LMFDB - Embedded newform 588.3.p.d.569.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,3,Mod(557,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("588.557");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.0218395444$
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			569.2
Root			$2.81174 + 1.04601i$ of defining polynomial
Character	$\chi$	$=$	588.569
Dual form			588.3.p.d.557.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	2.31174	−	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	0.915460	−	0.402408i	$-0.131827\pi$
$5$	5.12348	+	2.95804i	1.02470	+	0.591608i	0.109235	+	0.994016i	$0.465160\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.68826	−	8.84024i	0.187585	−	0.982248i
$10$		0			0
$11$	−5.12348	+	2.95804i	−0.465770	+	0.268913i	−0.714468	−	0.699669i	$-0.753331\pi$
$11$	−5.12348	+	2.95804i	−0.465770	+	0.268913i	0.248697	+	0.968581i	$0.419998\pi$
$12$		0			0
$13$	6.00000			0.461538			0.230769	−	0.973009i	$-0.425876\pi$
$13$	6.00000			0.461538			0.230769	+	0.973009i	$0.425876\pi$
$14$		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	$-0.626401\pi$
$19$	11.5000	−	19.9186i	0.605263	−	1.04835i	0.992010	−	0.126161i	$-0.0402654\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	35.8643	+	20.7063i	1.55932	+	0.900273i	0.997322	+	0.0731333i	$0.0232999\pi$
$23$	35.8643	+	20.7063i	1.55932	+	0.900273i	0.561996	+	0.827140i	$0.310033\pi$
$24$		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
$35$		0			0
$36$		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	$-0.582343\pi$
$43$	−22.0000			−0.511628			−0.255814	+	0.966726i	$0.582343\pi$
$44$		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
$49$		0			0
$50$		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	$0.397781\pi$
$61$	−40.5000	+	70.1481i	−0.663934	+	1.14997i	−0.979573	+	0.201089i	$0.935552\pi$
$62$		0			0
$63$		0			0
$64$		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	$-0.767749\pi$
$71$		−	94.6573i		−	1.33320i	0.745415	−	0.666601i	$-0.232251\pi$
$72$		0			0
$73$	−8.50000	−	14.7224i	−0.116438	−	0.201677i	0.801915	−	0.597438i	$-0.203814\pi$
$73$	−8.50000	−	14.7224i	−0.116438	−	0.201677i	−0.918354	+	0.395760i	$0.870481\pi$
$74$		0			0
$75$	28.1174	+	10.4601i	0.374898	+	0.139468i
$76$		0			0
$77$		0			0
$78$		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
$81$	−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	0.00167806	−	0.999999i	$-0.499466\pi$
$89$	−76.8521	−	44.3706i	−0.863507	−	0.498546i	−0.865185	+	0.501453i	$0.832799\pi$
$90$		0			0
$91$		0			0
$92$		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	$-0.638911\pi$
$97$	−82.0000			−0.845361			−0.422680	+	0.906279i	$0.638911\pi$
$98$		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	−0.804785	−	0.593566i	$-0.797720\pi$
$103$	11.5000	−	19.9186i	0.111650	−	0.193384i	0.916436	+	0.400182i	$0.131053\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−46.1113	−	26.6224i	−0.430947	−	0.248807i	0.268803	−	0.963195i	$-0.413372\pi$
$107$	−46.1113	−	26.6224i	−0.430947	−	0.248807i	−0.699750	+	0.714388i	$0.746705\pi$
$108$		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
$119$		0			0
$120$		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
$129$	−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
$133$		0			0
$134$		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
$147$		0			0
$148$		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	0.925888	−	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	$0.0118352\pi$
$157$	83.5000	+	144.626i	0.531847	+	0.921186i	−0.467462	+	0.884013i	$0.654831\pi$
$158$		0			0
$159$	−55.6944	+	149.710i	−0.350279	+	0.941573i
$160$		0			0
$161$		0			0
$162$		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
$165$	−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	−0.398398	−	0.917212i	$-0.630434\pi$
$173$	−240.803	−	139.028i	−1.39193	−	0.803629i	−0.993528	+	0.113583i	$0.963767\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	105.200	−	282.786i	0.594353	−	1.59766i
$178$		0			0
$179$	76.8521	−	44.3706i	0.429342	−	0.247880i	−0.269725	−	0.962938i	$-0.586933\pi$
$179$	76.8521	−	44.3706i	0.429342	−	0.247880i	0.699066	+	0.715057i	$0.253599\pi$
$180$		0			0
$181$	6.00000			0.0331492			0.0165746	−	0.999863i	$-0.494724\pi$
$181$	6.00000			0.0331492			0.0165746	+	0.999863i	$0.494724\pi$
$182$		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
$189$		0			0
$190$		0			0
$191$	−46.1113	−	26.6224i	−0.241420	−	0.139384i	0.374409	−	0.927264i	$-0.377846\pi$
$191$	−46.1113	−	26.6224i	−0.241420	−	0.139384i	−0.615829	+	0.787880i	$0.711179\pi$
$192$		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
$203$		0			0
$204$		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	$-0.628689\pi$
$211$	−166.000			−0.786730			−0.393365	+	0.919382i	$0.628689\pi$
$212$		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
$217$		0			0
$218$		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	$0.356302\pi$
$229$	−128.500	+	222.569i	−0.561135	+	0.971915i	−0.997398	+	0.0720955i	$0.977031\pi$
$230$		0			0
$231$		0			0
$232$		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	$0.202485\pi$
$239$			283.972i			1.18817i	−0.804404	+	0.594083i	$0.797515\pi$
$240$		0			0
$241$	−0.500000	−	0.866025i	−0.00207469	−	0.00359347i	0.864986	−	0.501796i	$-0.167327\pi$
$241$	−0.500000	−	0.866025i	−0.00207469	−	0.00359347i	−0.867061	+	0.498202i	$0.833994\pi$
$242$		0			0
$243$	−231.146	+	74.9715i	−0.951216	+	0.308525i
$244$		0			0
$245$		0			0
$246$		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	0.791468	−	0.611211i	$-0.209317\pi$
$257$	169.075	+	97.6153i	0.657878	+	0.379826i	−0.133590	+	0.991037i	$0.542650\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−418.396	−	79.9032i	−1.60305	−	0.306142i
$262$		0			0
$263$	−46.1113	+	26.6224i	−0.175328	+	0.101226i	−0.585096	−	0.810964i	$-0.698943\pi$
$263$	−46.1113	+	26.6224i	−0.175328	+	0.101226i	0.409768	+	0.912190i	$0.365610\pi$
$264$		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	−0.774537	−	0.632528i	$-0.782017\pi$
$271$	43.5000	−	75.3442i	0.160517	−	0.278023i	0.935054	+	0.354505i	$0.115351\pi$
$272$		0			0
$273$		0			0
$274$		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	$-0.922099\pi$
$293$		−	141.986i		−	0.484594i	0.970202	−	0.242297i	$-0.0779008\pi$
$294$		0			0
$295$	595.000			2.01695
$296$		0			0
$297$	136.605	+	82.7890i	0.459950	+	0.278751i
$298$		0			0
$299$	215.186	+	124.238i	0.719686	+	0.415511i
$300$		0			0
$301$		0			0
$302$		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	−0.994949	−	0.100380i	$-0.967994\pi$
$313$	−128.500	+	222.569i	−0.410543	+	0.711082i	0.584406	+	0.811461i	$0.301328\pi$
$314$		0			0
$315$		0			0
$316$		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
$329$		0			0
$330$		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
$333$	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
$343$		0			0
$344$		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	$-0.271523\pi$
$347$	568.706	−	328.342i	1.63892	−	0.946232i	0.981205	−	0.192966i	$-0.0618106\pi$
$348$		0			0
$349$	422.000			1.20917			0.604585	−	0.796541i	$-0.293339\pi$
$349$	422.000			1.20917			0.604585	+	0.796541i	$0.293339\pi$
$350$		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
$357$		0			0
$358$		0			0
$359$	117.840	+	68.0349i	0.328245	+	0.189512i	0.655062	−	0.755575i	$-0.272643\pi$
$359$	117.840	+	68.0349i	0.328245	+	0.189512i	−0.326817	+	0.945088i	$0.605976\pi$
$360$		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
$371$		0			0
$372$		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	$-0.248802\pi$
$379$	538.000			1.41953			0.709763	+	0.704441i	$0.248802\pi$
$380$		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
$385$		0			0
$386$		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	−0.886058	−	0.463574i	$-0.846567\pi$
$397$	−16.5000	+	28.5788i	−0.0415617	+	0.0719870i	0.844496	+	0.535561i	$0.179900\pi$
$398$		0			0
$399$		0			0
$400$		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	$-0.917444\pi$
$409$	−288.500	−	499.697i	−0.705379	−	1.22175i	0.261176	−	0.965291i	$-0.415890\pi$
$410$		0			0
$411$	−105.200	+	282.786i	−0.255962	+	0.688044i
$412$		0			0
$413$		0			0
$414$		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
$427$		0			0
$428$		0			0
$429$	−37.1296	+	99.8068i	−0.0865491	+	0.232650i
$430$		0			0
$431$	−537.965	+	310.594i	−1.24818	+	0.720636i	−0.970746	−	0.240109i	$-0.922817\pi$
$431$	−537.965	+	310.594i	−1.24818	+	0.720636i	−0.277433	+	0.960745i	$0.589483\pi$
$432$		0			0
$433$	622.000			1.43649			0.718245	−	0.695790i	$-0.244946\pi$
$433$	622.000			1.43649			0.718245	+	0.695790i	$0.244946\pi$
$434$		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
$441$		0			0
$442$		0			0
$443$	−210.062	−	121.280i	−0.474182	−	0.273769i	0.243807	−	0.969824i	$-0.421604\pi$
$443$	−210.062	−	121.280i	−0.474182	−	0.273769i	−0.717989	+	0.696055i	$0.754937\pi$
$444$		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
$455$		0			0
$456$		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	$-0.809008\pi$
$461$		−	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
$465$	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
$469$		0			0
$470$		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
$483$		0			0
$484$		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	$-0.953814\pi$
$491$		−	141.986i		−	0.289177i	0.989492	−	0.144589i	$-0.0461858\pi$
$492$		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
$497$		0			0
$498$		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
$501$	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	0.656804	−	0.754061i	$-0.271908\pi$
$509$	169.075	+	97.6153i	0.332170	+	0.191779i	−0.324634	+	0.945840i	$0.605241\pi$
$510$		0			0
$511$		0			0
$512$		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	−0.776689	−	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	−0.854822	−	0.518922i	$-0.826334\pi$
$523$	11.5000	−	19.9186i	0.0219885	−	0.0380852i	0.876810	+	0.480836i	$0.159667\pi$
$524$		0			0
$525$		0			0
$526$		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
$539$		0			0
$540$		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	$-0.515718\pi$
$547$	−54.0000			−0.0987203			−0.0493601	+	0.998781i	$0.515718\pi$
$548$		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
$553$		0			0
$554$		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
$567$		0			0
$568$		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	$-0.865191\pi$
$571$	−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	0.671567	−	0.740944i	$-0.265621\pi$
$577$	−176.500	−	305.707i	−0.305893	−	0.529821i	−0.977460	+	0.211122i	$0.932288\pi$
$578$		0			0
$579$	−402.078	−	149.579i	−0.694436	−	0.258340i
$580$		0			0
$581$		0			0
$582$		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	0.940004	−	0.341163i	$-0.110821\pi$
$593$	660.928	+	381.587i	1.11455	+	0.643486i	0.174546	+	0.984649i	$0.444154\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−475.184	−	176.775i	−0.795953	−	0.296106i
$598$		0			0
$599$	−537.965	+	310.594i	−0.898105	+	0.518521i	−0.876585	−	0.481247i	$-0.840184\pi$
$599$	−537.965	+	310.594i	−0.898105	+	0.518521i	−0.0215201	+	0.999768i	$0.506851\pi$
$600$		0			0
$601$	958.000			1.59401			0.797005	−	0.603973i	$-0.206416\pi$
$601$	958.000			1.59401			0.797005	+	0.603973i	$0.206416\pi$
$602$		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
$609$		0			0
$610$		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
$623$		0			0
$624$		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	$-0.320661\pi$
$631$	674.000			1.06815			0.534073	+	0.845438i	$0.320661\pi$
$632$		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
$637$		0			0
$638$		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
$651$		0			0
$652$		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	$0.154601\pi$
$659$			615.272i			0.933645i	−0.884351	+	0.466823i	$0.845399\pi$
$660$		0			0
$661$	−260.500	−	451.199i	−0.394100	−	0.682601i	0.598886	−	0.800834i	$-0.295610\pi$
$661$	−260.500	−	451.199i	−0.394100	−	0.682601i	−0.992986	+	0.118233i	$0.962277\pi$
$662$		0			0
$663$	37.1296	−	99.8068i	0.0560024	−	0.150538i
$664$		0			0
$665$		0			0
$666$		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	0.901139	−	0.433530i	$-0.142732\pi$
$677$	660.928	+	381.587i	0.976260	+	0.563644i	0.0751214	+	0.997174i	$0.476066\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−92.8239	+	249.517i	−0.136305	+	0.366398i
$682$		0			0
$683$	−169.075	+	97.6153i	−0.247547	+	0.142921i	−0.618641	−	0.785674i	$-0.712316\pi$
$683$	−169.075	+	97.6153i	−0.247547	+	0.142921i	0.371093	+	0.928596i	$0.378983\pi$
$684$		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
$693$		0			0
$694$		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
$707$		0			0
$708$		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
$721$		0			0
$722$		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	−0.743983	−	0.668198i	$-0.767066\pi$
$733$	151.500	−	262.406i	0.206685	−	0.357989i	0.950668	+	0.310209i	$0.100399\pi$
$734$		0			0
$735$		0			0
$736$		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	$-0.805665\pi$
$743$		−	851.915i		−	1.14659i	0.819349	−	0.573294i	$-0.194335\pi$
$744$		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
$749$		0			0
$750$		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
$753$	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	$-0.999499\pi$
$761$	−1142.54	−	659.643i	−1.50136	−	0.866811i	−0.501361	−	0.865238i	$-0.667167\pi$
$762$		0			0
$763$		0			0
$764$		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	$-0.710878\pi$
$769$	−946.000			−1.23017			−0.615085	+	0.788461i	$0.710878\pi$
$770$		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
$777$		0			0
$778$		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
$791$		0			0
$792$		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	$-0.703941\pi$
$797$		−	1277.87i		−	1.60335i	0.597757	−	0.801677i	$-0.296059\pi$
$798$		0			0
$799$	315.000			0.394243
$800$		0			0
$801$	−521.993	+	604.482i	−0.651677	+	0.754659i
$802$		0			0
$803$	87.0991	+	50.2867i	0.108467	+	0.0626235i
$804$		0			0
$805$		0			0
$806$		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
$819$		0			0
$820$		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	0.957524	−	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	$0.0273587\pi$
$827$			141.986i			0.171688i	−0.996309	+	0.0858440i	$0.972641\pi$
$828$		0			0
$829$	75.5000	+	130.770i	0.0910736	+	0.157744i	0.907963	−	0.419050i	$-0.137637\pi$
$829$	75.5000	+	130.770i	0.0910736	+	0.157744i	−0.816890	+	0.576794i	$0.804303\pi$
$830$		0			0
$831$	−874.450	−	325.308i	−1.05229	−	0.391466i
$832$		0			0
$833$		0			0
$834$		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
$847$		0			0
$848$		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	$-0.172341\pi$
$853$	1462.00			1.71395			0.856975	+	0.515357i	$0.172341\pi$
$854$		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	$-0.639432\pi$
$859$	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	0.423951	−	0.905685i	$-0.360643\pi$
$863$	−128.087	−	73.9510i	−0.148420	−	0.0856906i	−0.572371	+	0.819995i	$0.693976\pi$
$864$		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
$875$		0			0
$876$		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	$-0.443101\pi$
$883$	314.000			0.355606			0.177803	+	0.984066i	$0.443101\pi$
$884$		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
$889$		0			0
$890$		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
$903$		0			0
$904$		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	$-0.615271\pi$
$911$		−	1703.83i		−	1.87029i	0.354270	−	0.935143i	$-0.384729\pi$
$912$		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
$917$		0			0
$918$		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
$921$	−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	$0.00207252\pi$
$929$	1398.71	+	807.545i	1.50561	+	0.869263i	0.505628	+	0.862752i	$0.331261\pi$
$930$		0			0
$931$		0			0
$932$		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	$-0.625892\pi$
$937$	−722.000			−0.770544			−0.385272	+	0.922803i	$0.625892\pi$
$938$		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
$945$		0			0
$946$		0			0
$947$	−128.087	−	73.9510i	−0.135255	−	0.0780898i	0.430845	−	0.902426i	$-0.358215\pi$
$947$	−128.087	−	73.9510i	−0.135255	−	0.0780898i	−0.566101	+	0.824336i	$0.691549\pi$
$948$		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
$959$		0			0
$960$		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	$-0.419824\pi$
$967$	482.000			0.498449			0.249224	+	0.968446i	$0.419824\pi$
$968$		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
$973$		0			0
$974$		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
$987$		0			0
$988$		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	0.847140	−	0.531370i	$-0.178323\pi$
$997$	−36.5000	−	63.2199i	−0.0366098	−	0.0634101i	−0.883750	+	0.467960i	$0.844989\pi$
$998$		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	588.3.p.d.569.2		4
3.2	odd	2	inner	588.3.p.d.569.1		4
7.2	even	3		588.3.c.f.197.2		2
7.3	odd	6		84.3.p.c.53.2	yes	4
7.4	even	3	inner	588.3.p.d.557.1		4
7.5	odd	6		588.3.c.e.197.1		2
7.6	odd	2		84.3.p.c.65.1	yes	4
21.2	odd	6		588.3.c.f.197.1		2
21.5	even	6		588.3.c.e.197.2		2
21.11	odd	6	inner	588.3.p.d.557.2		4
21.17	even	6		84.3.p.c.53.1	✓	4
21.20	even	2		84.3.p.c.65.2	yes	4
28.3	even	6		336.3.bn.d.305.1		4
28.27	even	2		336.3.bn.d.65.2		4
84.59	odd	6		336.3.bn.d.305.2		4
84.83	odd	2		336.3.bn.d.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.p.c.53.1	✓	4	21.17	even	6
84.3.p.c.53.2	yes	4	7.3	odd	6
84.3.p.c.65.1	yes	4	7.6	odd	2
84.3.p.c.65.2	yes	4	21.20	even	2
336.3.bn.d.65.1		4	84.83	odd	2
336.3.bn.d.65.2		4	28.27	even	2
336.3.bn.d.305.1		4	28.3	even	6
336.3.bn.d.305.2		4	84.59	odd	6
588.3.c.e.197.1		2	7.5	odd	6
588.3.c.e.197.2		2	21.5	even	6
588.3.c.f.197.1		2	21.2	odd	6
588.3.c.f.197.2		2	7.2	even	3
588.3.p.d.557.1		4	7.4	even	3	inner
588.3.p.d.557.2		4	21.11	odd	6	inner
588.3.p.d.569.1		4	3.2	odd	2	inner
588.3.p.d.569.2		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.p (of order \(6\), degree \(2\), not minimal)

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