LMFDB - Embedded newform 336.3.be.a.319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(79,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 2]))

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

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

chi := DirichletCharacter("336.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.be (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:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			319.1
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	336.319
Dual form			336.3.be.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(-1.63746 - 2.83616i) q^{5} +(6.77492 + 1.76082i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.63746 - 2.83616i) q^{5} +(6.77492 + 1.76082i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-16.1873 - 9.34574i) q^{11} +10.2749 q^{13} +5.67232i q^{15} +(12.5498 - 21.7370i) q^{17} +(-26.7870 + 15.4655i) q^{19} +(-8.63746 - 8.50848i) q^{21} +(-4.54983 + 2.62685i) q^{23} +(7.13746 - 12.3624i) q^{25} -5.19615i q^{27} -42.0241 q^{29} +(-45.1495 - 26.0671i) q^{31} +(16.1873 + 28.0372i) q^{33} +(-6.09967 - 22.0980i) q^{35} +(-17.9622 - 31.1115i) q^{37} +(-15.4124 - 8.89834i) q^{39} -38.7492 q^{41} -31.5380i q^{43} +(4.91238 - 8.50848i) q^{45} +(21.0000 - 12.1244i) q^{47} +(42.7990 + 23.8589i) q^{49} +(-37.6495 + 21.7370i) q^{51} +(32.8127 - 56.8333i) q^{53} +61.2130i q^{55} +53.5739 q^{57} +(38.8368 + 22.4224i) q^{59} +(31.5498 + 54.6459i) q^{61} +(5.58762 + 20.2430i) q^{63} +(-16.8248 - 29.1413i) q^{65} +(19.2371 + 11.1066i) q^{67} +9.09967 q^{69} -97.5703i q^{71} +(-45.8625 + 79.4363i) q^{73} +(-21.4124 + 12.3624i) q^{75} +(-93.2114 - 91.8196i) q^{77} +(-8.02575 + 4.63367i) q^{79} +(-4.50000 + 7.79423i) q^{81} +51.1976i q^{83} -82.1993 q^{85} +(63.0361 + 36.3939i) q^{87} +(26.7251 + 46.2892i) q^{89} +(69.6117 + 18.0923i) q^{91} +(45.1495 + 78.2012i) q^{93} +(87.7251 + 50.6481i) q^{95} +129.522 q^{97} -56.0744i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + q^{5} + 12 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + q^5 + 12 * q^7 + 6 * q^9	$ 4 q - 6 q^{3} + q^{5} + 12 q^{7} + 6 q^{9} - 27 q^{11} + 26 q^{13} + 20 q^{17} - 9 q^{19} - 27 q^{21} + 12 q^{23} + 21 q^{25} - 2 q^{29} - 90 q^{31} + 27 q^{33} + 36 q^{35} - 19 q^{37} - 39 q^{39} - 4 q^{41} - 3 q^{45} + 84 q^{47} - 10 q^{49} - 60 q^{51} + 169 q^{53} + 18 q^{57} + 27 q^{59} + 96 q^{61} + 45 q^{63} - 22 q^{65} + 9 q^{67} - 24 q^{69} - 191 q^{73} - 63 q^{75} - 169 q^{77} - 168 q^{79} - 18 q^{81} - 208 q^{85} + 3 q^{87} + 122 q^{89} + 135 q^{91} + 90 q^{93} + 366 q^{95} + 50 q^{97}+O(q^{100}) $ 4 * q - 6 * q^3 + q^5 + 12 * q^7 + 6 * q^9 - 27 * q^11 + 26 * q^13 + 20 * q^17 - 9 * q^19 - 27 * q^21 + 12 * q^23 + 21 * q^25 - 2 * q^29 - 90 * q^31 + 27 * q^33 + 36 * q^35 - 19 * q^37 - 39 * q^39 - 4 * q^41 - 3 * q^45 + 84 * q^47 - 10 * q^49 - 60 * q^51 + 169 * q^53 + 18 * q^57 + 27 * q^59 + 96 * q^61 + 45 * q^63 - 22 * q^65 + 9 * q^67 - 24 * q^69 - 191 * q^73 - 63 * q^75 - 169 * q^77 - 168 * q^79 - 18 * q^81 - 208 * q^85 + 3 * q^87 + 122 * q^89 + 135 * q^91 + 90 * q^93 + 366 * q^95 + 50 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$		0			0
$5$	−1.63746	−	2.83616i	−0.327492	−	0.567232i	0.654522	−	0.756043i	$-0.272870\pi$
$5$	−1.63746	−	2.83616i	−0.327492	−	0.567232i	−0.982013	+	0.188811i	$0.939537\pi$
$6$		0			0
$7$	6.77492	+	1.76082i	0.967845	+	0.251546i
$7$	6.77492	+	1.76082i	0.967845	+	0.251546i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−16.1873	−	9.34574i	−1.47157	−	0.849613i	−0.472082	−	0.881554i	$-0.656498\pi$
$11$	−16.1873	−	9.34574i	−1.47157	−	0.849613i	−0.999490	+	0.0319419i	$0.989831\pi$
$12$		0			0
$13$	10.2749			0.790378			0.395189	−	0.918600i	$-0.370679\pi$
$13$	10.2749			0.790378			0.395189	+	0.918600i	$0.370679\pi$
$14$		0			0
$15$			5.67232i			0.378155i
$16$		0			0
$17$	12.5498	−	21.7370i	0.738226	−	1.27864i	−0.215068	−	0.976599i	$-0.568997\pi$
$17$	12.5498	−	21.7370i	0.738226	−	1.27864i	0.953294	−	0.302045i	$-0.0976693\pi$
$18$		0			0
$19$	−26.7870	+	15.4655i	−1.40984	+	0.813972i	−0.995372	−	0.0960925i	$-0.969366\pi$
$19$	−26.7870	+	15.4655i	−1.40984	+	0.813972i	−0.414468	+	0.910064i	$0.636032\pi$
$20$		0			0
$21$	−8.63746	−	8.50848i	−0.411308	−	0.405166i
$22$		0			0
$23$	−4.54983	+	2.62685i	−0.197819	+	0.114211i	−0.595638	−	0.803253i	$-0.703101\pi$
$23$	−4.54983	+	2.62685i	−0.197819	+	0.114211i	0.397819	+	0.917464i	$0.369767\pi$
$24$		0			0
$25$	7.13746	−	12.3624i	0.285498	−	0.494498i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−42.0241			−1.44911			−0.724553	−	0.689219i	$-0.757954\pi$
$29$	−42.0241			−1.44911			−0.724553	+	0.689219i	$0.757954\pi$
$30$		0			0
$31$	−45.1495	−	26.0671i	−1.45644	−	0.840873i	−0.457602	−	0.889157i	$-0.651292\pi$
$31$	−45.1495	−	26.0671i	−1.45644	−	0.840873i	−0.998834	+	0.0482837i	$0.984625\pi$
$32$		0			0
$33$	16.1873	+	28.0372i	0.490524	+	0.849613i
$34$		0			0
$35$	−6.09967	−	22.0980i	−0.174276	−	0.631372i
$36$		0			0
$37$	−17.9622	−	31.1115i	−0.485465	−	0.840850i	0.514395	−	0.857553i	$-0.328016\pi$
$37$	−17.9622	−	31.1115i	−0.485465	−	0.840850i	−0.999860	+	0.0167029i	$0.994683\pi$
$38$		0			0
$39$	−15.4124	−	8.89834i	−0.395189	−	0.228163i
$40$		0			0
$41$	−38.7492			−0.945102			−0.472551	−	0.881303i	$-0.656667\pi$
$41$	−38.7492			−0.945102			−0.472551	+	0.881303i	$0.656667\pi$
$42$		0			0
$43$		−	31.5380i		−	0.733442i	−0.930331	−	0.366721i	$-0.880480\pi$
$43$		−	31.5380i		−	0.733442i	0.930331	−	0.366721i	$-0.119520\pi$
$44$		0			0
$45$	4.91238	−	8.50848i	0.109164	−	0.189077i
$46$		0			0
$47$	21.0000	−	12.1244i	0.446809	−	0.257965i	−0.259673	−	0.965697i	$-0.583615\pi$
$47$	21.0000	−	12.1244i	0.446809	−	0.257965i	0.706481	+	0.707732i	$0.250281\pi$
$48$		0			0
$49$	42.7990	+	23.8589i	0.873449	+	0.486915i
$50$		0			0
$51$	−37.6495	+	21.7370i	−0.738226	+	0.426215i
$52$		0			0
$53$	32.8127	−	56.8333i	0.619108	−	1.07233i	−0.370541	−	0.928816i	$-0.620828\pi$
$53$	32.8127	−	56.8333i	0.619108	−	1.07233i	0.989649	−	0.143510i	$-0.0458389\pi$
$54$		0			0
$55$			61.2130i			1.11296i
$56$		0			0
$57$	53.5739			0.939893
$58$		0			0
$59$	38.8368	+	22.4224i	0.658251	+	0.380041i	0.791610	−	0.611026i	$-0.209243\pi$
$59$	38.8368	+	22.4224i	0.658251	+	0.380041i	−0.133359	+	0.991068i	$0.542576\pi$
$60$		0			0
$61$	31.5498	+	54.6459i	0.517210	+	0.895835i	0.999800	+	0.0199882i	$0.00636287\pi$
$61$	31.5498	+	54.6459i	0.517210	+	0.895835i	−0.482590	+	0.875846i	$0.660304\pi$
$62$		0			0
$63$	5.58762	+	20.2430i	0.0886924	+	0.321317i
$64$		0			0
$65$	−16.8248	−	29.1413i	−0.258842	−	0.448328i
$66$		0			0
$67$	19.2371	+	11.1066i	0.287121	+	0.165770i	0.636643	−	0.771159i	$-0.280323\pi$
$67$	19.2371	+	11.1066i	0.287121	+	0.165770i	−0.349522	+	0.936928i	$0.613656\pi$
$68$		0			0
$69$	9.09967			0.131879
$70$		0			0
$71$		−	97.5703i		−	1.37423i	−0.726549	−	0.687115i	$-0.758877\pi$
$71$		−	97.5703i		−	1.37423i	0.726549	−	0.687115i	$-0.241123\pi$
$72$		0			0
$73$	−45.8625	+	79.4363i	−0.628254	+	1.08817i	0.359648	+	0.933088i	$0.382897\pi$
$73$	−45.8625	+	79.4363i	−0.628254	+	1.08817i	−0.987902	+	0.155080i	$0.950437\pi$
$74$		0			0
$75$	−21.4124	+	12.3624i	−0.285498	+	0.164833i
$76$		0			0
$77$	−93.2114	−	91.8196i	−1.21054	−	1.19246i
$78$		0			0
$79$	−8.02575	+	4.63367i	−0.101592	+	0.0586540i	−0.549935	−	0.835207i	$-0.685348\pi$
$79$	−8.02575	+	4.63367i	−0.101592	+	0.0586540i	0.448343	+	0.893861i	$0.352014\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			51.1976i			0.616839i	0.951250	+	0.308419i	$0.0998000\pi$
$83$			51.1976i			0.616839i	−0.951250	+	0.308419i	$0.900200\pi$
$84$		0			0
$85$	−82.1993			−0.967051
$86$		0			0
$87$	63.0361	+	36.3939i	0.724553	+	0.418321i
$88$		0			0
$89$	26.7251	+	46.2892i	0.300282	+	0.520103i	0.976200	−	0.216874i	$-0.0695859\pi$
$89$	26.7251	+	46.2892i	0.300282	+	0.520103i	−0.675918	+	0.736977i	$0.736253\pi$
$90$		0			0
$91$	69.6117	+	18.0923i	0.764964	+	0.198817i
$92$		0			0
$93$	45.1495	+	78.2012i	0.485479	+	0.840873i
$94$		0			0
$95$	87.7251	+	50.6481i	0.923422	+	0.533138i
$96$		0			0
$97$	129.522			1.33528			0.667641	−	0.744483i	$-0.267304\pi$
$97$	129.522			1.33528			0.667641	+	0.744483i	$0.267304\pi$
$98$		0			0
$99$		−	56.0744i		−	0.566408i
$100$		0			0
$101$	−26.8488	+	46.5036i	−0.265830	+	0.460431i	−0.967781	−	0.251794i	$-0.918979\pi$
$101$	−26.8488	+	46.5036i	−0.265830	+	0.460431i	0.701951	+	0.712226i	$0.252313\pi$
$102$		0			0
$103$	27.8111	−	16.0567i	0.270010	−	0.155890i	−0.358882	−	0.933383i	$-0.616842\pi$
$103$	27.8111	−	16.0567i	0.270010	−	0.155890i	0.628892	+	0.777492i	$0.283509\pi$
$104$		0			0
$105$	−9.98796	+	38.4295i	−0.0951234	+	0.365995i
$106$		0			0
$107$	49.5860	−	28.6285i	0.463420	−	0.267556i	−0.250061	−	0.968230i	$-0.580451\pi$
$107$	49.5860	−	28.6285i	0.463420	−	0.267556i	0.713481	+	0.700674i	$0.247117\pi$
$108$		0			0
$109$	70.6873	−	122.434i	0.648507	−	1.12325i	−0.334972	−	0.942228i	$-0.608727\pi$
$109$	70.6873	−	122.434i	0.648507	−	1.12325i	0.983479	−	0.181020i	$-0.0579397\pi$
$110$		0			0
$111$			62.2229i			0.560567i
$112$		0			0
$113$	−72.1512			−0.638506			−0.319253	−	0.947670i	$-0.603432\pi$
$113$	−72.1512			−0.638506			−0.319253	+	0.947670i	$0.603432\pi$
$114$		0			0
$115$	14.9003	+	8.60271i	0.129568	+	0.0748062i
$116$		0			0
$117$	15.4124	+	26.6950i	0.131730	+	0.228163i
$118$		0			0
$119$	123.299	−	125.168i	1.03613	−	1.05183i
$120$		0			0
$121$	114.186	+	197.775i	0.943683	+	1.63451i
$122$		0			0
$123$	58.1238	+	33.5578i	0.472551	+	0.272827i
$124$		0			0
$125$	−128.622			−1.02898
$126$		0			0
$127$			150.887i			1.18809i	0.804433	+	0.594043i	$0.202469\pi$
$127$			150.887i			1.18809i	−0.804433	+	0.594043i	$0.797531\pi$
$128$		0			0
$129$	−27.3127	+	47.3070i	−0.211726	+	0.366721i
$130$		0			0
$131$	121.885	−	70.3703i	0.930420	−	0.537178i	0.0434754	−	0.999054i	$-0.486157\pi$
$131$	121.885	−	70.3703i	0.930420	−	0.537178i	0.886944	+	0.461876i	$0.152824\pi$
$132$		0			0
$133$	−208.711	+	57.6101i	−1.56926	+	0.433159i
$134$		0			0
$135$	−14.7371	+	8.50848i	−0.109164	+	0.0630258i
$136$		0			0
$137$	22.5257	−	39.0157i	0.164421	−	0.284786i	−0.772028	−	0.635588i	$-0.780758\pi$
$137$	22.5257	−	39.0157i	0.164421	−	0.284786i	0.936450	+	0.350802i	$0.114091\pi$
$138$		0			0
$139$		−	32.2285i		−	0.231860i	−0.993257	−	0.115930i	$-0.963015\pi$
$139$		−	32.2285i		−	0.231860i	0.993257	−	0.115930i	$-0.0369848\pi$
$140$		0			0
$141$	−42.0000			−0.297872
$142$		0			0
$143$	−166.323	−	96.0267i	−1.16310	−	0.671515i
$144$		0			0
$145$	68.8127	+	119.187i	0.474570	+	0.821980i
$146$		0			0
$147$	−43.5361	−	72.8533i	−0.296164	−	0.495601i
$148$		0			0
$149$	−78.5739	−	136.094i	−0.527342	−	0.913383i	−0.999492	−	0.0318647i	$-0.989855\pi$
$149$	−78.5739	−	136.094i	−0.527342	−	0.913383i	0.472150	−	0.881518i	$-0.343478\pi$
$150$		0			0
$151$	7.51370	+	4.33804i	0.0497596	+	0.0287287i	0.524673	−	0.851304i	$-0.324187\pi$
$151$	7.51370	+	4.33804i	0.0497596	+	0.0287287i	−0.474914	+	0.880032i	$0.657521\pi$
$152$		0			0
$153$	75.2990			0.492150
$154$		0			0
$155$			170.735i			1.10152i
$156$		0			0
$157$	55.0241	−	95.3045i	0.350472	−	0.607035i	−0.635860	−	0.771804i	$-0.719355\pi$
$157$	55.0241	−	95.3045i	0.350472	−	0.607035i	0.986332	+	0.164769i	$0.0526879\pi$
$158$		0			0
$159$	−98.4381	+	56.8333i	−0.619108	+	0.357442i
$160$		0			0
$161$	−35.4502	+	9.78523i	−0.220187	+	0.0607778i
$162$		0			0
$163$	127.849	−	73.8136i	0.784349	−	0.452844i	−0.0536205	−	0.998561i	$-0.517076\pi$
$163$	127.849	−	73.8136i	0.784349	−	0.452844i	0.837969	+	0.545717i	$0.183743\pi$
$164$		0			0
$165$	53.0120	−	91.8196i	0.321285	−	0.556482i
$166$		0			0
$167$		−	60.5642i		−	0.362660i	−0.983422	−	0.181330i	$-0.941960\pi$
$167$		−	60.5642i		−	0.362660i	0.983422	−	0.181330i	$-0.0580402\pi$
$168$		0			0
$169$	−63.4261			−0.375302
$170$		0			0
$171$	−80.3609	−	46.3964i	−0.469947	−	0.271324i
$172$		0			0
$173$	45.4261	+	78.6803i	0.262578	+	0.454799i	0.966926	−	0.255056i	$-0.0820938\pi$
$173$	45.4261	+	78.6803i	0.262578	+	0.454799i	−0.704348	+	0.709855i	$0.748760\pi$
$174$		0			0
$175$	70.1238	−	71.1867i	0.400707	−	0.406781i
$176$		0			0
$177$	−38.8368	−	67.2673i	−0.219417	−	0.380041i
$178$		0			0
$179$	275.973	+	159.333i	1.54175	+	0.890128i	0.998729	+	0.0504063i	$0.0160516\pi$
$179$	275.973	+	159.333i	1.54175	+	0.890128i	0.543018	+	0.839721i	$0.317282\pi$
$180$		0			0
$181$	31.6769			0.175011			0.0875053	−	0.996164i	$-0.472111\pi$
$181$	31.6769			0.175011			0.0875053	+	0.996164i	$0.472111\pi$
$182$		0			0
$183$		−	109.292i		−	0.597223i
$184$		0			0
$185$	−58.8248	+	101.887i	−0.317972	+	0.550743i
$186$		0			0
$187$	−406.296	+	234.575i	−2.17270	+	1.25441i
$188$		0			0
$189$	9.14950	−	35.2035i	0.0484101	−	0.186262i
$190$		0			0
$191$	−208.722	+	120.506i	−1.09278	+	0.630919i	−0.934316	−	0.356445i	$-0.883989\pi$
$191$	−208.722	+	120.506i	−1.09278	+	0.630919i	−0.158468	+	0.987364i	$0.550655\pi$
$192$		0			0
$193$	170.723	−	295.702i	0.884577	−	1.53213i	0.0383800	−	0.999263i	$-0.487780\pi$
$193$	170.723	−	295.702i	0.884577	−	1.53213i	0.846197	−	0.532870i	$-0.178886\pi$
$194$		0			0
$195$			58.2826i			0.298885i
$196$		0			0
$197$	−142.550			−0.723603			−0.361802	−	0.932255i	$-0.617838\pi$
$197$	−142.550			−0.723603			−0.361802	+	0.932255i	$0.617838\pi$
$198$		0			0
$199$	−4.54983	−	2.62685i	−0.0228635	−	0.0132002i	0.488525	−	0.872550i	$-0.337535\pi$
$199$	−4.54983	−	2.62685i	−0.0228635	−	0.0132002i	−0.511388	+	0.859350i	$0.670869\pi$
$200$		0			0
$201$	−19.2371	−	33.3197i	−0.0957071	−	0.165770i
$202$		0			0
$203$	−284.710	−	73.9970i	−1.40251	−	0.364517i
$204$		0			0
$205$	63.4502	+	109.899i	0.309513	+	0.536092i
$206$		0			0
$207$	−13.6495	−	7.88054i	−0.0659396	−	0.0380703i
$208$		0			0
$209$	578.145			2.76624
$210$		0			0
$211$		−	271.267i		−	1.28563i	−0.766023	−	0.642814i	$-0.777767\pi$
$211$		−	271.267i		−	1.28563i	0.766023	−	0.642814i	$-0.222233\pi$
$212$		0			0
$213$	−84.4983	+	146.355i	−0.396706	+	0.687115i
$214$		0			0
$215$	−89.4469	+	51.6422i	−0.416032	+	0.240196i
$216$		0			0
$217$	−259.985	−	256.103i	−1.19809	−	1.18020i
$218$		0			0
$219$	137.588	−	79.4363i	0.628254	−	0.362723i
$220$		0			0
$221$	128.949	−	223.345i	0.583477	−	1.01061i
$222$		0			0
$223$		−	76.8907i		−	0.344801i	−0.985027	−	0.172401i	$-0.944848\pi$
$223$		−	76.8907i		−	0.344801i	0.985027	−	0.172401i	$-0.0551524\pi$
$224$		0			0
$225$	42.8248			0.190332
$226$		0			0
$227$	−119.765	−	69.1461i	−0.527597	−	0.304608i	0.212440	−	0.977174i	$-0.431859\pi$
$227$	−119.765	−	69.1461i	−0.527597	−	0.304608i	−0.740037	+	0.672566i	$0.765192\pi$
$228$		0			0
$229$	−67.1856	−	116.369i	−0.293387	−	0.508161i	0.681221	−	0.732078i	$-0.261449\pi$
$229$	−67.1856	−	116.369i	−0.293387	−	0.508161i	−0.974608	+	0.223916i	$0.928116\pi$
$230$		0			0
$231$	60.2990	+	218.453i	0.261035	+	0.945683i
$232$		0			0
$233$	35.9244	+	62.2229i	0.154182	+	0.267051i	0.932761	−	0.360496i	$-0.117392\pi$
$233$	35.9244	+	62.2229i	0.154182	+	0.267051i	−0.778579	+	0.627547i	$0.784059\pi$
$234$		0			0
$235$	−68.7733	−	39.7063i	−0.292652	−	0.168963i
$236$		0			0
$237$	16.0515			0.0677278
$238$		0			0
$239$		−	331.308i		−	1.38623i	−0.720829	−	0.693113i	$-0.756239\pi$
$239$		−	331.308i		−	1.38623i	0.720829	−	0.693113i	$-0.243761\pi$
$240$		0			0
$241$	−53.2629	+	92.2540i	−0.221008	+	0.382797i	−0.955114	−	0.296238i	$-0.904268\pi$
$241$	−53.2629	+	92.2540i	−0.221008	+	0.382797i	0.734106	+	0.679034i	$0.237601\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−2.41403	−	160.453i	−0.00985319	−	0.654909i
$246$		0			0
$247$	−275.234	+	158.906i	−1.11431	+	0.643345i
$248$		0			0
$249$	44.3385	−	76.7965i	0.178066	−	0.308419i
$250$		0			0
$251$			251.100i			1.00040i	0.865910	+	0.500199i	$0.166740\pi$
$251$			251.100i			1.00040i	−0.865910	+	0.500199i	$0.833260\pi$
$252$		0			0
$253$	98.1993			0.388140
$254$		0			0
$255$	123.299	+	71.1867i	0.483526	+	0.279164i
$256$		0			0
$257$	203.199	+	351.952i	0.790659	+	1.36946i	0.925559	+	0.378602i	$0.123595\pi$
$257$	203.199	+	351.952i	0.790659	+	1.36946i	−0.134901	+	0.990859i	$0.543072\pi$
$258$		0			0
$259$	−66.9107	−	242.406i	−0.258343	−	0.935930i
$260$		0			0
$261$	−63.0361	−	109.182i	−0.241518	−	0.418321i
$262$		0			0
$263$	−48.8696	−	28.2149i	−0.185816	−	0.107281i	0.404206	−	0.914668i	$-0.367548\pi$
$263$	−48.8696	−	28.2149i	−0.185816	−	0.107281i	−0.590022	+	0.807387i	$0.700881\pi$
$264$		0			0
$265$	−214.918			−0.811011
$266$		0			0
$267$		−	92.5784i		−	0.346736i
$268$		0			0
$269$	68.2355	−	118.187i	0.253663	−	0.439358i	−0.710868	−	0.703325i	$-0.751698\pi$
$269$	68.2355	−	118.187i	0.253663	−	0.439358i	0.964532	+	0.263967i	$0.0850311\pi$
$270$		0			0
$271$	0.534478	−	0.308581i	0.00197225	−	0.00113868i	−0.499014	−	0.866594i	$-0.666304\pi$
$271$	0.534478	−	0.308581i	0.00197225	−	0.00113868i	0.500986	+	0.865456i	$0.332971\pi$
$272$		0			0
$273$	−88.7492	−	87.4240i	−0.325089	−	0.320234i
$274$		0			0
$275$	−231.072	+	133.410i	−0.840263	+	0.485126i
$276$		0			0
$277$	−195.632	+	338.845i	−0.706254	+	1.22327i	0.259982	+	0.965613i	$0.416283\pi$
$277$	−195.632	+	338.845i	−0.706254	+	1.22327i	−0.966237	+	0.257655i	$0.917050\pi$
$278$		0			0
$279$		−	156.402i		−	0.560582i
$280$		0			0
$281$	−534.248			−1.90124			−0.950618	−	0.310362i	$-0.899550\pi$
$281$	−534.248			−1.90124			−0.950618	+	0.310362i	$0.899550\pi$
$282$		0			0
$283$	55.4639	+	32.0221i	0.195985	+	0.113152i	0.594782	−	0.803887i	$-0.297239\pi$
$283$	55.4639	+	32.0221i	0.195985	+	0.113152i	−0.398796	+	0.917040i	$0.630572\pi$
$284$		0			0
$285$	−87.7251	−	151.944i	−0.307807	−	0.533138i
$286$		0			0
$287$	−262.522	−	68.2304i	−0.914712	−	0.237737i
$288$		0			0
$289$	−170.497	−	295.309i	−0.589954	−	1.02183i
$290$		0			0
$291$	−194.284	−	112.170i	−0.667641	−	0.385463i
$292$		0			0
$293$	88.6703			0.302629			0.151314	−	0.988486i	$-0.451649\pi$
$293$	88.6703			0.302629			0.151314	+	0.988486i	$0.451649\pi$
$294$		0			0
$295$		−	146.863i		−	0.497841i
$296$		0			0
$297$	−48.5619	+	84.1116i	−0.163508	+	0.283204i
$298$		0			0
$299$	−46.7492	+	26.9906i	−0.156352	+	0.0902697i
$300$		0			0
$301$	55.5328	−	213.667i	0.184494	−	0.709858i
$302$		0			0
$303$	80.5465	−	46.5036i	0.265830	−	0.153477i
$304$		0			0
$305$	103.323	−	178.961i	0.338764	−	0.586757i
$306$		0			0
$307$		−	147.004i		−	0.478841i	−0.970916	−	0.239421i	$-0.923043\pi$
$307$		−	147.004i		−	0.478841i	0.970916	−	0.239421i	$-0.0769575\pi$
$308$		0			0
$309$	−55.6221			−0.180007
$310$		0			0
$311$	−159.526	−	92.1022i	−0.512945	−	0.296149i	0.221099	−	0.975251i	$-0.429036\pi$
$311$	−159.526	−	92.1022i	−0.512945	−	0.296149i	−0.734043	+	0.679103i	$0.762369\pi$
$312$		0			0
$313$	111.521	+	193.160i	0.356296	+	0.617123i	0.987339	−	0.158625i	$-0.0507060\pi$
$313$	111.521	+	193.160i	0.356296	+	0.617123i	−0.631043	+	0.775748i	$0.717373\pi$
$314$		0			0
$315$	48.2629	−	48.9945i	0.153215	−	0.155538i
$316$		0			0
$317$	310.359	+	537.558i	0.979051	+	1.69577i	0.665861	+	0.746076i	$0.268065\pi$
$317$	310.359	+	537.558i	0.979051	+	1.69577i	0.313191	+	0.949690i	$0.398602\pi$
$318$		0			0
$319$	680.256	+	392.746i	2.13246	+	1.23118i
$320$		0			0
$321$	−99.1719			−0.308947
$322$		0			0
$323$			776.356i			2.40358i
$324$		0			0
$325$	73.3368	−	127.023i	0.225652	−	0.390840i
$326$		0			0
$327$	−212.062	+	122.434i	−0.648507	+	0.374416i
$328$		0			0
$329$	163.622	−	45.1642i	0.497332	−	0.137277i
$330$		0			0
$331$	314.787	−	181.742i	0.951018	−	0.549071i	0.0576210	−	0.998339i	$-0.481649\pi$
$331$	314.787	−	181.742i	0.951018	−	0.549071i	0.893397	+	0.449268i	$0.148315\pi$
$332$		0			0
$333$	53.8866	−	93.3344i	0.161822	−	0.280283i
$334$		0			0
$335$		−	72.7461i		−	0.217153i
$336$		0			0
$337$	−322.093			−0.955766			−0.477883	−	0.878424i	$-0.658596\pi$
$337$	−322.093			−0.955766			−0.477883	+	0.878424i	$0.658596\pi$
$338$		0			0
$339$	108.227	+	62.4847i	0.319253	+	0.184321i
$340$		0			0
$341$	487.232	+	843.911i	1.42883	+	2.47481i
$342$		0			0
$343$	247.949	+	237.003i	0.722882	+	0.690972i
$344$		0			0
$345$	−14.9003	−	25.8081i	−0.0431894	−	0.0748062i
$346$		0			0
$347$	305.093	+	176.146i	0.879231	+	0.507624i	0.870405	−	0.492337i	$-0.163857\pi$
$347$	305.093	+	176.146i	0.879231	+	0.507624i	0.00882601	+	0.999961i	$0.497191\pi$
$348$		0			0
$349$	221.395			0.634371			0.317185	−	0.948364i	$-0.397262\pi$
$349$	221.395			0.634371			0.317185	+	0.948364i	$0.397262\pi$
$350$		0			0
$351$		−	53.3900i		−	0.152108i
$352$		0			0
$353$	28.8729	−	50.0094i	0.0817930	−	0.141670i	−0.822227	−	0.569159i	$-0.807269\pi$
$353$	28.8729	−	50.0094i	0.0817930	−	0.141670i	0.904020	+	0.427490i	$0.140602\pi$
$354$		0			0
$355$	−276.725	+	159.767i	−0.779507	+	0.450049i
$356$		0			0
$357$	−293.347	+	80.9719i	−0.821701	+	0.226812i
$358$		0			0
$359$	243.117	−	140.364i	0.677207	−	0.390985i	−0.121595	−	0.992580i	$-0.538801\pi$
$359$	243.117	−	140.364i	0.677207	−	0.390985i	0.798802	+	0.601594i	$0.205468\pi$
$360$		0			0
$361$	297.861	−	515.910i	0.825099	−	1.42911i
$362$		0			0
$363$		−	395.551i		−	1.08967i
$364$		0			0
$365$	300.392			0.822992
$366$		0			0
$367$	80.2974	+	46.3597i	0.218794	+	0.126321i	0.605392	−	0.795928i	$-0.293016\pi$
$367$	80.2974	+	46.3597i	0.218794	+	0.126321i	−0.386598	+	0.922248i	$0.626350\pi$
$368$		0			0
$369$	−58.1238	−	100.673i	−0.157517	−	0.272827i
$370$		0			0
$371$	322.377	−	327.263i	0.868940	−	0.882112i
$372$		0			0
$373$	78.4365	+	135.856i	0.210285	+	0.364225i	0.951804	−	0.306707i	$-0.0992273\pi$
$373$	78.4365	+	135.856i	0.210285	+	0.364225i	−0.741518	+	0.670933i	$0.765894\pi$
$374$		0			0
$375$	192.933	+	111.390i	0.514488	+	0.297040i
$376$		0			0
$377$	−431.794			−1.14534
$378$		0			0
$379$		−	466.559i		−	1.23103i	−0.788127	−	0.615513i	$-0.788949\pi$
$379$		−	466.559i		−	1.23103i	0.788127	−	0.615513i	$-0.211051\pi$
$380$		0			0
$381$	130.672	−	226.330i	0.342971	−	0.594043i
$382$		0			0
$383$	429.625	−	248.044i	1.12174	−	0.647635i	0.179893	−	0.983686i	$-0.442425\pi$
$383$	429.625	−	248.044i	1.12174	−	0.647635i	0.941844	+	0.336051i	$0.109091\pi$
$384$		0			0
$385$	−107.785	+	414.713i	−0.279962	+	1.07718i
$386$		0			0
$387$	81.9381	−	47.3070i	0.211726	−	0.122240i
$388$		0			0
$389$	−324.148	+	561.441i	−0.833285	+	1.44329i	0.0621342	+	0.998068i	$0.480209\pi$
$389$	−324.148	+	561.441i	−0.833285	+	1.44329i	−0.895419	+	0.445224i	$0.853124\pi$
$390$		0			0
$391$			131.866i			0.337253i
$392$		0			0
$393$	−243.770			−0.620280
$394$		0			0
$395$	26.2837	+	15.1749i	0.0665409	+	0.0384174i
$396$		0			0
$397$	−156.210	−	270.563i	−0.393475	−	0.681519i	0.599430	−	0.800427i	$-0.295394\pi$
$397$	−156.210	−	270.563i	−0.393475	−	0.681519i	−0.992905	+	0.118908i	$0.962061\pi$
$398$		0			0
$399$	362.959	+	94.3342i	0.909671	+	0.236427i
$400$		0			0
$401$	−16.0000	−	27.7128i	−0.0399002	−	0.0691093i	0.845386	−	0.534156i	$-0.179371\pi$
$401$	−16.0000	−	27.7128i	−0.0399002	−	0.0691093i	−0.885286	+	0.465047i	$0.846037\pi$
$402$		0			0
$403$	−463.907	−	267.837i	−1.15114	−	0.664608i
$404$		0			0
$405$	29.4743			0.0727759
$406$		0			0
$407$			671.480i			1.64983i
$408$		0			0
$409$	−305.370	+	528.916i	−0.746625	+	1.29319i	0.202807	+	0.979219i	$0.434994\pi$
$409$	−305.370	+	528.916i	−0.746625	+	1.29319i	−0.949432	+	0.313974i	$0.898340\pi$
$410$		0			0
$411$	−67.5772	+	39.0157i	−0.164421	+	0.0949288i
$412$		0			0
$413$	223.634	+	220.295i	0.541487	+	0.533402i
$414$		0			0
$415$	145.205	−	83.8340i	0.349891	−	0.202010i
$416$		0			0
$417$	−27.9107	+	48.3428i	−0.0669322	+	0.115930i
$418$		0			0
$419$			674.432i			1.60962i	0.593530	+	0.804812i	$0.297734\pi$
$419$			674.432i			1.60962i	−0.593530	+	0.804812i	$0.702266\pi$
$420$		0			0
$421$	−97.9792			−0.232730			−0.116365	−	0.993207i	$-0.537124\pi$
$421$	−97.9792			−0.232730			−0.116365	+	0.993207i	$0.537124\pi$
$422$		0			0
$423$	63.0000	+	36.3731i	0.148936	+	0.0859883i
$424$		0			0
$425$	−179.148	−	310.293i	−0.421524	−	0.730102i
$426$		0			0
$427$	117.526	+	425.775i	0.275236	+	0.997132i
$428$		0			0
$429$	166.323	+	288.080i	0.387700	+	0.671515i
$430$		0			0
$431$	2.13038	+	1.22998i	0.00494288	+	0.00285377i	0.502469	−	0.864595i	$-0.332425\pi$
$431$	2.13038	+	1.22998i	0.00494288	+	0.00285377i	−0.497527	+	0.867449i	$0.665758\pi$
$432$		0			0
$433$	475.670			1.09855			0.549273	−	0.835643i	$-0.314905\pi$
$433$	475.670			1.09855			0.549273	+	0.835643i	$0.314905\pi$
$434$		0			0
$435$		−	238.374i		−	0.547987i
$436$		0			0
$437$	81.2508	−	140.731i	0.185929	−	0.322038i
$438$		0			0
$439$	118.686	−	68.5232i	0.270355	−	0.156089i	−0.358694	−	0.933455i	$-0.616778\pi$
$439$	118.686	−	68.5232i	0.270355	−	0.156089i	0.629049	+	0.777366i	$0.283445\pi$
$440$		0			0
$441$	2.21138	+	146.983i	0.00501447	+	0.333296i
$442$		0			0
$443$	139.459	−	80.5166i	0.314806	−	0.181753i	−0.334269	−	0.942478i	$-0.608489\pi$
$443$	139.459	−	80.5166i	0.314806	−	0.181753i	0.649075	+	0.760724i	$0.275156\pi$
$444$		0			0
$445$	87.5224	−	151.593i	0.196680	−	0.340659i
$446$		0			0
$447$			272.188i			0.608922i
$448$		0			0
$449$	279.643			0.622813			0.311406	−	0.950277i	$-0.399200\pi$
$449$	279.643			0.622813			0.311406	+	0.950277i	$0.399200\pi$
$450$		0			0
$451$	627.244	+	362.140i	1.39079	+	0.802970i
$452$		0			0
$453$	−7.51370	−	13.0141i	−0.0165865	−	0.0287287i
$454$		0			0
$455$	−62.6736	−	227.055i	−0.137744	−	0.499023i
$456$		0			0
$457$	−234.675	−	406.469i	−0.513513	−	0.889430i	−0.999877	−	0.0156739i	$-0.995011\pi$
$457$	−234.675	−	406.469i	−0.513513	−	0.889430i	0.486365	−	0.873756i	$-0.338323\pi$
$458$		0			0
$459$	−112.949	−	65.2109i	−0.246075	−	0.142072i
$460$		0			0
$461$	234.440			0.508547			0.254274	−	0.967132i	$-0.418164\pi$
$461$	234.440			0.508547			0.254274	+	0.967132i	$0.418164\pi$
$462$		0			0
$463$		−	515.120i		−	1.11257i	−0.830992	−	0.556285i	$-0.812226\pi$
$463$		−	515.120i		−	1.11257i	0.830992	−	0.556285i	$-0.187774\pi$
$464$		0			0
$465$	147.861	−	256.103i	0.317980	−	0.550758i
$466$		0			0
$467$	121.677	−	70.2502i	0.260550	−	0.150429i	−0.364035	−	0.931385i	$-0.618601\pi$
$467$	121.677	−	70.2502i	0.260550	−	0.150429i	0.624585	+	0.780956i	$0.285268\pi$
$468$		0			0
$469$	110.773	+	109.119i	0.236190	+	0.232664i
$470$		0			0
$471$	−165.072	+	95.3045i	−0.350472	+	0.202345i
$472$		0			0
$473$	−294.746	+	510.515i	−0.623141	+	1.07931i
$474$		0			0
$475$			441.536i			0.929550i
$476$		0			0
$477$	196.876			0.412738
$478$		0			0
$479$	−785.564	−	453.546i	−1.64001	−	0.946859i	−0.980828	−	0.194874i	$-0.937570\pi$
$479$	−785.564	−	453.546i	−1.64001	−	0.946859i	−0.659180	−	0.751985i	$-0.729097\pi$
$480$		0			0
$481$	−184.560	−	319.668i	−0.383701	−	0.664590i
$482$		0			0
$483$	61.6495	+	16.0229i	0.127639	+	0.0331737i
$484$		0			0
$485$	−212.088	−	367.347i	−0.437294	−	0.757416i
$486$		0			0
$487$	−251.153	−	145.003i	−0.515714	−	0.297748i	0.219465	−	0.975620i	$-0.429569\pi$
$487$	−251.153	−	145.003i	−0.515714	−	0.297748i	−0.735179	+	0.677873i	$0.762902\pi$
$488$		0			0
$489$	−255.698			−0.522899
$490$		0			0
$491$			353.412i			0.719779i	0.932995	+	0.359890i	$0.117186\pi$
$491$			353.412i			0.719779i	−0.932995	+	0.359890i	$0.882814\pi$
$492$		0			0
$493$	−527.395	+	913.476i	−1.06977	+	1.85289i
$494$		0			0
$495$	−159.036	+	91.8196i	−0.321285	+	0.185494i
$496$		0			0
$497$	171.804	−	661.031i	0.345682	−	1.33004i
$498$		0			0
$499$	284.543	−	164.281i	0.570226	−	0.329220i	−0.187014	−	0.982357i	$-0.559881\pi$
$499$	284.543	−	164.281i	0.570226	−	0.329220i	0.757240	+	0.653137i	$0.226548\pi$
$500$		0			0
$501$	−52.4502	+	90.8464i	−0.104691	+	0.181330i
$502$		0			0
$503$		−	791.625i		−	1.57381i	−0.617076	−	0.786904i	$-0.711683\pi$
$503$		−	791.625i		−	1.57381i	0.617076	−	0.786904i	$-0.288317\pi$
$504$		0			0
$505$	175.855			0.348229
$506$		0			0
$507$	95.1391	+	54.9286i	0.187651	+	0.108340i
$508$		0			0
$509$	217.637	+	376.959i	0.427579	+	0.740588i	0.996657	−	0.0816953i	$-0.0260334\pi$
$509$	217.637	+	376.959i	0.427579	+	0.740588i	−0.569079	+	0.822283i	$0.692700\pi$
$510$		0			0
$511$	−450.588	+	457.418i	−0.881777	+	0.895143i
$512$		0			0
$513$	80.3609	+	139.189i	0.156649	+	0.271324i
$514$		0			0
$515$	−91.0789	−	52.5844i	−0.176852	−	0.102106i
$516$		0			0
$517$	−453.244			−0.876681
$518$		0			0
$519$		−	157.361i		−	0.303200i
$520$		0			0
$521$	129.378	−	224.089i	0.248326	−	0.430113i	−0.714735	−	0.699395i	$-0.753453\pi$
$521$	129.378	−	224.089i	0.248326	−	0.430113i	0.963062	+	0.269282i	$0.0867862\pi$
$522$		0			0
$523$	809.523	−	467.378i	1.54784	−	0.893649i	0.549539	−	0.835468i	$-0.314803\pi$
$523$	809.523	−	467.378i	1.54784	−	0.893649i	0.998306	−	0.0581805i	$-0.0185299\pi$
$524$		0			0
$525$	−166.835	+	46.0511i	−0.317781	+	0.0877164i
$526$		0			0
$527$	−1133.24	+	654.275i	−2.15036	+	1.24151i
$528$		0			0
$529$	−250.699	+	434.224i	−0.473912	+	0.820839i
$530$		0			0
$531$			134.535i			0.253361i
$532$		0			0
$533$	−398.145			−0.746988
$534$		0			0
$535$	−162.390	−	93.7559i	−0.303533	−	0.175245i
$536$		0			0
$537$	−275.973	−	477.999i	−0.513915	−	0.890128i
$538$		0			0
$539$	−469.821	−	786.199i	−0.871654	−	1.45862i
$540$		0			0
$541$	−53.4572	−	92.5907i	−0.0988119	−	0.171147i	0.812381	−	0.583127i	$-0.198171\pi$
$541$	−53.4572	−	92.5907i	−0.0988119	−	0.171147i	−0.911193	+	0.411979i	$0.864838\pi$
$542$		0			0
$543$	−47.5154	−	27.4330i	−0.0875053	−	0.0505212i
$544$		0			0
$545$	−462.990			−0.849523
$546$		0			0
$547$		−	33.5534i		−	0.0613408i	−0.999530	−	0.0306704i	$-0.990236\pi$
$547$		−	33.5534i		−	0.0613408i	0.999530	−	0.0306704i	$-0.00976422\pi$
$548$		0			0
$549$	−94.6495	+	163.938i	−0.172403	+	0.298612i
$550$		0			0
$551$	1125.70	−	649.922i	2.04301	−	1.17953i
$552$		0			0
$553$	−62.5328	+	17.2608i	−0.113079	+	0.0312130i
$554$		0			0
$555$	176.474	−	101.887i	0.317972	−	0.183581i
$556$		0			0
$557$	484.954	−	839.965i	0.870653	−	1.50802i	0.00933136	−	0.999956i	$-0.497030\pi$
$557$	484.954	−	839.965i	0.870653	−	1.50802i	0.861322	−	0.508059i	$-0.169637\pi$
$558$		0			0
$559$		−	324.050i		−	0.579696i
$560$		0			0
$561$	812.591			1.44847
$562$		0			0
$563$	99.2629	+	57.3094i	0.176311	+	0.101793i	0.585558	−	0.810630i	$-0.300875\pi$
$563$	99.2629	+	57.3094i	0.176311	+	0.101793i	−0.409247	+	0.912423i	$0.634209\pi$
$564$		0			0
$565$	118.145	+	204.632i	0.209105	+	0.362181i
$566$		0			0
$567$	−44.2114	+	44.8816i	−0.0779742	+	0.0791562i
$568$		0			0
$569$	−152.275	−	263.748i	−0.267618	−	0.463529i	0.700628	−	0.713527i	$-0.252903\pi$
$569$	−152.275	−	263.748i	−0.267618	−	0.463529i	−0.968246	+	0.249998i	$0.919570\pi$
$570$		0			0
$571$	−709.636	−	409.708i	−1.24279	−	0.717528i	−0.273132	−	0.961976i	$-0.588060\pi$
$571$	−709.636	−	409.708i	−1.24279	−	0.717528i	−0.969662	+	0.244449i	$0.921393\pi$
$572$		0			0
$573$	417.444			0.728523
$574$		0			0
$575$			74.9961i			0.130428i
$576$		0			0
$577$	517.895	−	897.021i	0.897566	−	1.55463i	0.0669688	−	0.997755i	$-0.478667\pi$
$577$	517.895	−	897.021i	0.897566	−	1.55463i	0.830597	−	0.556874i	$-0.187999\pi$
$578$		0			0
$579$	−512.170	+	295.702i	−0.884577	+	0.510711i
$580$		0			0
$581$	−90.1500	+	346.860i	−0.155163	+	0.597005i
$582$		0			0
$583$	−1062.30	+	613.318i	−1.82212	+	1.05200i
$584$		0			0
$585$	50.4743	−	87.4240i	0.0862808	−	0.149443i
$586$		0			0
$587$			991.224i			1.68863i	0.535850	+	0.844313i	$0.319991\pi$
$587$			991.224i			1.68863i	−0.535850	+	0.844313i	$0.680009\pi$
$588$		0			0
$589$	1612.56			2.73779
$590$		0			0
$591$	213.825	+	123.452i	0.361802	+	0.208886i
$592$		0			0
$593$	−273.368	−	473.487i	−0.460992	−	0.798461i	0.538019	−	0.842933i	$-0.319173\pi$
$593$	−273.368	−	473.487i	−0.460992	−	0.798461i	−0.999011	+	0.0444719i	$0.985839\pi$
$594$		0			0
$595$	−556.894	−	144.738i	−0.935956	−	0.243258i
$596$		0			0
$597$	4.54983	+	7.88054i	0.00762116	+	0.0132002i
$598$		0			0
$599$	389.474	+	224.863i	0.650207	+	0.375397i	0.788536	−	0.614989i	$-0.210840\pi$
$599$	389.474	+	224.863i	0.650207	+	0.375397i	−0.138328	+	0.990386i	$0.544173\pi$
$600$		0			0
$601$	−392.106			−0.652423			−0.326212	−	0.945297i	$-0.605772\pi$
$601$	−392.106			−0.652423			−0.326212	+	0.945297i	$0.605772\pi$
$602$		0			0
$603$			66.6394i			0.110513i
$604$		0			0
$605$	373.949	−	647.698i	0.618097	−	1.07057i
$606$		0			0
$607$	−657.040	+	379.342i	−1.08244	+	0.624946i	−0.931553	−	0.363605i	$-0.881546\pi$
$607$	−657.040	+	379.342i	−1.08244	+	0.624946i	−0.150885	+	0.988551i	$0.548212\pi$
$608$		0			0
$609$	362.981	+	357.561i	0.596028	+	0.587129i
$610$		0			0
$611$	215.773	−	124.577i	0.353148	−	0.203890i
$612$		0			0
$613$	217.670	−	377.016i	0.355090	−	0.615034i	−0.632043	−	0.774933i	$-0.717783\pi$
$613$	217.670	−	377.016i	0.355090	−	0.615034i	0.987133	+	0.159899i	$0.0511168\pi$
$614$		0			0
$615$		−	219.798i		−	0.357395i
$616$		0			0
$617$	−145.189			−0.235315			−0.117658	−	0.993054i	$-0.537539\pi$
$617$	−145.189			−0.235315			−0.117658	+	0.993054i	$0.537539\pi$
$618$		0			0
$619$	−442.399	−	255.419i	−0.714700	−	0.412632i	0.0980990	−	0.995177i	$-0.468724\pi$
$619$	−442.399	−	255.419i	−0.714700	−	0.412632i	−0.812799	+	0.582545i	$0.802057\pi$
$620$		0			0
$621$	13.6495	+	23.6416i	0.0219799	+	0.0380703i
$622$		0			0
$623$	99.5531	+	360.664i	0.159796	+	0.578914i
$624$		0			0
$625$	32.1769	+	55.7320i	0.0514830	+	0.0891713i
$626$		0			0
$627$	−867.217	−	500.688i	−1.38312	−	0.798545i
$628$		0			0
$629$	−901.691			−1.43353
$630$		0			0
$631$			345.666i			0.547807i	0.961757	+	0.273904i	$0.0883150\pi$
$631$			345.666i			0.547807i	−0.961757	+	0.273904i	$0.911685\pi$
$632$		0			0
$633$	−234.924	+	406.901i	−0.371129	+	0.642814i
$634$		0			0
$635$	427.940	−	247.071i	0.673921	−	0.389088i
$636$		0			0
$637$	439.756	+	245.148i	0.690355	+	0.384847i
$638$		0			0
$639$	253.495	−	146.355i	0.396706	−	0.229038i
$640$		0			0
$641$	−452.072	+	783.012i	−0.705261	+	1.22155i	0.261336	+	0.965248i	$0.415837\pi$
$641$	−452.072	+	783.012i	−0.705261	+	1.22155i	−0.966597	+	0.256300i	$0.917497\pi$
$642$		0			0
$643$			265.621i			0.413096i	0.978436	+	0.206548i	$0.0662230\pi$
$643$			265.621i			0.413096i	−0.978436	+	0.206548i	$0.933777\pi$
$644$		0			0
$645$	178.894			0.277355
$646$		0			0
$647$	−306.807	−	177.135i	−0.474200	−	0.273779i	0.243796	−	0.969826i	$-0.421607\pi$
$647$	−306.807	−	177.135i	−0.474200	−	0.273779i	−0.717996	+	0.696047i	$0.754940\pi$
$648$		0			0
$649$	−419.108	−	725.917i	−0.645776	−	1.11852i
$650$		0			0
$651$	168.186	+	609.307i	0.258350	+	0.935956i
$652$		0			0
$653$	−390.483	−	676.336i	−0.597983	−	1.03574i	−0.993118	−	0.117114i	$-0.962636\pi$
$653$	−390.483	−	676.336i	−0.597983	−	1.03574i	0.395135	−	0.918623i	$-0.370698\pi$
$654$		0			0
$655$	−399.163	−	230.457i	−0.609409	−	0.351843i
$656$		0			0
$657$	−275.175			−0.418836
$658$		0			0
$659$		−	309.905i		−	0.470265i	−0.971963	−	0.235133i	$-0.924448\pi$
$659$		−	309.905i		−	0.470265i	0.971963	−	0.235133i	$-0.0755524\pi$
$660$		0			0
$661$	345.059	−	597.659i	0.522025	−	0.904174i	−0.477647	−	0.878552i	$-0.658510\pi$
$661$	345.059	−	597.659i	0.522025	−	0.904174i	0.999672	−	0.0256219i	$-0.00815660\pi$
$662$		0			0
$663$	−386.846	+	223.345i	−0.583477	+	0.336871i
$664$		0			0
$665$	505.148	+	497.605i	0.759621	+	0.748278i
$666$		0			0
$667$	191.203	−	110.391i	0.286661	−	0.165504i
$668$		0			0
$669$	−66.5893	+	115.336i	−0.0995355	+	0.172401i
$670$		0			0
$671$		−	1179.43i		−	1.75771i
$672$		0			0
$673$	714.238			1.06127			0.530637	−	0.847599i	$-0.321953\pi$
$673$	714.238			1.06127			0.530637	+	0.847599i	$0.321953\pi$
$674$		0			0
$675$	−64.2371	−	37.0873i	−0.0951661	−	0.0549442i
$676$		0			0
$677$	−589.205	−	1020.53i	−0.870317	−	1.50743i	−0.861669	−	0.507471i	$-0.830580\pi$
$677$	−589.205	−	1020.53i	−0.870317	−	1.50743i	−0.00864841	−	0.999963i	$-0.502753\pi$
$678$		0			0
$679$	877.504	+	228.066i	1.29235	+	0.335885i
$680$		0			0
$681$	119.765	+	207.438i	0.175866	+	0.304608i
$682$		0			0
$683$	−732.226	−	422.751i	−1.07207	−	0.618961i	−0.143326	−	0.989676i	$-0.545780\pi$
$683$	−732.226	−	422.751i	−1.07207	−	0.618961i	−0.928747	+	0.370714i	$0.879113\pi$
$684$		0			0
$685$	−147.540			−0.215387
$686$		0			0
$687$			232.738i			0.338774i
$688$		0			0
$689$	337.148	−	583.957i	0.489329	−	0.847543i
$690$		0			0
$691$	−871.598	+	503.218i	−1.26136	+	0.728245i	−0.973337	−	0.229379i	$-0.926331\pi$
$691$	−871.598	+	503.218i	−1.26136	+	0.728245i	−0.288021	+	0.957624i	$0.592997\pi$
$692$		0			0
$693$	98.7371	−	379.900i	0.142478	−	0.548196i
$694$		0			0
$695$	−91.4053	+	52.7729i	−0.131518	+	0.0759322i
$696$		0			0
$697$	−486.296	+	842.289i	−0.697698	+	1.20845i
$698$		0			0
$699$		−	124.446i		−	0.178034i
$700$		0			0
$701$	−1047.00			−1.49358			−0.746791	−	0.665059i	$-0.768406\pi$
$701$	−1047.00			−1.49358			−0.746791	+	0.665059i	$0.768406\pi$
$702$		0			0
$703$	962.306	+	555.588i	1.36886	+	0.790310i
$704$		0			0
$705$	68.7733	+	119.119i	0.0975507	+	0.168963i
$706$		0			0
$707$	−263.783	+	267.782i	−0.373102	+	0.378758i
$708$		0			0
$709$	664.485	+	1150.92i	0.937215	+	1.62330i	0.770637	+	0.637275i	$0.219938\pi$
$709$	664.485	+	1150.92i	0.937215	+	1.62330i	0.166578	+	0.986028i	$0.446728\pi$
$710$		0			0
$711$	−24.0772	−	13.9010i	−0.0338639	−	0.0195513i
$712$		0			0
$713$	273.897			0.384147
$714$		0			0
$715$			628.959i			0.879663i
$716$		0			0
$717$	−286.921	+	496.962i	−0.400169	+	0.693113i
$718$		0			0
$719$	1126.85	−	650.586i	1.56724	−	0.904849i	0.570756	−	0.821120i	$-0.306650\pi$
$719$	1126.85	−	650.586i	1.56724	−	0.904849i	0.996489	−	0.0837294i	$-0.0266831\pi$
$720$		0			0
$721$	216.691	−	59.8126i	0.300542	−	0.0829578i
$722$		0			0
$723$	159.789	−	92.2540i	0.221008	−	0.127599i
$724$		0			0
$725$	−299.945	+	519.520i	−0.413718	+	0.716580i
$726$		0			0
$727$		−	951.043i		−	1.30817i	−0.756419	−	0.654087i	$-0.773053\pi$
$727$		−	951.043i		−	1.30817i	0.756419	−	0.654087i	$-0.226947\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−685.540	−	395.797i	−0.937811	−	0.541445i
$732$		0			0
$733$	−365.313	−	632.740i	−0.498380	−	0.863220i	0.501618	−	0.865089i	$-0.332738\pi$
$733$	−365.313	−	632.740i	−0.498380	−	0.863220i	−0.999998	+	0.00186934i	$0.999405\pi$
$734$		0			0
$735$	−135.335	+	242.770i	−0.184129	+	0.330299i
$736$		0			0
$737$	−207.598	−	359.570i	−0.281680	−	0.487884i
$738$		0			0
$739$	197.107	+	113.800i	0.266721	+	0.153991i	0.627397	−	0.778700i	$-0.284121\pi$
$739$	197.107	+	113.800i	0.266721	+	0.153991i	−0.360676	+	0.932691i	$0.617454\pi$
$740$		0			0
$741$	550.468			0.742871
$742$		0			0
$743$			1129.94i			1.52078i	0.649470	+	0.760388i	$0.274991\pi$
$743$			1129.94i			1.52078i	−0.649470	+	0.760388i	$0.725009\pi$
$744$		0			0
$745$	−257.323	+	445.697i	−0.345400	+	0.598251i
$746$		0			0
$747$	−133.015	+	76.7965i	−0.178066	+	0.102806i
$748$		0			0
$749$	386.350	−	106.643i	0.515822	−	0.142381i
$750$		0			0
$751$	858.755	−	495.802i	1.14348	−	0.660190i	0.196192	−	0.980566i	$-0.437143\pi$
$751$	858.755	−	495.802i	1.14348	−	0.660190i	0.947290	+	0.320376i	$0.103809\pi$
$752$		0			0
$753$	217.459	−	376.650i	0.288790	−	0.500199i
$754$		0			0
$755$		−	28.4134i		−	0.0376337i
$756$		0			0
$757$	−373.286			−0.493112			−0.246556	−	0.969129i	$-0.579299\pi$
$757$	−373.286			−0.493112			−0.246556	+	0.969129i	$0.579299\pi$
$758$		0			0
$759$	−147.299	−	85.0431i	−0.194070	−	0.112046i
$760$		0			0
$761$	−113.106	−	195.906i	−0.148629	−	0.257432i	0.782092	−	0.623163i	$-0.214153\pi$
$761$	−113.106	−	195.906i	−0.148629	−	0.257432i	−0.930721	+	0.365730i	$0.880819\pi$
$762$		0			0
$763$	694.485	−	705.012i	0.910203	−	0.924000i
$764$		0			0
$765$	−123.299	−	213.560i	−0.161175	−	0.279164i
$766$		0			0
$767$	399.045	+	230.389i	0.520267	+	0.300376i
$768$		0			0
$769$	100.836			0.131126			0.0655628	−	0.997848i	$-0.479116\pi$
$769$	100.836			0.131126			0.0655628	+	0.997848i	$0.479116\pi$
$770$		0			0
$771$		−	703.903i		−	0.912974i
$772$		0			0
$773$	35.8040	−	62.0143i	0.0463182	−	0.0802255i	−0.841937	−	0.539576i	$-0.818585\pi$
$773$	35.8040	−	62.0143i	0.0463182	−	0.0802255i	0.888255	+	0.459351i	$0.151918\pi$
$774$		0			0
$775$	−644.505	+	372.105i	−0.831620	+	0.480136i
$776$		0			0
$777$	−109.564	+	421.555i	−0.141008	+	0.542542i
$778$		0			0
$779$	1037.97	−	599.274i	1.33244	−	0.769286i
$780$		0			0
$781$	−911.866	+	1579.40i	−1.16756	+	2.02228i
$782$		0			0
$783$			218.364i			0.278881i
$784$		0			0
$785$	−360.399			−0.459107
$786$		0			0
$787$	419.619	+	242.267i	0.533188	+	0.307836i	0.742314	−	0.670053i	$-0.233728\pi$
$787$	419.619	+	242.267i	0.533188	+	0.307836i	−0.209126	+	0.977889i	$0.567062\pi$
$788$		0			0
$789$	48.8696	+	84.6447i	0.0619387	+	0.107281i
$790$		0			0
$791$	−488.818	−	127.045i	−0.617975	−	0.160614i
$792$		0			0
$793$	324.172	+	561.482i	0.408792	+	0.708048i
$794$		0			0
$795$	322.377	+	186.124i	0.405505	+	0.234119i
$796$		0			0
$797$	−189.275			−0.237484			−0.118742	−	0.992925i	$-0.537886\pi$
$797$	−189.275			−0.237484			−0.118742	+	0.992925i	$0.537886\pi$
$798$		0			0
$799$		−	608.635i		−	0.761745i
$800$		0			0
$801$	−80.1752	+	138.868i	−0.100094	+	0.173368i
$802$		0			0
$803$	1484.78	−	857.239i	1.84904	−	1.06754i
$804$		0			0
$805$	85.8007	+	84.5195i	0.106585	+	0.104993i
$806$		0			0
$807$	−204.706	+	118.187i	−0.253663	+	0.146453i
$808$		0			0
$809$	−558.976	+	968.175i	−0.690947	+	1.19675i	0.280581	+	0.959830i	$0.409473\pi$
$809$	−558.976	+	968.175i	−0.690947	+	1.19675i	−0.971528	+	0.236925i	$0.923861\pi$
$810$		0			0
$811$			706.070i			0.870616i	0.900282	+	0.435308i	$0.143361\pi$
$811$			706.070i			0.870616i	−0.900282	+	0.435308i	$0.856639\pi$
$812$		0			0
$813$	−1.06896			−0.00131483
$814$		0			0
$815$	−418.694	−	241.733i	−0.513735	−	0.296605i
$816$		0			0
$817$	487.750	+	844.807i	0.597001	+	1.03404i
$818$		0			0
$819$	57.4124	+	207.995i	0.0701006	+	0.253962i
$820$		0			0
$821$	−424.211	−	734.756i	−0.516701	−	0.894952i	−0.999812	−	0.0193930i	$-0.993827\pi$
$821$	−424.211	−	734.756i	−0.516701	−	0.894952i	0.483111	−	0.875559i	$-0.339507\pi$
$822$		0			0
$823$	−29.0930	−	16.7969i	−0.0353500	−	0.0204093i	0.482221	−	0.876050i	$-0.339830\pi$
$823$	−29.0930	−	16.7969i	−0.0353500	−	0.0204093i	−0.517571	+	0.855640i	$0.673164\pi$
$824$		0			0
$825$	462.145			0.560175
$826$		0			0
$827$			1246.59i			1.50737i	0.657236	+	0.753685i	$0.271725\pi$
$827$			1246.59i			1.50737i	−0.657236	+	0.753685i	$0.728275\pi$
$828$		0			0
$829$	384.554	−	666.066i	0.463876	−	0.803458i	−0.535274	−	0.844679i	$-0.679791\pi$
$829$	384.554	−	666.066i	0.463876	−	0.803458i	0.999150	+	0.0412211i	$0.0131248\pi$
$830$		0			0
$831$	586.897	−	338.845i	0.706254	−	0.407756i
$832$		0			0
$833$	1055.74	−	630.895i	1.26739	−	0.757377i
$834$		0			0
$835$	−171.770	+	99.1714i	−0.205713	+	0.118768i
$836$		0			0
$837$	−135.449	+	234.604i	−0.161826	+	0.280291i
$838$		0			0
$839$			244.162i			0.291015i	0.989357	+	0.145508i	$0.0464815\pi$
$839$			244.162i			0.291015i	−0.989357	+	0.145508i	$0.953519\pi$
$840$		0			0
$841$	925.024			1.09991
$842$		0			0
$843$	801.371	+	462.672i	0.950618	+	0.548840i
$844$		0			0
$845$	103.858	+	179.887i	0.122908	+	0.212884i
$846$		0			0
$847$	425.351	+	1540.97i	0.502185	+	1.81933i
$848$		0			0
$849$	−55.4639	−	96.0662i	−0.0653285	−	0.113152i
$850$		0			0
$851$	163.450	+	94.3680i	0.192068	+	0.110891i
$852$		0			0
$853$	−594.722			−0.697212			−0.348606	−	0.937269i	$-0.613345\pi$
$853$	−594.722			−0.697212			−0.348606	+	0.937269i	$0.613345\pi$
$854$		0			0
$855$			303.889i			0.355425i
$856$		0			0
$857$	−151.172	+	261.837i	−0.176397	+	0.305528i	−0.940644	−	0.339396i	$-0.889777\pi$
$857$	−151.172	+	261.837i	−0.176397	+	0.305528i	0.764247	+	0.644924i	$0.223111\pi$
$858$		0			0
$859$	507.461	−	292.983i	0.590758	−	0.341074i	−0.174639	−	0.984632i	$-0.555876\pi$
$859$	507.461	−	292.983i	0.590758	−	0.341074i	0.765397	+	0.643558i	$0.222543\pi$
$860$		0			0
$861$	334.694	+	329.697i	0.388727	+	0.382923i
$862$		0			0
$863$	−37.7142	+	21.7743i	−0.0437013	+	0.0252310i	−0.521691	−	0.853134i	$-0.674699\pi$
$863$	−37.7142	+	21.7743i	−0.0437013	+	0.0252310i	0.477990	+	0.878365i	$0.341365\pi$
$864$		0			0
$865$	148.767	−	257.671i	0.171985	−	0.297886i
$866$		0			0
$867$			590.618i			0.681220i
$868$		0			0
$869$	173.220			0.199333
$870$		0			0
$871$	197.660	+	114.119i	0.226934	+	0.131021i
$872$		0			0
$873$	194.284	+	336.509i	0.222547	+	0.385463i
$874$		0			0
$875$	−871.404	−	226.481i	−0.995890	−	0.258835i
$876$		0			0
$877$	−702.014	−	1215.92i	−0.800472	−	1.38646i	−0.919306	−	0.393544i	$-0.871249\pi$
$877$	−702.014	−	1215.92i	−0.800472	−	1.38646i	0.118833	−	0.992914i	$-0.462085\pi$
$878$		0			0
$879$	−133.005	−	76.7907i	−0.151314	−	0.0873615i
$880$		0			0
$881$	−507.842			−0.576438			−0.288219	−	0.957564i	$-0.593063\pi$
$881$	−507.842			−0.576438			−0.288219	+	0.957564i	$0.593063\pi$
$882$		0			0
$883$			438.774i			0.496913i	0.968643	+	0.248457i	$0.0799233\pi$
$883$			438.774i			0.496913i	−0.968643	+	0.248457i	$0.920077\pi$
$884$		0			0
$885$	−127.187	+	220.295i	−0.143714	+	0.248921i
$886$		0			0
$887$	178.069	−	102.808i	0.200754	−	0.115905i	−0.396253	−	0.918141i	$-0.629690\pi$
$887$	178.069	−	102.808i	0.200754	−	0.115905i	0.597007	+	0.802236i	$0.296356\pi$
$888$		0			0
$889$	−265.685	+	1022.25i	−0.298858	+	1.14988i
$890$		0			0
$891$	145.686	−	84.1116i	0.163508	−	0.0944014i
$892$		0			0
$893$	−375.017	+	649.549i	−0.419952	+	0.727379i
$894$		0			0
$895$		−	1043.60i		−	1.16604i
$896$		0			0
$897$	93.4983			0.104234
$898$		0			0
$899$	1897.37	+	1095.45i	2.11053	+	1.21852i
$900$		0			0
$901$	−823.588	−	1426.50i	−0.914082	−	1.58324i
$902$		0			0
$903$	−268.341	+	272.408i	−0.297166	+	0.301670i
$904$		0			0
$905$	−51.8696	−	89.8408i	−0.0573145	−	0.0992716i
$906$		0			0
$907$	−609.240	−	351.745i	−0.671709	−	0.387812i	0.125015	−	0.992155i	$-0.460102\pi$
$907$	−609.240	−	351.745i	−0.671709	−	0.387812i	−0.796724	+	0.604343i	$0.793436\pi$
$908$		0			0
$909$	−161.093			−0.177220
$910$		0			0
$911$		−	372.699i		−	0.409110i	−0.978855	−	0.204555i	$-0.934425\pi$
$911$		−	372.699i		−	0.409110i	0.978855	−	0.204555i	$-0.0655747\pi$
$912$		0			0
$913$	478.480	−	828.751i	0.524074	−	0.907723i
$914$		0			0
$915$	−309.969	+	178.961i	−0.338764	+	0.195586i
$916$		0			0
$917$	949.670	−	262.135i	1.03563	−	0.285862i
$918$		0			0
$919$	255.983	−	147.792i	0.278545	−	0.160818i	−0.354219	−	0.935162i	$-0.615253\pi$
$919$	255.983	−	147.792i	0.278545	−	0.160818i	0.632765	+	0.774344i	$0.281920\pi$
$920$		0			0
$921$	−127.309	+	220.506i	−0.138230	+	0.239421i
$922$		0			0
$923$		−	1002.53i		−	1.08616i
$924$		0			0
$925$	−512.818			−0.554398
$926$		0			0
$927$	83.4332	+	48.1702i	0.0900034	+	0.0519635i
$928$		0			0
$929$	847.289	+	1467.55i	0.912044	+	1.57971i	0.811172	+	0.584808i	$0.198830\pi$
$929$	847.289	+	1467.55i	0.912044	+	1.57971i	0.100872	+	0.994899i	$0.467837\pi$
$930$		0			0
$931$	−1515.44	+	22.8000i	−1.62776	+	0.0244898i
$932$		0			0
$933$	159.526	+	276.307i	0.170982	+	0.296149i
$934$		0			0
$935$	1330.58	+	768.213i	1.42309	+	0.821619i
$936$		0			0
$937$	−246.691			−0.263278			−0.131639	−	0.991298i	$-0.542024\pi$
$937$	−246.691			−0.263278			−0.131639	+	0.991298i	$0.542024\pi$
$938$		0			0
$939$		−	386.319i		−	0.411416i
$940$		0			0
$941$	−163.858	+	283.810i	−0.174131	+	0.301604i	−0.939860	−	0.341559i	$-0.889045\pi$
$941$	−163.858	+	283.810i	−0.174131	+	0.301604i	0.765729	+	0.643163i	$0.222378\pi$
$942$		0			0
$943$	176.302	−	101.788i	0.186959	−	0.107941i
$944$		0			0
$945$	−114.825	+	31.6948i	−0.121508	+	0.0335395i
$946$		0			0
$947$	−8.02078	+	4.63080i	−0.00846967	+	0.00488997i	−0.504229	−	0.863570i	$-0.668223\pi$
$947$	−8.02078	+	4.63080i	−0.00846967	+	0.00488997i	0.495759	+	0.868460i	$0.334890\pi$
$948$		0			0
$949$	−471.234	+	816.201i	−0.496558	+	0.860064i
$950$		0			0
$951$		−	1075.12i		−	1.13051i
$952$		0			0
$953$	1300.02			1.36414			0.682068	−	0.731289i	$-0.261081\pi$
$953$	1300.02			1.36414			0.682068	+	0.731289i	$0.261081\pi$
$954$		0			0
$955$	683.547	+	394.646i	0.715756	+	0.413242i
$956$		0			0
$957$	−680.256	−	1178.24i	−0.710822	−	1.23118i
$958$		0			0
$959$	221.310	−	224.665i	0.230771	−	0.234270i
$960$		0			0
$961$	878.485	+	1521.58i	0.914136	+	1.58333i
$962$		0			0
$963$	148.758	+	85.8854i	0.154473	+	0.0891853i
$964$		0			0
$965$	−1118.21			−1.15877
$966$		0			0
$967$		−	669.581i		−	0.692432i	−0.938155	−	0.346216i	$-0.887466\pi$
$967$		−	669.581i		−	0.692432i	0.938155	−	0.346216i	$-0.112534\pi$
$968$		0			0
$969$	672.344	−	1164.53i	0.693853	−	1.20179i
$970$		0			0
$971$	−1078.54	+	622.695i	−1.11075	+	0.641292i	−0.939024	−	0.343853i	$-0.888268\pi$
$971$	−1078.54	+	622.695i	−1.11075	+	0.641292i	−0.171727	+	0.985145i	$0.554935\pi$
$972$		0			0
$973$	56.7487	−	218.346i	0.0583235	−	0.224405i
$974$		0			0
$975$	−220.010	+	127.023i	−0.225652	+	0.130280i
$976$		0			0
$977$	−108.257	+	187.507i	−0.110806	+	0.191922i	−0.916095	−	0.400960i	$-0.868677\pi$
$977$	−108.257	+	187.507i	−0.110806	+	0.191922i	0.805289	+	0.592882i	$0.202010\pi$
$978$		0			0
$979$		−	999.062i		−	1.02049i
$980$		0			0
$981$	424.124			0.432338
$982$		0			0
$983$	708.832	+	409.245i	0.721091	+	0.416322i	0.815154	−	0.579244i	$-0.196652\pi$
$983$	708.832	+	409.245i	0.721091	+	0.416322i	−0.0940632	+	0.995566i	$0.529986\pi$
$984$		0			0
$985$	233.419	+	404.294i	0.236974	+	0.410451i
$986$		0			0
$987$	−284.547	−	73.9546i	−0.288294	−	0.0749286i
$988$		0			0
$989$	82.8455	+	143.493i	0.0837670	+	0.145089i
$990$		0			0
$991$	616.301	+	355.821i	0.621898	+	0.359053i	0.777607	−	0.628750i	$-0.216433\pi$
$991$	616.301	+	355.821i	0.621898	+	0.359053i	−0.155710	+	0.987803i	$0.549766\pi$
$992$		0			0
$993$	−629.574			−0.634012
$994$		0			0
$995$			17.2054i			0.0172919i
$996$		0			0
$997$	−544.578	+	943.236i	−0.546216	+	0.946074i	0.452313	+	0.891859i	$0.350599\pi$
$997$	−544.578	+	943.236i	−0.546216	+	0.946074i	−0.998529	+	0.0542152i	$0.982734\pi$
$998$		0			0
$999$	−161.660	+	93.3344i	−0.161822	+	0.0934278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.be.a.319.1	yes	4
3.2	odd	2		1008.3.cd.g.991.2		4
4.3	odd	2		336.3.be.b.319.1	yes	4
7.2	even	3		336.3.be.b.79.1	yes	4
7.3	odd	6		2352.3.m.h.1471.1		4
7.4	even	3		2352.3.m.g.1471.4		4
12.11	even	2		1008.3.cd.f.991.2		4
21.2	odd	6		1008.3.cd.f.415.2		4
28.3	even	6		2352.3.m.h.1471.3		4
28.11	odd	6		2352.3.m.g.1471.2		4
28.23	odd	6	inner	336.3.be.a.79.1	✓	4
84.23	even	6		1008.3.cd.g.415.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.be.a.79.1	✓	4	28.23	odd	6	inner
336.3.be.a.319.1	yes	4	1.1	even	1	trivial
336.3.be.b.79.1	yes	4	7.2	even	3
336.3.be.b.319.1	yes	4	4.3	odd	2
1008.3.cd.f.415.2		4	21.2	odd	6
1008.3.cd.f.991.2		4	12.11	even	2
1008.3.cd.g.415.2		4	84.23	even	6
1008.3.cd.g.991.2		4	3.2	odd	2
2352.3.m.g.1471.2		4	28.11	odd	6
2352.3.m.g.1471.4		4	7.4	even	3
2352.3.m.h.1471.1		4	7.3	odd	6
2352.3.m.h.1471.3		4	28.3	even	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.63746 - 2.83616i) q^{5} +(6.77492 + 1.76082i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.63746 - 2.83616i) q^{5} +(6.77492 + 1.76082i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-16.1873 - 9.34574i) q^{11} +10.2749 q^{13} +5.67232i q^{15} +(12.5498 - 21.7370i) q^{17} +(-26.7870 + 15.4655i) q^{19} +(-8.63746 - 8.50848i) q^{21} +(-4.54983 + 2.62685i) q^{23} +(7.13746 - 12.3624i) q^{25} -5.19615i q^{27} -42.0241 q^{29} +(-45.1495 - 26.0671i) q^{31} +(16.1873 + 28.0372i) q^{33} +(-6.09967 - 22.0980i) q^{35} +(-17.9622 - 31.1115i) q^{37} +(-15.4124 - 8.89834i) q^{39} -38.7492 q^{41} -31.5380i q^{43} +(4.91238 - 8.50848i) q^{45} +(21.0000 - 12.1244i) q^{47} +(42.7990 + 23.8589i) q^{49} +(-37.6495 + 21.7370i) q^{51} +(32.8127 - 56.8333i) q^{53} +61.2130i q^{55} +53.5739 q^{57} +(38.8368 + 22.4224i) q^{59} +(31.5498 + 54.6459i) q^{61} +(5.58762 + 20.2430i) q^{63} +(-16.8248 - 29.1413i) q^{65} +(19.2371 + 11.1066i) q^{67} +9.09967 q^{69} -97.5703i q^{71} +(-45.8625 + 79.4363i) q^{73} +(-21.4124 + 12.3624i) q^{75} +(-93.2114 - 91.8196i) q^{77} +(-8.02575 + 4.63367i) q^{79} +(-4.50000 + 7.79423i) q^{81} +51.1976i q^{83} -82.1993 q^{85} +(63.0361 + 36.3939i) q^{87} +(26.7251 + 46.2892i) q^{89} +(69.6117 + 18.0923i) q^{91} +(45.1495 + 78.2012i) q^{93} +(87.7251 + 50.6481i) q^{95} +129.522 q^{97} -56.0744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + q^{5} + 12 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + q^5 + 12 * q^7 + 6 * q^9	\( 4 q - 6 q^{3} + q^{5} + 12 q^{7} + 6 q^{9} - 27 q^{11} + 26 q^{13} + 20 q^{17} - 9 q^{19} - 27 q^{21} + 12 q^{23} + 21 q^{25} - 2 q^{29} - 90 q^{31} + 27 q^{33} + 36 q^{35} - 19 q^{37} - 39 q^{39} - 4 q^{41} - 3 q^{45} + 84 q^{47} - 10 q^{49} - 60 q^{51} + 169 q^{53} + 18 q^{57} + 27 q^{59} + 96 q^{61} + 45 q^{63} - 22 q^{65} + 9 q^{67} - 24 q^{69} - 191 q^{73} - 63 q^{75} - 169 q^{77} - 168 q^{79} - 18 q^{81} - 208 q^{85} + 3 q^{87} + 122 q^{89} + 135 q^{91} + 90 q^{93} + 366 q^{95} + 50 q^{97}+O(q^{100}) \) 4 * q - 6 * q^3 + q^5 + 12 * q^7 + 6 * q^9 - 27 * q^11 + 26 * q^13 + 20 * q^17 - 9 * q^19 - 27 * q^21 + 12 * q^23 + 21 * q^25 - 2 * q^29 - 90 * q^31 + 27 * q^33 + 36 * q^35 - 19 * q^37 - 39 * q^39 - 4 * q^41 - 3 * q^45 + 84 * q^47 - 10 * q^49 - 60 * q^51 + 169 * q^53 + 18 * q^57 + 27 * q^59 + 96 * q^61 + 45 * q^63 - 22 * q^65 + 9 * q^67 - 24 * q^69 - 191 * q^73 - 63 * q^75 - 169 * q^77 - 168 * q^79 - 18 * q^81 - 208 * q^85 + 3 * q^87 + 122 * q^89 + 135 * q^91 + 90 * q^93 + 366 * q^95 + 50 * q^97

Introduction

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