LMFDB - Embedded newform 684.3.m.a.353.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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, 1, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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			353.13
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61882 - 2.52575i) q^{3} -0.497329i q^{5} +(5.73504 - 9.93338i) q^{7} +(-3.75887 + 8.17746i) q^{9} +O(q^{10})$	\(q+(-1.61882 - 2.52575i) q^{3} -0.497329i q^{5} +(5.73504 - 9.93338i) q^{7} +(-3.75887 + 8.17746i) q^{9} +(-7.37787 - 4.25962i) q^{11} +(8.81568 - 15.2692i) q^{13} +(-1.25613 + 0.805085i) q^{15} +(-16.4117 - 9.47532i) q^{17} +(8.90449 + 16.7842i) q^{19} +(-34.3732 + 1.59501i) q^{21} +(0.354632 + 0.204747i) q^{23} +24.7527 q^{25} +(26.7392 - 3.74381i) q^{27} -38.4425i q^{29} +(9.63763 + 16.6929i) q^{31} +(1.18467 + 25.5302i) q^{33} +(-4.94016 - 2.85220i) q^{35} -43.9804 q^{37} +(-52.8373 + 2.45178i) q^{39} -29.4070i q^{41} +(-4.11810 - 7.13276i) q^{43} +(4.06689 + 1.86940i) q^{45} +41.4322i q^{47} +(-41.2813 - 71.5014i) q^{49} +(2.63524 + 56.7908i) q^{51} +(-79.4128 + 45.8490i) q^{53} +(-2.11843 + 3.66923i) q^{55} +(27.9781 - 49.6611i) q^{57} +22.8606i q^{59} -42.6238 q^{61} +(59.6725 + 84.2364i) q^{63} +(-7.59383 - 4.38430i) q^{65} +(-20.7667 + 35.9690i) q^{67} +(-0.0569435 - 1.22716i) q^{69} +(-61.3593 - 35.4258i) q^{71} +(-6.81675 + 11.8070i) q^{73} +(-40.0700 - 62.5192i) q^{75} +(-84.6248 + 48.8581i) q^{77} +(-27.0355 - 46.8269i) q^{79} +(-52.7418 - 61.4761i) q^{81} +(-63.5614 - 36.6972i) q^{83} +(-4.71236 + 8.16204i) q^{85} +(-97.0962 + 62.2312i) q^{87} +(10.0596 - 5.80794i) q^{89} +(-101.117 - 175.139i) q^{91} +(26.5605 - 51.3650i) q^{93} +(8.34729 - 4.42846i) q^{95} +(35.5215 + 61.5250i) q^{97} +(62.5654 - 44.3209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.61882	−	2.52575i	−0.539605	−	0.841918i
$3$	−1.61882	−	2.52575i	−0.539605	−	0.841918i
$4$		0			0
$5$		−	0.497329i		−	0.0994659i	−0.998763	−	0.0497329i	$-0.984163\pi$
$5$		−	0.497329i		−	0.0994659i	0.998763	−	0.0497329i	$-0.0158370\pi$
$6$		0			0
$7$	5.73504	−	9.93338i	0.819291	−	1.41905i	−0.0869140	−	0.996216i	$-0.527701\pi$
$7$	5.73504	−	9.93338i	0.819291	−	1.41905i	0.906205	−	0.422838i	$-0.138966\pi$
$8$		0			0
$9$	−3.75887	+	8.17746i	−0.417653	+	0.908607i
$10$		0			0
$11$	−7.37787	−	4.25962i	−0.670716	−	0.387238i	0.125632	−	0.992077i	$-0.459904\pi$
$11$	−7.37787	−	4.25962i	−0.670716	−	0.387238i	−0.796348	+	0.604839i	$0.793237\pi$
$12$		0			0
$13$	8.81568	−	15.2692i	0.678130	−	1.17455i	−0.297414	−	0.954749i	$-0.596124\pi$
$13$	8.81568	−	15.2692i	0.678130	−	1.17455i	0.975544	−	0.219806i	$-0.0705425\pi$
$14$		0			0
$15$	−1.25613	+	0.805085i	−0.0837421	+	0.0536723i
$16$		0			0
$17$	−16.4117	−	9.47532i	−0.965397	−	0.557372i	−0.0675668	−	0.997715i	$-0.521524\pi$
$17$	−16.4117	−	9.47532i	−0.965397	−	0.557372i	−0.897830	+	0.440343i	$0.854857\pi$
$18$		0			0
$19$	8.90449	+	16.7842i	0.468657	+	0.883380i
$19$	8.90449	+	16.7842i	0.468657	+	0.883380i
$20$		0			0
$21$	−34.3732	+	1.59501i	−1.63682	+	0.0759527i
$22$		0			0
$23$	0.354632	+	0.204747i	0.0154188	+	0.00890204i	0.507690	−	0.861540i	$-0.330500\pi$
$23$	0.354632	+	0.204747i	0.0154188	+	0.00890204i	−0.492271	+	0.870442i	$0.663833\pi$
$24$		0			0
$25$	24.7527			0.990107
$26$		0			0
$27$	26.7392	−	3.74381i	0.990340	−	0.138660i
$28$		0			0
$29$		−	38.4425i		−	1.32560i	−0.748796	−	0.662801i	$-0.769368\pi$
$29$		−	38.4425i		−	1.32560i	0.748796	−	0.662801i	$-0.230632\pi$
$30$		0			0
$31$	9.63763	+	16.6929i	0.310891	+	0.538479i	0.978556	−	0.205983i	$-0.0660392\pi$
$31$	9.63763	+	16.6929i	0.310891	+	0.538479i	−0.667664	+	0.744462i	$0.732706\pi$
$32$		0			0
$33$	1.18467	+	25.5302i	0.0358990	+	0.773644i
$34$		0			0
$35$	−4.94016	−	2.85220i	−0.141147	−	0.0814915i
$36$		0			0
$37$	−43.9804			−1.18866			−0.594329	−	0.804222i	$-0.702582\pi$
$37$	−43.9804			−1.18866			−0.594329	+	0.804222i	$0.702582\pi$
$38$		0			0
$39$	−52.8373	+	2.45178i	−1.35480	+	0.0628663i
$40$		0			0
$41$		−	29.4070i		−	0.717243i	−0.933483	−	0.358621i	$-0.883247\pi$
$41$		−	29.4070i		−	0.717243i	0.933483	−	0.358621i	$-0.116753\pi$
$42$		0			0
$43$	−4.11810	−	7.13276i	−0.0957698	−	0.165878i	0.814160	−	0.580641i	$-0.197198\pi$
$43$	−4.11810	−	7.13276i	−0.0957698	−	0.165878i	−0.909930	+	0.414763i	$0.863865\pi$
$44$		0			0
$45$	4.06689	+	1.86940i	0.0903754	+	0.0415422i
$46$		0			0
$47$			41.4322i			0.881535i	0.897621	+	0.440768i	$0.145294\pi$
$47$			41.4322i			0.881535i	−0.897621	+	0.440768i	$0.854706\pi$
$48$		0			0
$49$	−41.2813	−	71.5014i	−0.842476	−	1.45921i
$50$		0			0
$51$	2.63524	+	56.7908i	0.0516714	+	1.11355i
$52$		0			0
$53$	−79.4128	+	45.8490i	−1.49836	+	0.865076i	−0.999998	−	0.00189596i	$-0.999396\pi$
$53$	−79.4128	+	45.8490i	−1.49836	+	0.865076i	−0.498357	+	0.866972i	$0.666063\pi$
$54$		0			0
$55$	−2.11843	+	3.66923i	−0.0385170	+	0.0667134i
$56$		0			0
$57$	27.9781	−	49.6611i	0.490844	−	0.871247i
$58$		0			0
$59$			22.8606i			0.387467i	0.981054	+	0.193734i	$0.0620597\pi$
$59$			22.8606i			0.387467i	−0.981054	+	0.193734i	$0.937940\pi$
$60$		0			0
$61$	−42.6238			−0.698751			−0.349375	−	0.936983i	$-0.613606\pi$
$61$	−42.6238			−0.698751			−0.349375	+	0.936983i	$0.613606\pi$
$62$		0			0
$63$	59.6725	+	84.2364i	0.947183	+	1.33709i
$64$		0			0
$65$	−7.59383	−	4.38430i	−0.116828	−	0.0674508i
$66$		0			0
$67$	−20.7667	+	35.9690i	−0.309951	+	0.536851i	−0.978351	−	0.206950i	$-0.933646\pi$
$67$	−20.7667	+	35.9690i	−0.309951	+	0.536851i	0.668400	+	0.743802i	$0.266979\pi$
$68$		0			0
$69$	−0.0569435	−	1.22716i	−0.000825267	−	0.0177850i
$70$		0			0
$71$	−61.3593	−	35.4258i	−0.864216	−	0.498955i	0.00120604	−	0.999999i	$-0.499616\pi$
$71$	−61.3593	−	35.4258i	−0.864216	−	0.498955i	−0.865422	+	0.501044i	$0.832949\pi$
$72$		0			0
$73$	−6.81675	+	11.8070i	−0.0933801	+	0.161739i	−0.908931	−	0.416946i	$-0.863101\pi$
$73$	−6.81675	+	11.8070i	−0.0933801	+	0.161739i	0.815551	+	0.578685i	$0.196434\pi$
$74$		0			0
$75$	−40.0700	−	62.5192i	−0.534267	−	0.833589i
$76$		0			0
$77$	−84.6248	+	48.8581i	−1.09902	+	0.634521i
$78$		0			0
$79$	−27.0355	−	46.8269i	−0.342222	−	0.592746i	0.642623	−	0.766183i	$-0.277846\pi$
$79$	−27.0355	−	46.8269i	−0.342222	−	0.592746i	−0.984845	+	0.173436i	$0.944513\pi$
$80$		0			0
$81$	−52.7418	−	61.4761i	−0.651133	−	0.758964i
$82$		0			0
$83$	−63.5614	−	36.6972i	−0.765801	−	0.442135i	0.0655740	−	0.997848i	$-0.479112\pi$
$83$	−63.5614	−	36.6972i	−0.765801	−	0.442135i	−0.831374	+	0.555713i	$0.812446\pi$
$84$		0			0
$85$	−4.71236	+	8.16204i	−0.0554395	+	0.0960240i
$86$		0			0
$87$	−97.0962	+	62.2312i	−1.11605	+	0.715302i
$88$		0			0
$89$	10.0596	−	5.80794i	0.113030	−	0.0652577i	−0.442419	−	0.896808i	$-0.645880\pi$
$89$	10.0596	−	5.80794i	0.113030	−	0.0652577i	0.555449	+	0.831551i	$0.312546\pi$
$90$		0			0
$91$	−101.117	−	175.139i	−1.11117	−	1.92461i
$92$		0			0
$93$	26.5605	−	51.3650i	0.285597	−	0.552311i
$94$		0			0
$95$	8.34729	−	4.42846i	0.0878662	−	0.0466154i
$96$		0			0
$97$	35.5215	+	61.5250i	0.366201	+	0.634278i	0.988968	−	0.148129i	$-0.0473250\pi$
$97$	35.5215	+	61.5250i	0.366201	+	0.634278i	−0.622767	+	0.782407i	$0.713992\pi$
$98$		0			0
$99$	62.5654	−	44.3209i	0.631973	−	0.447686i
$100$		0			0
$101$			90.2859i			0.893920i	0.894554	+	0.446960i	$0.147493\pi$
$101$			90.2859i			0.893920i	−0.894554	+	0.446960i	$0.852507\pi$
$102$		0			0
$103$	36.6465	+	63.4737i	0.355792	+	0.616249i	0.987253	−	0.159158i	$-0.0508779\pi$
$103$	36.6465	+	63.4737i	0.355792	+	0.616249i	−0.631461	+	0.775407i	$0.717545\pi$
$104$		0			0
$105$	0.793244	+	17.0948i	0.00755470	+	0.162808i
$106$		0			0
$107$			126.872i			1.18572i	0.805307	+	0.592858i	$0.202001\pi$
$107$			126.872i			1.18572i	−0.805307	+	0.592858i	$0.797999\pi$
$108$		0			0
$109$	48.3118	−	83.6785i	0.443227	−	0.767692i	−0.554700	−	0.832051i	$-0.687167\pi$
$109$	48.3118	−	83.6785i	0.443227	−	0.767692i	0.997927	+	0.0643585i	$0.0205001\pi$
$110$		0			0
$111$	71.1961	+	111.084i	0.641407	+	1.00075i
$112$		0			0
$113$	161.886	−	93.4652i	1.43262	−	0.827125i	0.435303	−	0.900284i	$-0.356641\pi$
$113$	161.886	−	93.4652i	1.43262	−	0.827125i	0.997320	+	0.0731588i	$0.0233080\pi$
$114$		0			0
$115$	0.101827	−	0.176369i	0.000885450	−	0.00153364i
$116$		0			0
$117$	91.7264	+	129.485i	0.783986	+	1.10671i
$118$		0			0
$119$	−188.244	+	108.683i	−1.58188	+	0.913300i
$120$		0			0
$121$	−24.2113	−	41.9352i	−0.200093	−	0.346572i
$122$		0			0
$123$	−74.2748	+	47.6044i	−0.603860	+	0.387028i
$124$		0			0
$125$		−	24.7435i		−	0.197948i
$126$		0			0
$127$	73.2518	+	126.876i	0.576786	+	0.999022i	0.995845	+	0.0910631i	$0.0290265\pi$
$127$	73.2518	+	126.876i	0.576786	+	0.999022i	−0.419060	+	0.907959i	$0.637640\pi$
$128$		0			0
$129$	−11.3492	+	21.9479i	−0.0879780	+	0.170139i
$130$		0			0
$131$		−	89.7482i		−	0.685101i	−0.939499	−	0.342550i	$-0.888709\pi$
$131$		−	89.7482i		−	0.685101i	0.939499	−	0.342550i	$-0.111291\pi$
$132$		0			0
$133$	217.792	+	7.80653i	1.63753	+	0.0586957i
$134$		0			0
$135$	−1.86191	−	13.2982i	−0.0137919	−	0.0985051i
$136$		0			0
$137$		−	74.0234i		−	0.540317i	−0.962816	−	0.270158i	$-0.912924\pi$
$137$		−	74.0234i		−	0.540317i	0.962816	−	0.270158i	$-0.0870760\pi$
$138$		0			0
$139$	123.835	−	214.489i	0.890902	−	1.54309i	0.0521064	−	0.998642i	$-0.483407\pi$
$139$	123.835	−	214.489i	0.890902	−	1.54309i	0.838796	−	0.544446i	$-0.183260\pi$
$140$		0			0
$141$	104.647	−	67.0710i	0.742181	−	0.475681i
$142$		0			0
$143$	−130.082	+	75.1029i	−0.909665	+	0.525195i
$144$		0			0
$145$	−19.1186			−0.131852
$146$		0			0
$147$	−113.768	+	220.014i	−0.773932	+	1.49669i
$148$		0			0
$149$		−	93.9704i		−	0.630674i	−0.948980	−	0.315337i	$-0.897882\pi$
$149$		−	93.9704i		−	0.630674i	0.948980	−	0.315337i	$-0.102118\pi$
$150$		0			0
$151$	−3.13122	+	5.42344i	−0.0207366	+	0.0359168i	−0.876207	−	0.481934i	$-0.839934\pi$
$151$	−3.13122	+	5.42344i	−0.0207366	+	0.0359168i	0.855471	+	0.517851i	$0.173268\pi$
$152$		0			0
$153$	139.174	−	98.5899i	0.909632	−	0.644378i
$154$		0			0
$155$	8.30185	−	4.79308i	0.0535603	−	0.0309231i
$156$		0			0
$157$	14.9879			0.0954644			0.0477322	−	0.998860i	$-0.484801\pi$
$157$	14.9879			0.0954644			0.0477322	+	0.998860i	$0.484801\pi$
$158$		0			0
$159$	244.358	+	126.356i	1.53684	+	0.794693i
$160$		0			0
$161$	4.06766	−	2.34846i	0.0252650	−	0.0145867i
$162$		0			0
$163$	0.718713			0.00440928			0.00220464	−	0.999998i	$-0.499298\pi$
$163$	0.718713			0.00440928			0.00220464	+	0.999998i	$0.499298\pi$
$164$		0			0
$165$	12.6969	−	0.589171i	0.0769511	−	0.00357073i
$166$		0			0
$167$	−277.850	−	160.417i	−1.66377	−	0.960580i	−0.970888	−	0.239533i	$-0.923006\pi$
$167$	−277.850	−	160.417i	−1.66377	−	0.960580i	−0.692886	−	0.721047i	$-0.743661\pi$
$168$		0			0
$169$	−70.9326	−	122.859i	−0.419720	−	0.726976i
$170$		0			0
$171$	−170.723	+	9.72634i	−0.998381	+	0.0568792i
$172$		0			0
$173$	121.498	−	70.1467i	0.702299	−	0.405473i	−0.105904	−	0.994376i	$-0.533774\pi$
$173$	121.498	−	70.1467i	0.702299	−	0.405473i	0.808203	+	0.588904i	$0.200440\pi$
$174$		0			0
$175$	141.957	−	245.878i	0.811186	−	1.40501i
$176$		0			0
$177$	57.7402	−	37.0070i	0.326216	−	0.209079i
$178$		0			0
$179$		−	91.6384i		−	0.511946i	−0.966684	−	0.255973i	$-0.917604\pi$
$179$		−	91.6384i		−	0.511946i	0.966684	−	0.255973i	$-0.0823959\pi$
$180$		0			0
$181$	−122.574	−	212.304i	−0.677203	−	1.17295i	−0.975820	−	0.218577i	$-0.929859\pi$
$181$	−122.574	−	212.304i	−0.677203	−	1.17295i	0.298617	−	0.954373i	$-0.403475\pi$
$182$		0			0
$183$	69.0001	+	107.657i	0.377050	+	0.588291i
$184$		0			0
$185$			21.8727i			0.118231i
$186$		0			0
$187$	80.7225	+	139.816i	0.431671	+	0.747676i
$188$		0			0
$189$	116.162	−	287.081i	0.614611	−	1.51895i
$190$		0			0
$191$	302.171	+	174.459i	1.58205	+	0.913396i	0.994560	+	0.104162i	$0.0332161\pi$
$191$	302.171	+	174.459i	1.58205	+	0.913396i	0.587487	+	0.809233i	$0.300117\pi$
$192$		0			0
$193$	122.335			0.633858			0.316929	−	0.948449i	$-0.397348\pi$
$193$	122.335			0.633858			0.316929	+	0.948449i	$0.397348\pi$
$194$		0			0
$195$	1.21934	+	26.2775i	0.00625305	+	0.134757i
$196$		0			0
$197$			55.4953i			0.281702i	0.990031	+	0.140851i	$0.0449839\pi$
$197$			55.4953i			0.281702i	−0.990031	+	0.140851i	$0.955016\pi$
$198$		0			0
$199$	−20.1790	−	34.9511i	−0.101402	−	0.175633i	0.810861	−	0.585239i	$-0.198999\pi$
$199$	−20.1790	−	34.9511i	−0.101402	−	0.175633i	−0.912263	+	0.409606i	$0.865666\pi$
$200$		0			0
$201$	124.467	−	5.77557i	0.619236	−	0.0287342i
$202$		0			0
$203$	−381.863	−	220.469i	−1.88110	−	1.08605i
$204$		0			0
$205$	−14.6249			−0.0713412
$206$		0			0
$207$	−3.00733	+	2.13037i	−0.0145282	+	0.0102917i
$208$		0			0
$209$	5.79819	−	161.762i	0.0277425	−	0.773979i
$210$		0			0
$211$	284.667			1.34913			0.674565	−	0.738215i	$-0.264331\pi$
$211$	284.667			1.34913			0.674565	+	0.738215i	$0.264331\pi$
$212$		0			0
$213$	9.85249	+	212.326i	0.0462558	+	0.996838i
$214$		0			0
$215$	−3.54733	+	2.04805i	−0.0164992	+	0.00952583i
$216$		0			0
$217$	221.089			1.01884
$218$		0			0
$219$	40.8565	−	1.89585i	0.186559	−	0.00865684i
$220$		0			0
$221$	−289.361	+	167.063i	−1.30933	+	0.755941i
$222$		0			0
$223$	99.7841	+	172.831i	0.447463	+	0.775028i	0.998220	−	0.0596374i	$-0.0189944\pi$
$223$	99.7841	+	172.831i	0.447463	+	0.775028i	−0.550758	+	0.834665i	$0.685661\pi$
$224$		0			0
$225$	−93.0421	+	202.414i	−0.413520	+	0.899618i
$226$		0			0
$227$	373.638	+	215.720i	1.64598	+	0.950307i	0.978647	+	0.205548i	$0.0658978\pi$
$227$	373.638	+	215.720i	1.64598	+	0.950307i	0.667334	+	0.744759i	$0.267436\pi$
$228$		0			0
$229$	−120.604	−	208.892i	−0.526655	−	0.912193i	−0.999518	−	0.0310572i	$-0.990113\pi$
$229$	−120.604	−	208.892i	−0.526655	−	0.912193i	0.472862	−	0.881136i	$-0.343221\pi$
$230$		0			0
$231$	260.396	+	134.649i	1.12725	+	0.582897i
$232$		0			0
$233$	−51.7582	−	29.8826i	−0.222138	−	0.128252i	0.384802	−	0.922999i	$-0.374270\pi$
$233$	−51.7582	−	29.8826i	−0.222138	−	0.128252i	−0.606940	+	0.794748i	$0.707603\pi$
$234$		0			0
$235$	20.6054			0.0876827
$236$		0			0
$237$	−74.5078	+	144.089i	−0.314379	+	0.607972i
$238$		0			0
$239$	−321.259	+	185.479i	−1.34418	+	0.776062i	−0.987418	−	0.158134i	$-0.949452\pi$
$239$	−321.259	+	185.479i	−1.34418	+	0.776062i	−0.356760	+	0.934196i	$0.616119\pi$
$240$		0			0
$241$	233.378			0.968374			0.484187	−	0.874965i	$-0.339116\pi$
$241$	233.378			0.968374			0.484187	+	0.874965i	$0.339116\pi$
$242$		0			0
$243$	−69.8943	+	232.731i	−0.287631	+	0.957741i
$244$		0			0
$245$	−35.5597	+	20.5304i	−0.145142	+	0.0837976i
$246$		0			0
$247$	334.781	+	11.9999i	1.35539	+	0.0485826i
$248$		0			0
$249$	10.2061	+	219.947i	0.0409883	+	0.883320i
$250$		0			0
$251$	284.054	−	163.999i	1.13169	−	0.653381i	0.187330	−	0.982297i	$-0.440017\pi$
$251$	284.054	−	163.999i	1.13169	−	0.653381i	0.944359	+	0.328916i	$0.106683\pi$
$252$		0			0
$253$	−1.74429	−	3.02120i	−0.00689442	−	0.0119415i
$254$		0			0
$255$	28.2438	−	1.31058i	0.110760	−	0.00513954i
$256$		0			0
$257$	271.570	+	156.791i	1.05669	+	0.610083i	0.924516	−	0.381143i	$-0.124470\pi$
$257$	271.570	+	156.791i	1.05669	+	0.610083i	0.132178	+	0.991226i	$0.457803\pi$
$258$		0			0
$259$	−252.229	+	436.874i	−0.973858	+	1.68677i
$260$		0			0
$261$	314.362	+	144.500i	1.20445	+	0.553641i
$262$		0			0
$263$	366.591	−	211.651i	1.39388	−	0.804758i	0.400140	−	0.916454i	$-0.368962\pi$
$263$	366.591	−	211.651i	1.39388	−	0.804758i	0.993742	+	0.111696i	$0.0356283\pi$
$264$		0			0
$265$	22.8021	+	39.4943i	0.0860455	+	0.149035i
$266$		0			0
$267$	−30.9541	−	16.0062i	−0.115933	−	0.0599483i
$268$		0			0
$269$	−286.799	−	165.584i	−1.06617	−	0.615553i	−0.139037	−	0.990287i	$-0.544401\pi$
$269$	−286.799	−	165.584i	−1.06617	−	0.615553i	−0.927132	+	0.374734i	$0.877734\pi$
$270$		0			0
$271$	136.655	−	236.694i	0.504263	−	0.873409i	−0.495725	−	0.868480i	$-0.665098\pi$
$271$	136.655	−	236.694i	0.504263	−	0.873409i	0.999988	−	0.00492935i	$-0.00156907\pi$
$272$		0			0
$273$	−278.669	+	538.914i	−1.02077	+	1.97404i
$274$		0			0
$275$	−182.622	−	105.437i	−0.664080	−	0.383407i
$276$		0			0
$277$	146.869	−	254.384i	0.530213	−	0.918355i	−0.469166	−	0.883110i	$-0.655445\pi$
$277$	146.869	−	254.384i	0.530213	−	0.918355i	0.999379	−	0.0352453i	$-0.0112212\pi$
$278$		0			0
$279$	−172.732	+	16.0650i	−0.619111	+	0.0575806i
$280$		0			0
$281$			220.492i			0.784670i	0.919822	+	0.392335i	$0.128333\pi$
$281$			220.492i			0.784670i	−0.919822	+	0.392335i	$0.871667\pi$
$282$		0			0
$283$	−172.057			−0.607974			−0.303987	−	0.952676i	$-0.598318\pi$
$283$	−172.057			−0.607974			−0.303987	+	0.952676i	$0.598318\pi$
$284$		0			0
$285$	−24.6979	−	13.9143i	−0.0866594	−	0.0488222i
$286$		0			0
$287$	−292.110	−	168.650i	−1.01781	−	0.587631i
$288$		0			0
$289$	35.0635	+	60.7318i	0.121327	+	0.210145i
$290$		0			0
$291$	97.8943	−	189.316i	0.336407	−	0.650571i
$292$		0			0
$293$	−387.752	+	223.869i	−1.32339	+	0.764057i	−0.984267	−	0.176686i	$-0.943462\pi$
$293$	−387.752	+	223.869i	−1.32339	+	0.764057i	−0.339119	+	0.940743i	$0.610129\pi$
$294$		0			0
$295$	11.3692			0.0385398
$296$		0			0
$297$	−213.226	−	86.2773i	−0.717931	−	0.290496i
$298$		0			0
$299$	6.25265	−	3.60997i	0.0209119	−	0.0120735i
$300$		0			0
$301$	−94.4699			−0.313854
$302$		0			0
$303$	228.040	−	146.156i	0.752608	−	0.482364i
$304$		0			0
$305$			21.1981i			0.0695019i
$306$		0			0
$307$	−98.5500	+	170.694i	−0.321010	+	0.556005i	−0.980697	−	0.195535i	$-0.937356\pi$
$307$	−98.5500	+	170.694i	−0.321010	+	0.556005i	0.659687	+	0.751541i	$0.270689\pi$
$308$		0			0
$309$	100.995	−	195.312i	0.326844	−	0.632079i
$310$		0			0
$311$	−143.204	+	82.6790i	−0.460464	+	0.265849i	−0.712239	−	0.701937i	$-0.752319\pi$
$311$	−143.204	+	82.6790i	−0.460464	+	0.265849i	0.251776	+	0.967786i	$0.418986\pi$
$312$		0			0
$313$	−482.577			−1.54178			−0.770890	−	0.636968i	$-0.780188\pi$
$313$	−482.577			−1.54178			−0.770890	+	0.636968i	$0.780188\pi$
$314$		0			0
$315$	41.8932	−	29.6769i	0.132994	−	0.0942124i
$316$		0			0
$317$			49.4053i			0.155853i	0.996959	+	0.0779264i	$0.0248299\pi$
$317$			49.4053i			0.155853i	−0.996959	+	0.0779264i	$0.975170\pi$
$318$		0			0
$319$	−163.750	+	283.624i	−0.513323	+	0.889102i
$320$		0			0
$321$	320.447	−	205.382i	0.998277	−	0.639819i
$322$		0			0
$323$	12.8978	−	359.831i	0.0399313	−	1.11403i
$324$		0			0
$325$	218.212	−	377.954i	0.671421	−	1.16293i
$326$		0			0
$327$	−289.559	+	13.4363i	−0.885502	+	0.0410896i
$328$		0			0
$329$	411.561	+	237.615i	1.25095	+	0.722234i
$330$		0			0
$331$	74.7326	−	129.441i	0.225778	−	0.391059i	−0.730774	−	0.682619i	$-0.760841\pi$
$331$	74.7326	−	129.441i	0.225778	−	0.391059i	0.956553	+	0.291560i	$0.0941742\pi$
$332$		0			0
$333$	165.317	−	359.648i	0.496446	−	1.08002i
$334$		0			0
$335$	17.8885	+	10.3279i	0.0533984	+	0.0308296i
$336$		0			0
$337$	528.937			1.56955			0.784773	−	0.619784i	$-0.212780\pi$
$337$	528.937			1.56955			0.784773	+	0.619784i	$0.212780\pi$
$338$		0			0
$339$	−498.134	−	257.582i	−1.46942	−	0.759830i
$340$		0			0
$341$		−	164.210i		−	0.481556i
$342$		0			0
$343$	−384.966			−1.12235
$344$		0			0
$345$	−0.610304	+	0.0283197i	−0.00176900	+	8.20860e-5i
$346$		0			0
$347$		−	410.266i		−	1.18232i	−0.806553	−	0.591161i	$-0.798670\pi$
$347$		−	410.266i		−	1.18232i	0.806553	−	0.591161i	$-0.201330\pi$
$348$		0			0
$349$	284.123	−	492.115i	0.814105	−	1.41007i	−0.0958635	−	0.995394i	$-0.530561\pi$
$349$	284.123	−	492.115i	0.814105	−	1.41007i	0.909969	−	0.414677i	$-0.136105\pi$
$350$		0			0
$351$	178.559	−	441.291i	0.508715	−	1.25724i
$352$		0			0
$353$	275.399	+	159.002i	0.780167	+	0.450430i	0.836490	−	0.547983i	$-0.184604\pi$
$353$	275.399	+	159.002i	0.780167	+	0.450430i	−0.0563223	+	0.998413i	$0.517937\pi$
$354$		0			0
$355$	−17.6183	+	30.5158i	−0.0496290	+	0.0859600i
$356$		0			0
$357$	579.238	+	299.521i	1.62252	+	0.838994i
$358$		0			0
$359$	400.232	+	231.074i	1.11485	+	0.643661i	0.940082	−	0.340948i	$-0.110748\pi$
$359$	400.232	+	231.074i	1.11485	+	0.643661i	0.174771	+	0.984609i	$0.444081\pi$
$360$		0			0
$361$	−202.420	+	298.910i	−0.560721	+	0.828005i
$362$		0			0
$363$	−66.7244	+	129.037i	−0.183814	+	0.355474i
$364$		0			0
$365$	5.87195	+	3.39017i	0.0160875	+	0.00928814i
$366$		0			0
$367$	−554.503			−1.51091			−0.755454	−	0.655201i	$-0.772584\pi$
$367$	−554.503			−1.51091			−0.755454	+	0.655201i	$0.772584\pi$
$368$		0			0
$369$	240.474	+	110.537i	0.651692	+	0.299558i
$370$		0			0
$371$			1051.78i			2.83500i
$372$		0			0
$373$	−297.536	−	515.347i	−0.797682	−	1.38163i	−0.921122	−	0.389274i	$-0.872726\pi$
$373$	−297.536	−	515.347i	−0.797682	−	1.38163i	0.123439	−	0.992352i	$-0.460608\pi$
$374$		0			0
$375$	−62.4959	+	40.0551i	−0.166656	+	0.106814i
$376$		0			0
$377$	−586.986	−	338.897i	−1.55699	−	0.898930i
$378$		0			0
$379$	−459.057			−1.21123			−0.605616	−	0.795757i	$-0.707073\pi$
$379$	−459.057			−1.21123			−0.605616	+	0.795757i	$0.707073\pi$
$380$		0			0
$381$	201.876	−	390.404i	0.529858	−	1.02468i
$382$		0			0
$383$			306.676i			0.800720i	0.916358	+	0.400360i	$0.131115\pi$
$383$			306.676i			0.800720i	−0.916358	+	0.400360i	$0.868885\pi$
$384$		0			0
$385$	24.2986	+	42.0864i	0.0631132	+	0.109315i
$386$		0			0
$387$	73.8073	−	6.86448i	0.190717	−	0.0177377i
$388$		0			0
$389$			152.250i			0.391389i	0.980665	+	0.195694i	$0.0626961\pi$
$389$			152.250i			0.391389i	−0.980665	+	0.195694i	$0.937304\pi$
$390$		0			0
$391$	−3.88009	−	6.72051i	−0.00992350	−	0.0171880i
$392$		0			0
$393$	−226.682	+	145.286i	−0.576799	+	0.369684i
$394$		0			0
$395$	−23.2884	+	13.4456i	−0.0589580	+	0.0340394i
$396$		0			0
$397$	106.852	−	185.072i	0.269148	−	0.466177i	−0.699494	−	0.714638i	$-0.746591\pi$
$397$	106.852	−	185.072i	0.269148	−	0.466177i	0.968642	+	0.248461i	$0.0799247\pi$
$398$		0			0
$399$	−332.847	−	562.725i	−0.834203	−	1.41034i
$400$		0			0
$401$			276.604i			0.689786i	0.938642	+	0.344893i	$0.112085\pi$
$401$			276.604i			0.689786i	−0.938642	+	0.344893i	$0.887915\pi$
$402$		0			0
$403$	339.849			0.843298
$404$		0			0
$405$	−30.5739	+	26.2300i	−0.0754910	+	0.0647655i
$406$		0			0
$407$	324.482	+	187.340i	0.797252	+	0.460294i
$408$		0			0
$409$	−182.327	+	315.800i	−0.445787	+	0.772126i	−0.998107	−	0.0615063i	$-0.980410\pi$
$409$	−182.327	+	315.800i	−0.445787	+	0.772126i	0.552319	+	0.833633i	$0.313743\pi$
$410$		0			0
$411$	−186.965	+	119.830i	−0.454902	+	0.291558i
$412$		0			0
$413$	227.083	+	131.106i	0.549837	+	0.317448i
$414$		0			0
$415$	−18.2506	+	31.6110i	−0.0439774	+	0.0761710i
$416$		0			0
$417$	−742.214	+	34.4406i	−1.77989	+	0.0825914i
$418$		0			0
$419$	−448.751	+	259.086i	−1.07100	+	0.618344i	−0.928456	−	0.371444i	$-0.878863\pi$
$419$	−448.751	+	259.086i	−1.07100	+	0.618344i	−0.142548	+	0.989788i	$0.545530\pi$
$420$		0			0
$421$	−178.083	−	308.449i	−0.423001	−	0.732659i	0.573231	−	0.819394i	$-0.305690\pi$
$421$	−178.083	−	308.449i	−0.423001	−	0.732659i	−0.996231	+	0.0867352i	$0.972357\pi$
$422$		0			0
$423$	−338.810	−	155.738i	−0.800969	−	0.368175i
$424$		0			0
$425$	−406.234	−	234.539i	−0.955845	−	0.551858i
$426$		0			0
$427$	−244.449	+	423.398i	−0.572480	+	0.991565i
$428$		0			0
$429$	400.270	+	206.978i	0.933031	+	0.482465i
$430$		0			0
$431$	733.752	−	423.632i	1.70244	−	0.982904i	0.759161	−	0.650902i	$-0.225609\pi$
$431$	733.752	−	423.632i	1.70244	−	0.982904i	0.943279	−	0.332002i	$-0.107724\pi$
$432$		0			0
$433$	22.9957	+	39.8296i	0.0531077	+	0.0919853i	0.891357	−	0.453302i	$-0.149754\pi$
$433$	22.9957	+	39.8296i	0.0531077	+	0.0919853i	−0.838249	+	0.545287i	$0.816421\pi$
$434$		0			0
$435$	30.9494	+	48.2888i	0.0711481	+	0.111009i
$436$		0			0
$437$	−0.278702	+	7.77539i	−0.000637761	+	0.0177927i
$438$		0			0
$439$	178.960	+	309.968i	0.407653	+	0.706076i	0.994626	−	0.103530i	$-0.0330138\pi$
$439$	178.960	+	309.968i	0.407653	+	0.706076i	−0.586973	+	0.809607i	$0.699680\pi$
$440$		0			0
$441$	739.871	−	68.8120i	1.67771	−	0.156036i
$442$		0			0
$443$		−	192.136i		−	0.433717i	−0.976203	−	0.216858i	$-0.930419\pi$
$443$		−	192.136i		−	0.433717i	0.976203	−	0.216858i	$-0.0695810\pi$
$444$		0			0
$445$	−2.88846	−	5.00296i	−0.00649092	−	0.0112426i
$446$		0			0
$447$	−237.346	+	152.121i	−0.530976	+	0.340315i
$448$		0			0
$449$		−	332.574i		−	0.740700i	−0.928892	−	0.370350i	$-0.879238\pi$
$449$		−	332.574i		−	0.740700i	0.928892	−	0.370350i	$-0.120762\pi$
$450$		0			0
$451$	−125.262	+	216.961i	−0.277744	+	0.481066i
$452$		0			0
$453$	18.7671	−	0.870844i	0.0414286	−	0.00192239i
$454$		0			0
$455$	−87.1018	+	50.2883i	−0.191433	+	0.110524i
$456$		0			0
$457$	391.702	−	678.447i	0.857115	−	1.48457i	−0.0175537	−	0.999846i	$-0.505588\pi$
$457$	391.702	−	678.447i	0.857115	−	1.48457i	0.874669	−	0.484721i	$-0.161079\pi$
$458$		0			0
$459$	−474.310	−	191.920i	−1.03336	−	0.418126i
$460$		0			0
$461$	16.7213	−	9.65408i	0.0362719	−	0.0209416i	−0.481754	−	0.876306i	$-0.660000\pi$
$461$	16.7213	−	9.65408i	0.0362719	−	0.0209416i	0.518026	+	0.855365i	$0.326667\pi$
$462$		0			0
$463$	−108.494	−	187.918i	−0.234329	−	0.405870i	0.724748	−	0.689014i	$-0.241956\pi$
$463$	−108.494	−	187.918i	−0.234329	−	0.405870i	−0.959078	+	0.283144i	$0.908623\pi$
$464$		0			0
$465$	−25.5453	−	13.2093i	−0.0549361	−	0.0284072i
$466$		0			0
$467$		−	472.704i		−	1.01221i	−0.862471	−	0.506107i	$-0.831084\pi$
$467$		−	472.704i		−	1.01221i	0.862471	−	0.506107i	$-0.168916\pi$
$468$		0			0
$469$	238.196	+	412.568i	0.507881	+	0.879675i
$470$		0			0
$471$	−24.2627	−	37.8558i	−0.0515131	−	0.0803733i
$472$		0			0
$473$			70.1662i			0.148343i
$474$		0			0
$475$	220.410	+	415.454i	0.464021	+	0.874640i
$476$		0			0
$477$	−76.4259	−	821.736i	−0.160222	−	1.72272i
$478$		0			0
$479$		−	729.153i		−	1.52224i	−0.648611	−	0.761120i	$-0.724650\pi$
$479$		−	729.153i		−	1.52224i	0.648611	−	0.761120i	$-0.275350\pi$
$480$		0			0
$481$	−387.717	+	671.546i	−0.806065	+	1.39615i
$482$		0			0
$483$	−12.5164	−	6.47218i	−0.0259139	−	0.0134000i
$484$		0			0
$485$	30.5982	−	17.6659i	0.0630891	−	0.0364245i
$486$		0			0
$487$	346.901			0.712323			0.356162	−	0.934424i	$-0.384085\pi$
$487$	346.901			0.712323			0.356162	+	0.934424i	$0.384085\pi$
$488$		0			0
$489$	−1.16346	−	1.81529i	−0.00237927	−	0.00371225i
$490$		0			0
$491$		−	956.995i		−	1.94907i	−0.224229	−	0.974536i	$-0.571986\pi$
$491$		−	956.995i		−	1.94907i	0.224229	−	0.974536i	$-0.428014\pi$
$492$		0			0
$493$	−364.255	+	630.908i	−0.738853	+	1.27973i
$494$		0			0
$495$	−22.0421	−	31.1156i	−0.0445295	−	0.0628598i
$496$		0			0
$497$	−703.796	+	406.337i	−1.41609	+	0.817579i
$498$		0			0
$499$	−620.566			−1.24362			−0.621810	−	0.783168i	$-0.713602\pi$
$499$	−620.566			−1.24362			−0.621810	+	0.783168i	$0.713602\pi$
$500$		0			0
$501$	44.6145	+	961.467i	0.0890510	+	1.91910i
$502$		0			0
$503$	−27.5529	+	15.9077i	−0.0547771	+	0.0316256i	−0.527138	−	0.849779i	$-0.676735\pi$
$503$	−27.5529	+	15.9077i	−0.0547771	+	0.0316256i	0.472361	+	0.881405i	$0.343402\pi$
$504$		0			0
$505$	44.9019			0.0889146
$506$		0			0
$507$	−195.485	+	378.044i	−0.385571	+	0.745649i
$508$		0			0
$509$	−8.37872	−	4.83746i	−0.0164611	−	0.00950385i	0.491747	−	0.870738i	$-0.336359\pi$
$509$	−8.37872	−	4.83746i	−0.0164611	−	0.00950385i	−0.508208	+	0.861234i	$0.669692\pi$
$510$		0			0
$511$	78.1886	+	135.427i	0.153011	+	0.265023i
$512$		0			0
$513$	300.936	+	415.460i	0.586619	+	0.809863i
$514$		0			0
$515$	31.5673	−	18.2254i	0.0612958	−	0.0353891i
$516$		0			0
$517$	176.485	−	305.681i	0.341364	−	0.591260i
$518$		0			0
$519$	−373.856	−	193.319i	−0.720339	−	0.372483i
$520$		0			0
$521$		−	758.567i		−	1.45598i	−0.685587	−	0.727991i	$-0.740454\pi$
$521$		−	758.567i		−	1.45598i	0.685587	−	0.727991i	$-0.259546\pi$
$522$		0			0
$523$	340.486	+	589.739i	0.651024	+	1.12761i	0.982875	+	0.184275i	$0.0589938\pi$
$523$	340.486	+	589.739i	0.651024	+	1.12761i	−0.331850	+	0.943332i	$0.607673\pi$
$524$		0			0
$525$	−850.829	+	39.4807i	−1.62063	+	0.0752013i
$526$		0			0
$527$		−	365.279i		−	0.693128i
$528$		0			0
$529$	−264.416	−	457.982i	−0.499842	−	0.865751i
$530$		0			0
$531$	−186.941	−	85.9299i	−0.352055	−	0.161827i
$532$		0			0
$533$	−449.021	−	259.242i	−0.842441	−	0.486384i
$534$		0			0
$535$	63.0970			0.117938
$536$		0			0
$537$	−231.456	+	148.346i	−0.431017	+	0.276249i
$538$		0			0
$539$			703.371i			1.30496i
$540$		0			0
$541$	−352.751	−	610.983i	−0.652035	−	1.12936i	−0.982628	−	0.185585i	$-0.940582\pi$
$541$	−352.751	−	610.983i	−0.652035	−	1.12936i	0.330593	−	0.943774i	$-0.392751\pi$
$542$		0			0
$543$	−337.803	+	653.272i	−0.622106	+	1.20308i
$544$		0			0
$545$	−41.6158	−	24.0269i	−0.0763592	−	0.0440860i
$546$		0			0
$547$	−184.307			−0.336942			−0.168471	−	0.985707i	$-0.553883\pi$
$547$	−184.307			−0.336942			−0.168471	+	0.985707i	$0.553883\pi$
$548$		0			0
$549$	160.217	−	348.554i	0.291835	−	0.634890i
$550$		0			0
$551$	645.227	−	342.310i	1.17101	−	0.621253i
$552$		0			0
$553$	−620.200			−1.12152
$554$		0			0
$555$	55.2452	−	35.4079i	0.0995409	−	0.0637981i
$556$		0			0
$557$	−406.427	+	234.651i	−0.729672	+	0.421276i	−0.818302	−	0.574788i	$-0.805084\pi$
$557$	−406.427	+	234.651i	−0.729672	+	0.421276i	0.0886301	+	0.996065i	$0.471751\pi$
$558$		0			0
$559$	−145.216			−0.259777
$560$		0			0
$561$	222.465	−	430.221i	0.396550	−	0.766882i
$562$		0			0
$563$	143.084	−	82.6098i	0.254146	−	0.146731i	−0.367515	−	0.930018i	$-0.619791\pi$
$563$	143.084	−	82.6098i	0.254146	−	0.146731i	0.621661	+	0.783286i	$0.286458\pi$
$564$		0			0
$565$	−46.4830	−	80.5109i	−0.0822708	−	0.142497i
$566$		0			0
$567$	−913.141	+	171.336i	−1.61048	+	0.302180i
$568$		0			0
$569$	45.8090	+	26.4478i	0.0805079	+	0.0464813i	0.539714	−	0.841849i	$-0.318533\pi$
$569$	45.8090	+	26.4478i	0.0805079	+	0.0464813i	−0.459206	+	0.888330i	$0.651866\pi$
$570$		0			0
$571$	−149.202	−	258.426i	−0.261300	−	0.452585i	0.705288	−	0.708921i	$-0.250818\pi$
$571$	−149.202	−	258.426i	−0.261300	−	0.452585i	−0.966588	+	0.256336i	$0.917484\pi$
$572$		0			0
$573$	−48.5197	−	1045.63i	−0.0846767	−	1.82483i
$574$		0			0
$575$	8.77809	+	5.06803i	0.0152662	+	0.00881397i
$576$		0			0
$577$	337.690			0.585251			0.292626	−	0.956227i	$-0.405471\pi$
$577$	337.690			0.585251			0.292626	+	0.956227i	$0.405471\pi$
$578$		0			0
$579$	−198.037	−	308.987i	−0.342033	−	0.533656i
$580$		0			0
$581$	−729.055	+	420.920i	−1.25483	+	0.724475i
$582$		0			0
$583$	781.197			1.33996
$584$		0			0
$585$	64.3967	−	45.6182i	0.110080	−	0.0779799i
$586$		0			0
$587$	−339.783	+	196.174i	−0.578846	+	0.334197i	−0.760675	−	0.649133i	$-0.775132\pi$
$587$	−339.783	+	196.174i	−0.578846	+	0.334197i	0.181829	+	0.983330i	$0.441798\pi$
$588$		0			0
$589$	−194.359	+	310.401i	−0.329981	+	0.526997i
$590$		0			0
$591$	140.168	−	89.8367i	0.237170	−	0.152008i
$592$		0			0
$593$	86.2134	−	49.7753i	0.145385	−	0.0839381i	−0.425543	−	0.904938i	$-0.639917\pi$
$593$	86.2134	−	49.7753i	0.145385	−	0.0839381i	0.570928	+	0.821000i	$0.306584\pi$
$594$		0			0
$595$	54.0511	+	93.6193i	0.0908422	+	0.157343i
$596$		0			0
$597$	−55.6117	+	107.547i	−0.0931519	+	0.180145i
$598$		0			0
$599$	967.688	+	558.695i	1.61551	+	0.932713i	0.988063	+	0.154050i	$0.0492318\pi$
$599$	967.688	+	558.695i	1.61551	+	0.932713i	0.627443	+	0.778662i	$0.284102\pi$
$600$		0			0
$601$	105.661	−	183.010i	0.175808	−	0.304508i	−0.764633	−	0.644466i	$-0.777080\pi$
$601$	105.661	−	183.010i	0.175808	−	0.304508i	0.940441	+	0.339958i	$0.110413\pi$
$602$		0			0
$603$	−216.076	−	305.022i	−0.358335	−	0.505841i
$604$		0			0
$605$	−20.8556	+	12.0410i	−0.0344721	+	0.0199025i
$606$		0			0
$607$	176.208	+	305.202i	0.290294	+	0.502803i	0.973879	−	0.227067i	$-0.0729137\pi$
$607$	176.208	+	305.202i	0.290294	+	0.502803i	−0.683585	+	0.729870i	$0.739580\pi$
$608$		0			0
$609$	61.3160	+	1321.39i	0.100683	+	2.16977i
$610$		0			0
$611$	632.637	+	365.253i	1.03541	+	0.597795i
$612$		0			0
$613$	−601.259	+	1041.41i	−0.980847	+	1.69888i	−0.321740	+	0.946828i	$0.604268\pi$
$613$	−601.259	+	1041.41i	−0.980847	+	1.69888i	−0.659107	+	0.752049i	$0.729066\pi$
$614$		0			0
$615$	23.6751	+	36.9390i	0.0384961	+	0.0600635i
$616$		0			0
$617$	699.402	+	403.800i	1.13355	+	0.654457i	0.944826	−	0.327572i	$-0.106231\pi$
$617$	699.402	+	403.800i	1.13355	+	0.654457i	0.188727	+	0.982030i	$0.439564\pi$
$618$		0			0
$619$	−134.510	+	232.978i	−0.217302	+	0.376378i	−0.953982	−	0.299863i	$-0.903059\pi$
$619$	−134.510	+	232.978i	−0.217302	+	0.376378i	0.736680	+	0.676241i	$0.236392\pi$
$620$		0			0
$621$	10.2491	+	4.14709i	0.0165042	+	0.00667809i
$622$		0			0
$623$		−	133.235i		−	0.213860i
$624$		0			0
$625$	606.511			0.970417
$626$		0			0
$627$	−417.956	+	247.217i	−0.666597	+	0.394286i
$628$		0			0
$629$	721.795	+	416.728i	1.14753	+	0.662525i
$630$		0			0
$631$	604.102	+	1046.34i	0.957373	+	1.65822i	0.728842	+	0.684682i	$0.240059\pi$
$631$	604.102	+	1046.34i	0.957373	+	1.65822i	0.228532	+	0.973537i	$0.426608\pi$
$632$		0			0
$633$	−460.823	−	718.998i	−0.727998	−	1.13586i
$634$		0			0
$635$	63.0991	−	36.4303i	0.0993686	−	0.0573705i
$636$		0			0
$637$	−1455.69			−2.28523
$638$		0			0
$639$	520.335	−	368.602i	0.814296	−	0.576842i
$640$		0			0
$641$	631.243	−	364.448i	0.984779	−	0.568562i	0.0810691	−	0.996708i	$-0.474167\pi$
$641$	631.243	−	364.448i	0.984779	−	0.568562i	0.903709	+	0.428146i	$0.140833\pi$
$642$		0			0
$643$	44.9271			0.0698711			0.0349356	−	0.999390i	$-0.488877\pi$
$643$	44.9271			0.0698711			0.0349356	+	0.999390i	$0.488877\pi$
$644$		0			0
$645$	10.9154	+	5.64427i	0.0169230	+	0.00875081i
$646$		0			0
$647$		−	1018.65i		−	1.57442i	−0.616686	−	0.787209i	$-0.711525\pi$
$647$		−	1018.65i		−	1.57442i	0.616686	−	0.787209i	$-0.288475\pi$
$648$		0			0
$649$	97.3772	−	168.662i	0.150042	−	0.259880i
$650$		0			0
$651$	−357.902	−	558.416i	−0.549772	−	0.857782i
$652$		0			0
$653$	−1025.90	+	592.301i	−1.57105	+	0.907046i	−0.575009	+	0.818147i	$0.695002\pi$
$653$	−1025.90	+	592.301i	−1.57105	+	0.907046i	−0.996041	+	0.0888993i	$0.971665\pi$
$654$		0			0
$655$	−44.6344			−0.0681441
$656$		0			0
$657$	−70.9276	−	100.125i	−0.107957	−	0.152397i
$658$		0			0
$659$			985.529i			1.49549i	0.663985	+	0.747746i	$0.268864\pi$
$659$			985.529i			1.49549i	−0.663985	+	0.747746i	$0.731136\pi$
$660$		0			0
$661$	8.48723	−	14.7003i	0.0128400	−	0.0222395i	−0.859534	−	0.511079i	$-0.829246\pi$
$661$	8.48723	−	14.7003i	0.0128400	−	0.0222395i	0.872374	+	0.488839i	$0.162579\pi$
$662$		0			0
$663$	890.383	+	460.412i	1.34296	+	0.694437i
$664$		0			0
$665$	3.88242	−	108.314i	0.00583822	−	0.162878i
$666$		0			0
$667$	7.87098	−	13.6329i	0.0118006	−	0.0204392i
$668$		0			0
$669$	274.997	−	531.812i	0.411057	−	0.794936i
$670$		0			0
$671$	314.473	+	181.561i	0.468663	+	0.270583i
$672$		0			0
$673$	−356.500	+	617.476i	−0.529718	+	0.917498i	0.469681	+	0.882836i	$0.344369\pi$
$673$	−356.500	+	617.476i	−0.529718	+	0.917498i	−0.999399	+	0.0346619i	$0.988965\pi$
$674$		0			0
$675$	661.866	−	92.6693i	0.980542	−	0.137288i
$676$		0			0
$677$	245.650	+	141.826i	0.362851	+	0.209492i	0.670331	−	0.742063i	$-0.266152\pi$
$677$	245.650	+	141.826i	0.362851	+	0.209492i	−0.307480	+	0.951555i	$0.599486\pi$
$678$		0			0
$679$	814.868			1.20010
$680$		0			0
$681$	−59.9952	−	1292.93i	−0.0880986	−	1.89857i
$682$		0			0
$683$			168.166i			0.246216i	0.992393	+	0.123108i	$0.0392862\pi$
$683$			168.166i			0.246216i	−0.992393	+	0.123108i	$0.960714\pi$
$684$		0			0
$685$	−36.8140			−0.0537431
$686$		0			0
$687$	−332.375	+	642.774i	−0.483806	+	0.935625i
$688$		0			0
$689$			1616.76i			2.34653i
$690$		0			0
$691$	−125.812	+	217.913i	−0.182073	+	0.315360i	−0.942586	−	0.333963i	$-0.891614\pi$
$691$	−125.812	+	217.913i	−0.182073	+	0.315360i	0.760513	+	0.649322i	$0.224947\pi$
$692$		0			0
$693$	−81.4418	−	875.667i	−0.117521	−	1.26359i
$694$		0			0
$695$	−106.672	−	61.5870i	−0.153485	−	0.0886144i
$696$		0			0
$697$	−278.640	+	482.619i	−0.399771	+	0.692424i
$698$		0			0
$699$	8.31084	+	179.103i	0.0118896	+	0.256228i
$700$		0			0
$701$	748.072	+	431.899i	1.06715	+	0.616119i	0.927401	−	0.374068i	$-0.122037\pi$
$701$	748.072	+	431.899i	1.06715	+	0.616119i	0.139748	+	0.990187i	$0.455371\pi$
$702$		0			0
$703$	−391.623	−	738.177i	−0.557074	−	1.05004i
$704$		0			0
$705$	−33.3564	−	52.0443i	−0.0473140	−	0.0738217i
$706$		0			0
$707$	896.844	+	517.793i	1.26852	+	0.732381i
$708$		0			0
$709$	−574.154			−0.809809			−0.404904	−	0.914359i	$-0.632695\pi$
$709$	−574.154			−0.809809			−0.404904	+	0.914359i	$0.632695\pi$
$710$		0			0
$711$	484.549	−	45.0656i	0.681503	−	0.0633835i
$712$		0			0
$713$			7.89310i			0.0110703i
$714$		0			0
$715$	37.3509	+	64.6936i	0.0522390	+	0.0904806i
$716$		0			0
$717$	988.532	+	511.164i	1.37871	+	0.712921i
$718$		0			0
$719$	73.5548	+	42.4669i	0.102302	+	0.0590638i	0.550278	−	0.834982i	$-0.314522\pi$
$719$	73.5548	+	42.4669i	0.102302	+	0.0590638i	−0.447976	+	0.894045i	$0.647855\pi$
$720$		0			0
$721$	840.677			1.16599
$722$		0			0
$723$	−377.796	−	589.456i	−0.522539	−	0.815291i
$724$		0			0
$725$		−	951.553i		−	1.31249i
$726$		0			0
$727$	−122.734	−	212.581i	−0.168822	−	0.292408i	0.769184	−	0.639027i	$-0.220663\pi$
$727$	−122.734	−	212.581i	−0.168822	−	0.292408i	−0.938006	+	0.346619i	$0.887330\pi$
$728$		0			0
$729$	700.968	−	200.213i	0.961547	−	0.274641i
$730$		0			0
$731$			156.081i			0.213518i
$732$		0			0
$733$	−588.181	−	1018.76i	−0.802430	−	1.38985i	−0.918012	−	0.396552i	$-0.870207\pi$
$733$	−588.181	−	1018.76i	−0.802430	−	1.38985i	0.115582	−	0.993298i	$-0.463127\pi$
$734$		0			0
$735$	109.419	+	56.5802i	0.148870	+	0.0769799i
$736$		0			0
$737$	306.429	−	176.917i	0.415779	−	0.240050i
$738$		0			0
$739$	639.622	−	1107.86i	0.865524	−	1.49913i	−0.00100273	−	0.999999i	$-0.500319\pi$
$739$	639.622	−	1107.86i	0.865524	−	1.49913i	0.866526	−	0.499131i	$-0.166347\pi$
$740$		0			0
$741$	−511.640	−	865.000i	−0.690472	−	1.16734i
$742$		0			0
$743$		−	1161.60i		−	1.56339i	−0.623658	−	0.781697i	$-0.714354\pi$
$743$		−	1161.60i		−	1.56339i	0.623658	−	0.781697i	$-0.285646\pi$
$744$		0			0
$745$	−46.7343			−0.0627305
$746$		0			0
$747$	539.009	−	381.831i	0.721565	−	0.511153i
$748$		0			0
$749$	1260.26	+	727.614i	1.68260	+	0.971447i
$750$		0			0
$751$	−390.247	+	675.928i	−0.519637	+	0.900037i	0.480103	+	0.877212i	$0.340599\pi$
$751$	−390.247	+	675.928i	−0.519637	+	0.900037i	−0.999739	+	0.0228248i	$0.992734\pi$
$752$		0			0
$753$	−874.052	−	451.967i	−1.16076	−	0.600222i
$754$		0			0
$755$	2.69723	+	1.55725i	0.00357250	+	0.00206258i
$756$		0			0
$757$	−117.799	+	204.034i	−0.155613	+	0.269529i	−0.933282	−	0.359144i	$-0.883069\pi$
$757$	−117.799	+	204.034i	−0.155613	+	0.269529i	0.777669	+	0.628674i	$0.216402\pi$
$758$		0			0
$759$	−4.80712	+	9.29640i	−0.00633349	+	0.0122482i
$760$		0			0
$761$	314.907	−	181.812i	0.413807	−	0.238911i	−0.278617	−	0.960402i	$-0.589876\pi$
$761$	314.907	−	181.812i	0.413807	−	0.238911i	0.692424	+	0.721491i	$0.256543\pi$
$762$		0			0
$763$	−554.140	−	959.798i	−0.726264	−	1.25793i
$764$		0			0
$765$	−49.0316	−	69.2152i	−0.0640936	−	0.0904774i
$766$		0			0
$767$	349.063	+	201.531i	0.455101	+	0.262753i
$768$		0			0
$769$	−546.768	+	947.030i	−0.711012	+	1.23151i	0.253466	+	0.967344i	$0.418429\pi$
$769$	−546.768	+	947.030i	−0.711012	+	1.23151i	−0.964478	+	0.264164i	$0.914904\pi$
$770$		0			0
$771$	−43.6062	−	939.736i	−0.0565579	−	1.21885i
$772$		0			0
$773$	1301.99	−	751.704i	1.68433	−	0.972451i	0.725612	−	0.688104i	$-0.241557\pi$
$773$	1301.99	−	751.704i	1.68433	−	0.972451i	0.958722	−	0.284347i	$-0.0917766\pi$
$774$		0			0
$775$	238.557	+	413.193i	0.307815	+	0.533152i
$776$		0			0
$777$	1511.75	−	70.1490i	1.94562	−	0.0902819i
$778$		0			0
$779$	493.573	−	261.854i	0.633598	−	0.336141i
$780$		0			0
$781$	301.801	+	522.734i	0.386429	+	0.669314i
$782$		0			0
$783$	−143.921	−	1027.92i	−0.183808	−	1.31280i
$784$		0			0
$785$		−	7.45393i		−	0.00949546i
$786$		0			0
$787$	308.357	+	534.090i	0.391813	+	0.678640i	0.992689	−	0.120703i	$-0.0385147\pi$
$787$	308.357	+	534.090i	0.391813	+	0.678640i	−0.600876	+	0.799342i	$0.705181\pi$
$788$		0			0
$789$	−1128.02	−	583.294i	−1.42969	−	0.739283i
$790$		0			0
$791$		−	2144.11i		−	2.71063i
$792$		0			0
$793$	−375.758	+	650.832i	−0.473844	+	0.820721i
$794$		0			0
$795$	62.8407	−	121.526i	0.0790449	−	0.152864i
$796$		0			0
$797$	175.903	−	101.558i	0.220707	−	0.127425i	−0.385571	−	0.922678i	$-0.625995\pi$
$797$	175.903	−	101.558i	0.220707	−	0.127425i	0.606278	+	0.795253i	$0.292662\pi$
$798$		0			0
$799$	392.583	−	679.974i	0.491343	−	0.851031i
$800$		0			0
$801$	9.68127	+	104.094i	0.0120865	+	0.129955i
$802$		0			0
$803$	100.586	−	58.0735i	0.125263	−	0.0723207i
$804$		0			0
$805$	−1.16796	−	2.02297i	−0.00145088	−	0.00251300i
$806$		0			0
$807$	46.0515	+	992.434i	0.0570651	+	1.22978i
$808$		0			0
$809$			589.547i			0.728736i	0.931255	+	0.364368i	$0.118715\pi$
$809$			589.547i			0.728736i	−0.931255	+	0.364368i	$0.881285\pi$
$810$		0			0
$811$	−332.344	−	575.637i	−0.409796	−	0.709787i	0.585071	−	0.810982i	$-0.301067\pi$
$811$	−332.344	−	575.637i	−0.409796	−	0.709787i	−0.994867	+	0.101195i	$0.967733\pi$
$812$		0			0
$813$	−819.050	+	38.0060i	−1.00744	+	0.0467479i
$814$		0			0
$815$		−	0.357437i		−	0.000438573i
$816$		0			0
$817$	83.0483	−	132.633i	0.101650	−	0.162341i
$818$		0			0
$819$	1812.28	−	168.552i	2.21279	−	0.205802i
$820$		0			0
$821$		−	966.861i		−	1.17766i	−0.808256	−	0.588831i	$-0.799588\pi$
$821$		−	966.861i		−	1.17766i	0.808256	−	0.588831i	$-0.200412\pi$
$822$		0			0
$823$	−358.318	+	620.625i	−0.435380	+	0.754101i	−0.997327	−	0.0730730i	$-0.976719\pi$
$823$	−358.318	+	620.625i	−0.435380	+	0.754101i	0.561946	+	0.827174i	$0.310053\pi$
$824$		0			0
$825$	29.3237	+	631.941i	0.0355439	+	0.765990i
$826$		0			0
$827$	−89.6846	+	51.7794i	−0.108446	+	0.0626112i	−0.553242	−	0.833021i	$-0.686609\pi$
$827$	−89.6846	+	51.7794i	−0.108446	+	0.0626112i	0.444796	+	0.895632i	$0.353276\pi$
$828$		0			0
$829$	33.8188			0.0407947			0.0203974	−	0.999792i	$-0.493507\pi$
$829$	33.8188			0.0407947			0.0203974	+	0.999792i	$0.493507\pi$
$830$		0			0
$831$	−880.266	+	40.8466i	−1.05929	+	0.0491536i
$832$		0			0
$833$			1564.62i			1.87829i
$834$		0			0
$835$	−79.7801	+	138.183i	−0.0955450	+	0.165489i
$836$		0			0
$837$	320.197	+	410.272i	0.382553	+	0.490170i
$838$		0			0
$839$	−342.384	+	197.675i	−0.408086	+	0.235608i	−0.689967	−	0.723841i	$-0.742375\pi$
$839$	−342.384	+	197.675i	−0.408086	+	0.235608i	0.281881	+	0.959449i	$0.409042\pi$
$840$		0			0
$841$	−636.822			−0.757220
$842$		0			0
$843$	556.909	−	356.936i	0.660628	−	0.423412i
$844$		0			0
$845$	−61.1013	+	35.2769i	−0.0723093	+	0.0417478i
$846$		0			0
$847$	−555.411			−0.655739
$848$		0			0
$849$	278.528	+	434.573i	0.328066	+	0.511864i
$850$		0			0
$851$	−15.5969	−	9.00485i	−0.0183277	−	0.0105815i
$852$		0			0
$853$	−350.270	−	606.686i	−0.410634	−	0.711238i	0.584326	−	0.811519i	$-0.301359\pi$
$853$	−350.270	−	606.686i	−0.410634	−	0.711238i	−0.994959	+	0.100281i	$0.968026\pi$
$854$		0			0
$855$	4.83720	+	84.9057i	0.00565754	+	0.0993049i
$856$		0			0
$857$	1104.62	−	637.752i	1.28894	−	0.744168i	0.310472	−	0.950583i	$-0.399513\pi$
$857$	1104.62	−	637.752i	1.28894	−	0.744168i	0.978465	+	0.206415i	$0.0661797\pi$
$858$		0			0
$859$	−187.439	+	324.654i	−0.218206	+	0.377944i	−0.954260	−	0.298979i	$-0.903354\pi$
$859$	−187.439	+	324.654i	−0.218206	+	0.377944i	0.736053	+	0.676924i	$0.236687\pi$
$860$		0			0
$861$	46.9043	+	1010.81i	0.0544765	+	1.17400i
$862$		0			0
$863$			282.004i			0.326772i	0.986562	+	0.163386i	$0.0522416\pi$
$863$			282.004i			0.326772i	−0.986562	+	0.163386i	$0.947758\pi$
$864$		0			0
$865$	−34.8860	−	60.4244i	−0.0403307	−	0.0698548i
$866$		0			0
$867$	96.6322	−	186.875i	0.111456	−	0.215543i
$868$		0			0
$869$			460.644i			0.530086i
$870$		0			0
$871$	366.146	+	634.184i	0.420374	+	0.728110i
$872$		0			0
$873$	−636.639	+	59.2109i	−0.729254	+	0.0678246i
$874$		0			0
$875$	−245.786	−	141.905i	−0.280899	−	0.162177i
$876$		0			0
$877$	518.048			0.590705			0.295353	−	0.955388i	$-0.404563\pi$
$877$	518.048			0.590705			0.295353	+	0.955388i	$0.404563\pi$
$878$		0			0
$879$	1193.14	+	616.965i	1.35738	+	0.701894i
$880$		0			0
$881$			489.787i			0.555945i	0.960589	+	0.277972i	$0.0896624\pi$
$881$			489.787i			0.555945i	−0.960589	+	0.277972i	$0.910338\pi$
$882$		0			0
$883$	292.251	+	506.194i	0.330975	+	0.573266i	0.982703	−	0.185187i	$-0.0592891\pi$
$883$	292.251	+	506.194i	0.330975	+	0.573266i	−0.651728	+	0.758453i	$0.725956\pi$
$884$		0			0
$885$	−18.4047	−	28.7159i	−0.0207963	−	0.0324473i
$886$		0			0
$887$	−877.206	−	506.455i	−0.988958	−	0.570975i	−0.0839953	−	0.996466i	$-0.526768\pi$
$887$	−877.206	−	506.455i	−0.988958	−	0.570975i	−0.904963	+	0.425491i	$0.860101\pi$
$888$		0			0
$889$	1680.41			1.89022
$890$		0			0
$891$	127.257	+	678.222i	0.142825	+	0.761192i
$892$		0			0
$893$	−695.407	+	368.932i	−0.778731	+	0.413138i
$894$		0			0
$895$	−45.5745			−0.0509212
$896$		0			0
$897$	−19.2398	−	9.94879i	−0.0214490	−	0.0110912i
$898$		0			0
$899$	641.715	−	370.494i	0.713809	−	0.412118i
$900$		0			0
$901$	1737.74			1.92868
$902$		0			0
$903$	152.929	+	238.608i	0.169357	+	0.264239i
$904$		0			0
$905$	−105.585	+	60.9595i	−0.116668	+	0.0673586i
$906$		0			0
$907$	840.726	+	1456.18i	0.926930	+	1.60549i	0.788427	+	0.615128i	$0.210896\pi$
$907$	840.726	+	1456.18i	0.926930	+	1.60549i	0.138503	+	0.990362i	$0.455771\pi$
$908$		0			0
$909$	−738.310	−	339.373i	−0.812222	−	0.373348i
$910$		0			0
$911$	282.331	+	163.004i	0.309913	+	0.178929i	0.646888	−	0.762585i	$-0.276070\pi$
$911$	282.331	+	163.004i	0.309913	+	0.178929i	−0.336974	+	0.941514i	$0.609404\pi$
$912$		0			0
$913$	312.632	+	541.495i	0.342423	+	0.593094i
$914$		0			0
$915$	53.5411	−	34.3158i	0.0585149	−	0.0375036i
$916$		0			0
$917$	−891.503	−	514.709i	−0.972195	−	0.561297i
$918$		0			0
$919$	429.757			0.467636			0.233818	−	0.972280i	$-0.424878\pi$
$919$	429.757			0.467636			0.233818	+	0.972280i	$0.424878\pi$
$920$		0			0
$921$	590.665	−	27.4084i	0.641330	−	0.0297593i
$922$		0			0
$923$	−1081.85	+	624.606i	−1.17210	+	0.676713i
$924$		0			0
$925$	−1088.63			−1.17690
$926$		0			0
$927$	−656.803	+	61.0863i	−0.708526	+	0.0658967i
$928$		0			0
$929$	253.818	−	146.542i	0.273216	−	0.157742i	−0.357132	−	0.934054i	$-0.616245\pi$
$929$	253.818	−	146.542i	0.273216	−	0.157742i	0.630348	+	0.776312i	$0.282912\pi$
$930$		0			0
$931$	832.506	−	1329.56i	0.894206	−	1.42810i
$932$		0			0
$933$	440.648	+	227.857i	0.472291	+	0.244219i
$934$		0			0
$935$	69.5344	−	40.1457i	0.0743683	−	0.0429366i
$936$		0			0
$937$	42.8606	+	74.2368i	0.0457424	+	0.0792282i	0.887990	−	0.459863i	$-0.152101\pi$
$937$	42.8606	+	74.2368i	0.0457424	+	0.0792282i	−0.842248	+	0.539091i	$0.818768\pi$
$938$		0			0
$939$	781.203	+	1218.87i	0.831952	+	1.29805i
$940$		0			0
$941$	−629.814	−	363.623i	−0.669303	−	0.386422i	0.126510	−	0.991965i	$-0.459622\pi$
$941$	−629.814	−	363.623i	−0.669303	−	0.386422i	−0.795812	+	0.605543i	$0.792956\pi$
$942$		0			0
$943$	6.02099	−	10.4287i	0.00638493	−	0.0110590i
$944$		0			0
$945$	−142.774	−	57.7706i	−0.151084	−	0.0611329i
$946$		0			0
$947$	1006.72	−	581.228i	1.06306	−	0.613757i	0.136782	−	0.990601i	$-0.456324\pi$
$947$	1006.72	−	581.228i	1.06306	−	0.613757i	0.926277	+	0.376844i	$0.122991\pi$
$948$		0			0
$949$	120.189	+	208.173i	0.126648	+	0.219360i
$950$		0			0
$951$	124.786	−	79.9781i	0.131215	−	0.0840989i
$952$		0			0
$953$	739.872	+	427.165i	0.776361	+	0.448232i	0.835139	−	0.550039i	$-0.185387\pi$
$953$	739.872	+	427.165i	0.776361	+	0.448232i	−0.0587783	+	0.998271i	$0.518720\pi$
$954$		0			0
$955$	86.7634	−	150.279i	0.0908517	−	0.157360i
$956$		0			0
$957$	981.445	−	45.5416i	1.02554	−	0.0475878i
$958$		0			0
$959$	−735.302	−	424.527i	−0.766738	−	0.442677i
$960$		0			0
$961$	294.732	−	510.491i	0.306693	−	0.531208i
$962$		0			0
$963$	−1037.49	−	476.895i	−1.07735	−	0.495218i
$964$		0			0
$965$		−	60.8406i		−	0.0630472i
$966$		0			0
$967$	1805.36			1.86697			0.933484	−	0.358620i	$-0.116753\pi$
$967$	1805.36			1.86697			0.933484	+	0.358620i	$0.116753\pi$
$968$		0			0
$969$	−929.725	+	549.924i	−0.959468	+	0.567517i
$970$		0			0
$971$	1237.85	+	714.672i	1.27482	+	0.736016i	0.975891	−	0.218260i	$-0.0700380\pi$
$971$	1237.85	+	714.672i	1.27482	+	0.736016i	0.298927	+	0.954276i	$0.403371\pi$
$972$		0			0
$973$	−1420.40	−	2460.21i	−1.45982	−	2.52848i
$974$		0			0
$975$	−1307.86	+	60.6882i	−1.34140	+	0.0622443i
$976$		0			0
$977$	−1263.88	+	729.700i	−1.29363	+	0.746878i	−0.979296	−	0.202435i	$-0.935115\pi$
$977$	−1263.88	+	729.700i	−1.29363	+	0.746878i	−0.314334	+	0.949312i	$0.601781\pi$
$978$		0			0
$979$	−98.9584			−0.101081
$980$		0			0
$981$	502.680	+	709.604i	0.512415	+	0.723348i
$982$		0			0
$983$	788.050	−	454.981i	0.801678	−	0.462849i	−0.0423795	−	0.999102i	$-0.513494\pi$
$983$	788.050	−	454.981i	0.801678	−	0.462849i	0.844058	+	0.536252i	$0.180161\pi$
$984$		0			0
$985$	27.5995			0.0280198
$986$		0			0
$987$	−66.0846	−	1424.16i	−0.0669550	−	1.44292i
$988$		0			0
$989$		−	3.37268i		−	0.00341019i
$990$		0			0
$991$	−428.060	+	741.421i	−0.431947	+	0.748155i	−0.997041	−	0.0768721i	$-0.975507\pi$
$991$	−428.060	+	741.421i	−0.431947	+	0.748155i	0.565094	+	0.825027i	$0.308840\pi$
$992$		0			0
$993$	−447.914	+	20.7843i	−0.451071	+	0.0209309i
$994$		0			0
$995$	−17.3822	+	10.0356i	−0.0174695	+	0.0100860i
$996$		0			0
$997$	1048.19			1.05135			0.525674	−	0.850686i	$-0.323813\pi$
$997$	1048.19			1.05135			0.525674	+	0.850686i	$0.323813\pi$
$998$		0			0
$999$	−1176.00	+	164.654i	−1.17718	+	0.164819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.13	✓	80
3.2	odd	2		2052.3.m.a.1493.22		80
9.4	even	3		2052.3.be.a.125.19		80
9.5	odd	6		684.3.be.a.581.39	yes	80
19.7	even	3		684.3.be.a.425.39	yes	80
57.26	odd	6		2052.3.be.a.197.19		80
171.121	even	3		2052.3.m.a.881.19		80
171.140	odd	6	inner	684.3.m.a.653.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.13	✓	80	1.1	even	1	trivial
684.3.m.a.653.13	yes	80	171.140	odd	6	inner
684.3.be.a.425.39	yes	80	19.7	even	3
684.3.be.a.581.39	yes	80	9.5	odd	6
2052.3.m.a.881.19		80	171.121	even	3
2052.3.m.a.1493.22		80	3.2	odd	2
2052.3.be.a.125.19		80	9.4	even	3
2052.3.be.a.197.19		80	57.26	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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61882 - 2.52575i) q^{3} -0.497329i q^{5} +(5.73504 - 9.93338i) q^{7} +(-3.75887 + 8.17746i) q^{9} +O(q^{10})\)	\(q+(-1.61882 - 2.52575i) q^{3} -0.497329i q^{5} +(5.73504 - 9.93338i) q^{7} +(-3.75887 + 8.17746i) q^{9} +(-7.37787 - 4.25962i) q^{11} +(8.81568 - 15.2692i) q^{13} +(-1.25613 + 0.805085i) q^{15} +(-16.4117 - 9.47532i) q^{17} +(8.90449 + 16.7842i) q^{19} +(-34.3732 + 1.59501i) q^{21} +(0.354632 + 0.204747i) q^{23} +24.7527 q^{25} +(26.7392 - 3.74381i) q^{27} -38.4425i q^{29} +(9.63763 + 16.6929i) q^{31} +(1.18467 + 25.5302i) q^{33} +(-4.94016 - 2.85220i) q^{35} -43.9804 q^{37} +(-52.8373 + 2.45178i) q^{39} -29.4070i q^{41} +(-4.11810 - 7.13276i) q^{43} +(4.06689 + 1.86940i) q^{45} +41.4322i q^{47} +(-41.2813 - 71.5014i) q^{49} +(2.63524 + 56.7908i) q^{51} +(-79.4128 + 45.8490i) q^{53} +(-2.11843 + 3.66923i) q^{55} +(27.9781 - 49.6611i) q^{57} +22.8606i q^{59} -42.6238 q^{61} +(59.6725 + 84.2364i) q^{63} +(-7.59383 - 4.38430i) q^{65} +(-20.7667 + 35.9690i) q^{67} +(-0.0569435 - 1.22716i) q^{69} +(-61.3593 - 35.4258i) q^{71} +(-6.81675 + 11.8070i) q^{73} +(-40.0700 - 62.5192i) q^{75} +(-84.6248 + 48.8581i) q^{77} +(-27.0355 - 46.8269i) q^{79} +(-52.7418 - 61.4761i) q^{81} +(-63.5614 - 36.6972i) q^{83} +(-4.71236 + 8.16204i) q^{85} +(-97.0962 + 62.2312i) q^{87} +(10.0596 - 5.80794i) q^{89} +(-101.117 - 175.139i) q^{91} +(26.5605 - 51.3650i) q^{93} +(8.34729 - 4.42846i) q^{95} +(35.5215 + 61.5250i) q^{97} +(62.5654 - 44.3209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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