-0.768508\pi$
$353$	−192.298	+	111.023i	−0.544753	+	0.314513i	0.202250	+	0.979334i	$0.435175\pi$
$354$		0			0
$355$	−245.099	+	424.523i	−0.690418	+	1.19584i
$356$	−51.2148	−	29.5689i	−0.143862	−	0.0830586i
$357$		0			0
$358$	−125.558	−	217.473i	−0.350721	−	0.607467i
$359$			316.242i			0.880898i	0.897778	+	0.440449i	$0.145181\pi$
$359$			316.242i			0.880898i	−0.897778	+	0.440449i	$0.854819\pi$
$360$		0			0
$361$	−348.824			−0.966272
$362$	51.4852	−	29.7250i	0.142224	−	0.0821133i
$363$		0			0
$364$	−21.2371	+	36.7837i	−0.0583436	+	0.101054i
$365$	−15.3690	−	8.87330i	−0.0421069	−	0.0243104i
$366$		0			0
$367$	232.627	+	402.922i	0.633862	+	1.09788i	0.986755	+	0.162217i	$0.0518646\pi$
$367$	232.627	+	402.922i	0.633862	+	1.09788i	−0.352893	+	0.935664i	$0.614802\pi$
$368$		−	151.390i		−	0.411386i
$369$		0			0
$370$	141.543			0.382549
$371$	146.167	−	84.3894i	0.393980	−	0.227465i
$372$		0			0
$373$	−39.8509	+	69.0237i	−0.106839	+	0.185050i	−0.914488	−	0.404613i	$-0.867406\pi$
$373$	−39.8509	+	69.0237i	−0.106839	+	0.185050i	0.807649	+	0.589663i	$0.200740\pi$
$374$	143.152	+	82.6489i	0.382760	+	0.220986i
$375$		0			0
$376$	85.1430	+	147.472i	0.226444	+	0.392213i
$377$			124.646i			0.330627i
$378$		0			0
$379$	135.902			0.358579			0.179290	−	0.983796i	$-0.442620\pi$
$379$	135.902			0.358579			0.179290	+	0.983796i	$0.442620\pi$
$380$	−31.4702	+	18.1693i	−0.0828162	+	0.0478140i
$381$		0			0
$382$	61.0462	−	105.735i	0.159807	−	0.276794i
$383$	−345.859	−	199.682i	−0.903027	−	0.521363i	−0.0248460	−	0.999691i	$-0.507910\pi$
$383$	−345.859	−	199.682i	−0.903027	−	0.521363i	−0.878181	+	0.478328i	$0.841243\pi$
$384$		0			0
$385$	91.2397	+	158.032i	0.236986	+	0.410472i
$386$		−	196.018i		−	0.507820i
$387$		0			0
$388$	163.186			0.420581
$389$	382.780	−	220.998i	0.984011	−	0.568119i	0.0805324	−	0.996752i	$-0.474338\pi$
$389$	382.780	−	220.998i	0.984011	−	0.568119i	0.903479	+	0.428633i	$0.141005\pi$
$390$		0			0
$391$	−166.989	+	289.233i	−0.427081	+	0.739726i
$392$	17.1464	+	9.89949i	0.0437409	+	0.0252538i
$393$		0			0
$394$	27.8818	+	48.2926i	0.0707659	+	0.122570i
$395$		−	813.227i		−	2.05880i
$396$		0			0
$397$	−384.151			−0.967635			−0.483817	−	0.875169i	$-0.660750\pi$
$397$	−384.151			−0.967635			−0.483817	+	0.875169i	$0.660750\pi$
$398$	107.830	−	62.2557i	0.270930	−	0.156421i
$399$		0			0
$400$	4.22689	−	7.32118i	0.0105672	−	0.0183030i
$401$	−224.637	−	129.694i	−0.560193	−	0.323427i	0.193030	−	0.981193i	$-0.438168\pi$
$401$	−224.637	−	129.694i	−0.560193	−	0.323427i	−0.753223	+	0.657765i	$0.771502\pi$
$402$		0			0
$403$	95.6542	+	165.678i	0.237355	+	0.411112i
$404$		−	1.43095i		−	0.00354196i
$405$		0			0
$406$	58.1029			0.143111
$407$	220.488	−	127.299i	0.541739	−	0.312773i
$408$		0			0
$409$	47.4549	−	82.1943i	0.116027	−	0.200964i	−0.802163	−	0.597105i	$-0.796318\pi$
$409$	47.4549	−	82.1943i	0.116027	−	0.200964i	0.918190	+	0.396141i	$0.129651\pi$
$410$	−215.533	−	124.438i	−0.525690	−	0.303507i
$411$		0			0
$412$	179.847	+	311.504i	0.436522	+	0.756079i
$413$			288.951i			0.699640i
$414$		0			0
$415$	−782.012			−1.88437
$416$	39.3234	−	22.7034i	0.0945274	−	0.0545754i
$417$		0			0
$418$	−32.6816	+	56.6063i	−0.0781857	+	0.135422i
$419$	139.448	+	80.5105i	0.332812	+	0.192149i	0.657089	−	0.753813i	$-0.271788\pi$
$419$	139.448	+	80.5105i	0.332812	+	0.192149i	−0.324277	+	0.945962i	$0.605121\pi$
$420$		0			0
$421$	−266.914	−	462.308i	−0.634000	−	1.09812i	−0.986726	−	0.162393i	$-0.948079\pi$
$421$	−266.914	−	462.308i	−0.634000	−	1.09812i	0.352727	−	0.935726i	$-0.385255\pi$
$422$			272.573i			0.645908i
$423$		0			0
$424$	−180.432			−0.425547
$425$	−16.1510	+	9.32481i	−0.0380025	+	0.0219407i
$426$		0			0
$427$	104.783	−	181.490i	0.245394	−	0.425035i
$428$	−110.345	−	63.7076i	−0.257815	−	0.148849i
$429$		0			0
$430$	−167.815	−	290.663i	−0.390266	−	0.675961i
$431$		−	224.292i		−	0.520399i	−0.965555	−	0.260200i	$-0.916212\pi$
$431$		−	224.292i		−	0.520399i	0.965555	−	0.260200i	$-0.0837884\pi$
$432$		0			0
$433$	−754.086			−1.74154			−0.870770	−	0.491691i	$-0.836379\pi$
$433$	−754.086			−1.74154			−0.870770	+	0.491691i	$0.836379\pi$
$434$	77.2295	−	44.5885i	0.177948	−	0.102738i
$435$		0			0
$436$	−184.582	+	319.705i	−0.423353	+	0.733268i
$437$	−114.371	−	66.0319i	−0.261718	−	0.151103i
$438$		0			0
$439$	−250.978	−	434.707i	−0.571705	−	0.990222i	−0.996391	−	0.0848812i	$-0.972949\pi$
$439$	−250.978	−	434.707i	−0.571705	−	0.990222i	0.424686	−	0.905341i	$-0.360384\pi$
$440$		−	195.079i		−	0.443361i
$441$		0			0
$442$	−100.170			−0.226630
$443$	213.379	−	123.194i	0.481668	−	0.278091i	−0.239443	−	0.970910i	$-0.576965\pi$
$443$	213.379	−	123.194i	0.481668	−	0.278091i	0.721111	+	0.692819i	$0.243632\pi$
$444$		0			0
$445$	76.9834	−	133.339i	0.172996	−	0.299639i
$446$	−220.384	−	127.239i	−0.494135	−	0.285289i
$447$		0			0
$448$	−10.5830	−	18.3303i	−0.0236228	−	0.0409159i
$449$			187.215i			0.416959i	0.978027	+	0.208480i	$0.0668515\pi$
$449$			187.215i			0.416959i	−0.978027	+	0.208480i	$0.933149\pi$
$450$		0			0
$451$	−447.660			−0.992594
$452$	−216.896	+	125.225i	−0.479858	+	0.277046i
$453$		0			0
$454$	67.1128	−	116.243i	0.147826	−	0.256041i
$455$	−95.7673	−	55.2913i	−0.210478	−	0.121519i
$456$		0			0
$457$	273.781	+	474.203i	0.599084	+	1.03764i	0.992957	+	0.118479i	$0.0378019\pi$
$457$	273.781	+	474.203i	0.599084	+	1.03764i	−0.393872	+	0.919165i	$0.628865\pi$
$458$		−	501.291i		−	1.09452i
$459$		0			0
$460$	394.149			0.856845
$461$	−126.424	+	72.9908i	−0.274238	+	0.158332i	−0.630812	−	0.775936i	$-0.717278\pi$
$461$	−126.424	+	72.9908i	−0.274238	+	0.158332i	0.356574	+	0.934267i	$0.383945\pi$
$462$		0			0
$463$	−95.3446	+	165.142i	−0.205928	+	0.356677i	−0.950428	−	0.310945i	$-0.899355\pi$
$463$	−95.3446	+	165.142i	−0.205928	+	0.356677i	0.744500	+	0.667622i	$0.232688\pi$
$464$	−53.7929	−	31.0573i	−0.115933	−	0.0669339i
$465$		0			0
$466$	−135.961	−	235.491i	−0.291761	−	0.505345i
$467$			728.372i			1.55968i	0.625977	+	0.779841i	$0.284700\pi$
$467$			728.372i			1.55968i	−0.625977	+	0.779841i	$0.715300\pi$
$468$		0			0
$469$	−282.475			−0.602293
$470$	−383.948	+	221.672i	−0.816910	+	0.471643i
$471$		0			0
$472$	154.451	−	267.517i	0.327226	−	0.566773i
$473$	−522.824	−	301.853i	−1.10534	−	0.638166i
$474$		0			0
$475$	−3.68729	−	6.38657i	−0.00776271	−	0.0134454i
$476$			46.6937i			0.0980960i
$477$		0			0
$478$	410.218			0.858196
$479$	−636.669	+	367.581i	−1.32916	+	0.767392i	−0.985170	−	0.171580i	$-0.945113\pi$
$479$	−636.669	+	367.581i	−1.32916	+	0.767392i	−0.343992	+	0.938972i	$0.611779\pi$
$480$		0			0
$481$	−77.1430	+	133.616i	−0.160380	+	0.277787i
$482$	137.075	+	79.1401i	0.284387	+	0.164191i
$483$		0			0
$484$	−54.4468	−	94.3045i	−0.112493	−	0.194844i
$485$			424.858i			0.875996i
$486$		0			0
$487$	−189.093			−0.388281			−0.194140	−	0.980974i	$-0.562192\pi$
$487$	−189.093			−0.388281			−0.194140	+	0.980974i	$0.562192\pi$
$488$	−194.021	+	112.018i	−0.397583	+	0.229545i
$489$		0			0
$490$	−25.7736	+	44.6412i	−0.0525992	+	0.0911045i
$491$	285.887	+	165.057i	0.582254	+	0.336164i	0.762029	−	0.647543i	$-0.224204\pi$
$491$	285.887	+	165.057i	0.582254	+	0.336164i	−0.179775	+	0.983708i	$0.557537\pi$
$492$		0			0
$493$	68.5147	+	118.671i	0.138975	+	0.240712i
$494$		−	39.6102i		−	0.0801825i
$495$		0			0
$496$	−95.3342			−0.192206
$497$	−215.704	+	124.537i	−0.434012	+	0.250577i
$498$		0			0
$499$	−153.572	+	265.994i	−0.307759	+	0.533054i	−0.977872	−	0.209205i	$-0.932912\pi$
$499$	−153.572	+	265.994i	−0.307759	+	0.533054i	0.670113	+	0.742259i	$0.266246\pi$
$500$	−206.411	−	119.172i	−0.412823	−	0.238343i
$501$		0			0
$502$	143.909	+	249.257i	0.286670	+	0.496528i
$503$			38.9199i			0.0773755i	0.999251	+	0.0386878i	$0.0123178\pi$
$503$			38.9199i			0.0773755i	−0.999251	+	0.0386878i	$0.987682\pi$
$504$		0			0
$505$	3.72552			0.00737727
$506$	613.983	−	354.483i	1.21340	−	0.700559i
$507$		0			0
$508$	186.865	−	323.659i	0.367844	−	0.637125i
$509$	−130.399	−	75.2856i	−0.256186	−	0.147909i	0.366408	−	0.930454i	$-0.380588\pi$
$509$	−130.399	−	75.2856i	−0.256186	−	0.147909i	−0.622593	+	0.782546i	$0.713921\pi$
$510$		0			0
$511$	−4.50860	−	7.80912i	−0.00882309	−	0.0152820i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−424.275			−0.825438
$515$	−811.011	+	468.237i	−1.57478	+	0.909198i
$516$		0			0
$517$	−398.728	+	690.617i	−0.771234	+	1.33582i
$518$	62.2839	+	35.9596i	0.120239	+	0.0694201i
$519$		0			0
$520$	59.1089	+	102.380i	0.113671	+	0.196884i
$521$		−	440.225i		−	0.844961i	−0.906372	−	0.422480i	$-0.861160\pi$
$521$		−	440.225i		−	0.844961i	0.906372	−	0.422480i	$-0.138840\pi$
$522$		0			0
$523$	324.153			0.619795			0.309898	−	0.950770i	$-0.399705\pi$
$523$	324.153			0.619795			0.309898	+	0.950770i	$0.399705\pi$
$524$	−25.0263	+	14.4489i	−0.0477601	+	0.0275743i
$525$		0			0
$526$	133.478	−	231.191i	0.253761	−	0.439526i
$527$	182.137	+	105.157i	0.345611	+	0.199539i
$528$		0			0
$529$	451.719	+	782.400i	0.853911	+	1.47902i
$530$		−	469.760i		−	0.886340i
$531$		0			0
$532$	−18.4640			−0.0347067
$533$	234.937	−	135.641i	0.440782	−	0.254486i
$534$		0			0
$535$	165.864	−	287.286i	0.310027	−	0.536982i
$536$	261.521	+	150.989i	0.487913	+	0.281697i
$537$		0			0
$538$	184.175	+	319.000i	0.342332	+	0.592937i
$539$			92.7194i			0.172021i
$540$		0			0
$541$	−476.266			−0.880344			−0.440172	−	0.897914i	$-0.645083\pi$
$541$	−476.266			−0.880344			−0.440172	+	0.897914i	$0.645083\pi$
$542$	−174.091	+	100.511i	−0.321200	+	0.185445i
$543$		0			0
$544$	24.9588	−	43.2300i	0.0458802	−	0.0794669i
$545$	−832.361	−	480.564i	−1.52727	−	0.881768i
$546$		0			0
$547$	169.902	+	294.279i	0.310607	+	0.537988i	0.978494	−	0.206275i	$-0.0661343\pi$
$547$	169.902	+	294.279i	0.310607	+	0.537988i	−0.667887	+	0.744263i	$0.732801\pi$
$548$			71.6663i			0.130778i
$549$		0			0
$550$	39.5893			0.0719806
$551$	−46.9257	+	27.0926i	−0.0851646	+	0.0491698i
$552$		0			0
$553$	206.604	−	357.848i	0.373605	−	0.647104i
$554$	13.0570	+	7.53845i	0.0235686	+	0.0136073i
$555$		0			0
$556$	35.0599	+	60.7255i	0.0630573	+	0.109219i
$557$			507.929i			0.911902i	0.890005	+	0.455951i	$0.150701\pi$
$557$			507.929i			0.911902i	−0.890005	+	0.455951i	$0.849299\pi$
$558$		0			0
$559$	365.845			0.654464
$560$	47.7235	−	27.5532i	0.0852205	−	0.0492021i
$561$		0			0
$562$	125.106	−	216.691i	0.222609	−	0.385570i
$563$	393.970	+	227.459i	0.699769	+	0.404012i	0.807261	−	0.590194i	$-0.200949\pi$
$563$	393.970	+	227.459i	0.699769	+	0.404012i	−0.107492	+	0.994206i	$0.534282\pi$
$564$		0			0
$565$	−326.026	−	564.694i	−0.577038	−	0.999458i
$566$		−	428.411i		−	0.756910i
$567$		0			0
$568$	266.271			0.468786
$569$	−382.086	+	220.597i	−0.671504	+	0.387693i	−0.796646	−	0.604446i	$-0.793395\pi$
$569$	−382.086	+	220.597i	−0.671504	+	0.387693i	0.125142	+	0.992139i	$0.460061\pi$
$570$		0			0
$571$	133.930	−	231.973i	0.234553	−	0.406258i	−0.724590	−	0.689181i	$-0.757971\pi$
$571$	133.930	−	231.973i	0.234553	−	0.406258i	0.959143	+	0.282923i	$0.0913039\pi$
$572$	184.153	+	106.321i	0.321946	+	0.185875i
$573$		0			0
$574$	−63.2280	−	109.514i	−0.110153	−	0.190791i
$575$			79.9887i			0.139111i
$576$		0			0
$577$	608.884			1.05526			0.527629	−	0.849475i	$-0.323081\pi$
$577$	608.884			1.05526			0.527629	+	0.849475i	$0.323081\pi$
$578$	258.583	−	149.293i	0.447375	−	0.258292i
$579$		0			0
$580$	80.8586	−	140.051i	0.139411	−	0.241468i
$581$	−344.113	−	198.674i	−0.592277	−	0.341951i
$582$		0			0
$583$	−422.485	−	731.766i	−0.724674	−	1.25517i
$584$			9.63979i			0.0165065i
$585$		0			0
$586$	759.515			1.29610
$587$	407.910	−	235.507i	0.694907	−	0.401205i	−0.110541	−	0.993872i	$-0.535258\pi$
$587$	407.910	−	235.507i	0.694907	−	0.401205i	0.805448	+	0.592667i	$0.201925\pi$
$588$		0			0
$589$	−41.5820	+	72.0221i	−0.0705976	+	0.122279i
$590$	696.488	+	402.117i	1.18049	+	0.681555i
$591$		0			0
$592$	−38.4424	−	66.5843i	−0.0649366	−	0.112473i
$593$			354.707i			0.598157i	0.954229	+	0.299078i	$0.0966792\pi$
$593$			354.707i			0.598157i	−0.954229	+	0.299078i	$0.903321\pi$
$594$		0			0
$595$	−121.568			−0.204317
$596$	−290.865	+	167.931i	−0.488028	+	0.281763i
$597$		0			0
$598$	−214.817	+	372.074i	−0.359225	+	0.622197i
$599$	5.34958	+	3.08858i	0.00893085	+	0.00515623i	0.504459	−	0.863436i	$-0.331692\pi$
$599$	5.34958	+	3.08858i	0.00893085	+	0.00515623i	−0.495528	+	0.868592i	$0.665025\pi$
$600$		0			0
$601$	13.6355	+	23.6173i	0.0226880	+	0.0392967i	0.877146	−	0.480223i	$-0.159444\pi$
$601$	13.6355	+	23.6173i	0.0226880	+	0.0392967i	−0.854459	+	0.519520i	$0.826111\pi$
$602$		−	170.536i		−	0.283282i
$603$		0			0
$604$	−388.002			−0.642387
$605$	245.525	−	141.754i	0.405826	−	0.234304i
$606$		0			0
$607$	−109.142	+	189.040i	−0.179806	+	0.311433i	−0.941814	−	0.336135i	$-0.890880\pi$
$607$	−109.142	+	189.040i	−0.179806	+	0.311433i	0.762008	+	0.647567i	$0.224214\pi$
$608$	17.0943	+	9.86941i	0.0281157	+	0.0162326i
$609$		0			0
$610$	−291.642	−	505.138i	−0.478101	−	0.828096i
$611$		−	483.258i		−	0.790930i
$612$		0			0
$613$	691.709			1.12840			0.564200	−	0.825638i	$-0.309185\pi$
$613$	691.709			1.12840			0.564200	+	0.825638i	$0.309185\pi$
$614$	624.107	−	360.328i	1.01646	−	0.586854i
$615$		0			0
$616$	49.5606	−	85.8415i	0.0804555	−	0.139353i
$617$	1066.69	+	615.852i	1.72883	+	0.998139i	0.894901	+	0.446264i	$0.147246\pi$
$617$	1066.69	+	615.852i	1.72883	+	0.998139i	0.833927	+	0.551875i	$0.186088\pi$
$618$		0			0
$619$	135.951	+	235.475i	0.219631	+	0.380411i	0.954695	−	0.297586i	$-0.0961815\pi$
$619$	135.951	+	235.475i	0.219631	+	0.380411i	−0.735064	+	0.677997i	$0.762848\pi$
$620$		−	248.205i		−	0.400331i
$621$		0			0
$622$	441.986			0.710588
$623$	67.7508	−	39.1159i	0.108749	−	0.0627864i
$624$		0			0
$625$	336.685	−	583.155i	0.538696	−	0.933048i
$626$	−692.183	−	399.632i	−1.10572	−	0.638390i
$627$		0			0
$628$	16.5048	+	28.5871i	0.0262815	+	0.0455209i
$629$			169.613i			0.269656i
$630$		0			0
$631$	−793.352			−1.25729			−0.628647	−	0.777691i	$-0.716391\pi$
$631$	−793.352			−1.25729			−0.628647	+	0.777691i	$0.716391\pi$
$632$	−382.556	+	220.869i	−0.605310	+	0.349476i
$633$		0			0
$634$	−96.3586	+	166.898i	−0.151985	+	0.263246i
$635$	842.656	+	486.508i	1.32702	+	0.766154i
$636$		0			0
$637$	−28.0940	−	48.6602i	−0.0441036	−	0.0763897i
$638$		−	290.885i		−	0.455933i
$639$		0			0
$640$	−58.9111			−0.0920486
$641$	714.591	−	412.569i	1.11481	−	0.643634i	0.174736	−	0.984615i	$-0.444093\pi$
$641$	714.591	−	412.569i	1.11481	−	0.643634i	0.940070	+	0.340982i	$0.110759\pi$
$642$		0			0
$643$	485.838	−	841.496i	0.755580	−	1.30870i	−0.189506	−	0.981880i	$-0.560689\pi$
$643$	485.838	−	841.496i	0.755580	−	1.30870i	0.945086	−	0.326823i	$-0.105978\pi$
$644$	173.439	+	100.135i	0.269316	+	0.155489i
$645$		0			0
$646$	−21.7726	−	37.7113i	−0.0337037	−	0.0583766i
$647$		−	234.968i		−	0.363166i	−0.983376	−	0.181583i	$-0.941878\pi$
$647$		−	234.968i		−	0.363166i	0.983376	−	0.181583i	$-0.0581221\pi$
$648$		0			0
$649$	1446.60			2.22897
$650$	−20.7769	+	11.9956i	−0.0319645	+	0.0184547i
$651$		0			0
$652$	−174.369	+	302.015i	−0.267436	+	0.463214i
$653$	−177.198	−	102.305i	−0.271360	−	0.156670i	0.358145	−	0.933666i	$-0.383409\pi$
$653$	−177.198	−	102.305i	−0.271360	−	0.156670i	−0.629506	+	0.776996i	$0.716743\pi$
$654$		0			0
$655$	−37.6182	−	65.1567i	−0.0574324	−	0.0994758i
$656$			135.187i			0.206078i
$657$		0			0
$658$	−225.267			−0.342351
$659$	888.097	−	512.743i	1.34764	−	0.778062i	0.359728	−	0.933057i	$-0.382870\pi$
$659$	888.097	−	512.743i	1.34764	−	0.778062i	0.987915	+	0.154995i	$0.0495363\pi$
$660$		0			0
$661$	−416.193	+	720.867i	−0.629641	+	1.09057i	0.357983	+	0.933728i	$0.383465\pi$
$661$	−416.193	+	720.867i	−0.629641	+	1.09057i	−0.987624	+	0.156842i	$0.949869\pi$
$662$	596.262	+	344.252i	0.900697	+	0.520018i
$663$		0			0
$664$	212.391	+	367.872i	0.319866	+	0.554024i
$665$		−	48.0715i		−	0.0722879i
$666$		0			0
$667$	587.722			0.881143
$668$	252.558	−	145.814i	0.378081	−	0.218285i
$669$		0			0
$670$	−393.105	+	680.878i	−0.586724	+	1.01624i
$671$	−908.606	−	524.584i	−1.35411	−	0.781794i
$672$		0			0
$673$	11.9190	+	20.6443i	0.0177102	+	0.0306750i	0.874745	−	0.484584i	$-0.161029\pi$
$673$	11.9190	+	20.6443i	0.0177102	+	0.0306750i	−0.857034	+	0.515259i	$0.827696\pi$
$674$		−	82.0484i		−	0.121734i
$675$		0			0
$676$	209.139			0.309378
$677$	878.026	−	506.929i	1.29694	−	0.748787i	0.317063	−	0.948405i	$-0.397303\pi$
$677$	878.026	−	506.929i	1.29694	−	0.748787i	0.979874	+	0.199618i	$0.0639700\pi$
$678$		0			0
$679$	−107.937	+	186.953i	−0.158965	+	0.275335i
$680$	112.550	+	64.9810i	0.165515	+	0.0955604i
$681$		0			0
$682$	−223.227	−	386.640i	−0.327312	−	0.566921i
$683$			1203.04i			1.76141i	0.473666	+	0.880704i	$0.342930\pi$
$683$			1203.04i			1.76141i	−0.473666	+	0.880704i	$0.657070\pi$
$684$		0			0
$685$	−186.585			−0.272387
$686$	−22.6826	+	13.0958i	−0.0330650	+	0.0190901i
$687$		0			0
$688$	−91.1553	+	157.886i	−0.132493	+	0.229485i
$689$	443.450	+	256.026i	0.643614	+	0.371591i
$690$		0			0
$691$	−460.688	−	797.935i	−0.666698	−	1.15475i	−0.978822	−	0.204713i	$-0.934374\pi$
$691$	−460.688	−	797.935i	−0.666698	−	1.15475i	0.312124	−	0.950041i	$-0.398960\pi$
$692$		−	116.273i		−	0.168025i
$693$		0			0
$694$	352.943			0.508564
$695$	−158.101	+	91.2794i	−0.227483	+	0.131337i
$696$		0			0
$697$	149.116	−	258.277i	0.213940	−	0.370555i
$698$	−274.854	−	158.687i	−0.393774	−	0.227345i
$699$		0			0
$700$	5.59164	+	9.68501i	0.00798806	+	0.0138357i
$701$			258.234i			0.368379i	0.982891	+	0.184189i	$0.0589660\pi$
$701$			258.234i			0.368379i	−0.982891	+	0.184189i	$0.941034\pi$
$702$		0			0
$703$	−67.0698			−0.0954051
$704$	−91.7684	+	52.9825i	−0.130353	+	0.0752593i
$705$		0			0
$706$	−157.010	+	271.950i	−0.222394	+	0.385198i
$707$	1.63936	+	0.946486i	0.00231876	+	0.00133873i
$708$		0			0
$709$	−54.5101	−	94.4143i	−0.0768831	−	0.133165i	0.825021	−	0.565103i	$-0.191164\pi$
$709$	−54.5101	−	94.4143i	−0.0768831	−	0.133165i	−0.901904	+	0.431937i	$0.857830\pi$
$710$			693.243i			0.976399i
$711$		0			0
$712$	−83.6334			−0.117463
$713$	781.191	−	451.021i	1.09564	−	0.632568i
$714$		0			0
$715$	−276.809	+	479.447i	−0.387146	+	0.670556i
$716$	−307.553	−	177.566i	−0.429544	−	0.247997i
$717$		0			0
$718$	223.617	+	387.316i	0.311444	+	0.539437i
$719$			736.032i			1.02369i	0.859078	+	0.511844i	$0.171038\pi$
$719$			736.032i			1.02369i	−0.859078	+	0.511844i	$0.828962\pi$
$720$		0			0
$721$	−475.831			−0.659960
$722$	−427.221	+	246.656i	−0.591719	+	0.341629i
$723$		0			0
$724$	42.0375	−	72.8111i	0.0580629	−	0.100568i
$725$	28.4220	+	16.4095i	0.0392028	+	0.0226338i
$726$		0			0
$727$	−216.054	−	374.217i	−0.297186	−	0.514741i	0.678305	−	0.734780i	$-0.262715\pi$
$727$	−216.054	−	374.217i	−0.297186	−	0.514741i	−0.975491	+	0.220039i	$0.929381\pi$
$728$			60.0675i			0.0825103i
$729$		0			0
$730$	−25.0975			−0.0343801
$731$	348.307	−	201.095i	0.476480	−	0.275096i
$732$		0			0
$733$	−267.895	+	464.008i	−0.365478	+	0.633026i	−0.988853	−	0.148897i	$-0.952428\pi$
$733$	−267.895	+	464.008i	−0.365478	+	0.633026i	0.623375	+	0.781923i	$0.285761\pi$
$734$	569.818	+	328.985i	0.776319	+	0.448208i
$735$		0			0
$736$	−107.049	−	185.414i	−0.145447	−	0.251922i
$737$			1414.18i			1.91883i
$738$		0			0
$739$	895.470			1.21173			0.605866	−	0.795567i	$-0.292827\pi$
$739$	895.470			1.21173			0.605866	+	0.795567i	$0.292827\pi$
$740$	173.354	−	100.086i	0.234262	−	0.135251i
$741$		0			0
$742$	119.345	−	206.711i	0.160842	−	0.278586i
$743$	−1157.51	−	668.291i	−1.55789	−	0.899450i	−0.997458	−	0.0712503i	$-0.977301\pi$
$743$	−1157.51	−	668.291i	−1.55789	−	0.899450i	−0.560434	−	0.828199i	$-0.689366\pi$
$744$		0			0
$745$	−437.213	−	757.274i	−0.586863	−	1.01648i
$746$			112.715i			0.151093i
$747$		0			0
$748$	233.766			0.312522
$749$	145.972	−	84.2772i	0.194890	−	0.112520i
$750$		0			0
$751$	570.632	−	988.364i	0.759830	−	1.31606i	−0.183107	−	0.983093i	$-0.558615\pi$
$751$	570.632	−	988.364i	0.759830	−	1.31606i	0.942937	−	0.332971i	$-0.108051\pi$
$752$	208.557	+	120.410i	0.277336	+	0.160120i
$753$		0			0
$754$	88.1383	+	152.660i	0.116894	+	0.202467i
$755$		−	1010.17i		−	1.33798i
$756$		0			0
$757$	775.634			1.02462			0.512308	−	0.858802i	$-0.328791\pi$
$757$	775.634			1.02462			0.512308	+	0.858802i	$0.328791\pi$
$758$	166.445	−	96.0969i	0.219584	−	0.126777i
$759$		0			0
$760$	−25.6953	+	44.5055i	−0.0338096	+	0.0585599i
$761$	−105.553	−	60.9413i	−0.138703	−	0.0800805i	0.429042	−	0.903284i	$-0.358851\pi$
$761$	−105.553	−	60.9413i	−0.138703	−	0.0800805i	−0.567746	+	0.823204i	$0.692184\pi$
$762$		0			0
$763$	−244.179	−	422.930i	−0.320024	−	0.554299i
$764$		−	172.665i		−	0.226001i
$765$		0			0
$766$	−564.786			−0.737319
$767$	−759.192	+	438.320i	−0.989820	+	0.571473i
$768$		0			0
$769$	−682.681	+	1182.44i	−0.887752	+	1.53763i	−0.0452251	+	0.998977i	$0.514401\pi$
$769$	−682.681	+	1182.44i	−0.887752	+	1.53763i	−0.842527	+	0.538655i	$0.818933\pi$
$770$	223.491	+	129.032i	0.290248	+	0.167575i
$771$		0			0
$772$	−138.606	−	240.073i	−0.179541	−	0.310975i
$773$			231.520i			0.299508i	0.988723	+	0.149754i	$0.0478482\pi$
$773$			231.520i			0.299508i	−0.988723	+	0.149754i	$0.952152\pi$
$774$		0			0
$775$	50.3709			0.0649947
$776$	199.861	−	115.390i	0.257552	−	0.148698i
$777$		0			0
$778$	312.539	−	541.333i	0.401721	−	0.695801i
$779$	102.130	+	58.9646i	0.131104	+	0.0756927i
$780$		0			0
$781$	623.478	+	1079.90i	0.798307	+	1.38271i
$782$			472.316i			0.603984i
$783$		0			0
$784$	28.0000			0.0357143
$785$	−74.4273	+	42.9706i	−0.0948119	+	0.0547397i
$786$		0			0
$787$	395.226	−	684.552i	0.502193	−	0.869824i	−0.497804	−	0.867290i	$-0.665860\pi$
$787$	395.226	−	684.552i	0.502193	−	0.869824i	0.999997	−	0.00253434i	$-0.000806706\pi$
$788$	68.2961	+	39.4308i	0.0866702	+	0.0500390i
$789$		0			0
$790$	−575.038	−	995.995i	−0.727896	−	1.26075i
$791$		−	331.314i		−	0.418854i
$792$		0			0
$793$	635.796			0.801760
$794$	−470.487	+	271.636i	−0.592553	+	0.342110i
$795$		0			0
$796$	88.0429	−	152.495i	0.110607	−	0.191576i
$797$	66.4876	+	38.3866i	0.0834223	+	0.0481639i	0.541131	−	0.840938i	$-0.317996\pi$
$797$	66.4876	+	38.3866i	0.0834223	+	0.0481639i	−0.457709	+	0.889102i	$0.651330\pi$
$798$		0			0
$799$	−265.634	−	460.091i	−0.332458	−	0.575834i
$800$		−	11.9554i		−	0.0149443i
$801$		0			0
$802$	−366.831			−0.457395
$803$	−39.0954	+	22.5718i	−0.0486867	+	0.0281093i
$804$		0			0
$805$	−260.705	+	451.554i	−0.323857	+	0.560937i
$806$	234.304	+	135.276i	0.290700	+	0.167836i
$807$		0			0
$808$	−1.01184	−	1.75255i	−0.00125227	−	0.00216900i
$809$		−	163.583i		−	0.202204i	−0.994876	−	0.101102i	$-0.967763\pi$
$809$		−	163.583i		−	0.202204i	0.994876	−	0.101102i	$-0.0322368\pi$
$810$		0			0
$811$	24.8546			0.0306469			0.0153235	−	0.999883i	$-0.495122\pi$
$811$	24.8546			0.0306469			0.0153235	+	0.999883i	$0.495122\pi$
$812$	71.1613	−	41.0850i	0.0876371	−	0.0505973i
$813$		0			0
$814$	180.027	−	311.817i	0.221164	−	0.383067i
$815$	−786.305	−	453.974i	−0.964792	−	0.557023i
$816$		0			0
$817$	79.5185	+	137.730i	0.0973299	+	0.168580i
$818$		−	134.223i		−	0.164087i
$819$		0			0
$820$	−351.964			−0.429224
$821$	251.574	−	145.246i	0.306424	−	0.176914i	−0.338901	−	0.940822i	$-0.610055\pi$
$821$	251.574	−	145.246i	0.306424	−	0.176914i	0.645325	+	0.763908i	$0.276722\pi$
$822$		0			0
$823$	−41.1232	+	71.2275i	−0.0499675	+	0.0865462i	−0.889927	−	0.456102i	$-0.849245\pi$
$823$	−41.1232	+	71.2275i	−0.0499675	+	0.0865462i	0.839960	+	0.542649i	$0.182578\pi$
$824$	440.534	+	254.342i	0.534628	+	0.308668i
$825$		0			0
$826$	204.319	+	353.891i	0.247360	+	0.428440i
$827$		−	1043.82i		−	1.26218i	−0.775709	−	0.631090i	$-0.782608\pi$
$827$		−	1043.82i		−	1.26218i	0.775709	−	0.631090i	$-0.217392\pi$
$828$		0			0
$829$	−121.734			−0.146844			−0.0734222	−	0.997301i	$-0.523392\pi$
$829$	−121.734			−0.146844			−0.0734222	+	0.997301i	$0.523392\pi$
$830$	−957.765	+	552.966i	−1.15393	+	0.666224i
$831$		0			0
$832$	32.1074	−	55.6117i	0.0385906	−	0.0668410i
$833$	−53.4944	−	30.8850i	−0.0642189	−	0.0370768i
$834$		0			0
$835$	379.632	+	657.542i	0.454649	+	0.787475i
$836$			92.4376i			0.110571i
$837$		0			0
$838$	227.718			0.271740
$839$	−873.889	+	504.540i	−1.04158	+	0.601359i	−0.920282	−	0.391257i	$-0.872040\pi$
$839$	−873.889	+	504.540i	−1.04158	+	0.601359i	−0.121303	+	0.992616i	$0.538707\pi$
$840$		0			0
$841$	−299.930	+	519.494i	−0.356635	+	0.617710i
$842$	−653.803	−	377.473i	−0.776488	−	0.448305i
$843$		0			0
$844$	192.738	+	333.832i	0.228363	+	0.395536i
$845$			544.500i			0.644379i
$846$		0			0
$847$	144.053			0.170074
$848$	−220.983	+	127.585i	−0.260593	+	0.150454i
$849$		0			0
$850$	−13.1873	+	22.8410i	−0.0155144	+	0.0268718i
$851$	630.013	+	363.738i	0.740321	+	0.427424i
$852$		0			0
$853$	−572.363	−	991.362i	−0.671000	−	1.16221i	−0.977621	−	0.210375i	$-0.932532\pi$
$853$	−572.363	−	991.362i	−0.671000	−	1.16221i	0.306620	−	0.951832i	$-0.400802\pi$
$854$		−	296.372i		−	0.347039i
$855$		0			0
$856$	−180.192			−0.210505
$857$	874.127	−	504.678i	1.01999	−	0.588889i	0.105886	−	0.994378i	$-0.466232\pi$
$857$	874.127	−	504.678i	1.01999	−	0.588889i	0.914100	+	0.405490i	$0.132899\pi$
$858$		0			0
$859$	−544.449	+	943.013i	−0.633817	+	1.09780i	0.352947	+	0.935643i	$0.385180\pi$
$859$	−544.449	+	943.013i	−0.633817	+	1.09780i	−0.986764	+	0.162160i	$0.948154\pi$
$860$	−411.060	−	237.326i	−0.477977	−	0.275960i
$861$		0			0
$862$	−158.598	−	274.701i	−0.183989	−	0.318678i
$863$		−	989.092i		−	1.14611i	−0.819517	−	0.573055i	$-0.805758\pi$
$863$		−	989.092i		−	1.14611i	0.819517	−	0.573055i	$-0.194242\pi$
$864$		0			0
$865$	302.721			0.349967
$866$	−923.564	+	533.220i	−1.06647	+	0.615727i
$867$		0			0
$868$	63.0577	−	109.219i	0.0726471	−	0.125828i
$869$	−1791.52	−	1034.34i	−2.06159	−	1.19026i
$870$		0			0
$871$	−428.496	−	742.177i	−0.491959	−	0.852098i
$872$			522.076i			0.598711i
$873$		0			0
$874$	−186.767			−0.213692
$875$	273.056	−	157.649i	0.312065	−	0.180171i
$876$		0			0
$877$	310.022	−	536.973i	0.353502	−	0.612284i	−0.633358	−	0.773859i	$-0.718324\pi$
$877$	310.022	−	536.973i	0.353502	−	0.612284i	0.986860	+	0.161575i	$0.0516573\pi$
$878$	−614.769	−	354.937i	−0.700193	−	0.404256i
$879$		0			0
$880$	−137.942	−	238.922i	−0.156752	−	0.271502i
$881$		−	636.200i		−	0.722134i	−0.932540	−	0.361067i	$-0.882413\pi$
$881$		−	636.200i		−	0.722134i	0.932540	−	0.361067i	$-0.117587\pi$
$882$		0			0
$883$	964.280			1.09205			0.546025	−	0.837769i	$-0.316140\pi$
$883$	964.280			1.09205			0.546025	+	0.837769i	$0.316140\pi$
$884$	−122.683	+	70.8312i	−0.138782	+	0.0801258i
$885$		0			0
$886$	174.223	−	301.763i	0.196640	−	0.340591i
$887$	443.953	+	256.316i	0.500510	+	0.288970i	0.728924	−	0.684594i	$-0.240021\pi$
$887$	443.953	+	256.316i	0.500510	+	0.288970i	−0.228414	+	0.973564i	$0.573354\pi$
$888$		0			0
$889$	247.199	+	428.161i	0.278064	+	0.481621i
$890$		−	217.742i		−	0.244654i
$891$		0			0
$892$	−359.886			−0.403459
$893$	181.933	−	105.039i	0.203732	−	0.117625i
$894$		0			0
$895$	462.298	−	800.724i	0.516534	−	0.894664i
$896$	−25.9230	−	14.9666i	−0.0289319	−	0.0167038i
$897$		0			0
$898$	132.381	+	229.290i	0.147417	+	0.255334i
$899$		−	370.103i		−	0.411683i
$900$		0			0
$901$	562.922			0.624775
$902$	−548.269	+	316.543i	−0.607837	+	0.350935i
$903$		0			0
$904$	−177.095	+	306.737i	−0.195901	+	0.339311i
$905$	189.566	+	109.446i	0.209465	+	0.120935i
$906$		0			0
$907$	607.985	+	1053.06i	0.670325	+	1.16104i	0.977812	+	0.209485i	$0.0671788\pi$
$907$	607.985	+	1053.06i	0.670325	+	1.16104i	−0.307486	+	0.951552i	$0.599488\pi$
$908$		−	189.824i		−	0.209057i
$909$		0			0
$910$	−156.387			−0.171854
$911$	−346.092	+	199.817i	−0.379904	+	0.219338i	−0.677776	−	0.735268i	$-0.737056\pi$
$911$	−346.092	+	199.817i	−0.379904	+	0.219338i	0.297873	+	0.954606i	$0.403723\pi$
$912$		0			0
$913$	−994.635	+	1722.76i	−1.08941	+	1.88692i
$914$	670.625	+	387.185i	0.733725	+	0.423616i
$915$		0			0
$916$	−354.467	−	613.954i	−0.386972	−	0.670256i
$917$		−	38.2283i		−	0.0416884i
$918$		0			0
$919$	−398.263			−0.433366			−0.216683	−	0.976242i	$-0.569524\pi$
$919$	−398.263			−0.433366			−0.216683	+	0.976242i	$0.569524\pi$
$920$	482.732	−	278.705i	0.524708	−	0.302941i
$921$		0			0
$922$	−103.225	+	178.790i	−0.111957	+	0.193916i
$923$	−654.417	−	377.828i	−0.709011	−	0.409347i
$924$		0			0
$925$	20.3115	+	35.1805i	0.0219584	+	0.0380330i
$926$			269.675i			0.291226i
$927$		0			0
$928$	−87.8434			−0.0946588
$929$	−1491.17	+	860.930i	−1.60514	+	0.926727i	−0.614702	+	0.788760i	$0.710724\pi$
$929$	−1491.17	+	860.930i	−1.60514	+	0.926727i	−0.990437	+	0.137968i	$0.955943\pi$
$930$		0			0
$931$	12.2128	−	21.1531i	0.0131179	−	0.0227209i
$932$	−333.035	−	192.278i	−0.357333	−	0.206306i
$933$		0			0
$934$	515.037	+	892.070i	0.551431	+	0.955107i
$935$			608.617i			0.650928i
$936$		0			0
$937$	−1714.27			−1.82953			−0.914765	−	0.403987i	$-0.867624\pi$
$937$	−1714.27			−1.82953			−0.914765	+	0.403987i	$0.867624\pi$
$938$	−345.960	+	199.740i	−0.368827	+	0.212943i
$939$		0			0
$940$	−313.492	+	542.984i	−0.333502	+	0.577642i
$941$	−76.8229	−	44.3537i	−0.0816396	−	0.0471347i	0.458624	−	0.888630i	$-0.348342\pi$
$941$	−76.8229	−	44.3537i	−0.0816396	−	0.0471347i	−0.540264	+	0.841496i	$0.681676\pi$
$942$		0			0
$943$	−639.563	−	1107.76i	−0.678221	−	1.17471i
$944$		−	436.853i		−	0.462768i
$945$		0			0
$946$	−853.768			−0.902503
$947$	−403.626	+	233.034i	−0.426215	+	0.246076i	−0.697733	−	0.716358i	$-0.745808\pi$
$947$	−403.626	+	233.034i	−0.426215	+	0.246076i	0.271518	+	0.962433i	$0.412474\pi$
$948$		0			0
$949$	13.6785	−	23.6918i	0.0144136	−	0.0249651i
$950$	−9.03197	−	5.21461i	−0.00950733	−	0.00548906i
$951$		0			0
$952$	33.0174	+	57.1879i	0.0346822	+	0.0600713i
$953$			1024.37i			1.07489i	0.843299	+	0.537445i	$0.180611\pi$
$953$			1024.37i			1.07489i	−0.843299	+	0.537445i	$0.819389\pi$
$954$		0			0
$955$	449.538			0.470720
$956$	502.412	−	290.068i	0.525536	−	0.303418i
$957$		0			0
$958$	−519.838	+	900.386i	−0.542628	+	0.939860i
$959$	−82.1040	−	47.4028i	−0.0856142	−	0.0494294i
$960$		0			0
$961$	196.481	+	340.315i	0.204455	+	0.354126i
$962$			218.193i			0.226812i
$963$		0			0
$964$	223.842			0.232201
$965$	625.036	−	360.865i	0.647706	−	0.373953i
$966$		0			0
$967$	−37.7510	+	65.3866i	−0.0390393	+	0.0676180i	−0.884885	−	0.465810i	$-0.845763\pi$
$967$	−37.7510	+	65.3866i	−0.0390393	+	0.0676180i	0.845846	+	0.533428i	$0.179096\pi$
$968$	−133.367	−	76.9993i	−0.137776	−	0.0795448i
$969$		0			0
$970$	300.420	+	520.343i	0.309712	+	0.536436i
$971$		−	1674.28i		−	1.72429i	−0.506664	−	0.862144i	$-0.669122\pi$
$971$		−	1674.28i		−	1.72429i	0.506664	−	0.862144i	$-0.330878\pi$
$972$		0			0
$973$	−92.7597			−0.0953337
$974$	−231.590	+	133.709i	−0.237772	+	0.137278i
$975$		0			0
$976$	−158.417	+	274.387i	−0.162313	+	0.281134i
$977$	933.331	+	538.859i	0.955303	+	0.551544i	0.894724	−	0.446619i	$-0.147372\pi$
$977$	933.331	+	538.859i	0.955303	+	0.551544i	0.0605785	+	0.998163i	$0.480705\pi$
$978$		0			0
$979$	−195.829	−	339.186i	−0.200030	−	0.346462i
$980$			72.8988i			0.0743865i
$981$		0			0
$982$	466.851			0.475408
$983$	−163.825	+	94.5846i	−0.166659	+	0.0962204i	−0.581009	−	0.813897i	$-0.697342\pi$
$983$	−163.825	+	94.5846i	−0.166659	+	0.0962204i	0.414351	+	0.910117i	$0.364009\pi$
$984$		0			0
$985$	−102.659	+	177.811i	−0.104222	+	0.180519i
$986$	167.826	+	96.8944i	0.170209	+	0.0982701i
$987$		0			0
$988$	−28.0086	−	48.5123i	−0.0283488	−	0.0491016i
$989$		−	1725.00i		−	1.74419i
$990$		0			0
$991$	−1637.86			−1.65273			−0.826367	−	0.563132i	$-0.809596\pi$
$991$	−1637.86			−1.65273			−0.826367	+	0.563132i	$0.809596\pi$
$992$	−116.760	+	67.4115i	−0.117702	+	0.0679551i
$993$		0			0
$994$	−176.122	+	305.051i	−0.177185	+	0.306893i
$995$	397.025	+	229.222i	0.399020	+	0.230374i
$996$		0			0
$997$	298.689	+	517.345i	0.299588	+	0.518902i	0.976042	−	0.217584i	$-0.0698174\pi$
$997$	298.689	+	517.345i	0.299588	+	0.518902i	−0.676454	+	0.736485i	$0.736484\pi$
$998$			434.366i			0.435237i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.q.a.71.12		24
3.2	odd	2		126.3.q.a.113.4	yes	24
9.2	odd	6	inner	378.3.q.a.197.12		24
9.4	even	3		1134.3.b.c.323.15		24
9.5	odd	6		1134.3.b.c.323.10		24
9.7	even	3		126.3.q.a.29.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.4	✓	24	9.7	even	3
126.3.q.a.113.4	yes	24	3.2	odd	2
378.3.q.a.71.12		24	1.1	even	1	trivial
378.3.q.a.197.12		24	9.2	odd	6	inner
1134.3.b.c.323.10		24	9.5	odd	6
1134.3.b.c.323.15		24	9.4	even	3

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50944 + 2.60353i) q^{5} +(1.32288 + 2.29129i) q^{7} -2.82843i q^{8} +7.36389 q^{10} +(11.4711 - 6.62282i) q^{11} +(-4.01343 + 6.95146i) q^{13} +(3.24037 + 1.87083i) q^{14} +(-2.00000 - 3.46410i) q^{16} +8.82428i q^{17} -3.48936 q^{19} +(9.01889 - 5.20706i) q^{20} +(9.36608 - 16.2225i) q^{22} +(32.7769 + 18.9238i) q^{23} +(1.05672 + 1.83030i) q^{25} +11.3517i q^{26} +5.29150 q^{28} +(13.4482 - 7.76433i) q^{29} +(11.9168 - 20.6405i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(6.23971 + 10.8075i) q^{34} +13.7766i q^{35} +19.2212 q^{37} +(-4.27358 + 2.46735i) q^{38} +(7.36389 - 12.7546i) q^{40} +(-29.2689 - 16.8984i) q^{41} +(-22.7888 - 39.4714i) q^{43} -26.4913i q^{44} +53.5245 q^{46} +(-52.1392 + 30.1026i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(2.58843 + 1.49443i) q^{50} +(8.02685 + 13.9029i) q^{52} -63.7924i q^{53} +68.9708 q^{55} +(6.48074 - 3.74166i) q^{56} +(10.9804 - 19.0187i) q^{58} +(94.5815 + 54.6066i) q^{59} +(-39.6043 - 68.5967i) q^{61} -33.7057i q^{62} -8.00000 q^{64} +(-36.1966 + 20.8981i) q^{65} +(-53.3828 + 92.4617i) q^{67} +(15.2841 + 8.82428i) q^{68} +(9.74151 + 16.8728i) q^{70} +94.1409i q^{71} -3.40818 q^{73} +(23.5411 - 13.5915i) q^{74} +(-3.48936 + 6.04375i) q^{76} +(30.3496 + 17.5223i) q^{77} +(-78.0889 - 135.254i) q^{79} -20.8282i q^{80} -47.7959 q^{82} +(-130.062 + 75.0915i) q^{83} +(-22.9743 + 39.7926i) q^{85} +(-55.8210 - 32.2283i) q^{86} +(-18.7322 - 32.4450i) q^{88} -29.5689i q^{89} -21.2371 q^{91} +(65.5539 - 37.8476i) q^{92} +(-42.5715 + 73.7360i) q^{94} +(-15.7351 - 9.08466i) q^{95} +(40.7964 + 70.6614i) q^{97} +9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{5} - 48 q^{16} + 24 q^{19} - 72 q^{20} + 24 q^{22} + 72 q^{23} + 72 q^{25} + 108 q^{29} - 60 q^{31} - 48 q^{34} - 168 q^{37} - 144 q^{38} - 108 q^{41} + 60 q^{43} + 324 q^{47} - 84 q^{49}+ \cdots + 48 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^5 - 48 * q^16 + 24 * q^19 - 72 * q^20 + 24 * q^22 + 72 * q^23 + 72 * q^25 + 108 * q^29 - 60 * q^31 - 48 * q^34 - 168 * q^37 - 144 * q^38 - 108 * q^41 + 60 * q^43 + 324 * q^47 - 84 * q^49 - 144 * q^50 + 264 * q^55 + 432 * q^59 - 192 * q^64 + 180 * q^65 + 72 * q^67 - 72 * q^68 + 24 * q^73 - 288 * q^74 + 24 * q^76 + 12 * q^79 - 288 * q^82 - 756 * q^83 - 156 * q^85 - 360 * q^86 - 48 * q^88 - 168 * q^91 + 144 * q^92 + 936 * q^95 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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