LMFDB - Embedded newform 336.3.bn.d.65.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(65,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.65"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bn (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-1,0,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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:	$\Q(\sqrt{-3}, \sqrt{-35})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} - 9x + 81 $ x^4 - x^3 - 8x^2 - 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$-2.31174 - 1.91203i$ of defining polynomial
Character	$\chi$	$=$	336.65
Dual form			336.3.bn.d.305.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.31174 - 1.91203i) q^{3} +(-5.12348 - 2.95804i) q^{5} +7.00000 q^{7} +(1.68826 - 8.84024i) q^{9} +(5.12348 - 2.95804i) q^{11} -6.00000 q^{13} +(-17.5000 + 2.95804i) q^{15} +(-5.12348 + 2.95804i) q^{17} +(11.5000 - 19.9186i) q^{19} +(16.1822 - 13.3842i) q^{21} +(-35.8643 - 20.7063i) q^{23} +(5.00000 + 8.66025i) q^{25} +(-13.0000 - 23.6643i) q^{27} -47.3286i q^{29} +(19.5000 + 33.7750i) q^{31} +(6.18826 - 16.6345i) q^{33} +(-35.8643 - 20.7063i) q^{35} +(-23.5000 + 40.7032i) q^{37} +(-13.8704 + 11.4722i) q^{39} +22.0000 q^{43} +(-34.7995 + 40.2988i) q^{45} +(46.1113 + 26.6224i) q^{47} +49.0000 q^{49} +(-6.18826 + 16.6345i) q^{51} +(-46.1113 + 26.6224i) q^{53} -35.0000 q^{55} +(-11.5000 - 68.0349i) q^{57} +(87.0991 - 50.2867i) q^{59} +(40.5000 - 70.1481i) q^{61} +(11.8178 - 61.8817i) q^{63} +(30.7409 + 17.7482i) q^{65} +(15.5000 + 26.8468i) q^{67} +(-122.500 + 20.7063i) q^{69} +94.6573i q^{71} +(8.50000 + 14.7224i) q^{73} +(28.1174 + 10.4601i) q^{75} +(35.8643 - 20.7063i) q^{77} +(-4.50000 + 7.79423i) q^{79} +(-75.2995 - 29.8493i) q^{81} -47.3286i q^{83} +35.0000 q^{85} +(-90.4939 - 109.411i) q^{87} +(76.8521 + 44.3706i) q^{89} -42.0000 q^{91} +(109.658 + 40.7943i) q^{93} +(-117.840 + 68.0349i) q^{95} +82.0000 q^{97} +(-17.5000 - 50.2867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 28 q^{7} + 17 q^{9} - 24 q^{13} - 70 q^{15} + 46 q^{19} - 7 q^{21} + 20 q^{25} - 52 q^{27} + 78 q^{31} + 35 q^{33} - 94 q^{37} + 6 q^{39} + 88 q^{43} + 35 q^{45} + 196 q^{49} - 35 q^{51}+ \cdots - 70 q^{99}+O(q^{100}) $ 4 * q - q^3 + 28 * q^7 + 17 * q^9 - 24 * q^13 - 70 * q^15 + 46 * q^19 - 7 * q^21 + 20 * q^25 - 52 * q^27 + 78 * q^31 + 35 * q^33 - 94 * q^37 + 6 * q^39 + 88 * q^43 + 35 * q^45 + 196 * q^49 - 35 * q^51 - 140 * q^55 - 46 * q^57 + 162 * q^61 + 119 * q^63 + 62 * q^67 - 490 * q^69 + 34 * q^73 + 10 * q^75 - 18 * q^79 - 127 * q^81 + 140 * q^85 - 280 * q^87 - 168 * q^91 + 39 * q^93 + 328 * q^97 - 70 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.31174	−	1.91203i	0.770579	−	0.637344i
$3$	2.31174	−	1.91203i	0.770579	−	0.637344i
$4$		0			0
$5$	−5.12348	−	2.95804i	−1.02470	−	0.591608i	−0.109235	−	0.994016i	$-0.534840\pi$
$5$	−5.12348	−	2.95804i	−1.02470	−	0.591608i	−0.915460	+	0.402408i	$0.868173\pi$
$6$		0			0
$7$	7.00000			1.00000
$7$	7.00000			1.00000
$8$		0			0
$9$	1.68826	−	8.84024i	0.187585	−	0.982248i
$10$		0			0
$11$	5.12348	−	2.95804i	0.465770	−	0.268913i	−0.248697	−	0.968581i	$-0.580002\pi$
$11$	5.12348	−	2.95804i	0.465770	−	0.268913i	0.714468	+	0.699669i	$0.246669\pi$
$12$		0			0
$13$	−6.00000			−0.461538			−0.230769	−	0.973009i	$-0.574124\pi$
$13$	−6.00000			−0.461538			−0.230769	+	0.973009i	$0.574124\pi$
$14$		0			0
$15$	−17.5000	+	2.95804i	−1.16667	+	0.197203i
$16$		0			0
$17$	−5.12348	+	2.95804i	−0.301381	+	0.174002i	−0.643063	−	0.765813i	$-0.722337\pi$
$17$	−5.12348	+	2.95804i	−0.301381	+	0.174002i	0.341682	+	0.939816i	$0.389003\pi$
$18$		0			0
$19$	11.5000	−	19.9186i	0.605263	−	1.04835i	−0.386747	−	0.922186i	$-0.626401\pi$
$19$	11.5000	−	19.9186i	0.605263	−	1.04835i	0.992010	−	0.126161i	$-0.0402654\pi$
$20$		0			0
$21$	16.1822	−	13.3842i	0.770579	−	0.637344i
$22$		0			0
$23$	−35.8643	−	20.7063i	−1.55932	−	0.900273i	−0.997322	−	0.0731333i	$-0.976700\pi$
$23$	−35.8643	−	20.7063i	−1.55932	−	0.900273i	−0.561996	−	0.827140i	$-0.689967\pi$
$24$		0			0
$25$	5.00000	+	8.66025i	0.200000	+	0.346410i
$26$		0			0
$27$	−13.0000	−	23.6643i	−0.481481	−	0.876456i
$28$		0			0
$29$		−	47.3286i		−	1.63202i	−0.578036	−	0.816011i	$-0.696181\pi$
$29$		−	47.3286i		−	1.63202i	0.578036	−	0.816011i	$-0.303819\pi$
$30$		0			0
$31$	19.5000	+	33.7750i	0.629032	+	1.08952i	0.987746	+	0.156068i	$0.0498820\pi$
$31$	19.5000	+	33.7750i	0.629032	+	1.08952i	−0.358714	+	0.933448i	$0.616785\pi$
$32$		0			0
$33$	6.18826	−	16.6345i	0.187523	−	0.504075i
$34$		0			0
$35$	−35.8643	−	20.7063i	−1.02470	−	0.591608i
$36$		0			0
$37$	−23.5000	+	40.7032i	−0.635135	+	1.10009i	0.351351	+	0.936244i	$0.385722\pi$
$37$	−23.5000	+	40.7032i	−0.635135	+	1.10009i	−0.986486	+	0.163843i	$0.947611\pi$
$38$		0			0
$39$	−13.8704	+	11.4722i	−0.355652	+	0.294159i
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	22.0000			0.511628			0.255814	−	0.966726i	$-0.417657\pi$
$43$	22.0000			0.511628			0.255814	+	0.966726i	$0.417657\pi$
$44$		0			0
$45$	−34.7995	+	40.2988i	−0.773323	+	0.895529i
$46$		0			0
$47$	46.1113	+	26.6224i	0.981091	+	0.566433i	0.902599	−	0.430482i	$-0.141656\pi$
$47$	46.1113	+	26.6224i	0.981091	+	0.566433i	0.0784917	+	0.996915i	$0.474990\pi$
$48$		0			0
$49$	49.0000			1.00000
$50$		0			0
$51$	−6.18826	+	16.6345i	−0.121338	+	0.326166i
$52$		0			0
$53$	−46.1113	+	26.6224i	−0.870024	+	0.502309i	−0.867356	−	0.497688i	$-0.834183\pi$
$53$	−46.1113	+	26.6224i	−0.870024	+	0.502309i	−0.00266787	+	0.999996i	$0.500849\pi$
$54$		0			0
$55$	−35.0000			−0.636364
$56$		0			0
$57$	−11.5000	−	68.0349i	−0.201754	−	1.19360i
$58$		0			0
$59$	87.0991	−	50.2867i	1.47626	−	0.852317i	0.476615	−	0.879112i	$-0.341864\pi$
$59$	87.0991	−	50.2867i	1.47626	−	0.852317i	0.999641	+	0.0267957i	$0.00853036\pi$
$60$		0			0
$61$	40.5000	−	70.1481i	0.663934	−	1.14997i	−0.315639	−	0.948879i	$-0.602219\pi$
$61$	40.5000	−	70.1481i	0.663934	−	1.14997i	0.979573	−	0.201089i	$-0.0644479\pi$
$62$		0			0
$63$	11.8178	−	61.8817i	0.187585	−	0.982248i
$64$		0			0
$65$	30.7409	+	17.7482i	0.472936	+	0.273050i
$66$		0			0
$67$	15.5000	+	26.8468i	0.231343	+	0.400698i	0.958204	−	0.286087i	$-0.0923546\pi$
$67$	15.5000	+	26.8468i	0.231343	+	0.400698i	−0.726860	+	0.686785i	$0.759021\pi$
$68$		0			0
$69$	−122.500	+	20.7063i	−1.77536	+	0.300091i
$70$		0			0
$71$			94.6573i			1.33320i	0.745415	+	0.666601i	$0.232251\pi$
$71$			94.6573i			1.33320i	−0.745415	+	0.666601i	$0.767749\pi$
$72$		0			0
$73$	8.50000	+	14.7224i	0.116438	+	0.201677i	0.918354	−	0.395760i	$-0.129519\pi$
$73$	8.50000	+	14.7224i	0.116438	+	0.201677i	−0.801915	+	0.597438i	$0.796186\pi$
$74$		0			0
$75$	28.1174	+	10.4601i	0.374898	+	0.139468i
$76$		0			0
$77$	35.8643	−	20.7063i	0.465770	−	0.268913i
$78$		0			0
$79$	−4.50000	+	7.79423i	−0.0569620	+	0.0986611i	−0.893100	−	0.449858i	$-0.851475\pi$
$79$	−4.50000	+	7.79423i	−0.0569620	+	0.0986611i	0.836138	+	0.548519i	$0.184808\pi$
$80$		0			0
$81$	−75.2995	−	29.8493i	−0.929624	−	0.368510i
$82$		0			0
$83$		−	47.3286i		−	0.570225i	−0.958494	−	0.285112i	$-0.907969\pi$
$83$		−	47.3286i		−	0.570225i	0.958494	−	0.285112i	$-0.0920309\pi$
$84$		0			0
$85$	35.0000			0.411765
$86$		0			0
$87$	−90.4939	−	109.411i	−1.04016	−	1.25760i
$88$		0			0
$89$	76.8521	+	44.3706i	0.863507	+	0.498546i	0.865185	−	0.501453i	$-0.167201\pi$
$89$	76.8521	+	44.3706i	0.863507	+	0.498546i	−0.00167806	+	0.999999i	$0.500534\pi$
$90$		0			0
$91$	−42.0000			−0.461538
$92$		0			0
$93$	109.658	+	40.7943i	1.17912	+	0.438648i
$94$		0			0
$95$	−117.840	+	68.0349i	−1.24042	+	0.716157i
$96$		0			0
$97$	82.0000			0.845361			0.422680	−	0.906279i	$-0.361089\pi$
$97$	82.0000			0.845361			0.422680	+	0.906279i	$0.361089\pi$
$98$		0			0
$99$	−17.5000	−	50.2867i	−0.176768	−	0.507946i
$100$		0			0
$101$	35.8643	−	20.7063i	0.355092	−	0.205013i	−0.311833	−	0.950137i	$-0.600943\pi$
$101$	35.8643	−	20.7063i	0.355092	−	0.205013i	0.666926	+	0.745124i	$0.267610\pi$
$102$		0			0
$103$	11.5000	−	19.9186i	0.111650	−	0.193384i	−0.804785	−	0.593566i	$-0.797720\pi$
$103$	11.5000	−	19.9186i	0.111650	−	0.193384i	0.916436	+	0.400182i	$0.131053\pi$
$104$		0			0
$105$	−122.500	+	20.7063i	−1.16667	+	0.197203i
$106$		0			0
$107$	46.1113	+	26.6224i	0.430947	+	0.248807i	0.699750	−	0.714388i	$-0.253295\pi$
$107$	46.1113	+	26.6224i	0.430947	+	0.248807i	−0.268803	+	0.963195i	$0.586628\pi$
$108$		0			0
$109$	68.5000	+	118.645i	0.628440	+	1.08849i	0.987865	+	0.155316i	$0.0496397\pi$
$109$	68.5000	+	118.645i	0.628440	+	1.08849i	−0.359424	+	0.933174i	$0.617027\pi$
$110$		0			0
$111$	23.5000	+	139.028i	0.211712	+	1.25250i
$112$		0			0
$113$			94.6573i			0.837675i	0.908061	+	0.418838i	$0.137562\pi$
$113$			94.6573i			0.837675i	−0.908061	+	0.418838i	$0.862438\pi$
$114$		0			0
$115$	122.500	+	212.176i	1.06522	+	1.84501i
$116$		0			0
$117$	−10.1296	+	53.0414i	−0.0865776	+	0.453345i
$118$		0			0
$119$	−35.8643	+	20.7063i	−0.301381	+	0.174002i
$120$		0			0
$121$	−43.0000	+	74.4782i	−0.355372	+	0.615522i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			88.7412i			0.709930i
$126$		0			0
$127$	78.0000			0.614173			0.307087	−	0.951682i	$-0.400646\pi$
$127$	78.0000			0.614173			0.307087	+	0.951682i	$0.400646\pi$
$128$		0			0
$129$	50.8582	−	42.0647i	0.394250	−	0.326083i
$130$		0			0
$131$	128.087	+	73.9510i	0.977762	+	0.564511i	0.901594	−	0.432584i	$-0.142398\pi$
$131$	128.087	+	73.9510i	0.977762	+	0.564511i	0.0761686	+	0.997095i	$0.475731\pi$
$132$		0			0
$133$	80.5000	−	139.430i	0.605263	−	1.04835i
$134$		0			0
$135$	−3.39482	+	159.698i	−0.0251468	+	1.18295i
$136$		0			0
$137$	−87.0991	+	50.2867i	−0.635760	+	0.367056i	−0.782979	−	0.622048i	$-0.786301\pi$
$137$	−87.0991	+	50.2867i	−0.635760	+	0.367056i	0.147220	+	0.989104i	$0.452968\pi$
$138$		0			0
$139$	−106.000			−0.762590			−0.381295	−	0.924453i	$-0.624522\pi$
$139$	−106.000			−0.762590			−0.381295	+	0.924453i	$0.624522\pi$
$140$		0			0
$141$	157.500	−	26.6224i	1.11702	−	0.188811i
$142$		0			0
$143$	−30.7409	+	17.7482i	−0.214971	+	0.124114i
$144$		0			0
$145$	−140.000	+	242.487i	−0.965517	+	1.67232i
$146$		0			0
$147$	113.275	−	93.6896i	0.770579	−	0.637344i
$148$		0			0
$149$	−169.075	−	97.6153i	−1.13473	−	0.655136i	−0.189609	−	0.981860i	$-0.560722\pi$
$149$	−169.075	−	97.6153i	−1.13473	−	0.655136i	−0.945120	+	0.326723i	$0.894055\pi$
$150$		0			0
$151$	−20.5000	−	35.5070i	−0.135762	−	0.235146i	0.790127	−	0.612944i	$-0.210015\pi$
$151$	−20.5000	−	35.5070i	−0.135762	−	0.235146i	−0.925888	+	0.377798i	$0.876681\pi$
$152$		0			0
$153$	17.5000	+	50.2867i	0.114379	+	0.328671i
$154$		0			0
$155$		−	230.727i		−	1.48856i
$156$		0			0
$157$	−83.5000	−	144.626i	−0.531847	−	0.921186i	−0.999309	−	0.0371729i	$-0.988165\pi$
$157$	−83.5000	−	144.626i	−0.531847	−	0.921186i	0.467462	−	0.884013i	$-0.345169\pi$
$158$		0			0
$159$	−55.6944	+	149.710i	−0.350279	+	0.941573i
$160$		0			0
$161$	−251.050	−	144.944i	−1.55932	−	0.900273i
$162$		0			0
$163$	131.500	−	227.765i	0.806748	−	1.39733i	−0.108356	−	0.994112i	$-0.534559\pi$
$163$	131.500	−	227.765i	0.806748	−	1.39733i	0.915104	−	0.403217i	$-0.132108\pi$
$164$		0			0
$165$	−80.9108	+	66.9211i	−0.490369	+	0.405583i
$166$		0			0
$167$			189.315i			1.13362i	0.823849	+	0.566810i	$0.191823\pi$
$167$			189.315i			1.13362i	−0.823849	+	0.566810i	$0.808177\pi$
$168$		0			0
$169$	−133.000			−0.786982
$170$		0			0
$171$	−156.670	−	135.291i	−0.916199	−	0.791173i
$172$		0			0
$173$	240.803	+	139.028i	1.39193	+	0.803629i	0.993528	−	0.113583i	$-0.0362328\pi$
$173$	240.803	+	139.028i	1.39193	+	0.803629i	0.398398	+	0.917212i	$0.369566\pi$
$174$		0			0
$175$	35.0000	+	60.6218i	0.200000	+	0.346410i
$176$		0			0
$177$	105.200	−	282.786i	0.594353	−	1.59766i
$178$		0			0
$179$	−76.8521	+	44.3706i	−0.429342	+	0.247880i	−0.699066	−	0.715057i	$-0.746401\pi$
$179$	−76.8521	+	44.3706i	−0.429342	+	0.247880i	0.269725	+	0.962938i	$0.413067\pi$
$180$		0			0
$181$	−6.00000			−0.0331492			−0.0165746	−	0.999863i	$-0.505276\pi$
$181$	−6.00000			−0.0331492			−0.0165746	+	0.999863i	$0.505276\pi$
$182$		0			0
$183$	−40.5000	−	239.601i	−0.221311	−	1.30930i
$184$		0			0
$185$	240.803	−	139.028i	1.30164	−	0.751502i
$186$		0			0
$187$	−17.5000	+	30.3109i	−0.0935829	+	0.162090i
$188$		0			0
$189$	−91.0000	−	165.650i	−0.481481	−	0.876456i
$190$		0			0
$191$	46.1113	+	26.6224i	0.241420	+	0.139384i	0.615829	−	0.787880i	$-0.288821\pi$
$191$	46.1113	+	26.6224i	0.241420	+	0.139384i	−0.374409	+	0.927264i	$0.622154\pi$
$192$		0			0
$193$	−71.5000	−	123.842i	−0.370466	−	0.641666i	0.619171	−	0.785256i	$-0.287469\pi$
$193$	−71.5000	−	123.842i	−0.370466	−	0.641666i	−0.989637	+	0.143590i	$0.954135\pi$
$194$		0			0
$195$	105.000	−	17.7482i	0.538462	−	0.0910166i
$196$		0			0
$197$			47.3286i			0.240247i	0.992759	+	0.120123i	$0.0383290\pi$
$197$			47.3286i			0.240247i	−0.992759	+	0.120123i	$0.961671\pi$
$198$		0			0
$199$	−84.5000	−	146.358i	−0.424623	−	0.735469i	0.571762	−	0.820420i	$-0.306260\pi$
$199$	−84.5000	−	146.358i	−0.424623	−	0.735469i	−0.996385	+	0.0849507i	$0.972927\pi$
$200$		0			0
$201$	87.1639	+	32.4262i	0.433651	+	0.161325i
$202$		0			0
$203$		−	331.300i		−	1.63202i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−243.597	+	282.091i	−1.17680	+	1.36276i
$208$		0			0
$209$		−	136.070i		−	0.651052i
$210$		0			0
$211$	166.000			0.786730			0.393365	−	0.919382i	$-0.371311\pi$
$211$	166.000			0.786730			0.393365	+	0.919382i	$0.371311\pi$
$212$		0			0
$213$	180.988	+	218.823i	0.849708	+	1.02734i
$214$		0			0
$215$	−112.716	−	65.0769i	−0.524263	−	0.302683i
$216$		0			0
$217$	136.500	+	236.425i	0.629032	+	1.08952i
$218$		0			0
$219$	47.7995	+	17.7821i	0.218263	+	0.0811969i
$220$		0			0
$221$	30.7409	−	17.7482i	0.139099	−	0.0803088i
$222$		0			0
$223$	142.000			0.636771			0.318386	−	0.947961i	$-0.396859\pi$
$223$	142.000			0.636771			0.318386	+	0.947961i	$0.396859\pi$
$224$		0			0
$225$	85.0000	−	29.5804i	0.377778	−	0.131468i
$226$		0			0
$227$	−76.8521	+	44.3706i	−0.338556	+	0.195465i	−0.659633	−	0.751588i	$-0.729288\pi$
$227$	−76.8521	+	44.3706i	−0.338556	+	0.195465i	0.321077	+	0.947053i	$0.395955\pi$
$228$		0			0
$229$	128.500	−	222.569i	0.561135	−	0.971915i	−0.436262	−	0.899820i	$-0.643698\pi$
$229$	128.500	−	222.569i	0.561135	−	0.971915i	0.997398	−	0.0720955i	$-0.0229686\pi$
$230$		0			0
$231$	43.3178	−	116.441i	0.187523	−	0.504075i
$232$		0			0
$233$	158.828	+	91.6992i	0.681664	+	0.393559i	0.800482	−	0.599357i	$-0.204577\pi$
$233$	158.828	+	91.6992i	0.681664	+	0.393559i	−0.118818	+	0.992916i	$0.537910\pi$
$234$		0			0
$235$	−157.500	−	272.798i	−0.670213	−	1.16084i
$236$		0			0
$237$	4.50000	+	26.6224i	0.0189873	+	0.112331i
$238$		0			0
$239$		−	283.972i		−	1.18817i	−0.804404	−	0.594083i	$-0.797515\pi$
$239$		−	283.972i		−	1.18817i	0.804404	−	0.594083i	$-0.202485\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.00207469	+	0.00359347i	0.867061	−	0.498202i	$-0.166006\pi$
$241$	0.500000	+	0.866025i	0.00207469	+	0.00359347i	−0.864986	+	0.501796i	$0.832673\pi$
$242$		0			0
$243$	−231.146	+	74.9715i	−0.951216	+	0.308525i
$244$		0			0
$245$	−251.050	−	144.944i	−1.02470	−	0.591608i
$246$		0			0
$247$	−69.0000	+	119.512i	−0.279352	+	0.483852i
$248$		0			0
$249$	−90.4939	−	109.411i	−0.363429	−	0.439403i
$250$		0			0
$251$			141.986i			0.565681i	0.959167	+	0.282840i	$0.0912767\pi$
$251$			141.986i			0.565681i	−0.959167	+	0.282840i	$0.908723\pi$
$252$		0			0
$253$	−245.000			−0.968379
$254$		0			0
$255$	80.9108	−	66.9211i	0.317297	−	0.262436i
$256$		0			0
$257$	−169.075	−	97.6153i	−0.657878	−	0.379826i	0.133590	−	0.991037i	$-0.457350\pi$
$257$	−169.075	−	97.6153i	−0.657878	−	0.379826i	−0.791468	+	0.611211i	$0.790683\pi$
$258$		0			0
$259$	−164.500	+	284.922i	−0.635135	+	1.10009i
$260$		0			0
$261$	−418.396	−	79.9032i	−1.60305	−	0.306142i
$262$		0			0
$263$	46.1113	−	26.6224i	0.175328	−	0.101226i	−0.409768	−	0.912190i	$-0.634390\pi$
$263$	46.1113	−	26.6224i	0.175328	−	0.101226i	0.585096	+	0.810964i	$0.301057\pi$
$264$		0			0
$265$	315.000			1.18868
$266$		0			0
$267$	262.500	−	44.3706i	0.983146	−	0.166182i
$268$		0			0
$269$	35.8643	−	20.7063i	0.133325	−	0.0769750i	−0.431854	−	0.901943i	$-0.642140\pi$
$269$	35.8643	−	20.7063i	0.133325	−	0.0769750i	0.565179	+	0.824968i	$0.308807\pi$
$270$		0			0
$271$	43.5000	−	75.3442i	0.160517	−	0.278023i	−0.774537	−	0.632528i	$-0.782017\pi$
$271$	43.5000	−	75.3442i	0.160517	−	0.278023i	0.935054	+	0.354505i	$0.115351\pi$
$272$		0			0
$273$	−97.0930	+	80.3054i	−0.355652	+	0.294159i
$274$		0			0
$275$	51.2348	+	29.5804i	0.186308	+	0.107565i
$276$		0			0
$277$	−155.500	−	269.334i	−0.561372	−	0.972325i	−0.997377	−	0.0723804i	$-0.976940\pi$
$277$	−155.500	−	269.334i	−0.561372	−	0.972325i	0.436005	−	0.899944i	$-0.356393\pi$
$278$		0			0
$279$	331.500	−	115.364i	1.18817	−	0.413489i
$280$		0			0
$281$		−	378.629i		−	1.34743i	−0.738989	−	0.673717i	$-0.764697\pi$
$281$		−	378.629i		−	1.34743i	0.738989	−	0.673717i	$-0.235303\pi$
$282$		0			0
$283$	159.500	+	276.262i	0.563604	+	0.976191i	0.997178	+	0.0750731i	$0.0239190\pi$
$283$	159.500	+	276.262i	0.563604	+	0.976191i	−0.433574	+	0.901118i	$0.642748\pi$
$284$		0			0
$285$	−142.330	+	382.593i	−0.499404	+	1.34243i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−127.000	+	219.970i	−0.439446	+	0.761143i
$290$		0			0
$291$	189.562	−	156.787i	0.651417	−	0.538786i
$292$		0			0
$293$			141.986i			0.484594i	0.970202	+	0.242297i	$0.0779008\pi$
$293$			141.986i			0.484594i	−0.970202	+	0.242297i	$0.922099\pi$
$294$		0			0
$295$	−595.000			−2.01695
$296$		0			0
$297$	−136.605	−	82.7890i	−0.459950	−	0.278751i
$298$		0			0
$299$	215.186	+	124.238i	0.719686	+	0.415511i
$300$		0			0
$301$	154.000			0.511628
$302$		0			0
$303$	43.3178	−	116.441i	0.142963	−	0.384295i
$304$		0			0
$305$	−415.002	+	239.601i	−1.36066	+	0.785578i
$306$		0			0
$307$	−442.000			−1.43974			−0.719870	−	0.694109i	$-0.755798\pi$
$307$	−442.000			−1.43974			−0.719870	+	0.694109i	$0.755798\pi$
$308$		0			0
$309$	−11.5000	−	68.0349i	−0.0372168	−	0.220178i
$310$		0			0
$311$	210.062	−	121.280i	0.675442	−	0.389967i	−0.122693	−	0.992445i	$-0.539153\pi$
$311$	210.062	−	121.280i	0.675442	−	0.389967i	0.798136	+	0.602478i	$0.205820\pi$
$312$		0			0
$313$	128.500	−	222.569i	0.410543	−	0.711082i	−0.584406	−	0.811461i	$-0.698672\pi$
$313$	128.500	−	222.569i	0.410543	−	0.711082i	0.994949	+	0.100380i	$0.0320058\pi$
$314$		0			0
$315$	−243.597	+	282.091i	−0.773323	+	0.895529i
$316$		0			0
$317$	76.8521	+	44.3706i	0.242436	+	0.139970i	0.616296	−	0.787515i	$-0.288633\pi$
$317$	76.8521	+	44.3706i	0.242436	+	0.139970i	−0.373860	+	0.927485i	$0.621966\pi$
$318$		0			0
$319$	−140.000	−	242.487i	−0.438871	−	0.760148i
$320$		0			0
$321$	157.500	−	26.6224i	0.490654	−	0.0829357i
$322$		0			0
$323$			136.070i			0.421269i
$324$		0			0
$325$	−30.0000	−	51.9615i	−0.0923077	−	0.159882i
$326$		0			0
$327$	385.208	+	143.303i	1.17801	+	0.438235i
$328$		0			0
$329$	322.779	+	186.357i	0.981091	+	0.566433i
$330$		0			0
$331$	−60.5000	+	104.789i	−0.182779	+	0.316583i	−0.942826	−	0.333285i	$-0.891843\pi$
$331$	−60.5000	+	104.789i	−0.182779	+	0.316583i	0.760047	+	0.649869i	$0.225176\pi$
$332$		0			0
$333$	320.152	+	276.463i	0.961416	+	0.830220i
$334$		0			0
$335$		−	183.398i		−	0.547458i
$336$		0			0
$337$	−78.0000			−0.231454			−0.115727	−	0.993281i	$-0.536920\pi$
$337$	−78.0000			−0.231454			−0.115727	+	0.993281i	$0.536920\pi$
$338$		0			0
$339$	180.988	+	218.823i	0.533887	+	0.645495i
$340$		0			0
$341$	199.816	+	115.364i	0.585969	+	0.338310i
$342$		0			0
$343$	343.000			1.00000
$344$		0			0
$345$	688.876	+	256.272i	1.99674	+	0.742817i
$346$		0			0
$347$	−568.706	+	328.342i	−1.63892	+	0.946232i	−0.657716	+	0.753266i	$0.728477\pi$
$347$	−568.706	+	328.342i	−1.63892	+	0.946232i	−0.981205	+	0.192966i	$0.938189\pi$
$348$		0			0
$349$	−422.000			−1.20917			−0.604585	−	0.796541i	$-0.706661\pi$
$349$	−422.000			−1.20917			−0.604585	+	0.796541i	$0.706661\pi$
$350$		0			0
$351$	78.0000	+	141.986i	0.222222	+	0.404518i
$352$		0			0
$353$	−169.075	+	97.6153i	−0.478965	+	0.276531i	−0.719985	−	0.693990i	$-0.755851\pi$
$353$	−169.075	+	97.6153i	−0.478965	+	0.276531i	0.241020	+	0.970520i	$0.422518\pi$
$354$		0			0
$355$	280.000	−	484.974i	0.788732	−	1.36612i
$356$		0			0
$357$	−43.3178	+	116.441i	−0.121338	+	0.326166i
$358$		0			0
$359$	−117.840	−	68.0349i	−0.328245	−	0.189512i	0.326817	−	0.945088i	$-0.394024\pi$
$359$	−117.840	−	68.0349i	−0.328245	−	0.189512i	−0.655062	+	0.755575i	$0.727357\pi$
$360$		0			0
$361$	−84.0000	−	145.492i	−0.232687	−	0.403026i
$362$		0			0
$363$	43.0000	+	254.391i	0.118457	+	0.700803i
$364$		0			0
$365$		−	100.573i		−	0.275543i
$366$		0			0
$367$	−36.5000	−	63.2199i	−0.0994550	−	0.172261i	0.812004	−	0.583652i	$-0.198377\pi$
$367$	−36.5000	−	63.2199i	−0.0994550	−	0.172261i	−0.911459	+	0.411390i	$0.865043\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−322.779	+	186.357i	−0.870024	+	0.502309i
$372$		0			0
$373$	200.500	−	347.276i	0.537534	−	0.931035i	−0.461503	−	0.887139i	$-0.652689\pi$
$373$	200.500	−	347.276i	0.537534	−	0.931035i	0.999036	−	0.0438965i	$-0.0139772\pi$
$374$		0			0
$375$	169.676	+	205.146i	0.452470	+	0.547057i
$376$		0			0
$377$			283.972i			0.753241i
$378$		0			0
$379$	−538.000			−1.41953			−0.709763	−	0.704441i	$-0.751198\pi$
$379$	−538.000			−1.41953			−0.709763	+	0.704441i	$0.751198\pi$
$380$		0			0
$381$	180.316	−	149.139i	0.473269	−	0.391440i
$382$		0			0
$383$	210.062	+	121.280i	0.548466	+	0.316657i	0.748503	−	0.663131i	$-0.230773\pi$
$383$	210.062	+	121.280i	0.548466	+	0.316657i	−0.200037	+	0.979788i	$0.564106\pi$
$384$		0			0
$385$	−245.000			−0.636364
$386$		0			0
$387$	37.1418	−	194.485i	0.0959736	−	0.502546i
$388$		0			0
$389$	35.8643	−	20.7063i	0.0921962	−	0.0532295i	−0.453193	−	0.891412i	$-0.649715\pi$
$389$	35.8643	−	20.7063i	0.0921962	−	0.0532295i	0.545389	+	0.838183i	$0.316382\pi$
$390$		0			0
$391$	245.000			0.626598
$392$		0			0
$393$	437.500	−	73.9510i	1.11323	−	0.188170i
$394$		0			0
$395$	46.1113	−	26.6224i	0.116737	−	0.0673984i
$396$		0			0
$397$	16.5000	−	28.5788i	0.0415617	−	0.0719870i	−0.844496	−	0.535561i	$-0.820100\pi$
$397$	16.5000	−	28.5788i	0.0415617	−	0.0719870i	0.886058	+	0.463574i	$0.153433\pi$
$398$		0			0
$399$	−80.5000	−	476.244i	−0.201754	−	1.19360i
$400$		0			0
$401$	322.779	+	186.357i	0.804935	+	0.464729i	0.845194	−	0.534460i	$-0.179485\pi$
$401$	322.779	+	186.357i	0.804935	+	0.464729i	−0.0402588	+	0.999189i	$0.512818\pi$
$402$		0			0
$403$	−117.000	−	202.650i	−0.290323	−	0.502853i
$404$		0			0
$405$	297.500	+	375.671i	0.734568	+	0.927583i
$406$		0			0
$407$			278.056i			0.683184i
$408$		0			0
$409$	288.500	+	499.697i	0.705379	+	1.22175i	0.966555	+	0.256461i	$0.0825565\pi$
$409$	288.500	+	499.697i	0.705379	+	1.22175i	−0.261176	+	0.965291i	$0.584110\pi$
$410$		0			0
$411$	−105.200	+	282.786i	−0.255962	+	0.688044i
$412$		0			0
$413$	609.694	−	352.007i	1.47626	−	0.852317i
$414$		0			0
$415$	−140.000	+	242.487i	−0.337349	+	0.584306i
$416$		0			0
$417$	−245.044	+	202.675i	−0.587636	+	0.486032i
$418$		0			0
$419$			141.986i			0.338869i	0.985541	+	0.169434i	$0.0541940\pi$
$419$			141.986i			0.338869i	−0.985541	+	0.169434i	$0.945806\pi$
$420$		0			0
$421$	−246.000			−0.584323			−0.292162	−	0.956369i	$-0.594374\pi$
$421$	−246.000			−0.584323			−0.292162	+	0.956369i	$0.594374\pi$
$422$		0			0
$423$	313.196	−	362.689i	0.740416	−	0.857421i
$424$		0			0
$425$	−51.2348	−	29.5804i	−0.120552	−	0.0696009i
$426$		0			0
$427$	283.500	−	491.036i	0.663934	−	1.14997i
$428$		0			0
$429$	−37.1296	+	99.8068i	−0.0865491	+	0.232650i
$430$		0			0
$431$	537.965	−	310.594i	1.24818	−	0.720636i	0.277433	−	0.960745i	$-0.410517\pi$
$431$	537.965	−	310.594i	1.24818	−	0.720636i	0.970746	+	0.240109i	$0.0771832\pi$
$432$		0			0
$433$	−622.000			−1.43649			−0.718245	−	0.695790i	$-0.755054\pi$
$433$	−622.000			−1.43649			−0.718245	+	0.695790i	$0.755054\pi$
$434$		0			0
$435$	140.000	+	828.251i	0.321839	+	1.90403i
$436$		0			0
$437$	−824.880	+	476.244i	−1.88760	+	1.08980i
$438$		0			0
$439$	−124.500	+	215.640i	−0.283599	+	0.491208i	−0.972268	−	0.233867i	$-0.924862\pi$
$439$	−124.500	+	215.640i	−0.283599	+	0.491208i	0.688669	+	0.725075i	$0.258195\pi$
$440$		0			0
$441$	82.7249	−	433.172i	0.187585	−	0.982248i
$442$		0			0
$443$	210.062	+	121.280i	0.474182	+	0.273769i	0.717989	−	0.696055i	$-0.245063\pi$
$443$	210.062	+	121.280i	0.474182	+	0.273769i	−0.243807	+	0.969824i	$0.578396\pi$
$444$		0			0
$445$	−262.500	−	454.663i	−0.589888	−	1.02172i
$446$		0			0
$447$	−577.500	+	97.6153i	−1.29195	+	0.218379i
$448$		0			0
$449$		−	473.286i		−	1.05409i	−0.849837	−	0.527045i	$-0.823300\pi$
$449$		−	473.286i		−	1.05409i	0.849837	−	0.527045i	$-0.176700\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−115.281	−	42.8863i	−0.254484	−	0.0946717i
$454$		0			0
$455$	215.186	+	124.238i	0.472936	+	0.273050i
$456$		0			0
$457$	−303.500	+	525.677i	−0.664114	+	1.15028i	0.315411	+	0.948955i	$0.397858\pi$
$457$	−303.500	+	525.677i	−0.664114	+	1.15028i	−0.979525	+	0.201324i	$0.935476\pi$
$458$		0			0
$459$	136.605	+	82.7890i	0.297615	+	0.180368i
$460$		0			0
$461$			520.615i			1.12932i	0.825325	+	0.564658i	$0.190992\pi$
$461$			520.615i			1.12932i	−0.825325	+	0.564658i	$0.809008\pi$
$462$		0			0
$463$	302.000			0.652268			0.326134	−	0.945324i	$-0.394254\pi$
$463$	302.000			0.652268			0.326134	+	0.945324i	$0.394254\pi$
$464$		0			0
$465$	−441.158	−	533.381i	−0.948726	−	1.14705i
$466$		0			0
$467$	128.087	+	73.9510i	0.274276	+	0.158353i	0.630829	−	0.775922i	$-0.282715\pi$
$467$	128.087	+	73.9510i	0.274276	+	0.158353i	−0.356553	+	0.934275i	$0.616048\pi$
$468$		0			0
$469$	108.500	+	187.928i	0.231343	+	0.400698i
$470$		0			0
$471$	−469.560	−	174.683i	−0.996943	−	0.370877i
$472$		0			0
$473$	112.716	−	65.0769i	0.238301	−	0.137583i
$474$		0			0
$475$	230.000			0.484211
$476$		0			0
$477$	157.500	+	452.580i	0.330189	+	0.948805i
$478$		0			0
$479$	128.087	−	73.9510i	0.267405	−	0.154386i	−0.360303	−	0.932835i	$-0.617327\pi$
$479$	128.087	−	73.9510i	0.267405	−	0.154386i	0.627708	+	0.778449i	$0.283993\pi$
$480$		0			0
$481$	141.000	−	244.219i	0.293139	−	0.507732i
$482$		0			0
$483$	−857.500	+	144.944i	−1.77536	+	0.300091i
$484$		0			0
$485$	−420.125	−	242.559i	−0.866237	−	0.500122i
$486$		0			0
$487$	323.500	+	560.318i	0.664271	+	1.15055i	0.979482	+	0.201530i	$0.0645913\pi$
$487$	323.500	+	560.318i	0.664271	+	1.15055i	−0.315211	+	0.949021i	$0.602075\pi$
$488$		0			0
$489$	−131.500	−	777.964i	−0.268916	−	1.59093i
$490$		0			0
$491$			141.986i			0.289177i	0.989492	+	0.144589i	$0.0461858\pi$
$491$			141.986i			0.289177i	−0.989492	+	0.144589i	$0.953814\pi$
$492$		0			0
$493$	140.000	+	242.487i	0.283976	+	0.491860i
$494$		0			0
$495$	−59.0892	+	309.408i	−0.119372	+	0.625067i
$496$		0			0
$497$			662.601i			1.33320i
$498$		0			0
$499$	51.5000	−	89.2006i	0.103206	−	0.178759i	−0.809798	−	0.586709i	$-0.800423\pi$
$499$	51.5000	−	89.2006i	0.103206	−	0.178759i	0.913004	+	0.407951i	$0.133756\pi$
$500$		0			0
$501$	361.976	+	437.646i	0.722506	+	0.873544i
$502$		0			0
$503$		−	283.972i		−	0.564556i	−0.959333	−	0.282278i	$-0.908910\pi$
$503$		−	283.972i		−	0.564556i	0.959333	−	0.282278i	$-0.0910901\pi$
$504$		0			0
$505$	−245.000			−0.485149
$506$		0			0
$507$	−307.461	+	254.300i	−0.606432	+	0.501579i
$508$		0			0
$509$	−169.075	−	97.6153i	−0.332170	−	0.191779i	0.324634	−	0.945840i	$-0.394759\pi$
$509$	−169.075	−	97.6153i	−0.332170	−	0.191779i	−0.656804	+	0.754061i	$0.728092\pi$
$510$		0			0
$511$	59.5000	+	103.057i	0.116438	+	0.201677i
$512$		0			0
$513$	−620.860	−	13.1981i	−1.21025	−	0.0257272i
$514$		0			0
$515$	−117.840	+	68.0349i	−0.228815	+	0.132107i
$516$		0			0
$517$	315.000			0.609284
$518$		0			0
$519$	822.500	−	139.028i	1.58478	−	0.267876i
$520$		0			0
$521$	322.779	−	186.357i	0.619537	−	0.357690i	−0.157152	−	0.987575i	$-0.550231\pi$
$521$	322.779	−	186.357i	0.619537	−	0.357690i	0.776689	+	0.629884i	$0.216898\pi$
$522$		0			0
$523$	11.5000	−	19.9186i	0.0219885	−	0.0380852i	−0.854822	−	0.518922i	$-0.826334\pi$
$523$	11.5000	−	19.9186i	0.0219885	−	0.0380852i	0.876810	+	0.480836i	$0.159667\pi$
$524$		0			0
$525$	196.822	+	73.2205i	0.374898	+	0.139468i
$526$		0			0
$527$	−199.816	−	115.364i	−0.379157	−	0.218906i
$528$		0			0
$529$	593.000	+	1027.11i	1.12098	+	1.94160i
$530$		0			0
$531$	−297.500	−	854.874i	−0.560264	−	1.60993i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−157.500	−	272.798i	−0.294393	−	0.509903i
$536$		0			0
$537$	−92.8239	+	249.517i	−0.172856	+	0.464650i
$538$		0			0
$539$	251.050	−	144.944i	0.465770	−	0.268913i
$540$		0			0
$541$	256.500	−	444.271i	0.474122	−	0.821203i	−0.525439	−	0.850831i	$-0.676099\pi$
$541$	256.500	−	444.271i	0.474122	−	0.821203i	0.999561	+	0.0296279i	$0.00943223\pi$
$542$		0			0
$543$	−13.8704	+	11.4722i	−0.0255441	+	0.0211274i
$544$		0			0
$545$		−	810.503i		−	1.48716i
$546$		0			0
$547$	54.0000			0.0987203			0.0493601	−	0.998781i	$-0.484282\pi$
$547$	54.0000			0.0987203			0.0493601	+	0.998781i	$0.484282\pi$
$548$		0			0
$549$	−551.751	−	476.458i	−1.00501	−	0.867865i
$550$		0			0
$551$	−942.719	−	544.279i	−1.71092	−	0.987803i
$552$		0			0
$553$	−31.5000	+	54.5596i	−0.0569620	+	0.0986611i
$554$		0			0
$555$	290.848	−	781.820i	0.524051	−	1.40868i
$556$		0			0
$557$	773.645	−	446.664i	1.38895	−	0.801910i	0.395752	−	0.918357i	$-0.370484\pi$
$557$	773.645	−	446.664i	1.38895	−	0.801910i	0.993197	+	0.116447i	$0.0371505\pi$
$558$		0			0
$559$	−132.000			−0.236136
$560$		0			0
$561$	17.5000	+	103.531i	0.0311943	+	0.184548i
$562$		0			0
$563$	−486.730	+	281.014i	−0.864530	+	0.499136i	−0.865527	−	0.500863i	$-0.833016\pi$
$563$	−486.730	+	281.014i	−0.864530	+	0.499136i	0.000996920		1.00000i	$0.499683\pi$
$564$		0			0
$565$	280.000	−	484.974i	0.495575	−	0.858361i
$566$		0			0
$567$	−527.097	−	208.945i	−0.929624	−	0.368510i
$568$		0			0
$569$	568.706	+	328.342i	0.999483	+	0.577052i	0.908095	−	0.418764i	$-0.137536\pi$
$569$	568.706	+	328.342i	0.999483	+	0.577052i	0.0913876	+	0.995815i	$0.470870\pi$
$570$		0			0
$571$	463.500	+	802.806i	0.811734	+	1.40596i	0.911650	+	0.410968i	$0.134809\pi$
$571$	463.500	+	802.806i	0.811734	+	1.40596i	−0.0999158	+	0.994996i	$0.531857\pi$
$572$		0			0
$573$	157.500	−	26.6224i	0.274869	−	0.0464614i
$574$		0			0
$575$		−	414.126i		−	0.720218i
$576$		0			0
$577$	176.500	+	305.707i	0.305893	+	0.529821i	0.977460	−	0.211122i	$-0.0677118\pi$
$577$	176.500	+	305.707i	0.305893	+	0.529821i	−0.671567	+	0.740944i	$0.734379\pi$
$578$		0			0
$579$	−402.078	−	149.579i	−0.694436	−	0.258340i
$580$		0			0
$581$		−	331.300i		−	0.570225i
$582$		0			0
$583$	−157.500	+	272.798i	−0.270154	+	0.467921i
$584$		0			0
$585$	208.797	−	241.793i	0.356918	−	0.413321i
$586$		0			0
$587$			236.643i			0.403140i	0.979474	+	0.201570i	$0.0646044\pi$
$587$			236.643i			0.403140i	−0.979474	+	0.201570i	$0.935396\pi$
$588$		0			0
$589$	897.000			1.52292
$590$		0			0
$591$	90.4939	+	109.411i	0.153120	+	0.185129i
$592$		0			0
$593$	−660.928	−	381.587i	−1.11455	−	0.643486i	−0.174546	−	0.984649i	$-0.555846\pi$
$593$	−660.928	−	381.587i	−1.11455	−	0.643486i	−0.940004	+	0.341163i	$0.889179\pi$
$594$		0			0
$595$	245.000			0.411765
$596$		0			0
$597$	−475.184	−	176.775i	−0.795953	−	0.296106i
$598$		0			0
$599$	537.965	−	310.594i	0.898105	−	0.518521i	0.0215201	−	0.999768i	$-0.493149\pi$
$599$	537.965	−	310.594i	0.898105	−	0.518521i	0.876585	+	0.481247i	$0.159816\pi$
$600$		0			0
$601$	−958.000			−1.59401			−0.797005	−	0.603973i	$-0.793584\pi$
$601$	−958.000			−1.59401			−0.797005	+	0.603973i	$0.793584\pi$
$602$		0			0
$603$	263.500	−	91.6992i	0.436982	−	0.152072i
$604$		0			0
$605$	440.619	−	254.391i	0.728296	−	0.420482i
$606$		0			0
$607$	403.500	−	698.883i	0.664745	−	1.15137i	−0.314610	−	0.949221i	$-0.601874\pi$
$607$	403.500	−	698.883i	0.664745	−	1.15137i	0.979354	−	0.202150i	$-0.0647930\pi$
$608$		0			0
$609$	−633.457	−	765.880i	−1.04016	−	1.25760i
$610$		0			0
$611$	−276.668	−	159.734i	−0.452811	−	0.261431i
$612$		0			0
$613$	−259.500	−	449.467i	−0.423328	−	0.733225i	0.572935	−	0.819601i	$-0.305805\pi$
$613$	−259.500	−	449.467i	−0.423328	−	0.733225i	−0.996263	+	0.0863756i	$0.972472\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			757.258i			1.22732i	0.789569	+	0.613661i	$0.210304\pi$
$617$			757.258i			1.22732i	−0.789569	+	0.613661i	$0.789696\pi$
$618$		0			0
$619$	−344.500	−	596.692i	−0.556543	−	0.963960i	−0.997782	−	0.0665707i	$-0.978794\pi$
$619$	−344.500	−	596.692i	−0.556543	−	0.963960i	0.441239	−	0.897390i	$-0.354539\pi$
$620$		0			0
$621$	−23.7637	+	1117.89i	−0.0382669	+	1.80014i
$622$		0			0
$623$	537.965	+	310.594i	0.863507	+	0.498546i
$624$		0			0
$625$	387.500	−	671.170i	0.620000	−	1.07387i
$626$		0			0
$627$	−260.170	−	314.558i	−0.414944	−	0.501687i
$628$		0			0
$629$		−	278.056i		−	0.442060i
$630$		0			0
$631$	−674.000			−1.06815			−0.534073	−	0.845438i	$-0.679339\pi$
$631$	−674.000			−1.06815			−0.534073	+	0.845438i	$0.679339\pi$
$632$		0			0
$633$	383.748	−	317.397i	0.606238	−	0.501418i
$634$		0			0
$635$	−399.631	−	230.727i	−0.629340	−	0.363350i
$636$		0			0
$637$	−294.000			−0.461538
$638$		0			0
$639$	836.793	+	159.806i	1.30953	+	0.250088i
$640$		0			0
$641$	−742.904	+	428.916i	−1.15898	+	0.669135i	−0.951059	−	0.309011i	$-0.900002\pi$
$641$	−742.904	+	428.916i	−1.15898	+	0.669135i	−0.207918	+	0.978146i	$0.566669\pi$
$642$		0			0
$643$	−218.000			−0.339036			−0.169518	−	0.985527i	$-0.554221\pi$
$643$	−218.000			−0.339036			−0.169518	+	0.985527i	$0.554221\pi$
$644$		0			0
$645$	−385.000	+	65.0769i	−0.596899	+	0.100894i
$646$		0			0
$647$	−445.742	+	257.349i	−0.688937	+	0.397758i	−0.803214	−	0.595691i	$-0.796878\pi$
$647$	−445.742	+	257.349i	−0.688937	+	0.397758i	0.114277	+	0.993449i	$0.463545\pi$
$648$		0			0
$649$	297.500	−	515.285i	0.458398	−	0.793968i
$650$		0			0
$651$	767.604	+	285.560i	1.17912	+	0.438648i
$652$		0			0
$653$	−906.855	−	523.573i	−1.38875	−	0.801796i	−0.395577	−	0.918433i	$-0.629456\pi$
$653$	−906.855	−	523.573i	−1.38875	−	0.801796i	−0.993175	+	0.116636i	$0.962789\pi$
$654$		0			0
$655$	−437.500	−	757.772i	−0.667939	−	1.15690i
$656$		0			0
$657$	144.500	−	50.2867i	0.219939	−	0.0765398i
$658$		0			0
$659$		−	615.272i		−	0.933645i	−0.884351	−	0.466823i	$-0.845399\pi$
$659$		−	615.272i		−	0.933645i	0.884351	−	0.466823i	$-0.154601\pi$
$660$		0			0
$661$	260.500	+	451.199i	0.394100	+	0.682601i	0.992986	−	0.118233i	$-0.0377231\pi$
$661$	260.500	+	451.199i	0.394100	+	0.682601i	−0.598886	+	0.800834i	$0.704390\pi$
$662$		0			0
$663$	37.1296	−	99.8068i	0.0560024	−	0.150538i
$664$		0			0
$665$	−824.880	+	476.244i	−1.24042	+	0.716157i
$666$		0			0
$667$	−980.000	+	1697.41i	−1.46927	+	2.54484i
$668$		0			0
$669$	328.267	−	271.509i	0.490683	−	0.405843i
$670$		0			0
$671$		−	479.202i		−	0.714162i
$672$		0			0
$673$	818.000			1.21545			0.607727	−	0.794146i	$-0.292082\pi$
$673$	818.000			1.21545			0.607727	+	0.794146i	$0.292082\pi$
$674$		0			0
$675$	139.939	−	230.905i	0.207317	−	0.342081i
$676$		0			0
$677$	−660.928	−	381.587i	−0.976260	−	0.563644i	−0.0751214	−	0.997174i	$-0.523934\pi$
$677$	−660.928	−	381.587i	−0.976260	−	0.563644i	−0.901139	+	0.433530i	$0.857268\pi$
$678$		0			0
$679$	574.000			0.845361
$680$		0			0
$681$	−92.8239	+	249.517i	−0.136305	+	0.366398i
$682$		0			0
$683$	169.075	−	97.6153i	0.247547	−	0.142921i	−0.371093	−	0.928596i	$-0.621017\pi$
$683$	169.075	−	97.6153i	0.247547	−	0.142921i	0.618641	+	0.785674i	$0.287684\pi$
$684$		0			0
$685$	595.000			0.868613
$686$		0			0
$687$	−128.500	−	760.216i	−0.187045	−	1.10657i
$688$		0			0
$689$	276.668	−	159.734i	0.401550	−	0.231835i
$690$		0			0
$691$	179.500	−	310.903i	0.259768	−	0.449932i	−0.706411	−	0.707802i	$-0.749687\pi$
$691$	179.500	−	310.903i	0.259768	−	0.449932i	0.966180	+	0.257869i	$0.0830204\pi$
$692$		0			0
$693$	−122.500	−	352.007i	−0.176768	−	0.507946i
$694$		0			0
$695$	543.088	+	313.552i	0.781422	+	0.451154i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	542.500	−	91.6992i	0.776109	−	0.131186i
$700$		0			0
$701$			804.587i			1.14777i	0.818936	+	0.573885i	$0.194564\pi$
$701$			804.587i			1.14777i	−0.818936	+	0.573885i	$0.805436\pi$
$702$		0			0
$703$	540.500	+	936.173i	0.768848	+	1.33168i
$704$		0			0
$705$	−885.697	−	329.492i	−1.25631	−	0.467365i
$706$		0			0
$707$	251.050	−	144.944i	0.355092	−	0.205013i
$708$		0			0
$709$	−215.500	+	373.257i	−0.303949	+	0.526455i	−0.977027	−	0.213116i	$-0.931639\pi$
$709$	−215.500	+	373.257i	−0.303949	+	0.526455i	0.673078	+	0.739572i	$0.264972\pi$
$710$		0			0
$711$	61.3056	+	52.9398i	0.0862245	+	0.0744582i
$712$		0			0
$713$		−	1615.09i		−	2.26520i
$714$		0			0
$715$	210.000			0.293706
$716$		0			0
$717$	−542.963	−	656.468i	−0.757271	−	0.915577i
$718$		0			0
$719$	−199.816	−	115.364i	−0.277908	−	0.160450i	0.354568	−	0.935030i	$-0.384628\pi$
$719$	−199.816	−	115.364i	−0.277908	−	0.160450i	−0.632476	+	0.774580i	$0.717961\pi$
$720$		0			0
$721$	80.5000	−	139.430i	0.111650	−	0.193384i
$722$		0			0
$723$	2.81174	+	1.04601i	0.00388899	+	0.00144676i
$724$		0			0
$725$	409.878	−	236.643i	0.565349	−	0.326404i
$726$		0			0
$727$	734.000			1.00963			0.504814	−	0.863228i	$-0.331561\pi$
$727$	734.000			1.00963			0.504814	+	0.863228i	$0.331561\pi$
$728$		0			0
$729$	−391.000	+	615.272i	−0.536351	+	0.843995i
$730$		0			0
$731$	−112.716	+	65.0769i	−0.154195	+	0.0890245i
$732$		0			0
$733$	−151.500	+	262.406i	−0.206685	+	0.357989i	−0.950668	−	0.310209i	$-0.899601\pi$
$733$	−151.500	+	262.406i	−0.206685	+	0.357989i	0.743983	+	0.668198i	$0.232934\pi$
$734$		0			0
$735$	−857.500	+	144.944i	−1.16667	+	0.197203i
$736$		0			0
$737$	158.828	+	91.6992i	0.215506	+	0.124422i
$738$		0			0
$739$	295.500	+	511.821i	0.399865	+	0.692586i	0.993709	−	0.111994i	$-0.0357238\pi$
$739$	295.500	+	511.821i	0.399865	+	0.692586i	−0.593844	+	0.804580i	$0.702390\pi$
$740$		0			0
$741$	69.0000	+	408.210i	0.0931174	+	0.550890i
$742$		0			0
$743$			851.915i			1.14659i	0.819349	+	0.573294i	$0.194335\pi$
$743$			851.915i			1.14659i	−0.819349	+	0.573294i	$0.805665\pi$
$744$		0			0
$745$	577.500	+	1000.26i	0.775168	+	1.34263i
$746$		0			0
$747$	−418.396	−	79.9032i	−0.560102	−	0.106965i
$748$		0			0
$749$	322.779	+	186.357i	0.430947	+	0.248807i
$750$		0			0
$751$	499.500	−	865.159i	0.665113	−	1.15201i	−0.314141	−	0.949376i	$-0.601717\pi$
$751$	499.500	−	865.159i	0.665113	−	1.15201i	0.979255	−	0.202634i	$-0.0649501\pi$
$752$		0			0
$753$	271.482	+	328.234i	0.360533	+	0.435902i
$754$		0			0
$755$			242.559i			0.321271i
$756$		0			0
$757$	−1398.00			−1.84676			−0.923382	−	0.383883i	$-0.874587\pi$
$757$	−1398.00			−1.84676			−0.923382	+	0.383883i	$0.874587\pi$
$758$		0			0
$759$	−566.376	+	468.448i	−0.746213	+	0.617191i
$760$		0			0
$761$	1142.54	+	659.643i	1.50136	+	0.866811i	0.999999	+	0.00157261i	$0.000500578\pi$
$761$	1142.54	+	659.643i	1.50136	+	0.866811i	0.501361	+	0.865238i	$0.332833\pi$
$762$		0			0
$763$	479.500	+	830.518i	0.628440	+	1.08849i
$764$		0			0
$765$	59.0892	−	309.408i	0.0772408	−	0.404455i
$766$		0			0
$767$	−522.594	+	301.720i	−0.681349	+	0.393377i
$768$		0			0
$769$	946.000			1.23017			0.615085	−	0.788461i	$-0.289122\pi$
$769$	946.000			1.23017			0.615085	+	0.788461i	$0.289122\pi$
$770$		0			0
$771$	−577.500	+	97.6153i	−0.749027	+	0.126609i
$772$		0			0
$773$	−455.989	+	263.266i	−0.589896	+	0.340576i	−0.765056	−	0.643963i	$-0.777289\pi$
$773$	−455.989	+	263.266i	−0.589896	+	0.340576i	0.175161	+	0.984540i	$0.443956\pi$
$774$		0			0
$775$	−195.000	+	337.750i	−0.251613	+	0.435806i
$776$		0			0
$777$	164.500	+	973.195i	0.211712	+	1.25250i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	280.000	+	484.974i	0.358515	+	0.620966i
$782$		0			0
$783$	−1120.00	+	615.272i	−1.43040	+	0.785788i
$784$		0			0
$785$			987.985i			1.25858i
$786$		0			0
$787$	223.500	+	387.113i	0.283990	+	0.491885i	0.972364	−	0.233471i	$-0.0750085\pi$
$787$	223.500	+	387.113i	0.283990	+	0.491885i	−0.688374	+	0.725356i	$0.741675\pi$
$788$		0			0
$789$	55.6944	−	149.710i	0.0705885	−	0.189747i
$790$		0			0
$791$			662.601i			0.837675i
$792$		0			0
$793$	−243.000	+	420.888i	−0.306431	+	0.530755i
$794$		0			0
$795$	728.197	−	602.290i	0.915972	−	0.757598i
$796$		0			0
$797$			1277.87i			1.60335i	0.597757	+	0.801677i	$0.296059\pi$
$797$			1277.87i			1.60335i	−0.597757	+	0.801677i	$0.703941\pi$
$798$		0			0
$799$	−315.000			−0.394243
$800$		0			0
$801$	521.993	−	604.482i	0.651677	−	0.754659i
$802$		0			0
$803$	87.0991	+	50.2867i	0.108467	+	0.0626235i
$804$		0			0
$805$	857.500	+	1485.23i	1.06522	+	1.84501i
$806$		0			0
$807$	43.3178	−	116.441i	0.0536776	−	0.144289i
$808$		0			0
$809$	1142.54	−	659.643i	1.41228	−	0.815381i	0.416678	−	0.909054i	$-0.363194\pi$
$809$	1142.54	−	659.643i	1.41228	−	0.815381i	0.995603	+	0.0936737i	$0.0298611\pi$
$810$		0			0
$811$	86.0000			0.106042			0.0530210	−	0.998593i	$-0.483115\pi$
$811$	86.0000			0.106042			0.0530210	+	0.998593i	$0.483115\pi$
$812$		0			0
$813$	−43.5000	−	257.349i	−0.0535055	−	0.316543i
$814$		0			0
$815$	−1347.47	+	777.964i	−1.65334	+	0.954558i
$816$		0			0
$817$	253.000	−	438.209i	0.309670	−	0.536363i
$818$		0			0
$819$	−70.9070	+	371.290i	−0.0865776	+	0.453345i
$820$		0			0
$821$	−333.026	−	192.273i	−0.405634	−	0.234193i	0.283278	−	0.959038i	$-0.408578\pi$
$821$	−333.026	−	192.273i	−0.405634	−	0.234193i	−0.688912	+	0.724845i	$0.741911\pi$
$822$		0			0
$823$	−188.500	−	326.492i	−0.229040	−	0.396709i	0.728484	−	0.685063i	$-0.240225\pi$
$823$	−188.500	−	326.492i	−0.229040	−	0.396709i	−0.957524	+	0.288354i	$0.906892\pi$
$824$		0			0
$825$	175.000	−	29.5804i	0.212121	−	0.0358550i
$826$		0			0
$827$		−	141.986i		−	0.171688i	−0.996309	−	0.0858440i	$-0.972641\pi$
$827$		−	141.986i		−	0.171688i	0.996309	−	0.0858440i	$-0.0273587\pi$
$828$		0			0
$829$	−75.5000	−	130.770i	−0.0910736	−	0.157744i	0.816890	−	0.576794i	$-0.195697\pi$
$829$	−75.5000	−	130.770i	−0.0910736	−	0.157744i	−0.907963	+	0.419050i	$0.862363\pi$
$830$		0			0
$831$	−874.450	−	325.308i	−1.05229	−	0.391466i
$832$		0			0
$833$	−251.050	+	144.944i	−0.301381	+	0.174002i
$834$		0			0
$835$	560.000	−	969.948i	0.670659	−	1.16161i
$836$		0			0
$837$	545.762	−	900.529i	0.652046	−	1.07590i
$838$		0			0
$839$		−	473.286i		−	0.564108i	−0.959399	−	0.282054i	$-0.908984\pi$
$839$		−	473.286i		−	0.564108i	0.959399	−	0.282054i	$-0.0910157\pi$
$840$		0			0
$841$	−1399.00			−1.66350
$842$		0			0
$843$	−723.951	−	875.291i	−0.858780	−	1.03831i
$844$		0			0
$845$	681.422	+	393.419i	0.806417	+	0.465585i
$846$		0			0
$847$	−301.000	+	521.347i	−0.355372	+	0.615522i
$848$		0			0
$849$	896.944	+	333.676i	1.05647	+	0.393023i
$850$		0			0
$851$	1685.62	−	973.195i	1.98076	−	1.14359i
$852$		0			0
$853$	−1462.00			−1.71395			−0.856975	−	0.515357i	$-0.827659\pi$
$853$	−1462.00			−1.71395			−0.856975	+	0.515357i	$0.827659\pi$
$854$		0			0
$855$	402.500	+	1156.59i	0.470760	+	1.35274i
$856$		0			0
$857$	−169.075	+	97.6153i	−0.197287	+	0.113904i	−0.595389	−	0.803437i	$-0.703002\pi$
$857$	−169.075	+	97.6153i	−0.197287	+	0.113904i	0.398103	+	0.917341i	$0.369669\pi$
$858$		0			0
$859$	491.500	−	851.303i	0.572177	−	0.991040i	−0.424165	−	0.905585i	$-0.639432\pi$
$859$	491.500	−	851.303i	0.572177	−	0.991040i	0.996342	−	0.0854547i	$-0.0272343\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	128.087	+	73.9510i	0.148420	+	0.0856906i	0.572371	−	0.819995i	$-0.306024\pi$
$863$	128.087	+	73.9510i	0.148420	+	0.0856906i	−0.423951	+	0.905685i	$0.639357\pi$
$864$		0			0
$865$	−822.500	−	1424.61i	−0.950867	−	1.64695i
$866$		0			0
$867$	127.000	+	751.342i	0.146482	+	0.866600i
$868$		0			0
$869$			53.2447i			0.0612713i
$870$		0			0
$871$	−93.0000	−	161.081i	−0.106774	−	0.184938i
$872$		0			0
$873$	138.438	−	724.899i	0.158577	−	0.830354i
$874$		0			0
$875$			621.188i			0.709930i
$876$		0			0
$877$	176.500	−	305.707i	0.201254	−	0.348583i	−0.747679	−	0.664061i	$-0.768832\pi$
$877$	176.500	−	305.707i	0.201254	−	0.348583i	0.948933	+	0.315478i	$0.102165\pi$
$878$		0			0
$879$	271.482	+	328.234i	0.308853	+	0.373418i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$		0			0
$883$	−314.000			−0.355606			−0.177803	−	0.984066i	$-0.556899\pi$
$883$	−314.000			−0.355606			−0.177803	+	0.984066i	$0.556899\pi$
$884$		0			0
$885$	−1375.48	+	1137.66i	−1.55422	+	1.28549i
$886$		0			0
$887$	537.965	+	310.594i	0.606499	+	0.350163i	0.771594	−	0.636115i	$-0.219460\pi$
$887$	537.965	+	310.594i	0.606499	+	0.350163i	−0.165095	+	0.986278i	$0.552793\pi$
$888$		0			0
$889$	546.000			0.614173
$890$		0			0
$891$	−474.091	+	69.8070i	−0.532088	+	0.0783468i
$892$		0			0
$893$	1060.56	−	612.314i	1.18764	−	0.685682i
$894$		0			0
$895$	525.000			0.586592
$896$		0			0
$897$	735.000	−	124.238i	0.819398	−	0.138504i
$898$		0			0
$899$	1598.52	−	922.908i	1.77811	−	1.02659i
$900$		0			0
$901$	157.500	−	272.798i	0.174806	−	0.302772i
$902$		0			0
$903$	356.008	−	294.453i	0.394250	−	0.326083i
$904$		0			0
$905$	30.7409	+	17.7482i	0.0339678	+	0.0196113i
$906$		0			0
$907$	−376.500	−	652.117i	−0.415105	−	0.718983i	0.580335	−	0.814378i	$-0.302922\pi$
$907$	−376.500	−	652.117i	−0.415105	−	0.718983i	−0.995439	+	0.0953956i	$0.969588\pi$
$908$		0			0
$909$	−122.500	−	352.007i	−0.134763	−	0.387246i
$910$		0			0
$911$			1703.83i			1.87029i	0.354270	+	0.935143i	$0.384729\pi$
$911$			1703.83i			1.87029i	−0.354270	+	0.935143i	$0.615271\pi$
$912$		0			0
$913$	−140.000	−	242.487i	−0.153341	−	0.265594i
$914$		0			0
$915$	−501.249	+	1347.39i	−0.547813	+	1.47256i
$916$		0			0
$917$	896.608	+	517.657i	0.977762	+	0.564511i
$918$		0			0
$919$	−284.500	+	492.768i	−0.309576	+	0.536201i	−0.978270	−	0.207337i	$-0.933520\pi$
$919$	−284.500	+	492.768i	−0.309576	+	0.536201i	0.668694	+	0.743538i	$0.266854\pi$
$920$		0			0
$921$	−1021.79	+	845.118i	−1.10943	+	0.917610i
$922$		0			0
$923$		−	567.944i		−	0.615324i
$924$		0			0
$925$	−470.000			−0.508108
$926$		0			0
$927$	−156.670	−	135.291i	−0.169008	−	0.145944i
$928$		0			0
$929$	−1398.71	−	807.545i	−1.50561	−	0.869263i	−0.999979	−	0.00651097i	$-0.997927\pi$
$929$	−1398.71	−	807.545i	−1.50561	−	0.869263i	−0.505628	−	0.862752i	$-0.668739\pi$
$930$		0			0
$931$	563.500	−	976.011i	0.605263	−	1.04835i
$932$		0			0
$933$	253.719	−	682.013i	0.271939	−	0.730989i
$934$		0			0
$935$	179.322	−	103.531i	0.191788	−	0.110729i
$936$		0			0
$937$	722.000			0.770544			0.385272	−	0.922803i	$-0.374108\pi$
$937$	722.000			0.770544			0.385272	+	0.922803i	$0.374108\pi$
$938$		0			0
$939$	−128.500	−	760.216i	−0.136848	−	0.809602i
$940$		0			0
$941$	−455.989	+	263.266i	−0.484579	+	0.279772i	−0.722323	−	0.691556i	$-0.756926\pi$
$941$	−455.989	+	263.266i	−0.484579	+	0.279772i	0.237743	+	0.971328i	$0.423592\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−23.7637	+	1117.89i	−0.0251468	+	1.18295i
$946$		0			0
$947$	128.087	+	73.9510i	0.135255	+	0.0780898i	0.566101	−	0.824336i	$-0.308451\pi$
$947$	128.087	+	73.9510i	0.135255	+	0.0780898i	−0.430845	+	0.902426i	$0.641785\pi$
$948$		0			0
$949$	−51.0000	−	88.3346i	−0.0537408	−	0.0930818i
$950$		0			0
$951$	262.500	−	44.3706i	0.276025	−	0.0466568i
$952$		0			0
$953$		−	378.629i		−	0.397302i	−0.980070	−	0.198651i	$-0.936344\pi$
$953$		−	378.629i		−	0.397302i	0.980070	−	0.198651i	$-0.0636561\pi$
$954$		0			0
$955$	−157.500	−	272.798i	−0.164921	−	0.285652i
$956$		0			0
$957$	−787.287	−	292.882i	−0.822661	−	0.306042i
$958$		0			0
$959$	−609.694	+	352.007i	−0.635760	+	0.367056i
$960$		0			0
$961$	−280.000	+	484.974i	−0.291363	+	0.504656i
$962$		0			0
$963$	313.196	−	362.689i	0.325229	−	0.376624i
$964$		0			0
$965$			845.999i			0.876683i
$966$		0			0
$967$	−482.000			−0.498449			−0.249224	−	0.968446i	$-0.580176\pi$
$967$	−482.000			−0.498449			−0.249224	+	0.968446i	$0.580176\pi$
$968$		0			0
$969$	260.170	+	314.558i	0.268493	+	0.324621i
$970$		0			0
$971$	−199.816	−	115.364i	−0.205783	−	0.118809i	0.393567	−	0.919296i	$-0.371241\pi$
$971$	−199.816	−	115.364i	−0.205783	−	0.118809i	−0.599350	+	0.800487i	$0.704574\pi$
$972$		0			0
$973$	−742.000			−0.762590
$974$		0			0
$975$	−168.704	−	62.7604i	−0.173030	−	0.0643697i
$976$		0			0
$977$	−169.075	+	97.6153i	−0.173055	+	0.0999133i	−0.584026	−	0.811735i	$-0.698523\pi$
$977$	−169.075	+	97.6153i	−0.173055	+	0.0999133i	0.410971	+	0.911649i	$0.365190\pi$
$978$		0			0
$979$	525.000			0.536261
$980$		0			0
$981$	1164.50	−	405.251i	1.18705	−	0.413100i
$982$		0			0
$983$	1275.75	−	736.552i	1.29781	−	0.749290i	0.317783	−	0.948163i	$-0.397062\pi$
$983$	1275.75	−	736.552i	1.29781	−	0.749290i	0.980025	+	0.198874i	$0.0637283\pi$
$984$		0			0
$985$	140.000	−	242.487i	0.142132	−	0.246180i
$986$		0			0
$987$	1102.50	−	186.357i	1.11702	−	0.188811i
$988$		0			0
$989$	−789.015	−	455.538i	−0.797791	−	0.460605i
$990$		0			0
$991$	−180.500	−	312.635i	−0.182139	−	0.315474i	0.760470	−	0.649374i	$-0.224969\pi$
$991$	−180.500	−	312.635i	−0.182139	−	0.315474i	−0.942609	+	0.333899i	$0.891636\pi$
$992$		0			0
$993$	60.5000	+	357.923i	0.0609265	+	0.360446i
$994$		0			0
$995$			999.817i			1.00484i
$996$		0			0
$997$	36.5000	+	63.2199i	0.0366098	+	0.0634101i	0.883750	−	0.467960i	$-0.155011\pi$
$997$	36.5000	+	63.2199i	0.0366098	+	0.0634101i	−0.847140	+	0.531370i	$0.821677\pi$
$998$		0			0
$999$	1268.71	+	26.9700i	1.26998	+	0.0269970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bn.d.65.2		4
3.2	odd	2	inner	336.3.bn.d.65.1		4
4.3	odd	2		84.3.p.c.65.1	yes	4
7.4	even	3	inner	336.3.bn.d.305.1		4
12.11	even	2		84.3.p.c.65.2	yes	4
21.11	odd	6	inner	336.3.bn.d.305.2		4
28.3	even	6		588.3.p.d.557.1		4
28.11	odd	6		84.3.p.c.53.2	yes	4
28.19	even	6		588.3.c.f.197.2		2
28.23	odd	6		588.3.c.e.197.1		2
28.27	even	2		588.3.p.d.569.2		4
84.11	even	6		84.3.p.c.53.1	✓	4
84.23	even	6		588.3.c.e.197.2		2
84.47	odd	6		588.3.c.f.197.1		2
84.59	odd	6		588.3.p.d.557.2		4
84.83	odd	2		588.3.p.d.569.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.p.c.53.1	✓	4	84.11	even	6
84.3.p.c.53.2	yes	4	28.11	odd	6
84.3.p.c.65.1	yes	4	4.3	odd	2
84.3.p.c.65.2	yes	4	12.11	even	2
336.3.bn.d.65.1		4	3.2	odd	2	inner
336.3.bn.d.65.2		4	1.1	even	1	trivial
336.3.bn.d.305.1		4	7.4	even	3	inner
336.3.bn.d.305.2		4	21.11	odd	6	inner
588.3.c.e.197.1		2	28.23	odd	6
588.3.c.e.197.2		2	84.23	even	6
588.3.c.f.197.1		2	84.47	odd	6
588.3.c.f.197.2		2	28.19	even	6
588.3.p.d.557.1		4	28.3	even	6
588.3.p.d.557.2		4	84.59	odd	6
588.3.p.d.569.1		4	84.83	odd	2
588.3.p.d.569.2		4	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.31174 - 1.91203i) q^{3} +(-5.12348 - 2.95804i) q^{5} +7.00000 q^{7} +(1.68826 - 8.84024i) q^{9} +(5.12348 - 2.95804i) q^{11} -6.00000 q^{13} +(-17.5000 + 2.95804i) q^{15} +(-5.12348 + 2.95804i) q^{17} +(11.5000 - 19.9186i) q^{19} +(16.1822 - 13.3842i) q^{21} +(-35.8643 - 20.7063i) q^{23} +(5.00000 + 8.66025i) q^{25} +(-13.0000 - 23.6643i) q^{27} -47.3286i q^{29} +(19.5000 + 33.7750i) q^{31} +(6.18826 - 16.6345i) q^{33} +(-35.8643 - 20.7063i) q^{35} +(-23.5000 + 40.7032i) q^{37} +(-13.8704 + 11.4722i) q^{39} +22.0000 q^{43} +(-34.7995 + 40.2988i) q^{45} +(46.1113 + 26.6224i) q^{47} +49.0000 q^{49} +(-6.18826 + 16.6345i) q^{51} +(-46.1113 + 26.6224i) q^{53} -35.0000 q^{55} +(-11.5000 - 68.0349i) q^{57} +(87.0991 - 50.2867i) q^{59} +(40.5000 - 70.1481i) q^{61} +(11.8178 - 61.8817i) q^{63} +(30.7409 + 17.7482i) q^{65} +(15.5000 + 26.8468i) q^{67} +(-122.500 + 20.7063i) q^{69} +94.6573i q^{71} +(8.50000 + 14.7224i) q^{73} +(28.1174 + 10.4601i) q^{75} +(35.8643 - 20.7063i) q^{77} +(-4.50000 + 7.79423i) q^{79} +(-75.2995 - 29.8493i) q^{81} -47.3286i q^{83} +35.0000 q^{85} +(-90.4939 - 109.411i) q^{87} +(76.8521 + 44.3706i) q^{89} -42.0000 q^{91} +(109.658 + 40.7943i) q^{93} +(-117.840 + 68.0349i) q^{95} +82.0000 q^{97} +(-17.5000 - 50.2867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 28 q^{7} + 17 q^{9} - 24 q^{13} - 70 q^{15} + 46 q^{19} - 7 q^{21} + 20 q^{25} - 52 q^{27} + 78 q^{31} + 35 q^{33} - 94 q^{37} + 6 q^{39} + 88 q^{43} + 35 q^{45} + 196 q^{49} - 35 q^{51}+ \cdots - 70 q^{99}+O(q^{100}) \) 4 * q - q^3 + 28 * q^7 + 17 * q^9 - 24 * q^13 - 70 * q^15 + 46 * q^19 - 7 * q^21 + 20 * q^25 - 52 * q^27 + 78 * q^31 + 35 * q^33 - 94 * q^37 + 6 * q^39 + 88 * q^43 + 35 * q^45 + 196 * q^49 - 35 * q^51 - 140 * q^55 - 46 * q^57 + 162 * q^61 + 119 * q^63 + 62 * q^67 - 490 * q^69 + 34 * q^73 + 10 * q^75 - 18 * q^79 - 127 * q^81 + 140 * q^85 - 280 * q^87 - 168 * q^91 + 39 * q^93 + 328 * q^97 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more