LMFDB - Embedded newform 684.3.s.a.445.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.16
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.719501 + 2.91244i) q^{3} +(-1.98064 - 3.43056i) q^{5} +(2.79341 + 4.83834i) q^{7} +(-7.96464 - 4.19101i) q^{9} +O(q^{10})$	\(q+(-0.719501 + 2.91244i) q^{3} +(-1.98064 - 3.43056i) q^{5} +(2.79341 + 4.83834i) q^{7} +(-7.96464 - 4.19101i) q^{9} +(-6.63076 - 11.4848i) q^{11} +25.1234i q^{13} +(11.4164 - 3.30019i) q^{15} +(5.39015 - 9.33602i) q^{17} +(12.0131 - 14.7202i) q^{19} +(-16.1012 + 4.65447i) q^{21} -43.7153 q^{23} +(4.65417 - 8.06125i) q^{25} +(17.9366 - 20.1811i) q^{27} +(-24.1872 - 13.9645i) q^{29} +(4.29533 + 2.47991i) q^{31} +(38.2197 - 11.0484i) q^{33} +(11.0655 - 19.1660i) q^{35} -25.3930i q^{37} +(-73.1704 - 18.0763i) q^{39} +(28.4041 - 16.3991i) q^{41} -39.9131 q^{43} +(1.39753 + 35.6240i) q^{45} +(9.60811 - 16.6417i) q^{47} +(8.89367 - 15.4043i) q^{49} +(23.3124 + 22.4158i) q^{51} +(73.0025 - 42.1480i) q^{53} +(-26.2662 + 45.4944i) q^{55} +(34.2284 + 45.5787i) q^{57} +(-12.1135 + 6.99374i) q^{59} +(-31.7016 + 54.9088i) q^{61} +(-1.97102 - 50.2428i) q^{63} +(86.1873 - 49.7602i) q^{65} -79.8298i q^{67} +(31.4532 - 127.318i) q^{69} +(-63.5140 - 36.6698i) q^{71} +(49.7782 - 86.2184i) q^{73} +(20.1293 + 19.3551i) q^{75} +(37.0449 - 64.1636i) q^{77} -79.2932i q^{79} +(45.8709 + 66.7597i) q^{81} +(9.92316 + 17.1874i) q^{83} -42.7037 q^{85} +(58.0735 - 60.3964i) q^{87} +(2.17243 - 1.25425i) q^{89} +(-121.555 + 70.1800i) q^{91} +(-10.3131 + 10.7256i) q^{93} +(-74.2922 - 12.0563i) q^{95} -77.4269i q^{97} +(4.67863 + 119.262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.719501	+	2.91244i	−0.239834	+	0.970814i
$3$	−0.719501	+	2.91244i	−0.239834	+	0.970814i
$4$		0			0
$5$	−1.98064	−	3.43056i	−0.396127	−	0.686112i	0.597117	−	0.802154i	$-0.296313\pi$
$5$	−1.98064	−	3.43056i	−0.396127	−	0.686112i	−0.993244	+	0.116042i	$0.962979\pi$
$6$		0			0
$7$	2.79341	+	4.83834i	0.399059	+	0.691191i	0.993610	−	0.112867i	$-0.0360035\pi$
$7$	2.79341	+	4.83834i	0.399059	+	0.691191i	−0.594551	+	0.804058i	$0.702670\pi$
$8$		0			0
$9$	−7.96464	−	4.19101i	−0.884960	−	0.465668i
$10$		0			0
$11$	−6.63076	−	11.4848i	−0.602796	−	1.04407i	−0.992396	−	0.123089i	$-0.960720\pi$
$11$	−6.63076	−	11.4848i	−0.602796	−	1.04407i	0.389600	−	0.920984i	$-0.372613\pi$
$12$		0			0
$13$			25.1234i			1.93257i	0.257481	+	0.966283i	$0.417108\pi$
$13$			25.1234i			1.93257i	−0.257481	+	0.966283i	$0.582892\pi$
$14$		0			0
$15$	11.4164	−	3.30019i	0.761092	−	0.220013i
$16$		0			0
$17$	5.39015	−	9.33602i	0.317068	−	0.549178i	−0.662807	−	0.748790i	$-0.730635\pi$
$17$	5.39015	−	9.33602i	0.317068	−	0.549178i	0.979875	+	0.199613i	$0.0639684\pi$
$18$		0			0
$19$	12.0131	−	14.7202i	0.632269	−	0.774749i
$19$	12.0131	−	14.7202i	0.632269	−	0.774749i
$20$		0			0
$21$	−16.1012	+	4.65447i	−0.766725	+	0.221641i
$22$		0			0
$23$	−43.7153			−1.90067			−0.950333	−	0.311235i	$-0.899257\pi$
$23$	−43.7153			−1.90067			−0.950333	+	0.311235i	$0.899257\pi$
$24$		0			0
$25$	4.65417	−	8.06125i	0.186167	−	0.322450i
$26$		0			0
$27$	17.9366	−	20.1811i	0.664320	−	0.747448i
$28$		0			0
$29$	−24.1872	−	13.9645i	−0.834042	−	0.481534i	0.0211926	−	0.999775i	$-0.493254\pi$
$29$	−24.1872	−	13.9645i	−0.834042	−	0.481534i	−0.855235	+	0.518241i	$0.826587\pi$
$30$		0			0
$31$	4.29533	+	2.47991i	0.138559	+	0.0799971i	0.567677	−	0.823251i	$-0.307842\pi$
$31$	4.29533	+	2.47991i	0.138559	+	0.0799971i	−0.429118	+	0.903248i	$0.641176\pi$
$32$		0			0
$33$	38.2197	−	11.0484i	1.15817	−	0.334799i
$34$		0			0
$35$	11.0655	−	19.1660i	0.316156	−	0.547599i
$36$		0			0
$37$		−	25.3930i		−	0.686298i	−0.939281	−	0.343149i	$-0.888506\pi$
$37$		−	25.3930i		−	0.686298i	0.939281	−	0.343149i	$-0.111494\pi$
$38$		0			0
$39$	−73.1704	−	18.0763i	−1.87616	−	0.463495i
$40$		0			0
$41$	28.4041	−	16.3991i	0.692782	−	0.399978i	−0.111871	−	0.993723i	$-0.535684\pi$
$41$	28.4041	−	16.3991i	0.692782	−	0.399978i	0.804654	+	0.593745i	$0.202351\pi$
$42$		0			0
$43$	−39.9131			−0.928212			−0.464106	−	0.885780i	$-0.653624\pi$
$43$	−39.9131			−0.928212			−0.464106	+	0.885780i	$0.653624\pi$
$44$		0			0
$45$	1.39753	+	35.6240i	0.0310562	+	0.791645i
$46$		0			0
$47$	9.60811	−	16.6417i	0.204428	−	0.354080i	−0.745522	−	0.666481i	$-0.767800\pi$
$47$	9.60811	−	16.6417i	0.204428	−	0.354080i	0.949950	+	0.312401i	$0.101133\pi$
$48$		0			0
$49$	8.89367	−	15.4043i	0.181504	−	0.314373i
$50$		0			0
$51$	23.3124	+	22.4158i	0.457106	+	0.439525i
$52$		0			0
$53$	73.0025	−	42.1480i	1.37741	−	0.795246i	0.385559	−	0.922683i	$-0.374009\pi$
$53$	73.0025	−	42.1480i	1.37741	−	0.795246i	0.991847	+	0.127438i	$0.0406753\pi$
$54$		0			0
$55$	−26.2662	+	45.4944i	−0.477568	+	0.827171i
$56$		0			0
$57$	34.2284	+	45.5787i	0.600498	+	0.799627i
$58$		0			0
$59$	−12.1135	+	6.99374i	−0.205314	+	0.118538i	−0.599132	−	0.800651i	$-0.704487\pi$
$59$	−12.1135	+	6.99374i	−0.205314	+	0.118538i	0.393818	+	0.919188i	$0.371154\pi$
$60$		0			0
$61$	−31.7016	+	54.9088i	−0.519699	+	0.900144i	0.480039	+	0.877247i	$0.340622\pi$
$61$	−31.7016	+	54.9088i	−0.519699	+	0.900144i	−0.999738	+	0.0228974i	$0.992711\pi$
$62$		0			0
$63$	−1.97102	−	50.2428i	−0.0312860	−	0.797505i
$64$		0			0
$65$	86.1873	−	49.7602i	1.32596	−	0.765542i
$66$		0			0
$67$		−	79.8298i		−	1.19149i	−0.803174	−	0.595745i	$-0.796857\pi$
$67$		−	79.8298i		−	1.19149i	0.803174	−	0.595745i	$-0.203143\pi$
$68$		0			0
$69$	31.4532	−	127.318i	0.455844	−	1.84519i
$70$		0			0
$71$	−63.5140	−	36.6698i	−0.894564	−	0.516476i	−0.0191311	−	0.999817i	$-0.506090\pi$
$71$	−63.5140	−	36.6698i	−0.894564	−	0.516476i	−0.875432	+	0.483341i	$0.839423\pi$
$72$		0			0
$73$	49.7782	−	86.2184i	0.681893	−	1.18107i	−0.292509	−	0.956263i	$-0.594490\pi$
$73$	49.7782	−	86.2184i	0.681893	−	1.18107i	0.974402	−	0.224811i	$-0.0721764\pi$
$74$		0			0
$75$	20.1293	+	19.3551i	0.268390	+	0.258068i
$76$		0			0
$77$	37.0449	−	64.1636i	0.481102	−	0.833294i
$78$		0			0
$79$		−	79.2932i		−	1.00371i	−0.864951	−	0.501856i	$-0.832651\pi$
$79$		−	79.2932i		−	1.00371i	0.864951	−	0.501856i	$-0.167349\pi$
$80$		0			0
$81$	45.8709	+	66.7597i	0.566307	+	0.824194i
$82$		0			0
$83$	9.92316	+	17.1874i	0.119556	+	0.207077i	0.919592	−	0.392875i	$-0.128520\pi$
$83$	9.92316	+	17.1874i	0.119556	+	0.207077i	−0.800036	+	0.599952i	$0.795186\pi$
$84$		0			0
$85$	−42.7037			−0.502397
$86$		0			0
$87$	58.0735	−	60.3964i	0.667512	−	0.694211i
$88$		0			0
$89$	2.17243	−	1.25425i	0.0244093	−	0.0140927i	−0.487746	−	0.872986i	$-0.662181\pi$
$89$	2.17243	−	1.25425i	0.0244093	−	0.0140927i	0.512155	+	0.858893i	$0.328847\pi$
$90$		0			0
$91$	−121.555	+	70.1800i	−1.33577	+	0.771209i
$92$		0			0
$93$	−10.3131	+	10.7256i	−0.110893	+	0.115329i
$94$		0			0
$95$	−74.2922	−	12.0563i	−0.782024	−	0.126909i
$96$		0			0
$97$		−	77.4269i		−	0.798215i	−0.916904	−	0.399108i	$-0.869320\pi$
$97$		−	77.4269i		−	0.798215i	0.916904	−	0.399108i	$-0.130680\pi$
$98$		0			0
$99$	4.67863	+	119.262i	0.0472589	+	1.20467i
$100$		0			0
$101$	−29.9666	+	51.9036i	−0.296699	+	0.513897i	−0.975379	−	0.220537i	$-0.929219\pi$
$101$	−29.9666	+	51.9036i	−0.296699	+	0.513897i	0.678680	+	0.734434i	$0.262552\pi$
$102$		0			0
$103$	96.2690	+	55.5809i	0.934651	+	0.539621i	0.888279	−	0.459303i	$-0.151901\pi$
$103$	96.2690	+	55.5809i	0.934651	+	0.539621i	0.0463713	+	0.998924i	$0.485234\pi$
$104$		0			0
$105$	47.8581	+	46.0175i	0.455792	+	0.438262i
$106$		0			0
$107$		−	39.3147i		−	0.367427i	−0.982980	−	0.183713i	$-0.941188\pi$
$107$		−	39.3147i		−	0.367427i	0.982980	−	0.183713i	$-0.0588118\pi$
$108$		0			0
$109$	9.98429	+	5.76443i	0.0915990	+	0.0528847i	0.545100	−	0.838371i	$-0.316492\pi$
$109$	9.98429	+	5.76443i	0.0915990	+	0.0528847i	−0.453501	+	0.891256i	$0.649825\pi$
$110$		0			0
$111$	73.9557	+	18.2703i	0.666267	+	0.164597i
$112$		0			0
$113$	−56.0972	−	32.3877i	−0.496436	−	0.286617i	0.230805	−	0.973000i	$-0.425864\pi$
$113$	−56.0972	−	32.3877i	−0.496436	−	0.286617i	−0.727240	+	0.686383i	$0.759197\pi$
$114$		0			0
$115$	86.5841	+	149.968i	0.752905	+	1.30407i
$116$		0			0
$117$	105.292	−	200.099i	0.899934	−	1.71024i
$118$		0			0
$119$	60.2277			0.506115
$120$		0			0
$121$	−27.4338	+	47.5168i	−0.226726	+	0.392701i
$122$		0			0
$123$	27.3247	+	94.5244i	0.222152	+	0.768491i
$124$		0			0
$125$	−135.905			−1.08724
$126$		0			0
$127$	−114.338	+	66.0128i	−0.900296	+	0.519786i	−0.877296	−	0.479949i	$-0.840655\pi$
$127$	−114.338	+	66.0128i	−0.900296	+	0.519786i	−0.0229998	+	0.999735i	$0.507322\pi$
$128$		0			0
$129$	28.7175	−	116.245i	0.222617	−	0.901122i
$130$		0			0
$131$	49.7841	+	86.2286i	0.380031	+	0.658233i	0.991066	−	0.133370i	$-0.0425799\pi$
$131$	49.7841	+	86.2286i	0.380031	+	0.658233i	−0.611035	+	0.791604i	$0.709247\pi$
$132$		0			0
$133$	104.779	+	17.0038i	0.787812	+	0.127848i
$134$		0			0
$135$	−104.758	−	21.5613i	−0.775989	−	0.159713i
$136$		0			0
$137$	−54.5400	+	94.4660i	−0.398102	+	0.689533i	−0.993492	−	0.113904i	$-0.963664\pi$
$137$	−54.5400	+	94.4660i	−0.398102	+	0.689533i	0.595390	+	0.803437i	$0.296998\pi$
$138$		0			0
$139$	4.21609			0.0303316			0.0151658	−	0.999885i	$-0.495172\pi$
$139$	4.21609			0.0303316			0.0151658	+	0.999885i	$0.495172\pi$
$140$		0			0
$141$	41.5551	+	39.9568i	0.294717	+	0.283382i
$142$		0			0
$143$	288.537	−	166.587i	2.01774	−	1.16494i
$144$		0			0
$145$			110.634i			0.762995i
$146$		0			0
$147$	38.4651	+	36.9857i	0.261667	+	0.251604i
$148$		0			0
$149$	−133.072	−	230.487i	−0.893100	−	1.54690i	−0.836138	−	0.548519i	$-0.815192\pi$
$149$	−133.072	−	230.487i	−0.893100	−	1.54690i	−0.0569625	−	0.998376i	$-0.518142\pi$
$150$		0			0
$151$	−199.036	+	114.913i	−1.31812	+	0.761016i	−0.983426	−	0.181311i	$-0.941966\pi$
$151$	−199.036	+	114.913i	−1.31812	+	0.761016i	−0.334693	+	0.942327i	$0.608633\pi$
$152$		0			0
$153$	−82.0580	+	51.7678i	−0.536327	+	0.338352i
$154$		0			0
$155$		−	19.6472i		−	0.126756i
$156$		0			0
$157$	−66.7469	−	115.609i	−0.425139	−	0.736363i	0.571294	−	0.820745i	$-0.306442\pi$
$157$	−66.7469	−	115.609i	−0.425139	−	0.736363i	−0.996433	+	0.0843824i	$0.973108\pi$
$158$		0			0
$159$	70.2283	+	242.941i	0.441687	+	1.52793i
$160$		0			0
$161$	−122.115	−	211.509i	−0.758478	−	1.31372i
$162$		0			0
$163$	−215.134			−1.31984			−0.659921	−	0.751335i	$-0.729410\pi$
$163$	−215.134			−1.31984			−0.659921	+	0.751335i	$0.729410\pi$
$164$		0			0
$165$	−113.601	−	109.232i	−0.688493	−	0.662013i
$166$		0			0
$167$		−	104.289i		−	0.624487i	−0.950002	−	0.312243i	$-0.898920\pi$
$167$		−	104.289i		−	0.624487i	0.950002	−	0.312243i	$-0.101080\pi$
$168$		0			0
$169$	−462.184			−2.73481
$170$		0			0
$171$	−157.373	+	66.8942i	−0.920308	+	0.391194i
$172$		0			0
$173$			334.413i			1.93302i	0.256623	+	0.966512i	$0.417390\pi$
$173$			334.413i			1.93302i	−0.256623	+	0.966512i	$0.582610\pi$
$174$		0			0
$175$	52.0041			0.297166
$176$		0			0
$177$	−11.6532	−	40.3119i	−0.0658372	−	0.227751i
$178$		0			0
$179$			147.280i			0.822793i	0.911456	+	0.411397i	$0.134959\pi$
$179$			147.280i			0.822793i	−0.911456	+	0.411397i	$0.865041\pi$
$180$		0			0
$181$	−181.475	+	104.775i	−1.00263	+	0.578867i	−0.909024	−	0.416743i	$-0.863172\pi$
$181$	−181.475	+	104.775i	−1.00263	+	0.578867i	−0.0936021	+	0.995610i	$0.529838\pi$
$182$		0			0
$183$	−137.109	−	131.836i	−0.749232	−	0.720416i
$184$		0			0
$185$	−87.1123	+	50.2943i	−0.470877	+	0.271861i
$186$		0			0
$187$	−142.963			−0.764509
$188$		0			0
$189$	147.747	+	30.4093i	0.781732	+	0.160896i
$190$		0			0
$191$	−130.504	−	226.039i	−0.683266	−	1.18345i	−0.973978	−	0.226641i	$-0.927225\pi$
$191$	−130.504	−	226.039i	−0.683266	−	1.18345i	0.290712	−	0.956811i	$-0.406108\pi$
$192$		0			0
$193$	274.813	−	158.663i	1.42390	−	0.822090i	0.427272	−	0.904123i	$-0.359475\pi$
$193$	274.813	−	158.663i	1.42390	−	0.822090i	0.996630	+	0.0820329i	$0.0261413\pi$
$194$		0			0
$195$	82.9120	+	286.818i	0.425190	+	1.47086i
$196$		0			0
$197$	117.271			0.595286			0.297643	−	0.954677i	$-0.403800\pi$
$197$	117.271			0.595286			0.297643	+	0.954677i	$0.403800\pi$
$198$		0			0
$199$	113.149	+	195.981i	0.568590	+	0.984827i	0.996706	+	0.0811029i	$0.0258442\pi$
$199$	113.149	+	195.981i	0.568590	+	0.984827i	−0.428116	+	0.903724i	$0.640822\pi$
$200$		0			0
$201$	232.500	+	57.4376i	1.15671	+	0.285759i
$202$		0			0
$203$		−	156.034i		−	0.768643i
$204$		0			0
$205$	−112.516	−	64.9613i	−0.548860	−	0.316884i
$206$		0			0
$207$	348.177	+	183.211i	1.68201	+	0.885079i
$208$		0			0
$209$	−248.715	−	40.3621i	−1.19002	−	0.193120i
$210$		0			0
$211$	−104.403	+	60.2773i	−0.494803	+	0.285674i	−0.726565	−	0.687098i	$-0.758884\pi$
$211$	−104.403	+	60.2773i	−0.494803	+	0.285674i	0.231762	+	0.972773i	$0.425551\pi$
$212$		0			0
$213$	152.497	−	158.597i	0.715949	−	0.744586i
$214$		0			0
$215$	79.0534	+	136.924i	0.367690	+	0.636858i
$216$		0			0
$217$			27.7097i			0.127694i
$218$		0			0
$219$	215.291	+	207.010i	0.983062	+	0.945253i
$220$		0			0
$221$	234.552	+	135.419i	1.06132	+	0.612755i
$222$		0			0
$223$			68.1444i			0.305580i	0.988259	+	0.152790i	$0.0488259\pi$
$223$			68.1444i			0.305580i	−0.988259	+	0.152790i	$0.951174\pi$
$224$		0			0
$225$	−70.8535	+	44.6993i	−0.314905	+	0.198664i
$226$		0			0
$227$	54.7779	−	31.6260i	0.241312	−	0.139322i	−0.374467	−	0.927240i	$-0.622174\pi$
$227$	54.7779	−	31.6260i	0.241312	−	0.139322i	0.615780	+	0.787918i	$0.288841\pi$
$228$		0			0
$229$	−53.9886	+	93.5111i	−0.235758	+	0.408345i	−0.959493	−	0.281733i	$-0.909091\pi$
$229$	−53.9886	+	93.5111i	−0.235758	+	0.408345i	0.723735	+	0.690079i	$0.242424\pi$
$230$		0			0
$231$	160.219	+	154.057i	0.693589	+	0.666913i
$232$		0			0
$233$	201.984	−	349.846i	0.866884	−	1.50149i	0.00171917	−	0.999999i	$-0.499453\pi$
$233$	201.984	−	349.846i	0.866884	−	1.50149i	0.865165	−	0.501488i	$-0.167214\pi$
$234$		0			0
$235$	−76.1207			−0.323918
$236$		0			0
$237$	230.937	+	57.0515i	0.974417	+	0.240724i
$238$		0			0
$239$	−117.285	+	203.144i	−0.490734	+	0.849977i	−0.999943	−	0.0106663i	$-0.996605\pi$
$239$	−117.285	+	203.144i	−0.490734	+	0.849977i	0.509209	+	0.860643i	$0.329938\pi$
$240$		0			0
$241$	86.4868	+	49.9332i	0.358866	+	0.207192i	0.668583	−	0.743637i	$-0.266901\pi$
$241$	86.4868	+	49.9332i	0.358866	+	0.207192i	−0.309717	+	0.950829i	$0.600234\pi$
$242$		0			0
$243$	−227.438	+	85.5626i	−0.935959	+	0.352109i
$244$		0			0
$245$	−70.4605			−0.287594
$246$		0			0
$247$	369.822	+	301.810i	1.49725	+	1.22190i
$248$		0			0
$249$	−57.1971	+	16.5343i	−0.229707	+	0.0664027i
$250$		0			0
$251$	54.7583	+	94.8441i	0.218160	+	0.377865i	0.954246	−	0.299024i	$-0.0966610\pi$
$251$	54.7583	+	94.8441i	0.218160	+	0.377865i	−0.736085	+	0.676889i	$0.763328\pi$
$252$		0			0
$253$	289.866	+	502.062i	1.14571	+	1.98443i
$254$		0			0
$255$	30.7254	−	124.372i	0.120492	−	0.487734i
$256$		0			0
$257$			248.204i			0.965775i	0.875682	+	0.482888i	$0.160412\pi$
$257$			248.204i			0.965775i	−0.875682	+	0.482888i	$0.839588\pi$
$258$		0			0
$259$	122.860	−	70.9332i	0.474363	−	0.273873i
$260$		0			0
$261$	134.117	+	212.591i	0.513858	+	0.814525i
$262$		0			0
$263$	−463.434			−1.76210			−0.881052	−	0.473019i	$-0.843164\pi$
$263$	−463.434			−1.76210			−0.881052	+	0.473019i	$0.843164\pi$
$264$		0			0
$265$	−289.183	−	166.960i	−1.09126	−	0.630037i
$266$		0			0
$267$	2.08987	+	7.22952i	0.00782725	+	0.0270768i
$268$		0			0
$269$	208.925	+	120.623i	0.776673	+	0.448412i	0.835250	−	0.549871i	$-0.185323\pi$
$269$	208.925	+	120.623i	0.776673	+	0.448412i	−0.0585770	+	0.998283i	$0.518656\pi$
$270$		0			0
$271$	−49.7374	+	86.1478i	−0.183533	+	0.317888i	−0.943081	−	0.332563i	$-0.892087\pi$
$271$	−49.7374	+	86.1478i	−0.183533	+	0.317888i	0.759548	+	0.650451i	$0.225420\pi$
$272$		0			0
$273$	−116.936	−	404.517i	−0.428337	−	1.48175i
$274$		0			0
$275$	−123.443			−0.448882
$276$		0			0
$277$	235.476	+	407.856i	0.850093	+	1.47240i	0.881124	+	0.472886i	$0.156788\pi$
$277$	235.476	+	407.856i	0.850093	+	1.47240i	−0.0310310	+	0.999518i	$0.509879\pi$
$278$		0			0
$279$	−23.8174	−	37.7533i	−0.0853671	−	0.135317i
$280$		0			0
$281$	−225.286	−	130.069i	−0.801729	−	0.462878i	0.0423465	−	0.999103i	$-0.486517\pi$
$281$	−225.286	−	130.069i	−0.801729	−	0.462878i	−0.844075	+	0.536225i	$0.819850\pi$
$282$		0			0
$283$	−79.5473	−	137.780i	−0.281086	−	0.486855i	0.690567	−	0.723269i	$-0.257361\pi$
$283$	−79.5473	−	137.780i	−0.281086	−	0.486855i	−0.971652	+	0.236414i	$0.924028\pi$
$284$		0			0
$285$	88.5667	−	207.697i	0.310760	−	0.728762i
$286$		0			0
$287$	158.689	+	91.6190i	0.552922	+	0.319230i
$288$		0			0
$289$	86.3925	+	149.636i	0.298936	+	0.517772i
$290$		0			0
$291$	225.501	+	55.7087i	0.774918	+	0.191439i
$292$		0			0
$293$	36.6938	+	21.1852i	0.125235	+	0.0723043i	0.561309	−	0.827607i	$-0.310298\pi$
$293$	36.6938	+	21.1852i	0.125235	+	0.0723043i	−0.436074	+	0.899911i	$0.643631\pi$
$294$		0			0
$295$	47.9849	+	27.7041i	0.162661	+	0.0939122i
$296$		0			0
$297$	−350.710	−	72.1828i	−1.18084	−	0.243040i
$298$		0			0
$299$		−	1098.28i		−	3.67316i
$300$		0			0
$301$	−111.494	−	193.113i	−0.370412	−	0.641572i
$302$		0			0
$303$	−129.605	−	124.621i	−0.427740	−	0.411289i
$304$		0			0
$305$	251.157			0.823467
$306$		0			0
$307$	−136.415	−	78.7594i	−0.444349	−	0.256545i	0.261092	−	0.965314i	$-0.415918\pi$
$307$	−136.415	−	78.7594i	−0.444349	−	0.256545i	−0.705441	+	0.708769i	$0.749251\pi$
$308$		0			0
$309$	−231.142	+	240.387i	−0.748032	+	0.777953i
$310$		0			0
$311$	−25.7344	+	44.5733i	−0.0827474	+	0.143323i	−0.904429	−	0.426624i	$-0.859703\pi$
$311$	−25.7344	+	44.5733i	−0.0827474	+	0.143323i	0.821682	+	0.569947i	$0.193036\pi$
$312$		0			0
$313$	205.217	−	355.446i	0.655646	−	1.13561i	−0.326086	−	0.945340i	$-0.605730\pi$
$313$	205.217	−	355.446i	0.655646	−	1.13561i	0.981732	−	0.190271i	$-0.0609368\pi$
$314$		0			0
$315$	−168.457	+	106.274i	−0.534785	+	0.337379i
$316$		0			0
$317$	70.9840	+	40.9826i	0.223924	+	0.129283i	0.607766	−	0.794116i	$-0.292066\pi$
$317$	70.9840	+	40.9826i	0.223924	+	0.129283i	−0.383842	+	0.923399i	$0.625399\pi$
$318$		0			0
$319$			370.381i			1.16107i
$320$		0			0
$321$	114.502	+	28.2869i	0.356703	+	0.0881213i
$322$		0			0
$323$	−72.6758	−	191.499i	−0.225002	−	0.592876i
$324$		0			0
$325$	202.526	+	116.928i	0.623156	+	0.359780i
$326$		0			0
$327$	−23.9723	+	24.9312i	−0.0733098	+	0.0762421i
$328$		0			0
$329$	107.358			0.326315
$330$		0			0
$331$	−409.814	+	236.606i	−1.23811	+	0.714822i	−0.968707	−	0.248207i	$-0.920159\pi$
$331$	−409.814	+	236.606i	−1.23811	+	0.714822i	−0.269400	+	0.963028i	$0.586825\pi$
$332$		0			0
$333$	−106.422	+	202.246i	−0.319587	+	0.607346i
$334$		0			0
$335$	−273.861	+	158.114i	−0.817496	+	0.471981i
$336$		0			0
$337$	−21.5323	+	12.4317i	−0.0638942	+	0.0368893i	−0.531607	−	0.846991i	$-0.678412\pi$
$337$	−21.5323	+	12.4317i	−0.0638942	+	0.0368893i	0.467713	+	0.883881i	$0.345078\pi$
$338$		0			0
$339$	134.689	−	140.077i	0.397314	−	0.413206i
$340$		0			0
$341$		−	65.7747i		−	0.192888i
$342$		0			0
$343$	373.129			1.08784
$344$		0			0
$345$	−499.071	+	144.269i	−1.44658	+	0.418171i
$346$		0			0
$347$	118.491	+	205.232i	0.341473	+	0.591448i	0.984706	−	0.174222i	$-0.0557410\pi$
$347$	118.491	+	205.232i	0.341473	+	0.591448i	−0.643234	+	0.765670i	$0.722408\pi$
$348$		0			0
$349$	−316.275	−	547.805i	−0.906233	−	1.56964i	−0.819254	−	0.573431i	$-0.805612\pi$
$349$	−316.275	−	547.805i	−0.906233	−	1.56964i	−0.0869793	−	0.996210i	$-0.527721\pi$
$350$		0			0
$351$	507.017	+	450.629i	1.44449	+	1.28384i
$352$		0			0
$353$	18.7051	+	32.3982i	0.0529891	+	0.0917797i	0.891303	−	0.453408i	$-0.149792\pi$
$353$	18.7051	+	32.3982i	0.0529891	+	0.0917797i	−0.838314	+	0.545187i	$0.816458\pi$
$354$		0			0
$355$			290.518i			0.818361i
$356$		0			0
$357$	−43.3339	+	175.410i	−0.121383	+	0.491344i
$358$		0			0
$359$	311.259	−	539.116i	0.867017	−	1.50172i	0.00198589	−	0.999998i	$-0.499368\pi$
$359$	311.259	−	539.116i	0.867017	−	1.50172i	0.865031	−	0.501719i	$-0.167299\pi$
$360$		0			0
$361$	−72.3702	−	353.672i	−0.200471	−	0.979700i
$362$		0			0
$363$	−118.651	−	114.088i	−0.326863	−	0.314292i
$364$		0			0
$365$	−394.370			−1.08047
$366$		0			0
$367$	280.673	−	486.140i	0.764776	−	1.32463i	−0.175589	−	0.984464i	$-0.556183\pi$
$367$	280.673	−	486.140i	0.764776	−	1.32463i	0.940365	−	0.340167i	$-0.110484\pi$
$368$		0			0
$369$	−294.957	+	11.5711i	−0.799341	+	0.0313581i
$370$		0			0
$371$	407.852	+	235.474i	1.09933	+	0.634700i
$372$		0			0
$373$	−165.463	−	95.5303i	−0.443601	−	0.256113i	0.261523	−	0.965197i	$-0.415775\pi$
$373$	−165.463	−	95.5303i	−0.443601	−	0.256113i	−0.705124	+	0.709084i	$0.749109\pi$
$374$		0			0
$375$	97.7835	−	395.814i	0.260756	−	1.05550i
$376$		0			0
$377$	350.835	−	607.664i	0.930597	−	1.61184i
$378$		0			0
$379$		−	284.754i		−	0.751329i	−0.926756	−	0.375665i	$-0.877414\pi$
$379$		−	284.754i		−	0.751329i	0.926756	−	0.375665i	$-0.122586\pi$
$380$		0			0
$381$	−109.993	−	380.498i	−0.288694	−	0.998682i
$382$		0			0
$383$	−224.972	+	129.887i	−0.587393	+	0.339132i	−0.764066	−	0.645138i	$-0.776800\pi$
$383$	−224.972	+	129.887i	−0.587393	+	0.339132i	0.176673	+	0.984270i	$0.443466\pi$
$384$		0			0
$385$	−293.490			−0.762311
$386$		0			0
$387$	317.894	+	167.276i	0.821430	+	0.432239i
$388$		0			0
$389$	−184.925	+	320.300i	−0.475386	+	0.823393i	−0.999603	−	0.0281922i	$-0.991025\pi$
$389$	−184.925	+	320.300i	−0.475386	+	0.823393i	0.524216	+	0.851585i	$0.324358\pi$
$390$		0			0
$391$	−235.632	+	408.127i	−0.602640	+	1.04380i
$392$		0			0
$393$	−286.955	+	82.9517i	−0.730166	+	0.211073i
$394$		0			0
$395$	−272.020	+	157.051i	−0.688659	+	0.397597i
$396$		0			0
$397$	279.296	−	483.754i	0.703515	−	1.21852i	−0.263709	−	0.964602i	$-0.584946\pi$
$397$	279.296	−	483.754i	0.703515	−	1.21852i	0.967225	−	0.253922i	$-0.0817207\pi$
$398$		0			0
$399$	−124.911	+	292.929i	−0.313060	+	0.734157i
$400$		0			0
$401$	661.224	−	381.758i	1.64894	−	0.952015i	0.671444	−	0.741055i	$-0.265674\pi$
$401$	661.224	−	381.758i	1.64894	−	0.952015i	0.977495	−	0.210960i	$-0.0676590\pi$
$402$		0			0
$403$	−62.3037	+	107.913i	−0.154600	+	0.267775i
$404$		0			0
$405$	138.170	−	289.590i	0.341160	−	0.715036i
$406$		0			0
$407$	−291.634	+	168.375i	−0.716545	+	0.413697i
$408$		0			0
$409$		−	675.395i		−	1.65133i	−0.564159	−	0.825666i	$-0.690800\pi$
$409$		−	675.395i		−	1.65133i	0.564159	−	0.825666i	$-0.309200\pi$
$410$		0			0
$411$	−235.885	−	226.813i	−0.573930	−	0.551856i
$412$		0			0
$413$	−67.6761	−	39.0728i	−0.163865	−	0.0946073i
$414$		0			0
$415$	39.3083	−	68.0840i	0.0947188	−	0.164058i
$416$		0			0
$417$	−3.03348	+	12.2791i	−0.00727454	+	0.0294464i
$418$		0			0
$419$	−280.195	+	485.312i	−0.668724	+	1.15826i	0.309538	+	0.950887i	$0.399826\pi$
$419$	−280.195	+	485.312i	−0.668724	+	1.15826i	−0.978261	+	0.207376i	$0.933508\pi$
$420$		0			0
$421$		−	379.086i		−	0.900443i	−0.892917	−	0.450221i	$-0.851345\pi$
$421$		−	379.086i		−	0.900443i	0.892917	−	0.450221i	$-0.148655\pi$
$422$		0			0
$423$	−146.271	+	92.2777i	−0.345794	+	0.218151i
$424$		0			0
$425$	−50.1733	−	86.9028i	−0.118055	−	0.204477i
$426$		0			0
$427$	−354.223			−0.829562
$428$		0			0
$429$	277.572	+	960.207i	0.647021	+	2.23824i
$430$		0			0
$431$	406.143	−	234.487i	0.942328	−	0.544053i	0.0516388	−	0.998666i	$-0.483556\pi$
$431$	406.143	−	234.487i	0.942328	−	0.544053i	0.890689	+	0.454612i	$0.150222\pi$
$432$		0			0
$433$	−190.975	+	110.259i	−0.441050	+	0.254640i	−0.704043	−	0.710157i	$-0.748624\pi$
$433$	−190.975	+	110.259i	−0.441050	+	0.254640i	0.262993	+	0.964798i	$0.415290\pi$
$434$		0			0
$435$	−322.216	−	79.6015i	−0.740726	−	0.182992i
$436$		0			0
$437$	−525.157	+	643.499i	−1.20173	+	1.47254i
$438$		0			0
$439$			527.944i			1.20261i	0.799021	+	0.601303i	$0.205352\pi$
$439$			527.944i			1.20261i	−0.799021	+	0.601303i	$0.794648\pi$
$440$		0			0
$441$	−135.394	+	85.4162i	−0.307017	+	0.193687i
$442$		0			0
$443$	2.16032	−	3.74178i	0.00487657	−	0.00844646i	−0.863577	−	0.504217i	$-0.831781\pi$
$443$	2.16032	−	3.74178i	0.00487657	−	0.00844646i	0.868453	+	0.495771i	$0.165114\pi$
$444$		0			0
$445$	−8.60559	−	4.96844i	−0.0193384	−	0.0111650i
$446$		0			0
$447$	767.027	−	221.728i	1.71594	−	0.496037i
$448$		0			0
$449$			139.442i			0.310561i	0.987870	+	0.155281i	$0.0496281\pi$
$449$			139.442i			0.310561i	−0.987870	+	0.155281i	$0.950372\pi$
$450$		0			0
$451$	−376.681	−	217.477i	−0.835213	−	0.482210i
$452$		0			0
$453$	−191.472	−	662.361i	−0.422676	−	1.46217i
$454$		0			0
$455$	481.513	+	278.002i	1.05827	+	0.610993i
$456$		0			0
$457$	−23.1575	−	40.1100i	−0.0506729	−	0.0877680i	0.839576	−	0.543242i	$-0.182803\pi$
$457$	−23.1575	−	40.1100i	−0.0506729	−	0.0877680i	−0.890249	+	0.455474i	$0.849470\pi$
$458$		0			0
$459$	−91.7300	−	276.236i	−0.199847	−	0.601821i
$460$		0			0
$461$	239.445			0.519404			0.259702	−	0.965689i	$-0.416376\pi$
$461$	239.445			0.519404			0.259702	+	0.965689i	$0.416376\pi$
$462$		0			0
$463$	−24.8923	+	43.1147i	−0.0537631	+	0.0931204i	−0.891654	−	0.452717i	$-0.850455\pi$
$463$	−24.8923	+	43.1147i	−0.0537631	+	0.0931204i	0.837891	+	0.545837i	$0.183788\pi$
$464$		0			0
$465$	57.2213	+	14.1362i	0.123057	+	0.0304004i
$466$		0			0
$467$	−412.789			−0.883917			−0.441958	−	0.897036i	$-0.645716\pi$
$467$	−412.789			−0.883917			−0.441958	+	0.897036i	$0.645716\pi$
$468$		0			0
$469$	386.243	−	222.998i	0.823547	−	0.475475i
$470$		0			0
$471$	384.729	−	111.216i	0.816834	−	0.236127i
$472$		0			0
$473$	264.654	+	458.395i	0.559523	+	0.969122i
$474$		0			0
$475$	−62.7524	−	165.351i	−0.132110	−	0.348108i
$476$		0			0
$477$	−758.081	+	29.7394i	−1.58927	+	0.0623468i
$478$		0			0
$479$	216.233	−	374.527i	0.451426	−	0.781893i	−0.547049	−	0.837101i	$-0.684249\pi$
$479$	216.233	−	374.527i	0.451426	−	0.781893i	0.998475	+	0.0552080i	$0.0175822\pi$
$480$		0			0
$481$	637.958			1.32632
$482$		0			0
$483$	703.870	−	203.472i	1.45729	−	0.421266i
$484$		0			0
$485$	−265.618	+	153.354i	−0.547665	+	0.316195i
$486$		0			0
$487$		−	566.439i		−	1.16312i	−0.813504	−	0.581559i	$-0.802443\pi$
$487$		−	566.439i		−	1.16312i	0.813504	−	0.581559i	$-0.197557\pi$
$488$		0			0
$489$	154.789	−	626.566i	0.316542	−	1.28132i
$490$		0			0
$491$	114.618	+	198.523i	0.233437	+	0.404325i	0.958817	−	0.284024i	$-0.0916694\pi$
$491$	114.618	+	198.523i	0.233437	+	0.404325i	−0.725380	+	0.688348i	$0.758336\pi$
$492$		0			0
$493$	−260.746	+	150.542i	−0.528896	+	0.305358i
$494$		0			0
$495$	399.868	−	252.265i	0.807815	−	0.509625i
$496$		0			0
$497$		−	409.736i		−	0.824419i
$498$		0			0
$499$	273.965	+	474.521i	0.549028	+	0.950945i	0.998341	+	0.0575705i	$0.0183354\pi$
$499$	273.965	+	474.521i	0.549028	+	0.950945i	−0.449313	+	0.893374i	$0.648331\pi$
$500$		0			0
$501$	303.737	+	75.0363i	0.606261	+	0.149773i
$502$		0			0
$503$	37.9593	+	65.7474i	0.0754658	+	0.130711i	0.901289	−	0.433219i	$-0.142622\pi$
$503$	37.9593	+	65.7474i	0.0754658	+	0.130711i	−0.825823	+	0.563929i	$0.809289\pi$
$504$		0			0
$505$	237.411			0.470121
$506$		0			0
$507$	332.542	−	1346.08i	0.655901	−	2.65500i
$508$		0			0
$509$		−	102.887i		−	0.202135i	−0.994880	−	0.101067i	$-0.967774\pi$
$509$		−	102.887i		−	0.202135i	0.994880	−	0.101067i	$-0.0322258\pi$
$510$		0			0
$511$	556.205			1.08846
$512$		0			0
$513$	−81.5956	−	506.469i	−0.159056	−	0.987270i
$514$		0			0
$515$		−	440.342i		−	0.855034i
$516$		0			0
$517$	−254.836			−0.492913
$518$		0			0
$519$	−973.958	−	240.610i	−1.87661	−	0.463604i
$520$		0			0
$521$			478.933i			0.919258i	0.888111	+	0.459629i	$0.152018\pi$
$521$			478.933i			0.919258i	−0.888111	+	0.459629i	$0.847982\pi$
$522$		0			0
$523$	−863.569	+	498.582i	−1.65118	+	0.953311i	−0.674597	+	0.738187i	$0.735682\pi$
$523$	−863.569	+	498.582i	−1.65118	+	0.953311i	−0.976587	+	0.215125i	$0.930984\pi$
$524$		0			0
$525$	−37.4170	+	151.459i	−0.0712704	+	0.288493i
$526$		0			0
$527$	46.3050	−	26.7342i	0.0878652	−	0.0507290i
$528$		0			0
$529$	1382.03			2.61253
$530$		0			0
$531$	125.791	−	4.93475i	0.236894	−	0.00929331i
$532$		0			0
$533$	412.001	+	713.606i	0.772985	+	1.33885i
$534$		0			0
$535$	−134.871	+	77.8680i	−0.252096	+	0.145548i
$536$		0			0
$537$	−428.944	−	105.968i	−0.798779	−	0.197333i
$538$		0			0
$539$	−235.887			−0.437638
$540$		0			0
$541$	99.7528	+	172.777i	0.184386	+	0.319366i	0.943369	−	0.331744i	$-0.107637\pi$
$541$	99.7528	+	172.777i	0.184386	+	0.319366i	−0.758983	+	0.651110i	$0.774304\pi$
$542$		0			0
$543$	−174.579	−	603.922i	−0.321508	−	1.11220i
$544$		0			0
$545$		−	45.6690i		−	0.0837963i
$546$		0			0
$547$	378.396	+	218.467i	0.691765	+	0.399391i	0.804273	−	0.594260i	$-0.202555\pi$
$547$	378.396	+	218.467i	0.691765	+	0.399391i	−0.112508	+	0.993651i	$0.535888\pi$
$548$		0			0
$549$	482.615	−	304.467i	0.879080	−	0.554585i
$550$		0			0
$551$	−496.124	+	188.284i	−0.900407	+	0.341714i
$552$		0			0
$553$	383.647	−	221.499i	0.693756	−	0.400540i
$554$		0			0
$555$	−83.8019	−	289.896i	−0.150994	−	0.522336i
$556$		0			0
$557$	−288.865	−	500.329i	−0.518609	−	0.898257i	−0.999766	−	0.0216224i	$-0.993117\pi$
$557$	−288.865	−	500.329i	−0.518609	−	0.898257i	0.481158	−	0.876634i	$-0.340216\pi$
$558$		0			0
$559$		−	1002.75i		−	1.79383i
$560$		0			0
$561$	102.862	−	416.372i	0.183355	−	0.742196i
$562$		0			0
$563$	−48.9658	−	28.2704i	−0.0869730	−	0.0502139i	0.455883	−	0.890040i	$-0.349324\pi$
$563$	−48.9658	−	28.2704i	−0.0869730	−	0.0502139i	−0.542856	+	0.839826i	$0.682657\pi$
$564$		0			0
$565$			256.593i			0.454147i
$566$		0			0
$567$	−194.870	+	408.426i	−0.343685	+	0.720329i
$568$		0			0
$569$	−133.057	+	76.8207i	−0.233844	+	0.135010i	−0.612344	−	0.790591i	$-0.709773\pi$
$569$	−133.057	+	76.8207i	−0.233844	+	0.135010i	0.378500	+	0.925601i	$0.376440\pi$
$570$		0			0
$571$	−112.166	+	194.277i	−0.196438	+	0.340241i	−0.947371	−	0.320138i	$-0.896271\pi$
$571$	−112.166	+	194.277i	−0.196438	+	0.340241i	0.750933	+	0.660378i	$0.229604\pi$
$572$		0			0
$573$	752.224	−	217.449i	1.31278	−	0.379493i
$574$		0			0
$575$	−203.458	+	352.400i	−0.353841	+	0.612870i
$576$		0			0
$577$	149.144			0.258483			0.129241	−	0.991613i	$-0.458746\pi$
$577$	149.144			0.258483			0.129241	+	0.991613i	$0.458746\pi$
$578$		0			0
$579$	264.370	+	914.536i	0.456597	+	1.57951i
$580$		0			0
$581$	−55.4390	+	96.0231i	−0.0954199	+	0.165272i
$582$		0			0
$583$	−968.123	−	558.946i	−1.66059	−	0.958742i
$584$		0			0
$585$	−894.996	+	35.1106i	−1.52991	+	0.0600181i
$586$		0			0
$587$	−860.561			−1.46603			−0.733016	−	0.680211i	$-0.761888\pi$
$587$	−860.561			−1.46603			−0.733016	+	0.680211i	$0.761888\pi$
$588$		0			0
$589$	88.1051	−	33.4368i	0.149584	−	0.0567687i
$590$		0			0
$591$	−84.3768	+	341.546i	−0.142770	+	0.577912i
$592$		0			0
$593$	258.516	+	447.763i	0.435946	+	0.755081i	0.997372	−	0.0724456i	$-0.0230804\pi$
$593$	258.516	+	447.763i	0.435946	+	0.755081i	−0.561426	+	0.827527i	$0.689747\pi$
$594$		0			0
$595$	−119.289	−	206.615i	−0.200486	−	0.347252i
$596$		0			0
$597$	−652.193	+	188.533i	−1.09245	+	0.315801i
$598$		0			0
$599$		−	995.005i		−	1.66111i	−0.556936	−	0.830555i	$-0.688023\pi$
$599$		−	995.005i		−	1.66111i	0.556936	−	0.830555i	$-0.311977\pi$
$600$		0			0
$601$	1005.66	−	580.617i	1.67331	−	0.966085i	0.707542	−	0.706672i	$-0.249804\pi$
$601$	1005.66	−	580.617i	1.67331	−	0.966085i	0.965766	−	0.259413i	$-0.0835292\pi$
$602$		0			0
$603$	−334.567	+	635.815i	−0.554838	+	1.05442i
$604$		0			0
$605$	217.346			0.359249
$606$		0			0
$607$	−272.695	−	157.440i	−0.449250	−	0.259375i	0.258263	−	0.966075i	$-0.416850\pi$
$607$	−272.695	−	157.440i	−0.449250	−	0.259375i	−0.707513	+	0.706700i	$0.750183\pi$
$608$		0			0
$609$	454.441	+	112.267i	0.746209	+	0.184346i
$610$		0			0
$611$	418.097	+	241.388i	0.684283	+	0.395071i
$612$		0			0
$613$	1.68671	−	2.92147i	0.00275157	−	0.00476586i	−0.864646	−	0.502381i	$-0.832457\pi$
$613$	1.68671	−	2.92147i	0.00275157	−	0.00476586i	0.867398	+	0.497615i	$0.165791\pi$
$614$		0			0
$615$	270.152	−	280.957i	0.439271	−	0.456841i
$616$		0			0
$617$	85.9129			0.139243			0.0696215	−	0.997573i	$-0.477821\pi$
$617$	85.9129			0.139243			0.0696215	+	0.997573i	$0.477821\pi$
$618$		0			0
$619$	−174.074	−	301.505i	−0.281218	−	0.487084i	0.690467	−	0.723364i	$-0.257405\pi$
$619$	−174.074	−	301.505i	−0.281218	−	0.487084i	−0.971685	+	0.236280i	$0.924072\pi$
$620$		0			0
$621$	−784.106	+	882.223i	−1.26265	+	1.42065i
$622$		0			0
$623$	12.1370	+	7.00730i	0.0194815	+	0.0112477i
$624$		0			0
$625$	152.823	+	264.698i	0.244517	+	0.423516i
$626$		0			0
$627$	296.503	−	695.327i	0.472891	−	1.10898i
$628$		0			0
$629$	−237.070	−	136.872i	−0.376899	−	0.217603i
$630$		0			0
$631$	178.654	+	309.437i	0.283128	+	0.490391i	0.972153	−	0.234345i	$-0.0752947\pi$
$631$	178.654	+	309.437i	0.283128	+	0.490391i	−0.689026	+	0.724737i	$0.741961\pi$
$632$		0			0
$633$	−100.436	−	347.438i	−0.158666	−	0.548876i
$634$		0			0
$635$	452.922	+	261.495i	0.713263	+	0.411803i
$636$		0			0
$637$	387.008	+	223.439i	0.607548	+	0.350768i
$638$		0			0
$639$	352.182	+	558.250i	0.551146	+	0.873630i
$640$		0			0
$641$		−	142.047i		−	0.221603i	−0.993843	−	0.110801i	$-0.964658\pi$
$641$		−	142.047i		−	0.221603i	0.993843	−	0.110801i	$-0.0353417\pi$
$642$		0			0
$643$	−435.578	−	754.443i	−0.677415	−	1.17332i	−0.975757	−	0.218858i	$-0.929767\pi$
$643$	−435.578	−	754.443i	−0.677415	−	1.17332i	0.298342	−	0.954459i	$-0.403566\pi$
$644$		0			0
$645$	−455.663	+	131.721i	−0.706455	+	0.204219i
$646$		0			0
$647$	594.022			0.918117			0.459058	−	0.888406i	$-0.348187\pi$
$647$	594.022			0.918117			0.459058	+	0.888406i	$0.348187\pi$
$648$		0			0
$649$	160.643	+	92.7475i	0.247525	+	0.142908i
$650$		0			0
$651$	−80.7028	−	19.9371i	−0.123967	−	0.0306254i
$652$		0			0
$653$	−391.470	+	678.046i	−0.599495	+	1.03836i	0.393401	+	0.919367i	$0.371298\pi$
$653$	−391.470	+	678.046i	−0.599495	+	1.03836i	−0.992896	+	0.118988i	$0.962035\pi$
$654$		0			0
$655$	197.208	−	341.575i	0.301081	−	0.521488i
$656$		0			0
$657$	−757.807	+	478.077i	−1.15344	+	0.727667i
$658$		0			0
$659$	−184.847	−	106.722i	−0.280497	−	0.161945i	0.353152	−	0.935566i	$-0.385110\pi$
$659$	−184.847	−	106.722i	−0.280497	−	0.161945i	−0.633648	+	0.773621i	$0.718443\pi$
$660$		0			0
$661$			476.262i			0.720517i	0.932852	+	0.360259i	$0.117312\pi$
$661$			476.262i			0.720517i	−0.932852	+	0.360259i	$0.882688\pi$
$662$		0			0
$663$	−563.160	+	585.686i	−0.849412	+	0.883387i
$664$		0			0
$665$	−149.196	−	393.129i	−0.224356	−	0.591172i
$666$		0			0
$667$	1057.35	+	610.462i	1.58523	+	0.915236i
$668$		0			0
$669$	−198.467	−	49.0300i	−0.296662	−	0.0732884i
$670$		0			0
$671$	840.823			1.25309
$672$		0			0
$673$	1023.15	−	590.714i	1.52028	−	0.877732i	0.520563	−	0.853823i	$-0.325722\pi$
$673$	1023.15	−	590.714i	1.52028	−	0.877732i	0.999714	−	0.0239093i	$-0.00761130\pi$
$674$		0			0
$675$	−79.2049	−	238.518i	−0.117341	−	0.353360i
$676$		0			0
$677$	1014.38	−	585.651i	1.49834	−	0.865067i	0.498342	−	0.866980i	$-0.333942\pi$
$677$	1014.38	−	585.651i	1.49834	−	0.865067i	0.999998	+	0.00191292i	$0.000608900\pi$
$678$		0			0
$679$	374.617	−	216.285i	0.551719	−	0.318535i
$680$		0			0
$681$	52.6962	+	182.292i	0.0773806	+	0.267683i
$682$		0			0
$683$			795.560i			1.16480i	0.812902	+	0.582401i	$0.197887\pi$
$683$			795.560i			1.16480i	−0.812902	+	0.582401i	$0.802113\pi$
$684$		0			0
$685$	432.095			0.630796
$686$		0			0
$687$	−233.501	−	224.520i	−0.339885	−	0.326812i
$688$		0			0
$689$	1058.90	+	1834.07i	1.53687	+	2.66193i
$690$		0			0
$691$	278.681	+	482.690i	0.403302	+	0.698539i	0.994122	−	0.108264i	$-0.0345292\pi$
$691$	278.681	+	482.690i	0.403302	+	0.698539i	−0.590820	+	0.806803i	$0.701196\pi$
$692$		0			0
$693$	−563.960	+	355.785i	−0.813794	+	0.513398i
$694$		0			0
$695$	−8.35055	−	14.4636i	−0.0120152	−	0.0208109i
$696$		0			0
$697$		−	353.575i		−	0.507281i
$698$		0			0
$699$	873.580	+	839.981i	1.24976	+	1.20169i
$700$		0			0
$701$	394.685	−	683.614i	0.563031	−	0.975198i	−0.434199	−	0.900817i	$-0.642968\pi$
$701$	394.685	−	683.614i	0.563031	−	0.975198i	0.997230	−	0.0743813i	$-0.0236982\pi$
$702$		0			0
$703$	−373.791	−	305.049i	−0.531708	−	0.433925i
$704$		0			0
$705$	54.7689	−	221.697i	0.0776864	−	0.314464i
$706$		0			0
$707$	−334.836			−0.473601
$708$		0			0
$709$	−596.941	+	1033.93i	−0.841948	+	1.45830i	0.0462968	+	0.998928i	$0.485258\pi$
$709$	−596.941	+	1033.93i	−0.841948	+	1.45830i	−0.888245	+	0.459370i	$0.848075\pi$
$710$		0			0
$711$	−332.319	+	631.542i	−0.467396	+	0.888244i
$712$		0			0
$713$	−187.772	−	108.410i	−0.263354	−	0.152048i
$714$		0			0
$715$	−1142.97	−	659.896i	−1.59856	−	0.922931i
$716$		0			0
$717$	−507.259	−	487.750i	−0.707475	−	0.680265i
$718$		0			0
$719$	−171.089	+	296.335i	−0.237954	+	0.412148i	−0.960127	−	0.279564i	$-0.909810\pi$
$719$	−171.089	+	296.335i	−0.237954	+	0.412148i	0.722173	+	0.691712i	$0.243143\pi$
$720$		0			0
$721$			621.042i			0.861363i
$722$		0			0
$723$	−207.655	+	215.961i	−0.287213	+	0.298701i
$724$		0			0
$725$	−225.143	+	129.986i	−0.310542	+	0.179291i
$726$		0			0
$727$	541.308			0.744577			0.372289	−	0.928117i	$-0.378573\pi$
$727$	541.308			0.744577			0.372289	+	0.928117i	$0.378573\pi$
$728$		0			0
$729$	−85.5542	−	723.962i	−0.117358	−	0.993090i
$730$		0			0
$731$	−215.138	+	372.630i	−0.294306	+	0.509753i
$732$		0			0
$733$	642.502	−	1112.85i	0.876538	−	1.51821i	0.0214218	−	0.999771i	$-0.493181\pi$
$733$	642.502	−	1112.85i	0.876538	−	1.51821i	0.855116	−	0.518437i	$-0.173486\pi$
$734$		0			0
$735$	50.6964	−	205.212i	0.0689747	−	0.279200i
$736$		0			0
$737$	−916.830	+	529.332i	−1.24400	+	0.718225i
$738$		0			0
$739$	371.062	−	642.698i	0.502113	−	0.869686i	−0.497884	−	0.867244i	$-0.665889\pi$
$739$	371.062	−	642.698i	0.502113	−	0.869686i	0.999997	−	0.00244211i	$-0.000777349\pi$
$740$		0			0
$741$	−1145.09	+	859.932i	−1.54533	+	1.16050i
$742$		0			0
$743$	455.142	−	262.776i	0.612573	−	0.353669i	−0.161399	−	0.986889i	$-0.551600\pi$
$743$	455.142	−	262.776i	0.612573	−	0.353669i	0.773972	+	0.633220i	$0.218267\pi$
$744$		0			0
$745$	−527.134	+	913.023i	−0.707563	+	1.22553i
$746$		0			0
$747$	−7.00173	−	178.480i	−0.00937314	−	0.238928i
$748$		0			0
$749$	190.218	−	109.822i	0.253962	−	0.146625i
$750$		0			0
$751$			168.525i			0.224401i	0.993686	+	0.112200i	$0.0357898\pi$
$751$			168.525i			0.224401i	−0.993686	+	0.112200i	$0.964210\pi$
$752$		0			0
$753$	−315.627	+	91.2399i	−0.419159	+	0.121168i
$754$		0			0
$755$	788.435	+	455.203i	1.04429	+	0.602918i
$756$		0			0
$757$	510.495	−	884.204i	0.674366	−	1.16804i	−0.302287	−	0.953217i	$-0.597750\pi$
$757$	510.495	−	884.204i	0.674366	−	1.16804i	0.976654	−	0.214820i	$-0.0689164\pi$
$758$		0			0
$759$	−1670.78	+	482.983i	−2.20130	+	0.636341i
$760$		0			0
$761$	−505.546	+	875.632i	−0.664318	+	1.15063i	0.315151	+	0.949041i	$0.397945\pi$
$761$	−505.546	+	875.632i	−0.664318	+	1.15063i	−0.979470	+	0.201592i	$0.935389\pi$
$762$		0			0
$763$			64.4098i			0.0844165i
$764$		0			0
$765$	340.120	+	178.972i	0.444601	+	0.233950i
$766$		0			0
$767$	−175.706	−	304.332i	−0.229083	−	0.396783i
$768$		0			0
$769$	−56.6415			−0.0736560			−0.0368280	−	0.999322i	$-0.511725\pi$
$769$	−56.6415			−0.0736560			−0.0368280	+	0.999322i	$0.511725\pi$
$770$		0			0
$771$	−722.880	−	178.583i	−0.937588	−	0.231625i
$772$		0			0
$773$	−1027.30	+	593.110i	−1.32897	+	0.767283i	−0.985141	−	0.171749i	$-0.945058\pi$
$773$	−1027.30	+	593.110i	−1.32897	+	0.767283i	−0.343832	+	0.939031i	$0.611725\pi$
$774$		0			0
$775$	39.9824	−	23.0838i	0.0515901	−	0.0297856i
$776$		0			0
$777$	118.191	+	408.859i	0.152112	+	0.526202i
$778$		0			0
$779$	99.8229	−	615.119i	0.128142	−	0.789626i
$780$		0			0
$781$			972.595i			1.24532i
$782$		0			0
$783$	−715.656	+	237.649i	−0.913993	+	0.303511i
$784$		0			0
$785$	−264.403	+	457.959i	−0.336818	+	0.583387i
$786$		0			0
$787$	574.530	+	331.705i	0.730026	+	0.421481i	0.818432	−	0.574604i	$-0.194844\pi$
$787$	574.530	+	331.705i	0.730026	+	0.421481i	−0.0884057	+	0.996085i	$0.528177\pi$
$788$		0			0
$789$	333.441	−	1349.72i	0.422612	−	1.71068i
$790$		0			0
$791$		−	361.890i		−	0.457509i
$792$		0			0
$793$	−1379.49	−	796.451i	−1.73959	−	1.00435i
$794$		0			0
$795$	694.328	−	722.100i	0.873368	−	0.908302i
$796$		0			0
$797$	31.4026	+	18.1303i	0.0394010	+	0.0227482i	0.519571	−	0.854427i	$-0.326092\pi$
$797$	31.4026	+	18.1303i	0.0394010	+	0.0227482i	−0.480170	+	0.877175i	$0.659425\pi$
$798$		0			0
$799$	−103.578	−	179.403i	−0.129635	−	0.224535i
$800$		0			0
$801$	−22.5592	+	0.884995i	−0.0281638	+	0.00110486i
$802$		0			0
$803$	−1320.27			−1.64417
$804$		0			0
$805$	−483.730	+	837.846i	−0.600907	+	1.04080i
$806$		0			0
$807$	−501.629	+	521.694i	−0.621597	+	0.646460i
$808$		0			0
$809$	526.840			0.651224			0.325612	−	0.945504i	$-0.394430\pi$
$809$	526.840			0.651224			0.325612	+	0.945504i	$0.394430\pi$
$810$		0			0
$811$	−753.632	+	435.109i	−0.929262	+	0.536510i	−0.886578	−	0.462579i	$-0.846924\pi$
$811$	−753.632	+	435.109i	−0.929262	+	0.536510i	−0.0426841	+	0.999089i	$0.513591\pi$
$812$		0			0
$813$	−215.114	−	206.841i	−0.264593	−	0.254417i
$814$		0			0
$815$	426.102	+	738.031i	0.522825	+	0.905559i
$816$		0			0
$817$	−479.481	+	587.530i	−0.586880	+	0.719131i
$818$		0			0
$819$	1262.27	−	49.5187i	1.54123	−	0.0604623i
$820$		0			0
$821$	−648.515	+	1123.26i	−0.789909	+	1.36816i	0.136113	+	0.990693i	$0.456539\pi$
$821$	−648.515	+	1123.26i	−0.789909	+	1.36816i	−0.926022	+	0.377469i	$0.876794\pi$
$822$		0			0
$823$	−177.845			−0.216094			−0.108047	−	0.994146i	$-0.534460\pi$
$823$	−177.845			−0.216094			−0.108047	+	0.994146i	$0.534460\pi$
$824$		0			0
$825$	88.8170	−	359.519i	0.107657	−	0.435781i
$826$		0			0
$827$	1246.60	−	719.723i	1.50737	−	0.870282i	0.507409	−	0.861705i	$-0.330603\pi$
$827$	1246.60	−	719.723i	1.50737	−	0.870282i	0.999963	−	0.00857684i	$-0.00273013\pi$
$828$		0			0
$829$			365.186i			0.440514i	0.975442	+	0.220257i	$0.0706896\pi$
$829$			365.186i			0.440514i	−0.975442	+	0.220257i	$0.929310\pi$
$830$		0			0
$831$	−1357.28	+	392.357i	−1.63331	+	0.472150i
$832$		0			0
$833$	−95.8765	−	166.063i	−0.115098	−	0.199355i
$834$		0			0
$835$	−357.771	+	206.559i	−0.428468	+	0.247376i
$836$		0			0
$837$	127.091	−	42.2033i	0.151841	−	0.0504221i
$838$		0			0
$839$		−	1058.02i		−	1.26105i	−0.776170	−	0.630524i	$-0.782840\pi$
$839$		−	1058.02i		−	1.26105i	0.776170	−	0.630524i	$-0.217160\pi$
$840$		0			0
$841$	−30.4857	−	52.8028i	−0.0362494	−	0.0627857i
$842$		0			0
$843$	540.911	−	562.547i	0.641650	−	0.667316i
$844$		0			0
$845$	915.417	+	1585.55i	1.08333	+	1.87639i
$846$		0			0
$847$	−306.536			−0.361908
$848$		0			0
$849$	458.511	−	132.544i	0.540060	−	0.156118i
$850$		0			0
$851$			1110.06i			1.30442i
$852$		0			0
$853$	168.558			0.197606			0.0988030	−	0.995107i	$-0.468499\pi$
$853$	168.558			0.197606			0.0988030	+	0.995107i	$0.468499\pi$
$854$		0			0
$855$	541.183	+	407.384i	0.632962	+	0.476472i
$856$		0			0
$857$		−	134.996i		−	0.157522i	−0.996894	−	0.0787611i	$-0.974904\pi$
$857$		−	134.996i		−	0.157522i	0.996894	−	0.0787611i	$-0.0250964\pi$
$858$		0			0
$859$	297.949			0.346856			0.173428	−	0.984847i	$-0.444516\pi$
$859$	297.949			0.346856			0.173428	+	0.984847i	$0.444516\pi$
$860$		0			0
$861$	−381.012	+	396.252i	−0.442522	+	0.460223i
$862$		0			0
$863$		−	9.77430i		−	0.0113260i	−0.999984	−	0.00566298i	$-0.998197\pi$
$863$		−	9.77430i		−	0.0113260i	0.999984	−	0.00566298i	$-0.00180259\pi$
$864$		0			0
$865$	1147.22	−	662.350i	1.32627	−	0.765723i
$866$		0			0
$867$	−497.966	+	143.950i	−0.574355	+	0.166032i
$868$		0			0
$869$	−910.667	+	525.774i	−1.04795	+	0.605033i
$870$		0			0
$871$	2005.59			2.30263
$872$		0			0
$873$	−324.497	+	616.677i	−0.371703	+	0.706388i
$874$		0			0
$875$	−379.638	−	657.552i	−0.433872	−	0.751488i
$876$		0			0
$877$	−44.6279	+	25.7659i	−0.0508870	+	0.0293796i	−0.525228	−	0.850962i	$-0.676020\pi$
$877$	−44.6279	+	25.7659i	−0.0508870	+	0.0293796i	0.474341	+	0.880341i	$0.342687\pi$
$878$		0			0
$879$	−88.1018	+	91.6258i	−0.100230	+	0.104239i
$880$		0			0
$881$	−1119.78			−1.27103			−0.635515	−	0.772089i	$-0.719212\pi$
$881$	−1119.78			−1.27103			−0.635515	+	0.772089i	$0.719212\pi$
$882$		0			0
$883$	295.782	+	512.309i	0.334974	+	0.580192i	0.983480	−	0.181018i	$-0.0579392\pi$
$883$	295.782	+	512.309i	0.334974	+	0.580192i	−0.648506	+	0.761210i	$0.724606\pi$
$884$		0			0
$885$	−115.212	+	119.820i	−0.130183	+	0.135390i
$886$		0			0
$887$			1446.56i			1.63085i	0.578863	+	0.815424i	$0.303496\pi$
$887$			1446.56i			1.63085i	−0.578863	+	0.815424i	$0.696504\pi$
$888$		0			0
$889$	−638.784	−	368.802i	−0.718543	−	0.414851i
$890$		0			0
$891$	462.564	−	969.486i	0.519152	−	1.08809i
$892$		0			0
$893$	−129.547	−	341.353i	−0.145069	−	0.382254i
$894$		0			0
$895$	505.253	−	291.708i	0.564528	−	0.325931i
$896$		0			0
$897$	3198.66	+	790.211i	3.56596	+	0.880948i
$898$		0			0
$899$	−69.2614	−	119.964i	−0.0770427	−	0.133442i
$900$		0			0
$901$		−	908.737i		−	1.00859i
$902$		0			0
$903$	642.651	−	185.774i	0.711684	−	0.205730i
$904$		0			0
$905$	718.873	+	415.042i	0.794335	+	0.458610i
$906$		0			0
$907$		−	569.512i		−	0.627908i	−0.949438	−	0.313954i	$-0.898346\pi$
$907$		−	569.512i		−	0.627908i	0.949438	−	0.313954i	$-0.101654\pi$
$908$		0			0
$909$	456.201	−	287.803i	0.501872	−	0.316615i
$910$		0			0
$911$	−800.123	+	461.951i	−0.878290	+	0.507081i	−0.870094	−	0.492885i	$-0.835942\pi$
$911$	−800.123	+	461.951i	−0.878290	+	0.507081i	−0.00819605	+	0.999966i	$0.502609\pi$
$912$		0			0
$913$	131.596	−	227.931i	0.144136	−	0.249651i
$914$		0			0
$915$	−180.708	+	731.481i	−0.197495	+	0.799433i
$916$		0			0
$917$	−278.135	+	481.744i	−0.303310	+	0.525348i
$918$		0			0
$919$	−894.580			−0.973427			−0.486714	−	0.873562i	$-0.661804\pi$
$919$	−894.580			−0.973427			−0.486714	+	0.873562i	$0.661804\pi$
$920$		0			0
$921$	327.533	−	340.634i	0.355627	−	0.369852i
$922$		0			0
$923$	921.270	−	1595.69i	0.998125	−	1.72880i
$924$		0			0
$925$	−204.700	−	118.183i	−0.221297	−	0.127766i
$926$		0			0
$927$	−533.808	−	846.146i	−0.575844	−	0.912779i
$928$		0			0
$929$	−755.243			−0.812963			−0.406482	−	0.913659i	$-0.633244\pi$
$929$	−755.243			−0.812963			−0.406482	+	0.913659i	$0.633244\pi$
$930$		0			0
$931$	−119.914	−	315.970i	−0.128801	−	0.339388i
$932$		0			0
$933$	−111.301	−	107.021i	−0.119294	−	0.114706i
$934$		0			0
$935$	283.158	+	490.444i	0.302843	+	0.524539i
$936$		0			0
$937$	514.651	+	891.402i	0.549254	+	0.951336i	0.998326	+	0.0578406i	$0.0184215\pi$
$937$	514.651	+	891.402i	0.549254	+	0.951336i	−0.449071	+	0.893496i	$0.648245\pi$
$938$		0			0
$939$	887.563	+	853.427i	0.945222	+	0.908868i
$940$		0			0
$941$			623.200i			0.662274i	0.943583	+	0.331137i	$0.107432\pi$
$941$			623.200i			0.662274i	−0.943583	+	0.331137i	$0.892568\pi$
$942$		0			0
$943$	−1241.69	+	716.892i	−1.31675	+	0.760225i
$944$		0			0
$945$	−188.313	−	567.086i	−0.199273	−	0.600091i
$946$		0			0
$947$	82.7527			0.0873840			0.0436920	−	0.999045i	$-0.486088\pi$
$947$	82.7527			0.0873840			0.0436920	+	0.999045i	$0.486088\pi$
$948$		0			0
$949$	2166.10	+	1250.60i	2.28250	+	1.31780i
$950$		0			0
$951$	−170.433	+	177.250i	−0.179214	+	0.186383i
$952$		0			0
$953$	684.789	+	395.363i	0.718561	+	0.414861i	0.814223	−	0.580553i	$-0.197163\pi$
$953$	684.789	+	395.363i	0.718561	+	0.414861i	−0.0956618	+	0.995414i	$0.530497\pi$
$954$		0			0
$955$	−516.961	+	895.403i	−0.541321	+	0.937595i
$956$		0			0
$957$	−1078.71	−	266.489i	−1.12718	−	0.278463i
$958$		0			0
$959$	−609.411			−0.635465
$960$		0			0
$961$	−468.200	−	810.946i	−0.487201	−	0.843857i
$962$		0			0
$963$	−164.768	+	313.127i	−0.171099	+	0.325158i
$964$		0			0
$965$	−1088.61	−	628.509i	−1.12809	−	0.651304i
$966$		0			0
$967$	887.257	+	1536.77i	0.917536	+	1.58922i	0.803145	+	0.595783i	$0.203158\pi$
$967$	887.257	+	1536.77i	0.917536	+	1.58922i	0.114391	+	0.993436i	$0.463508\pi$
$968$		0			0
$969$	610.020	−	73.8804i	0.629535	−	0.0762439i
$970$		0			0
$971$	−1346.24	−	777.253i	−1.38645	−	0.800466i	−0.393535	−	0.919309i	$-0.628748\pi$
$971$	−1346.24	−	777.253i	−1.38645	−	0.800466i	−0.992913	+	0.118843i	$0.962081\pi$
$972$		0			0
$973$	11.7773	+	20.3989i	0.0121041	+	0.0209649i
$974$		0			0
$975$	−486.265	+	505.715i	−0.498733	+	0.518682i
$976$		0			0
$977$	−44.5449	−	25.7180i	−0.0455936	−	0.0263235i	0.477030	−	0.878887i	$-0.341713\pi$
$977$	−44.5449	−	25.7180i	−0.0455936	−	0.0263235i	−0.522624	+	0.852564i	$0.675047\pi$
$978$		0			0
$979$	−28.8097	−	16.6333i	−0.0294277	−	0.0169901i
$980$		0			0
$981$	−55.3625	−	87.7559i	−0.0564347	−	0.0894556i
$982$		0			0
$983$		−	1132.32i		−	1.15190i	−0.817484	−	0.575951i	$-0.804632\pi$
$983$		−	1132.32i		−	1.15190i	0.817484	−	0.575951i	$-0.195368\pi$
$984$		0			0
$985$	−232.272	−	402.306i	−0.235809	−	0.408433i
$986$		0			0
$987$	−77.2440	+	312.673i	−0.0782614	+	0.316792i
$988$		0			0
$989$	1744.81			1.76422
$990$		0			0
$991$	−391.151	−	225.831i	−0.394704	−	0.227882i	0.289492	−	0.957180i	$-0.406513\pi$
$991$	−391.151	−	225.831i	−0.394704	−	0.227882i	−0.684196	+	0.729298i	$0.739847\pi$
$992$		0			0
$993$	−394.240	−	1363.80i	−0.397019	−	1.37341i
$994$		0			0
$995$	448.216	−	776.332i	0.450468	−	0.780233i
$996$		0			0
$997$	−398.740	+	690.638i	−0.399940	+	0.692716i	−0.993718	−	0.111913i	$-0.964302\pi$
$997$	−398.740	+	690.638i	−0.399940	+	0.692716i	0.593778	+	0.804629i	$0.297636\pi$
$998$		0			0
$999$	−512.459	−	455.465i	−0.512972	−	0.455921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.16	✓	80
3.2	odd	2		2052.3.s.a.901.28		80
9.2	odd	6		2052.3.bl.a.1585.13		80
9.7	even	3		684.3.bl.a.673.30	yes	80
19.12	odd	6		684.3.bl.a.373.30	yes	80
57.50	even	6		2052.3.bl.a.145.13		80
171.88	odd	6	inner	684.3.s.a.601.16	yes	80
171.164	even	6		2052.3.s.a.829.28		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.16	✓	80	1.1	even	1	trivial
684.3.s.a.601.16	yes	80	171.88	odd	6	inner
684.3.bl.a.373.30	yes	80	19.12	odd	6
684.3.bl.a.673.30	yes	80	9.7	even	3
2052.3.s.a.829.28		80	171.164	even	6
2052.3.s.a.901.28		80	3.2	odd	2
2052.3.bl.a.145.13		80	57.50	even	6
2052.3.bl.a.1585.13		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.719501 + 2.91244i) q^{3} +(-1.98064 - 3.43056i) q^{5} +(2.79341 + 4.83834i) q^{7} +(-7.96464 - 4.19101i) q^{9} +O(q^{10})\)	\(q+(-0.719501 + 2.91244i) q^{3} +(-1.98064 - 3.43056i) q^{5} +(2.79341 + 4.83834i) q^{7} +(-7.96464 - 4.19101i) q^{9} +(-6.63076 - 11.4848i) q^{11} +25.1234i q^{13} +(11.4164 - 3.30019i) q^{15} +(5.39015 - 9.33602i) q^{17} +(12.0131 - 14.7202i) q^{19} +(-16.1012 + 4.65447i) q^{21} -43.7153 q^{23} +(4.65417 - 8.06125i) q^{25} +(17.9366 - 20.1811i) q^{27} +(-24.1872 - 13.9645i) q^{29} +(4.29533 + 2.47991i) q^{31} +(38.2197 - 11.0484i) q^{33} +(11.0655 - 19.1660i) q^{35} -25.3930i q^{37} +(-73.1704 - 18.0763i) q^{39} +(28.4041 - 16.3991i) q^{41} -39.9131 q^{43} +(1.39753 + 35.6240i) q^{45} +(9.60811 - 16.6417i) q^{47} +(8.89367 - 15.4043i) q^{49} +(23.3124 + 22.4158i) q^{51} +(73.0025 - 42.1480i) q^{53} +(-26.2662 + 45.4944i) q^{55} +(34.2284 + 45.5787i) q^{57} +(-12.1135 + 6.99374i) q^{59} +(-31.7016 + 54.9088i) q^{61} +(-1.97102 - 50.2428i) q^{63} +(86.1873 - 49.7602i) q^{65} -79.8298i q^{67} +(31.4532 - 127.318i) q^{69} +(-63.5140 - 36.6698i) q^{71} +(49.7782 - 86.2184i) q^{73} +(20.1293 + 19.3551i) q^{75} +(37.0449 - 64.1636i) q^{77} -79.2932i q^{79} +(45.8709 + 66.7597i) q^{81} +(9.92316 + 17.1874i) q^{83} -42.7037 q^{85} +(58.0735 - 60.3964i) q^{87} +(2.17243 - 1.25425i) q^{89} +(-121.555 + 70.1800i) q^{91} +(-10.3131 + 10.7256i) q^{93} +(-74.2922 - 12.0563i) q^{95} -77.4269i q^{97} +(4.67863 + 119.262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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