LMFDB - Embedded newform 84.3.p.c.65.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [84,3,Mod(53,84)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(84, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("84.53"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	84.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.28883422063$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$2.81174 - 1.04601i$ of defining polynomial
Character	$\chi$	$=$	84.65
Dual form			84.3.p.c.53.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.81174 - 1.04601i) q^{3} +(5.12348 + 2.95804i) q^{5} -7.00000 q^{7} +(6.81174 - 5.88220i) q^{9} +(5.12348 - 2.95804i) q^{11} -6.00000 q^{13} +(17.5000 + 2.95804i) q^{15} +(5.12348 - 2.95804i) q^{17} +(-11.5000 + 19.9186i) q^{19} +(-19.6822 + 7.32205i) q^{21} +(-35.8643 - 20.7063i) q^{23} +(5.00000 + 8.66025i) q^{25} +(13.0000 - 23.6643i) q^{27} +47.3286i q^{29} +(-19.5000 - 33.7750i) q^{31} +(11.3117 - 13.6764i) q^{33} +(-35.8643 - 20.7063i) q^{35} +(-23.5000 + 40.7032i) q^{37} +(-16.8704 + 6.27604i) q^{39} -22.0000 q^{43} +(52.2995 - 9.98789i) q^{45} +(46.1113 + 26.6224i) q^{47} +49.0000 q^{49} +(11.3117 - 13.6764i) q^{51} +(46.1113 - 26.6224i) q^{53} +35.0000 q^{55} +(-11.5000 + 68.0349i) q^{57} +(87.0991 - 50.2867i) q^{59} +(40.5000 - 70.1481i) q^{61} +(-47.6822 + 41.1754i) q^{63} +(-30.7409 - 17.7482i) q^{65} +(-15.5000 - 26.8468i) q^{67} +(-122.500 - 20.7063i) q^{69} +94.6573i q^{71} +(8.50000 + 14.7224i) q^{73} +(23.1174 + 19.1203i) q^{75} +(-35.8643 + 20.7063i) q^{77} +(4.50000 - 7.79423i) q^{79} +(11.7995 - 80.1360i) q^{81} -47.3286i q^{83} +35.0000 q^{85} +(49.5061 + 133.076i) q^{87} +(-76.8521 - 44.3706i) q^{89} +42.0000 q^{91} +(-90.1578 - 74.5693i) q^{93} +(-117.840 + 68.0349i) q^{95} +82.0000 q^{97} +(17.5000 - 50.2867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	2.81174	−	1.04601i	0.937246	−	0.348669i
$3$	2.81174	−	1.04601i	0.937246	−	0.348669i
$4$		0			0
$5$	5.12348	+	2.95804i	1.02470	+	0.591608i	0.915460	−	0.402408i	$-0.131827\pi$
$5$	5.12348	+	2.95804i	1.02470	+	0.591608i	0.109235	+	0.994016i	$0.465160\pi$
$6$		0			0
$7$	−7.00000			−1.00000
$7$	−7.00000			−1.00000
$8$		0			0
$9$	6.81174	−	5.88220i	0.756860	−	0.653577i
$10$		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	−0.341682	−	0.939816i	$-0.610997\pi$
$17$	5.12348	−	2.95804i	0.301381	−	0.174002i	0.643063	+	0.765813i	$0.277663\pi$
$18$		0			0
$19$	−11.5000	+	19.9186i	−0.605263	+	1.04835i	0.386747	+	0.922186i	$0.373599\pi$
$19$	−11.5000	+	19.9186i	−0.605263	+	1.04835i	−0.992010	+	0.126161i	$0.959735\pi$
$20$		0			0
$21$	−19.6822	+	7.32205i	−0.937246	+	0.348669i
$22$		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	$0.303819\pi$
$29$			47.3286i			1.63202i	−0.578036	+	0.816011i	$0.696181\pi$
$30$		0			0
$31$	−19.5000	−	33.7750i	−0.629032	−	1.08952i	−0.987746	−	0.156068i	$-0.950118\pi$
$31$	−19.5000	−	33.7750i	−0.629032	−	1.08952i	0.358714	−	0.933448i	$-0.383215\pi$
$32$		0			0
$33$	11.3117	−	13.6764i	0.342780	−	0.414437i
$34$		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
$39$	−16.8704	+	6.27604i	−0.432575	+	0.160924i
$40$		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	$-0.582343\pi$
$43$	−22.0000			−0.511628			−0.255814	+	0.966726i	$0.582343\pi$
$44$		0			0
$45$	52.2995	−	9.98789i	1.16221	−	0.221953i
$46$		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
$51$	11.3117	−	13.6764i	0.221799	−	0.268165i
$52$		0			0
$53$	46.1113	−	26.6224i	0.870024	−	0.502309i	0.00266787	−	0.999996i	$-0.499151\pi$
$53$	46.1113	−	26.6224i	0.870024	−	0.502309i	0.867356	+	0.497688i	$0.165817\pi$
$54$		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
$63$	−47.6822	+	41.1754i	−0.756860	+	0.653577i
$64$		0			0
$65$	−30.7409	−	17.7482i	−0.472936	−	0.273050i
$66$		0			0
$67$	−15.5000	−	26.8468i	−0.231343	−	0.400698i	0.726860	−	0.686785i	$-0.240979\pi$
$67$	−15.5000	−	26.8468i	−0.231343	−	0.400698i	−0.958204	+	0.286087i	$0.907645\pi$
$68$		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
$75$	23.1174	+	19.1203i	0.308232	+	0.254938i
$76$		0			0
$77$	−35.8643	+	20.7063i	−0.465770	+	0.268913i
$78$		0			0
$79$	4.50000	−	7.79423i	0.0569620	−	0.0986611i	−0.836138	−	0.548519i	$-0.815192\pi$
$79$	4.50000	−	7.79423i	0.0569620	−	0.0986611i	0.893100	+	0.449858i	$0.148525\pi$
$80$		0			0
$81$	11.7995	−	80.1360i	0.145673	−	0.989333i
$82$		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
$87$	49.5061	+	133.076i	0.569036	+	1.52961i
$88$		0			0
$89$	−76.8521	−	44.3706i	−0.863507	−	0.498546i	0.00167806	−	0.999999i	$-0.499466\pi$
$89$	−76.8521	−	44.3706i	−0.863507	−	0.498546i	−0.865185	+	0.501453i	$0.832799\pi$
$90$		0			0
$91$	42.0000			0.461538
$92$		0			0
$93$	−90.1578	−	74.5693i	−0.969438	−	0.801820i
$94$		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	−0.666926	−	0.745124i	$-0.732390\pi$
$101$	−35.8643	+	20.7063i	−0.355092	+	0.205013i	0.311833	+	0.950137i	$0.399057\pi$
$102$		0			0
$103$	−11.5000	+	19.9186i	−0.111650	+	0.193384i	−0.916436	−	0.400182i	$-0.868947\pi$
$103$	−11.5000	+	19.9186i	−0.111650	+	0.193384i	0.804785	+	0.593566i	$0.202280\pi$
$104$		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	$-0.862438\pi$
$113$		−	94.6573i		−	0.837675i	0.908061	−	0.418838i	$-0.137562\pi$
$114$		0			0
$115$	−122.500	−	212.176i	−1.06522	−	1.84501i
$116$		0			0
$117$	−40.8704	+	35.2932i	−0.349320	+	0.301651i
$118$		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	$-0.599354\pi$
$127$	−78.0000			−0.614173			−0.307087	+	0.951682i	$0.599354\pi$
$128$		0			0
$129$	−61.8582	+	23.0122i	−0.479521	+	0.178389i
$130$		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
$135$	136.605	−	82.7890i	1.01189	−	0.613252i
$136$		0			0
$137$	87.0991	−	50.2867i	0.635760	−	0.367056i	−0.147220	−	0.989104i	$-0.547032\pi$
$137$	87.0991	−	50.2867i	0.635760	−	0.367056i	0.782979	+	0.622048i	$0.213699\pi$
$138$		0			0
$139$	106.000			0.762590			0.381295	−	0.924453i	$-0.375478\pi$
$139$	106.000			0.762590			0.381295	+	0.924453i	$0.375478\pi$
$140$		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
$147$	137.775	−	51.2544i	0.937246	−	0.348669i
$148$		0			0
$149$	169.075	+	97.6153i	1.13473	+	0.655136i	0.945120	−	0.326723i	$-0.105945\pi$
$149$	169.075	+	97.6153i	1.13473	+	0.655136i	0.189609	+	0.981860i	$0.439278\pi$
$150$		0			0
$151$	20.5000	+	35.5070i	0.135762	+	0.235146i	0.925888	−	0.377798i	$-0.123319\pi$
$151$	20.5000	+	35.5070i	0.135762	+	0.235146i	−0.790127	+	0.612944i	$0.789985\pi$
$152$		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
$159$	101.806	−	123.088i	0.640287	−	0.774137i
$160$		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	$0.465441\pi$
$163$	−131.500	+	227.765i	−0.806748	+	1.39733i	−0.915104	+	0.403217i	$0.867892\pi$
$164$		0			0
$165$	98.4108	−	36.6103i	0.596429	−	0.221880i
$166$		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
$171$	38.8300	+	203.325i	0.227076	+	1.18904i
$172$		0			0
$173$	−240.803	−	139.028i	−1.39193	−	0.803629i	−0.398398	−	0.917212i	$-0.630434\pi$
$173$	−240.803	−	139.028i	−1.39193	−	0.803629i	−0.993528	+	0.113583i	$0.963767\pi$
$174$		0			0
$175$	−35.0000	−	60.6218i	−0.200000	−	0.346410i
$176$		0			0
$177$	192.300	−	232.499i	1.08644	−	1.31355i
$178$		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	$-0.961671\pi$
$197$		−	47.3286i		−	0.240247i	0.992759	−	0.120123i	$-0.0383290\pi$
$198$		0			0
$199$	84.5000	+	146.358i	0.424623	+	0.735469i	0.996385	−	0.0849507i	$-0.0270733\pi$
$199$	84.5000	+	146.358i	0.424623	+	0.735469i	−0.571762	+	0.820420i	$0.693740\pi$
$200$		0			0
$201$	−71.6639	−	59.2730i	−0.356537	−	0.294891i
$202$		0			0
$203$		−	331.300i		−	1.63202i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−366.097	+	69.9153i	−1.76858	+	0.337755i
$208$		0			0
$209$			136.070i			0.651052i
$210$		0			0
$211$	−166.000			−0.786730			−0.393365	−	0.919382i	$-0.628689\pi$
$211$	−166.000			−0.786730			−0.393365	+	0.919382i	$0.628689\pi$
$212$		0			0
$213$	99.0122	+	266.151i	0.464846	+	1.24954i
$214$		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
$219$	39.2995	+	32.5046i	0.179450	+	0.148423i
$220$		0			0
$221$	−30.7409	+	17.7482i	−0.139099	+	0.0803088i
$222$		0			0
$223$	−142.000			−0.636771			−0.318386	−	0.947961i	$-0.603141\pi$
$223$	−142.000			−0.636771			−0.318386	+	0.947961i	$0.603141\pi$
$224$		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
$231$	−79.1822	+	95.7350i	−0.342780	+	0.414437i
$232$		0			0
$233$	−158.828	−	91.6992i	−0.681664	−	0.393559i	0.118818	−	0.992916i	$-0.462090\pi$
$233$	−158.828	−	91.6992i	−0.681664	−	0.393559i	−0.800482	+	0.599357i	$0.795423\pi$
$234$		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
$243$	−50.6456	−	237.664i	−0.208418	−	0.978040i
$244$		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
$249$	−49.5061	−	133.076i	−0.198820	−	0.534441i
$250$		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
$255$	98.4108	−	36.6103i	0.385925	−	0.143570i
$256$		0			0
$257$	169.075	+	97.6153i	0.657878	+	0.379826i	0.791468	−	0.611211i	$-0.209317\pi$
$257$	169.075	+	97.6153i	0.657878	+	0.379826i	−0.133590	+	0.991037i	$0.542650\pi$
$258$		0			0
$259$	164.500	−	284.922i	0.635135	−	1.10009i
$260$		0			0
$261$	278.396	+	322.390i	1.06665	+	1.23521i
$262$		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	−0.565179	−	0.824968i	$-0.691193\pi$
$269$	−35.8643	+	20.7063i	−0.133325	+	0.0769750i	0.431854	+	0.901943i	$0.357860\pi$
$270$		0			0
$271$	−43.5000	+	75.3442i	−0.160517	+	0.278023i	−0.935054	−	0.354505i	$-0.884649\pi$
$271$	−43.5000	+	75.3442i	−0.160517	+	0.278023i	0.774537	+	0.632528i	$0.217983\pi$
$272$		0			0
$273$	118.093	−	43.9323i	0.432575	−	0.160924i
$274$		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	$0.235303\pi$
$281$			378.629i			1.34743i	−0.738989	+	0.673717i	$0.764697\pi$
$282$		0			0
$283$	−159.500	−	276.262i	−0.563604	−	0.976191i	−0.997178	−	0.0750731i	$-0.976081\pi$
$283$	−159.500	−	276.262i	−0.563604	−	0.976191i	0.433574	−	0.901118i	$-0.357252\pi$
$284$		0			0
$285$	−260.170	+	314.558i	−0.912877	+	1.10371i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−127.000	+	219.970i	−0.439446	+	0.761143i
$290$		0			0
$291$	230.562	−	85.7726i	0.792311	−	0.294751i
$292$		0			0
$293$		−	141.986i		−	0.484594i	−0.970202	−	0.242297i	$-0.922099\pi$
$293$		−	141.986i		−	0.484594i	0.970202	−	0.242297i	$-0.0779008\pi$
$294$		0			0
$295$	595.000			2.01695
$296$		0			0
$297$	−3.39482	−	159.698i	−0.0114304	−	0.537704i
$298$		0			0
$299$	215.186	+	124.238i	0.719686	+	0.415511i
$300$		0			0
$301$	154.000			0.511628
$302$		0			0
$303$	−79.1822	+	95.7350i	−0.261327	+	0.315957i
$304$		0			0
$305$	415.002	−	239.601i	1.36066	−	0.785578i
$306$		0			0
$307$	442.000			1.43974			0.719870	−	0.694109i	$-0.244202\pi$
$307$	442.000			1.43974			0.719870	+	0.694109i	$0.244202\pi$
$308$		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
$315$	−366.097	+	69.9153i	−1.16221	+	0.221953i
$316$		0			0
$317$	−76.8521	−	44.3706i	−0.242436	−	0.139970i	0.373860	−	0.927485i	$-0.378034\pi$
$317$	−76.8521	−	44.3706i	−0.242436	−	0.139970i	−0.616296	+	0.787515i	$0.711367\pi$
$318$		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
$327$	316.708	+	261.948i	0.968526	+	0.801066i
$328$		0			0
$329$	−322.779	−	186.357i	−0.981091	−	0.566433i
$330$		0			0
$331$	60.5000	−	104.789i	0.182779	−	0.316583i	−0.760047	−	0.649869i	$-0.774824\pi$
$331$	60.5000	−	104.789i	0.182779	−	0.316583i	0.942826	+	0.333285i	$0.108157\pi$
$332$		0			0
$333$	79.3483	+	415.491i	0.238283	+	1.24772i
$334$		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
$339$	−99.0122	−	266.151i	−0.292071	−	0.785107i
$340$		0			0
$341$	−199.816	−	115.364i	−0.585969	−	0.338310i
$342$		0			0
$343$	−343.000			−1.00000
$344$		0			0
$345$	−566.376	−	468.448i	−1.64167	−	1.35782i
$346$		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	−0.241020	−	0.970520i	$-0.577482\pi$
$353$	169.075	−	97.6153i	0.478965	−	0.276531i	0.719985	+	0.693990i	$0.244149\pi$
$354$		0			0
$355$	−280.000	+	484.974i	−0.788732	+	1.36612i
$356$		0			0
$357$	−79.1822	+	95.7350i	−0.221799	+	0.268165i
$358$		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	0.911459	−	0.411390i	$-0.134957\pi$
$367$	36.5000	+	63.2199i	0.0994550	+	0.172261i	−0.812004	+	0.583652i	$0.801623\pi$
$368$		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
$375$	−92.8239	−	249.517i	−0.247530	−	0.665379i
$376$		0			0
$377$		−	283.972i		−	0.753241i
$378$		0			0
$379$	538.000			1.41953			0.709763	−	0.704441i	$-0.248802\pi$
$379$	538.000			1.41953			0.709763	+	0.704441i	$0.248802\pi$
$380$		0			0
$381$	−219.316	+	81.5886i	−0.575631	+	0.214143i
$382$		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
$387$	−149.858	+	129.408i	−0.387231	+	0.334388i
$388$		0			0
$389$	−35.8643	+	20.7063i	−0.0921962	+	0.0532295i	−0.545389	−	0.838183i	$-0.683618\pi$
$389$	−35.8643	+	20.7063i	−0.0921962	+	0.0532295i	0.453193	+	0.891412i	$0.350285\pi$
$390$		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	0.0402588	−	0.999189i	$-0.487182\pi$
$401$	−322.779	−	186.357i	−0.804935	−	0.464729i	−0.845194	+	0.534460i	$0.820515\pi$
$402$		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
$411$	192.300	−	232.499i	0.467882	−	0.565692i
$412$		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
$417$	298.044	−	110.877i	0.714734	−	0.265892i
$418$		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
$423$	470.696	−	89.8911i	1.11276	−	0.212508i
$424$		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
$429$	−67.8704	+	82.0585i	−0.158206	+	0.191279i
$430$		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	−0.688669	−	0.725075i	$-0.741805\pi$
$439$	124.500	−	215.640i	0.283599	−	0.491208i	0.972268	+	0.233867i	$0.0751382\pi$
$440$		0			0
$441$	333.775	−	288.228i	0.756860	−	0.653577i
$442$		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	$0.176700\pi$
$449$			473.286i			1.05409i	−0.849837	+	0.527045i	$0.823300\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	94.7812	+	78.3933i	0.209230	+	0.173054i
$454$		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
$459$	−3.39482	−	159.698i	−0.00739612	−	0.347926i
$460$		0			0
$461$		−	520.615i		−	1.12932i	−0.825325	−	0.564658i	$-0.809008\pi$
$461$		−	520.615i		−	1.12932i	0.825325	−	0.564658i	$-0.190992\pi$
$462$		0			0
$463$	−302.000			−0.652268			−0.326134	−	0.945324i	$-0.605746\pi$
$463$	−302.000			−0.652268			−0.326134	+	0.945324i	$0.605746\pi$
$464$		0			0
$465$	−241.342	−	648.744i	−0.519016	−	1.39515i
$466$		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
$471$	−386.060	−	319.309i	−0.819661	−	0.677939i
$472$		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	$-0.935409\pi$
$487$	−323.500	−	560.318i	−0.664271	−	1.15055i	0.315211	−	0.949021i	$-0.397925\pi$
$488$		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
$495$	238.411	−	205.877i	0.481638	−	0.415913i
$496$		0			0
$497$		−	662.601i		−	1.33320i
$498$		0			0
$499$	−51.5000	+	89.2006i	−0.103206	+	0.178759i	−0.913004	−	0.407951i	$-0.866244\pi$
$499$	−51.5000	+	89.2006i	−0.103206	+	0.178759i	0.809798	+	0.586709i	$0.199577\pi$
$500$		0			0
$501$	198.024	+	532.303i	0.395258	+	1.06248i
$502$		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
$507$	−373.961	+	139.119i	−0.737596	+	0.274396i
$508$		0			0
$509$	169.075	+	97.6153i	0.332170	+	0.191779i	0.656804	−	0.754061i	$-0.271908\pi$
$509$	169.075	+	97.6153i	0.332170	+	0.191779i	−0.324634	+	0.945840i	$0.605241\pi$
$510$		0			0
$511$	−59.5000	−	103.057i	−0.116438	−	0.201677i
$512$		0			0
$513$	321.860	+	531.081i	0.627407	+	1.03525i
$514$		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	−0.776689	−	0.629884i	$-0.783102\pi$
$521$	−322.779	+	186.357i	−0.619537	+	0.357690i	0.157152	+	0.987575i	$0.449769\pi$
$522$		0			0
$523$	−11.5000	+	19.9186i	−0.0219885	+	0.0380852i	−0.876810	−	0.480836i	$-0.840333\pi$
$523$	−11.5000	+	19.9186i	−0.0219885	+	0.0380852i	0.854822	+	0.518922i	$0.173666\pi$
$524$		0			0
$525$	−161.822	−	133.842i	−0.308232	−	0.254938i
$526$		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
$537$	−169.676	+	205.146i	−0.315970	+	0.382023i
$538$		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
$543$	−16.8704	+	6.27604i	−0.0310689	+	0.0115581i
$544$		0			0
$545$			810.503i			1.48716i
$546$		0			0
$547$	−54.0000			−0.0987203			−0.0493601	−	0.998781i	$-0.515718\pi$
$547$	−54.0000			−0.0987203			−0.0493601	+	0.998781i	$0.515718\pi$
$548$		0			0
$549$	−136.749	−	716.059i	−0.249088	−	1.30430i
$550$		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
$555$	−531.652	+	642.792i	−0.957931	+	1.15818i
$556$		0			0
$557$	−773.645	+	446.664i	−1.38895	+	0.801910i	−0.993197	−	0.116447i	$-0.962849\pi$
$557$	−773.645	+	446.664i	−1.38895	+	0.801910i	−0.395752	+	0.918357i	$0.629516\pi$
$558$		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
$567$	−82.5968	+	560.952i	−0.145673	+	0.989333i
$568$		0			0
$569$	−568.706	−	328.342i	−0.999483	−	0.577052i	−0.0913876	−	0.995815i	$-0.529130\pi$
$569$	−568.706	−	328.342i	−0.999483	−	0.577052i	−0.908095	+	0.418764i	$0.862464\pi$
$570$		0			0
$571$	−463.500	−	802.806i	−0.811734	−	1.40596i	−0.911650	−	0.410968i	$-0.865191\pi$
$571$	−463.500	−	802.806i	−0.811734	−	1.40596i	0.0999158	−	0.994996i	$-0.468143\pi$
$572$		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
$579$	−330.578	−	273.421i	−0.570947	−	0.472229i
$580$		0			0
$581$			331.300i			0.570225i
$582$		0			0
$583$	157.500	−	272.798i	0.270154	−	0.467921i
$584$		0			0
$585$	−313.797	+	59.9274i	−0.536406	+	0.102440i
$586$		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
$591$	−49.5061	−	133.076i	−0.0837667	−	0.225170i
$592$		0			0
$593$	660.928	+	381.587i	1.11455	+	0.643486i	0.940004	−	0.341163i	$-0.110821\pi$
$593$	660.928	+	381.587i	1.11455	+	0.643486i	0.174546	+	0.984649i	$0.444154\pi$
$594$		0			0
$595$	−245.000			−0.411765
$596$		0			0
$597$	390.684	+	323.134i	0.654412	+	0.541262i
$598$		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	$0.398126\pi$
$607$	−403.500	+	698.883i	−0.664745	+	1.15137i	−0.979354	+	0.202150i	$0.935207\pi$
$608$		0			0
$609$	−346.543	−	931.530i	−0.569036	−	1.52961i
$610$		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	$-0.789696\pi$
$617$		−	757.258i		−	1.22732i	0.789569	−	0.613661i	$-0.210304\pi$
$618$		0			0
$619$	344.500	+	596.692i	0.556543	+	0.963960i	0.997782	+	0.0665707i	$0.0212058\pi$
$619$	344.500	+	596.692i	0.556543	+	0.963960i	−0.441239	+	0.897390i	$0.645461\pi$
$620$		0			0
$621$	−956.236	+	579.523i	−1.53983	+	0.933210i
$622$		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
$627$	142.330	+	382.593i	0.227002	+	0.610196i
$628$		0			0
$629$			278.056i			0.442060i
$630$		0			0
$631$	674.000			1.06815			0.534073	−	0.845438i	$-0.320661\pi$
$631$	674.000			1.06815			0.534073	+	0.845438i	$0.320661\pi$
$632$		0			0
$633$	−466.748	+	173.637i	−0.737359	+	0.274308i
$634$		0			0
$635$	−399.631	−	230.727i	−0.629340	−	0.363350i
$636$		0			0
$637$	−294.000			−0.461538
$638$		0			0
$639$	556.793	+	644.781i	0.871350	+	1.00905i
$640$		0			0
$641$	742.904	−	428.916i	1.15898	−	0.669135i	0.207918	−	0.978146i	$-0.433331\pi$
$641$	742.904	−	428.916i	1.15898	−	0.669135i	0.951059	+	0.309011i	$0.0999980\pi$
$642$		0			0
$643$	218.000			0.339036			0.169518	−	0.985527i	$-0.445779\pi$
$643$	218.000			0.339036			0.169518	+	0.985527i	$0.445779\pi$
$644$		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
$651$	631.104	+	521.985i	0.969438	+	0.801820i
$652$		0			0
$653$	906.855	+	523.573i	1.38875	+	0.801796i	0.993175	−	0.116636i	$-0.0372112\pi$
$653$	906.855	+	523.573i	1.38875	+	0.801796i	0.395577	+	0.918433i	$0.370544\pi$
$654$		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
$663$	−67.8704	+	82.0585i	−0.102369	+	0.123769i
$664$		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
$669$	−399.267	+	148.533i	−0.596811	+	0.222022i
$670$		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
$675$	269.939	−	5.73829i	0.399910	−	0.00850118i
$676$		0			0
$677$	660.928	+	381.587i	0.976260	+	0.563644i	0.901139	−	0.433530i	$-0.142732\pi$
$677$	660.928	+	381.587i	0.976260	+	0.563644i	0.0751214	+	0.997174i	$0.476066\pi$
$678$		0			0
$679$	−574.000			−0.845361
$680$		0			0
$681$	−169.676	+	205.146i	−0.249157	+	0.301243i
$682$		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	−0.966180	−	0.257869i	$-0.916980\pi$
$691$	−179.500	+	310.903i	−0.259768	+	0.449932i	0.706411	+	0.707802i	$0.250313\pi$
$692$		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	$-0.805436\pi$
$701$		−	804.587i		−	1.14777i	0.818936	−	0.573885i	$-0.194564\pi$
$702$		0			0
$703$	−540.500	−	936.173i	−0.768848	−	1.33168i
$704$		0			0
$705$	728.197	+	602.290i	1.03290	+	0.854312i
$706$		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
$711$	−15.1944	−	79.5621i	−0.0213704	−	0.111902i
$712$		0			0
$713$			1615.09i			2.26520i
$714$		0			0
$715$	−210.000			−0.293706
$716$		0			0
$717$	−297.037	−	798.454i	−0.414277	−	1.11360i
$718$		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
$723$	2.31174	+	1.91203i	0.00319742	+	0.00264458i
$724$		0			0
$725$	−409.878	+	236.643i	−0.565349	+	0.326404i
$726$		0			0
$727$	−734.000			−1.00963			−0.504814	−	0.863228i	$-0.668439\pi$
$727$	−734.000			−1.00963			−0.504814	+	0.863228i	$0.668439\pi$
$728$		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	0.593844	−	0.804580i	$-0.297610\pi$
$739$	−295.500	−	511.821i	−0.399865	−	0.692586i	−0.993709	+	0.111994i	$0.964276\pi$
$740$		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
$747$	−278.396	−	322.390i	−0.372686	−	0.431580i
$748$		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	$0.398283\pi$
$751$	−499.500	+	865.159i	−0.665113	+	1.15201i	−0.979255	+	0.202634i	$0.935050\pi$
$752$		0			0
$753$	148.518	+	399.227i	0.197235	+	0.530182i
$754$		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
$759$	−688.876	+	256.272i	−0.907610	+	0.337644i
$760$		0			0
$761$	−1142.54	−	659.643i	−1.50136	−	0.866811i	−0.999999	−	0.00157261i	$-0.999499\pi$
$761$	−1142.54	−	659.643i	−1.50136	−	0.866811i	−0.501361	−	0.865238i	$-0.667167\pi$
$762$		0			0
$763$	−479.500	−	830.518i	−0.628440	−	1.08849i
$764$		0			0
$765$	238.411	−	205.877i	0.311648	−	0.269120i
$766$		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	−0.175161	−	0.984540i	$-0.556044\pi$
$773$	455.989	−	263.266i	0.589896	−	0.340576i	0.765056	+	0.643963i	$0.222711\pi$
$774$		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	0.688374	−	0.725356i	$-0.258325\pi$
$787$	−223.500	−	387.113i	−0.283990	−	0.491885i	−0.972364	+	0.233471i	$0.924992\pi$
$788$		0			0
$789$	101.806	−	123.088i	0.129031	−	0.156005i
$790$		0			0
$791$			662.601i			0.837675i
$792$		0			0
$793$	−243.000	+	420.888i	−0.306431	+	0.530755i
$794$		0			0
$795$	885.697	−	329.492i	1.11408	−	0.414456i
$796$		0			0
$797$		−	1277.87i		−	1.60335i	−0.597757	−	0.801677i	$-0.703941\pi$
$797$		−	1277.87i		−	1.60335i	0.597757	−	0.801677i	$-0.296059\pi$
$798$		0			0
$799$	315.000			0.394243
$800$		0			0
$801$	−784.493	+	149.818i	−0.979392	+	0.187039i
$802$		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
$807$	−79.1822	+	95.7350i	−0.0981192	+	0.118631i
$808$		0			0
$809$	−1142.54	+	659.643i	−1.41228	+	0.815381i	−0.995603	−	0.0936737i	$-0.970139\pi$
$809$	−1142.54	+	659.643i	−1.41228	+	0.815381i	−0.416678	+	0.909054i	$0.636806\pi$
$810$		0			0
$811$	−86.0000			−0.106042			−0.0530210	−	0.998593i	$-0.516885\pi$
$811$	−86.0000			−0.106042			−0.0530210	+	0.998593i	$0.516885\pi$
$812$		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
$819$	286.093	−	247.052i	0.349320	−	0.301651i
$820$		0			0
$821$	333.026	+	192.273i	0.405634	+	0.234193i	0.688912	−	0.724845i	$-0.258089\pi$
$821$	333.026	+	192.273i	0.405634	+	0.234193i	−0.283278	+	0.959038i	$0.591422\pi$
$822$		0			0
$823$	188.500	+	326.492i	0.229040	+	0.396709i	0.957524	−	0.288354i	$-0.0931080\pi$
$823$	188.500	+	326.492i	0.229040	+	0.396709i	−0.728484	+	0.685063i	$0.759775\pi$
$824$		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
$831$	−718.950	−	594.642i	−0.865163	−	0.715574i
$832$		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
$837$	−1052.76	+	22.3793i	−1.25778	+	0.0267376i
$838$		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
$843$	396.049	+	1064.61i	0.469809	+	1.26288i
$844$		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
$849$	−737.444	−	609.938i	−0.868603	−	0.718420i
$850$		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	−0.398103	−	0.917341i	$-0.630331\pi$
$857$	169.075	−	97.6153i	0.197287	−	0.113904i	0.595389	+	0.803437i	$0.296998\pi$
$858$		0			0
$859$	−491.500	+	851.303i	−0.572177	+	0.991040i	0.424165	+	0.905585i	$0.360568\pi$
$859$	−491.500	+	851.303i	−0.572177	+	0.991040i	−0.996342	+	0.0854547i	$0.972766\pi$
$860$		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
$873$	558.562	−	482.340i	0.639820	−	0.552509i
$874$		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
$879$	−148.518	−	399.227i	−0.168963	−	0.454183i
$880$		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	$-0.443101\pi$
$883$	314.000			0.355606			0.177803	+	0.984066i	$0.443101\pi$
$884$		0			0
$885$	1672.98	−	622.374i	1.89038	−	0.703248i
$886$		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
$891$	−176.591	−	445.478i	−0.198194	−	0.499975i
$892$		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
$903$	433.008	−	161.085i	0.479521	−	0.178389i
$904$		0			0
$905$	−30.7409	−	17.7482i	−0.0339678	−	0.0196113i
$906$		0			0
$907$	376.500	+	652.117i	0.415105	+	0.718983i	0.995439	−	0.0953956i	$-0.0304116\pi$
$907$	376.500	+	652.117i	0.415105	+	0.718983i	−0.580335	+	0.814378i	$0.697078\pi$
$908$		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
$915$	916.251	−	1107.79i	1.00137	−	1.21070i
$916$		0			0
$917$	−896.608	−	517.657i	−0.977762	−	0.564511i
$918$		0			0
$919$	284.500	−	492.768i	0.309576	−	0.536201i	−0.668694	−	0.743538i	$-0.733146\pi$
$919$	284.500	−	492.768i	0.309576	−	0.536201i	0.978270	+	0.207337i	$0.0664797\pi$
$920$		0			0
$921$	1242.79	−	462.335i	1.34939	−	0.501993i
$922$		0			0
$923$		−	567.944i		−	0.615324i
$924$		0			0
$925$	−470.000			−0.508108
$926$		0			0
$927$	38.8300	+	203.325i	0.0418878	+	0.219337i
$928$		0			0
$929$	1398.71	+	807.545i	1.50561	+	0.869263i	0.999979	+	0.00651097i	$0.00207252\pi$
$929$	1398.71	+	807.545i	1.50561	+	0.869263i	0.505628	+	0.862752i	$0.331261\pi$
$930$		0			0
$931$	−563.500	+	976.011i	−0.605263	+	1.04835i
$932$		0			0
$933$	463.781	−	560.733i	0.497086	−	0.601000i
$934$		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	−0.237743	−	0.971328i	$-0.576408\pi$
$941$	455.989	−	263.266i	0.484579	−	0.279772i	0.722323	+	0.691556i	$0.243074\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−956.236	+	579.523i	−1.01189	+	0.613252i
$946$		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	$0.0636561\pi$
$953$			378.629i			0.397302i	−0.980070	+	0.198651i	$0.936344\pi$
$954$		0			0
$955$	157.500	+	272.798i	0.164921	+	0.285652i
$956$		0			0
$957$	647.287	+	535.369i	0.676370	+	0.559424i
$958$		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
$963$	470.696	−	89.8911i	0.488781	−	0.0933448i
$964$		0			0
$965$		−	845.999i		−	0.876683i
$966$		0			0
$967$	482.000			0.498449			0.249224	−	0.968446i	$-0.419824\pi$
$967$	482.000			0.498449			0.249224	+	0.968446i	$0.419824\pi$
$968$		0			0
$969$	142.330	+	382.593i	0.146883	+	0.394832i
$970$		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
$975$	−138.704	−	114.722i	−0.142261	−	0.117664i
$976$		0			0
$977$	169.075	−	97.6153i	0.173055	−	0.0999133i	−0.410971	−	0.911649i	$-0.634810\pi$
$977$	169.075	−	97.6153i	0.173055	−	0.0999133i	0.584026	+	0.811735i	$0.301477\pi$
$978$		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	0.942609	−	0.333899i	$-0.108364\pi$
$991$	180.500	+	312.635i	0.182139	+	0.315474i	−0.760470	+	0.649374i	$0.775031\pi$
$992$		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
$999$	657.713	+	1085.25i	0.658372	+	1.08634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.3.p.c.65.2	yes	4
3.2	odd	2	inner	84.3.p.c.65.1	yes	4
4.3	odd	2		336.3.bn.d.65.1		4
7.2	even	3		588.3.c.e.197.2		2
7.3	odd	6		588.3.p.d.557.2		4
7.4	even	3	inner	84.3.p.c.53.1	✓	4
7.5	odd	6		588.3.c.f.197.1		2
7.6	odd	2		588.3.p.d.569.1		4
12.11	even	2		336.3.bn.d.65.2		4
21.2	odd	6		588.3.c.e.197.1		2
21.5	even	6		588.3.c.f.197.2		2
21.11	odd	6	inner	84.3.p.c.53.2	yes	4
21.17	even	6		588.3.p.d.557.1		4
21.20	even	2		588.3.p.d.569.2		4
28.11	odd	6		336.3.bn.d.305.2		4
84.11	even	6		336.3.bn.d.305.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.p.c.53.1	✓	4	7.4	even	3	inner
84.3.p.c.53.2	yes	4	21.11	odd	6	inner
84.3.p.c.65.1	yes	4	3.2	odd	2	inner
84.3.p.c.65.2	yes	4	1.1	even	1	trivial
336.3.bn.d.65.1		4	4.3	odd	2
336.3.bn.d.65.2		4	12.11	even	2
336.3.bn.d.305.1		4	84.11	even	6
336.3.bn.d.305.2		4	28.11	odd	6
588.3.c.e.197.1		2	21.2	odd	6
588.3.c.e.197.2		2	7.2	even	3
588.3.c.f.197.1		2	7.5	odd	6
588.3.c.f.197.2		2	21.5	even	6
588.3.p.d.557.1		4	21.17	even	6
588.3.p.d.557.2		4	7.3	odd	6
588.3.p.d.569.1		4	7.6	odd	2
588.3.p.d.569.2		4	21.20	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	84.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81174 - 1.04601i) q^{3} +(5.12348 + 2.95804i) q^{5} -7.00000 q^{7} +(6.81174 - 5.88220i) q^{9} +(5.12348 - 2.95804i) q^{11} -6.00000 q^{13} +(17.5000 + 2.95804i) q^{15} +(5.12348 - 2.95804i) q^{17} +(-11.5000 + 19.9186i) q^{19} +(-19.6822 + 7.32205i) q^{21} +(-35.8643 - 20.7063i) q^{23} +(5.00000 + 8.66025i) q^{25} +(13.0000 - 23.6643i) q^{27} +47.3286i q^{29} +(-19.5000 - 33.7750i) q^{31} +(11.3117 - 13.6764i) q^{33} +(-35.8643 - 20.7063i) q^{35} +(-23.5000 + 40.7032i) q^{37} +(-16.8704 + 6.27604i) q^{39} -22.0000 q^{43} +(52.2995 - 9.98789i) q^{45} +(46.1113 + 26.6224i) q^{47} +49.0000 q^{49} +(11.3117 - 13.6764i) q^{51} +(46.1113 - 26.6224i) q^{53} +35.0000 q^{55} +(-11.5000 + 68.0349i) q^{57} +(87.0991 - 50.2867i) q^{59} +(40.5000 - 70.1481i) q^{61} +(-47.6822 + 41.1754i) q^{63} +(-30.7409 - 17.7482i) q^{65} +(-15.5000 - 26.8468i) q^{67} +(-122.500 - 20.7063i) q^{69} +94.6573i q^{71} +(8.50000 + 14.7224i) q^{73} +(23.1174 + 19.1203i) q^{75} +(-35.8643 + 20.7063i) q^{77} +(4.50000 - 7.79423i) q^{79} +(11.7995 - 80.1360i) q^{81} -47.3286i q^{83} +35.0000 q^{85} +(49.5061 + 133.076i) q^{87} +(-76.8521 - 44.3706i) q^{89} +42.0000 q^{91} +(-90.1578 - 74.5693i) q^{93} +(-117.840 + 68.0349i) q^{95} +82.0000 q^{97} +(17.5000 - 50.2867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 28 q^{7} + 17 q^{9} - 24 q^{13} + 70 q^{15} - 46 q^{19} - 7 q^{21} + 20 q^{25} + 52 q^{27} - 78 q^{31} + 35 q^{33} - 94 q^{37} - 6 q^{39} - 88 q^{43} + 35 q^{45} + 196 q^{49} + 35 q^{51}+ \cdots + 70 q^{99}+O(q^{100}) \) 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

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