LMFDB - Embedded newform 588.3.g.d.295.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(295,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.295"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,0,2,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.489494783471841.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 11 x^{9} + 18 x^{8} - 22 x^{7} + 33 x^{6} - 44 x^{5} + 72 x^{4} + \cdots + 64 $ x^12 - 3x^11 + 7x^10 - 11x^9 + 18x^8 - 22x^7 + 33x^6 - 44x^5 + 72x^4 - 88x^3 + 112x^2 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.4
Root			$0.0311486 - 1.41387i$ of defining polynomial
Character	$\chi$	$=$	588.295
Dual form			588.3.g.d.295.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.51951 + 1.30042i) q^{2} -1.73205i q^{3} +(0.617841 - 3.95200i) q^{4} -7.86764 q^{5} +(2.25238 + 2.63187i) q^{6} +(4.20042 + 6.80856i) q^{8} -3.00000 q^{9} +(11.9550 - 10.2312i) q^{10} +11.2993i q^{11} +(-6.84506 - 1.07013i) q^{12} +10.5494 q^{13} +13.6272i q^{15} +(-15.2365 - 4.88341i) q^{16} -25.9378 q^{17} +(4.55854 - 3.90125i) q^{18} -1.33925i q^{19} +(-4.86096 + 31.0929i) q^{20} +(-14.6938 - 17.1694i) q^{22} -11.0460i q^{23} +(11.7928 - 7.27534i) q^{24} +36.8998 q^{25} +(-16.0300 + 13.7186i) q^{26} +5.19615i q^{27} -20.4217 q^{29} +(-17.7210 - 20.7066i) q^{30} +36.9764i q^{31} +(29.5026 - 12.3934i) q^{32} +19.5710 q^{33} +(39.4128 - 33.7299i) q^{34} +(-1.85352 + 11.8560i) q^{36} +24.2482 q^{37} +(1.74158 + 2.03501i) q^{38} -18.2721i q^{39} +(-33.0474 - 53.5673i) q^{40} +77.6185 q^{41} -77.7251i q^{43} +(44.6548 + 6.98118i) q^{44} +23.6029 q^{45} +(14.3644 + 16.7846i) q^{46} +0.795833i q^{47} +(-8.45832 + 26.3905i) q^{48} +(-56.0698 + 47.9851i) q^{50} +44.9255i q^{51} +(6.51787 - 41.6913i) q^{52} +74.4459 q^{53} +(-6.75715 - 7.89562i) q^{54} -88.8989i q^{55} -2.31965 q^{57} +(31.0311 - 26.5567i) q^{58} -64.6353i q^{59} +(53.8545 + 8.41942i) q^{60} +0.601583 q^{61} +(-48.0847 - 56.1861i) q^{62} +(-28.7130 + 57.1976i) q^{64} -82.9991 q^{65} +(-29.7383 + 25.4504i) q^{66} -50.3015i q^{67} +(-16.0254 + 102.506i) q^{68} -19.1323 q^{69} -101.650i q^{71} +(-12.6013 - 20.4257i) q^{72} +100.183 q^{73} +(-36.8455 + 31.5327i) q^{74} -63.9124i q^{75} +(-5.29271 - 0.827444i) q^{76} +(23.7614 + 27.7647i) q^{78} -33.4197i q^{79} +(119.876 + 38.4210i) q^{80} +9.00000 q^{81} +(-117.942 + 100.936i) q^{82} +58.7583i q^{83} +204.069 q^{85} +(101.075 + 118.104i) q^{86} +35.3715i q^{87} +(-76.9320 + 47.4618i) q^{88} +53.9641 q^{89} +(-35.8650 + 30.6936i) q^{90} +(-43.6538 - 6.82468i) q^{92} +64.0450 q^{93} +(-1.03491 - 1.20928i) q^{94} +10.5367i q^{95} +(-21.4660 - 51.1000i) q^{96} +39.9964 q^{97} -33.8979i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{4} - 8 q^{5} + 12 q^{6} - 10 q^{8} - 36 q^{9} - 28 q^{10} - 24 q^{12} + 24 q^{13} - 14 q^{16} + 40 q^{17} - 6 q^{18} + 20 q^{20} - 88 q^{22} + 36 q^{24} + 180 q^{25} - 100 q^{26} + 72 q^{29}+ \cdots + 264 q^{97}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^4 - 8 * q^5 + 12 * q^6 - 10 * q^8 - 36 * q^9 - 28 * q^10 - 24 * q^12 + 24 * q^13 - 14 * q^16 + 40 * q^17 - 6 * q^18 + 20 * q^20 - 88 * q^22 + 36 * q^24 + 180 * q^25 - 100 * q^26 + 72 * q^29 + 72 * q^30 + 142 * q^32 + 100 * q^34 - 6 * q^36 - 88 * q^37 - 128 * q^38 + 28 * q^40 + 200 * q^41 - 40 * q^44 + 24 * q^45 - 24 * q^46 - 48 * q^48 - 346 * q^50 + 364 * q^52 + 104 * q^53 - 36 * q^54 + 148 * q^58 + 96 * q^60 - 104 * q^61 - 64 * q^62 - 70 * q^64 + 176 * q^65 - 24 * q^66 - 188 * q^68 + 192 * q^69 + 30 * q^72 - 312 * q^73 + 4 * q^74 - 432 * q^76 + 48 * q^78 + 564 * q^80 + 108 * q^81 - 332 * q^82 + 352 * q^85 + 160 * q^86 + 328 * q^88 + 552 * q^89 + 84 * q^90 + 232 * q^92 - 48 * q^93 + 144 * q^94 + 108 * q^96 + 264 * q^97

Character values

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

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.51951	+	1.30042i	−0.759757	+	0.650208i
$2$	−1.51951	+	1.30042i	−0.759757	+	0.650208i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	0.617841	−	3.95200i	0.154460	−	0.987999i
$5$	−7.86764			−1.57353			−0.786764	−	0.617253i	$-0.788245\pi$
$5$	−7.86764			−1.57353			−0.786764	+	0.617253i	$0.788245\pi$
$6$	2.25238	+	2.63187i	0.375397	+	0.438646i
$7$		0			0
$7$		0			0
$8$	4.20042	+	6.80856i	0.525052	+	0.851070i
$9$	−3.00000			−0.333333
$10$	11.9550	−	10.2312i	1.19550	−	1.02312i
$11$			11.2993i			1.02721i	0.858027	+	0.513605i	$0.171690\pi$
$11$			11.2993i			1.02721i	−0.858027	+	0.513605i	$0.828310\pi$
$12$	−6.84506	−	1.07013i	−0.570421	−	0.0891777i
$13$	10.5494			0.811494			0.405747	−	0.913985i	$-0.367011\pi$
$13$	10.5494			0.811494			0.405747	+	0.913985i	$0.367011\pi$
$14$		0			0
$15$			13.6272i			0.908477i
$16$	−15.2365	−	4.88341i	−0.952284	−	0.305213i
$17$	−25.9378			−1.52575			−0.762875	−	0.646545i	$-0.776213\pi$
$17$	−25.9378			−1.52575			−0.762875	+	0.646545i	$0.776213\pi$
$18$	4.55854	−	3.90125i	0.253252	−	0.216736i
$19$		−	1.33925i		−	0.0704869i	−0.999379	−	0.0352434i	$-0.988779\pi$
$19$		−	1.33925i		−	0.0704869i	0.999379	−	0.0352434i	$-0.0112207\pi$
$20$	−4.86096	+	31.0929i	−0.243048	+	1.55464i
$21$		0			0
$22$	−14.6938	−	17.1694i	−0.667899	−	0.780429i
$23$		−	11.0460i		−	0.480261i	−0.970741	−	0.240131i	$-0.922810\pi$
$23$		−	11.0460i		−	0.480261i	0.970741	−	0.240131i	$-0.0771903\pi$
$24$	11.7928	−	7.27534i	0.491366	−	0.303139i
$25$	36.8998			1.47599
$26$	−16.0300	+	13.7186i	−0.616538	+	0.527639i
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−20.4217			−0.704198			−0.352099	−	0.935963i	$-0.614532\pi$
$29$	−20.4217			−0.704198			−0.352099	+	0.935963i	$0.614532\pi$
$30$	−17.7210	−	20.7066i	−0.590699	−	0.690222i
$31$			36.9764i			1.19279i	0.802692	+	0.596394i	$0.203400\pi$
$31$			36.9764i			1.19279i	−0.802692	+	0.596394i	$0.796600\pi$
$32$	29.5026	−	12.3934i	0.921956	−	0.387294i
$33$	19.5710			0.593060
$34$	39.4128	−	33.7299i	1.15920	−	0.992055i
$35$		0			0
$36$	−1.85352	+	11.8560i	−0.0514868	+	0.329333i
$37$	24.2482			0.655357			0.327679	−	0.944789i	$-0.393734\pi$
$37$	24.2482			0.655357			0.327679	+	0.944789i	$0.393734\pi$
$38$	1.74158	+	2.03501i	0.0458311	+	0.0535529i
$39$		−	18.2721i		−	0.468516i
$40$	−33.0474	−	53.5673i	−0.826185	−	1.33918i
$41$	77.6185			1.89313			0.946567	−	0.322508i	$-0.104526\pi$
$41$	77.6185			1.89313			0.946567	+	0.322508i	$0.104526\pi$
$42$		0			0
$43$		−	77.7251i		−	1.80756i	−0.427997	−	0.903780i	$-0.640780\pi$
$43$		−	77.7251i		−	1.80756i	0.427997	−	0.903780i	$-0.359220\pi$
$44$	44.6548	+	6.98118i	1.01488	+	0.158663i
$45$	23.6029			0.524510
$46$	14.3644	+	16.7846i	0.312270	+	0.364882i
$47$			0.795833i			0.0169326i	0.999964	+	0.00846631i	$0.00269494\pi$
$47$			0.795833i			0.0169326i	−0.999964	+	0.00846631i	$0.997305\pi$
$48$	−8.45832	+	26.3905i	−0.176215	+	0.549801i
$49$		0			0
$50$	−56.0698	+	47.9851i	−1.12140	+	0.959702i
$51$			44.9255i			0.880893i
$52$	6.51787	−	41.6913i	0.125344	−	0.801755i
$53$	74.4459			1.40464			0.702320	−	0.711862i	$-0.252148\pi$
$53$	74.4459			1.40464			0.702320	+	0.711862i	$0.252148\pi$
$54$	−6.75715	−	7.89562i	−0.125132	−	0.146215i
$55$		−	88.8989i		−	1.61634i
$56$		0			0
$57$	−2.31965			−0.0406956
$58$	31.0311	−	26.5567i	0.535019	−	0.457875i
$59$		−	64.6353i		−	1.09551i	−0.836637	−	0.547757i	$-0.815482\pi$
$59$		−	64.6353i		−	1.09551i	0.836637	−	0.547757i	$-0.184518\pi$
$60$	53.8545	+	8.41942i	0.897575	+	0.140324i
$61$	0.601583			0.00986201			0.00493101	−	0.999988i	$-0.498430\pi$
$61$	0.601583			0.00986201			0.00493101	+	0.999988i	$0.498430\pi$
$62$	−48.0847	−	56.1861i	−0.775559	−	0.906228i
$63$		0			0
$64$	−28.7130	+	57.1976i	−0.448641	+	0.893712i
$65$	−82.9991			−1.27691
$66$	−29.7383	+	25.4504i	−0.450581	+	0.385612i
$67$		−	50.3015i		−	0.750769i	−0.926869	−	0.375385i	$-0.877511\pi$
$67$		−	50.3015i		−	0.750769i	0.926869	−	0.375385i	$-0.122489\pi$
$68$	−16.0254	+	102.506i	−0.235668	+	1.50744i
$69$	−19.1323			−0.277279
$70$		0			0
$71$		−	101.650i		−	1.43168i	−0.698262	−	0.715842i	$-0.746043\pi$
$71$		−	101.650i		−	1.43168i	0.698262	−	0.715842i	$-0.253957\pi$
$72$	−12.6013	−	20.4257i	−0.175017	−	0.283690i
$73$	100.183			1.37237			0.686185	−	0.727427i	$-0.259284\pi$
$73$	100.183			1.37237			0.686185	+	0.727427i	$0.259284\pi$
$74$	−36.8455	+	31.5327i	−0.497912	+	0.426118i
$75$		−	63.9124i		−	0.852165i
$76$	−5.29271	−	0.827444i	−0.0696410	−	0.0108874i
$77$		0			0
$78$	23.7614	+	27.7647i	0.304633	+	0.355958i
$79$		−	33.4197i		−	0.423034i	−0.977374	−	0.211517i	$-0.932160\pi$
$79$		−	33.4197i		−	0.423034i	0.977374	−	0.211517i	$-0.0678404\pi$
$80$	119.876	+	38.4210i	1.49845	+	0.480262i
$81$	9.00000			0.111111
$82$	−117.942	+	100.936i	−1.43832	+	1.23093i
$83$			58.7583i			0.707932i	0.935258	+	0.353966i	$0.115167\pi$
$83$			58.7583i			0.707932i	−0.935258	+	0.353966i	$0.884833\pi$
$84$		0			0
$85$	204.069			2.40081
$86$	101.075	+	118.104i	1.17529	+	1.37331i
$87$			35.3715i			0.406569i
$88$	−76.9320	+	47.4618i	−0.874227	+	0.539339i
$89$	53.9641			0.606338			0.303169	−	0.952937i	$-0.401955\pi$
$89$	53.9641			0.606338			0.303169	+	0.952937i	$0.401955\pi$
$90$	−35.8650	+	30.6936i	−0.398500	+	0.341040i
$91$		0			0
$92$	−43.6538	−	6.82468i	−0.474498	−	0.0741813i
$93$	64.0450			0.688656
$94$	−1.03491	−	1.20928i	−0.0110097	−	0.0128647i
$95$			10.5367i			0.110913i
$96$	−21.4660	−	51.1000i	−0.223605	−	0.532292i
$97$	39.9964			0.412334			0.206167	−	0.978517i	$-0.433901\pi$
$97$	39.9964			0.412334			0.206167	+	0.978517i	$0.433901\pi$
$98$		0			0
$99$		−	33.8979i		−	0.342403i
$100$	22.7982	−	145.828i	0.227982	−	1.45828i
$101$	−45.8279			−0.453741			−0.226871	−	0.973925i	$-0.572849\pi$
$101$	−45.8279			−0.453741			−0.226871	+	0.973925i	$0.572849\pi$
$102$	−58.4218	−	68.2649i	−0.572763	−	0.669264i
$103$		−	29.5754i		−	0.287140i	−0.989640	−	0.143570i	$-0.954142\pi$
$103$		−	29.5754i		−	0.287140i	0.989640	−	0.143570i	$-0.0458582\pi$
$104$	44.3120	+	71.8264i	0.426077	+	0.690638i
$105$		0			0
$106$	−113.122	+	96.8106i	−1.06718	+	0.913307i
$107$			200.948i			1.87802i	0.343886	+	0.939012i	$0.388257\pi$
$107$			200.948i			1.87802i	−0.343886	+	0.939012i	$0.611743\pi$
$108$	20.5352	+	3.21040i	0.190140	+	0.0297259i
$109$	−3.84730			−0.0352963			−0.0176482	−	0.999844i	$-0.505618\pi$
$109$	−3.84730			−0.0352963			−0.0176482	+	0.999844i	$0.505618\pi$
$110$	115.605	+	135.083i	1.05096	+	1.22803i
$111$		−	41.9991i		−	0.378371i
$112$		0			0
$113$	67.4772			0.597144			0.298572	−	0.954387i	$-0.403490\pi$
$113$	67.4772			0.597144			0.298572	+	0.954387i	$0.403490\pi$
$114$	3.52474	−	3.01651i	0.0309188	−	0.0264606i
$115$			86.9061i			0.755705i
$116$	−12.6174	+	80.7066i	−0.108771	+	0.695747i
$117$	−31.6483			−0.270498
$118$	84.0528	+	98.2143i	0.712312	+	0.832324i
$119$		0			0
$120$	−92.7813	+	57.2398i	−0.773178	+	0.476998i
$121$	−6.67429			−0.0551594
$122$	−0.914113	+	0.782307i	−0.00749273	+	0.00641235i
$123$		−	134.439i		−	1.09300i
$124$	146.131	+	22.8455i	1.17847	+	0.184238i
$125$	−93.6236			−0.748988
$126$		0			0
$127$			194.583i			1.53215i	0.642751	+	0.766075i	$0.277793\pi$
$127$			194.583i			1.53215i	−0.642751	+	0.766075i	$0.722207\pi$
$128$	−30.7508	−	124.251i	−0.240241	−	0.970713i
$129$	−134.624			−1.04360
$130$	126.118	−	107.933i	0.970140	−	0.830256i
$131$		−	43.2285i		−	0.329989i	−0.986294	−	0.164994i	$-0.947239\pi$
$131$		−	43.2285i		−	0.329989i	0.986294	−	0.164994i	$-0.0527606\pi$
$132$	12.0918	−	77.3444i	0.0916042	−	0.585942i
$133$		0			0
$134$	65.4129	+	76.4339i	0.488156	+	0.570402i
$135$		−	40.8815i		−	0.302826i
$136$	−108.949	−	176.599i	−0.801099	−	1.29852i
$137$	−64.3080			−0.469401			−0.234701	−	0.972068i	$-0.575411\pi$
$137$	−64.3080			−0.469401			−0.234701	+	0.972068i	$0.575411\pi$
$138$	29.0717	−	24.8799i	0.210665	−	0.180289i
$139$		−	192.002i		−	1.38131i	−0.723185	−	0.690654i	$-0.757323\pi$
$139$		−	192.002i		−	1.38131i	0.723185	−	0.690654i	$-0.242677\pi$
$140$		0			0
$141$	1.37842			0.00977605
$142$	132.187	+	154.458i	0.930892	+	1.08773i
$143$			119.201i			0.833574i
$144$	45.7096	+	14.6502i	0.317428	+	0.101738i
$145$	160.671			1.10808
$146$	−152.230	+	130.280i	−1.04267	+	0.892326i
$147$		0			0
$148$	14.9815	−	95.8288i	0.101227	−	0.647492i
$149$	83.3468			0.559375			0.279687	−	0.960091i	$-0.409769\pi$
$149$	83.3468			0.559375			0.279687	+	0.960091i	$0.409769\pi$
$150$	83.1126	+	97.1157i	0.554084	+	0.647438i
$151$			167.386i			1.10852i	0.832344	+	0.554259i	$0.186998\pi$
$151$			167.386i			1.10852i	−0.832344	+	0.554259i	$0.813002\pi$
$152$	9.11837	−	5.62541i	0.0599893	−	0.0370093i
$153$	77.8133			0.508584
$154$		0			0
$155$		−	290.917i		−	1.87688i
$156$	−72.2114	−	11.2893i	−0.462893	−	0.0723672i
$157$	−84.8631			−0.540529			−0.270265	−	0.962786i	$-0.587111\pi$
$157$	−84.8631			−0.540529			−0.270265	+	0.962786i	$0.587111\pi$
$158$	43.4595	+	50.7817i	0.275060	+	0.321403i
$159$		−	128.944i		−	0.810969i
$160$	−232.116	+	97.5070i	−1.45072	+	0.609419i
$161$		0			0
$162$	−13.6756	+	11.7037i	−0.0844174	+	0.0722453i
$163$		−	126.615i		−	0.776780i	−0.921495	−	0.388390i	$-0.873031\pi$
$163$		−	126.615i		−	0.776780i	0.921495	−	0.388390i	$-0.126969\pi$
$164$	47.9559	−	306.748i	0.292414	−	1.87041i
$165$	−153.977			−0.933197
$166$	−76.4102	−	89.2841i	−0.460303	−	0.537856i
$167$		−	17.8740i		−	0.107030i	−0.998567	−	0.0535149i	$-0.982958\pi$
$167$		−	17.8740i		−	0.107030i	0.998567	−	0.0535149i	$-0.0170425\pi$
$168$		0			0
$169$	−57.7098			−0.341478
$170$	−310.086	+	265.375i	−1.82403	+	1.56103i
$171$			4.01775i			0.0234956i
$172$	−307.169	−	48.0218i	−1.78587	−	0.279196i
$173$	−21.3963			−0.123678			−0.0618392	−	0.998086i	$-0.519697\pi$
$173$	−21.3963			−0.123678			−0.0618392	+	0.998086i	$0.519697\pi$
$174$	−45.9976	−	53.7474i	−0.264354	−	0.308893i
$175$		0			0
$176$	55.1792	−	172.162i	0.313518	−	0.978195i
$177$	−111.952			−0.632495
$178$	−81.9991	+	70.1757i	−0.460669	+	0.394245i
$179$		−	34.8434i		−	0.194656i	−0.995252	−	0.0973280i	$-0.968970\pi$
$179$		−	34.8434i		−	0.194656i	0.995252	−	0.0973280i	$-0.0310296\pi$
$180$	14.5829	−	93.2787i	0.0810159	−	0.518215i
$181$	45.6228			0.252059			0.126030	−	0.992026i	$-0.459777\pi$
$181$	45.6228			0.252059			0.126030	+	0.992026i	$0.459777\pi$
$182$		0			0
$183$		−	1.04197i		−	0.00569384i
$184$	75.2074	−	46.3978i	0.408736	−	0.252162i
$185$	−190.776			−1.03122
$186$	−97.3172	+	83.2851i	−0.523211	+	0.447769i
$187$		−	293.079i		−	1.56727i
$188$	3.14513	+	0.491698i	0.0167294	+	0.00261542i
$189$		0			0
$190$	−13.7021	−	16.0107i	−0.0721165	−	0.0842670i
$191$		−	28.3252i		−	0.148300i	−0.997247	−	0.0741498i	$-0.976376\pi$
$191$		−	28.3252i		−	0.148300i	0.997247	−	0.0741498i	$-0.0236243\pi$
$192$	99.0691	+	49.7324i	0.515985	+	0.259023i
$193$	−122.494			−0.634683			−0.317341	−	0.948311i	$-0.602790\pi$
$193$	−122.494			−0.634683			−0.317341	+	0.948311i	$0.602790\pi$
$194$	−60.7751	+	52.0119i	−0.313274	+	0.268103i
$195$			143.759i			0.737224i
$196$		0			0
$197$	131.382			0.666912			0.333456	−	0.942766i	$-0.391785\pi$
$197$	131.382			0.666912			0.333456	+	0.942766i	$0.391785\pi$
$198$	44.0814	+	51.5083i	0.222633	+	0.260143i
$199$			321.715i			1.61666i	0.588732	+	0.808328i	$0.299627\pi$
$199$			321.715i			1.61666i	−0.588732	+	0.808328i	$0.700373\pi$
$200$	154.995	+	251.235i	0.774973	+	1.25617i
$201$	−87.1248			−0.433457
$202$	69.6361	−	59.5953i	0.344733	−	0.295026i
$203$		0			0
$204$	177.546	+	27.7568i	0.870321	+	0.136063i
$205$	−610.674			−2.97890
$206$	38.4603	+	44.9402i	0.186700	+	0.218156i
$207$			33.1380i			0.160087i
$208$	−160.737	−	51.5172i	−0.772773	−	0.247679i
$209$	15.1326			0.0724048
$210$		0			0
$211$		−	149.843i		−	0.710158i	−0.934836	−	0.355079i	$-0.884454\pi$
$211$		−	149.843i		−	0.710158i	0.934836	−	0.355079i	$-0.115546\pi$
$212$	45.9957	−	294.210i	0.216961	−	1.38778i
$213$	−176.062			−0.826583
$214$	−261.316	−	305.344i	−1.22110	−	1.42684i
$215$			611.513i			2.84425i
$216$	−35.3783	+	21.8260i	−0.163789	+	0.101046i
$217$		0			0
$218$	5.84603	−	5.00309i	0.0268166	−	0.0229499i
$219$		−	173.522i		−	0.792339i
$220$	−351.328	−	54.9254i	−1.59695	−	0.249661i
$221$	−273.628			−1.23814
$222$	54.6163	+	63.8182i	0.246019	+	0.287470i
$223$			241.710i			1.08390i	0.840410	+	0.541952i	$0.182314\pi$
$223$			241.710i			1.08390i	−0.840410	+	0.541952i	$0.817686\pi$
$224$		0			0
$225$	−110.699			−0.491998
$226$	−102.533	+	87.7484i	−0.453684	+	0.388267i
$227$		−	388.566i		−	1.71174i	−0.517189	−	0.855871i	$-0.673021\pi$
$227$		−	388.566i		−	1.71174i	0.517189	−	0.855871i	$-0.326979\pi$
$228$	−1.43318	+	9.16725i	−0.00628586	+	0.0402072i
$229$	−82.0654			−0.358364			−0.179182	−	0.983816i	$-0.557345\pi$
$229$	−82.0654			−0.358364			−0.179182	+	0.983816i	$0.557345\pi$
$230$	−113.014	−	132.055i	−0.491365	−	0.574152i
$231$		0			0
$232$	−85.7798	−	139.043i	−0.369740	−	0.599322i
$233$	226.287			0.971191			0.485595	−	0.874184i	$-0.338603\pi$
$233$	226.287			0.971191			0.485595	+	0.874184i	$0.338603\pi$
$234$	48.0899	−	41.1559i	0.205513	−	0.175880i
$235$		−	6.26133i		−	0.0266440i
$236$	−255.439	−	39.9344i	−1.08237	−	0.169213i
$237$	−57.8847			−0.244239
$238$		0			0
$239$			174.441i			0.729878i	0.931031	+	0.364939i	$0.118910\pi$
$239$			174.441i			0.729878i	−0.931031	+	0.364939i	$0.881090\pi$
$240$	66.5470	−	207.631i	0.277279	−	0.865128i
$241$	346.058			1.43592			0.717962	−	0.696082i	$-0.245075\pi$
$241$	346.058			1.43592			0.717962	+	0.696082i	$0.245075\pi$
$242$	10.1417	−	8.67934i	0.0419077	−	0.0358651i
$243$		−	15.5885i		−	0.0641500i
$244$	0.371683	−	2.37745i	0.00152329	−	0.00974366i
$245$		0			0
$246$	174.827	+	204.282i	0.710678	+	0.830415i
$247$		−	14.1283i		−	0.0571996i
$248$	−251.756	+	155.316i	−1.01515	+	0.626275i
$249$	101.772			0.408725
$250$	142.262	−	121.749i	0.569049	−	0.486998i
$251$		−	108.787i		−	0.433414i	−0.976237	−	0.216707i	$-0.930468\pi$
$251$		−	108.787i		−	0.433414i	0.976237	−	0.216707i	$-0.0695316\pi$
$252$		0			0
$253$	124.812			0.493329
$254$	−253.039	−	295.671i	−0.996215	−	1.16406i
$255$		−	353.458i		−	1.38611i
$256$	208.305	+	148.813i	0.813690	+	0.581299i
$257$	362.184			1.40928			0.704639	−	0.709566i	$-0.251109\pi$
$257$	362.184			1.40928			0.704639	+	0.709566i	$0.251109\pi$
$258$	204.563	−	175.067i	0.792879	−	0.678554i
$259$		0			0
$260$	−51.2803	+	328.012i	−0.197232	+	1.26158i
$261$	61.2652			0.234733
$262$	56.2151	+	65.6864i	0.214561	+	0.250711i
$263$			262.474i			0.997999i	0.866602	+	0.499000i	$0.166299\pi$
$263$			262.474i			0.997999i	−0.866602	+	0.499000i	$0.833701\pi$
$264$	82.2062	+	133.250i	0.311387	+	0.504735i
$265$	−585.714			−2.21024
$266$		0			0
$267$		−	93.4685i		−	0.350069i
$268$	−198.791	−	31.0784i	−0.741759	−	0.115964i
$269$	45.9518			0.170824			0.0854122	−	0.996346i	$-0.472779\pi$
$269$	45.9518			0.170824			0.0854122	+	0.996346i	$0.472779\pi$
$270$	53.1629	+	62.1199i	0.196900	+	0.230074i
$271$		−	26.2165i		−	0.0967400i	−0.998829	−	0.0483700i	$-0.984597\pi$
$271$		−	26.2165i		−	0.0967400i	0.998829	−	0.0483700i	$-0.0154027\pi$
$272$	395.202	+	126.665i	1.45295	+	0.465679i
$273$		0			0
$274$	97.7168	−	83.6271i	0.356631	−	0.305208i
$275$			416.942i			1.51615i
$276$	−11.8207	+	75.6106i	−0.0428286	+	0.273951i
$277$	530.046			1.91352			0.956761	−	0.290874i	$-0.0939462\pi$
$277$	530.046			1.91352			0.956761	+	0.290874i	$0.0939462\pi$
$278$	249.682	+	291.749i	0.898137	+	1.04946i
$279$		−	110.929i		−	0.397596i
$280$		0			0
$281$	−268.974			−0.957201			−0.478601	−	0.878033i	$-0.658856\pi$
$281$	−268.974			−0.957201			−0.478601	+	0.878033i	$0.658856\pi$
$282$	−2.09453	+	1.79252i	−0.00742742	+	0.00635646i
$283$		−	58.6271i		−	0.207163i	−0.994621	−	0.103581i	$-0.966970\pi$
$283$		−	58.6271i		−	0.207163i	0.994621	−	0.103581i	$-0.0330302\pi$
$284$	−401.719	−	62.8033i	−1.41450	−	0.221138i
$285$	18.2502			0.0640357
$286$	−155.011	−	181.128i	−0.541996	−	0.633313i
$287$		0			0
$288$	−88.5078	+	37.1803i	−0.307319	+	0.129098i
$289$	383.768			1.32792
$290$	−244.142	+	208.939i	−0.841868	+	0.720479i
$291$		−	69.2758i		−	0.238061i
$292$	61.8972	−	395.923i	0.211977	−	1.35590i
$293$	202.002			0.689426			0.344713	−	0.938708i	$-0.387976\pi$
$293$	202.002			0.689426			0.344713	+	0.938708i	$0.387976\pi$
$294$		0			0
$295$			508.528i			1.72382i
$296$	101.853	+	165.095i	0.344097	+	0.557755i
$297$	−58.7129			−0.197687
$298$	−126.647	+	108.385i	−0.424989	+	0.363710i
$299$		−	116.529i		−	0.389729i
$300$	−252.581	−	39.4877i	−0.841938	−	0.131626i
$301$		0			0
$302$	−217.671	−	254.345i	−0.720766	−	0.842204i
$303$			79.3762i			0.261968i
$304$	−6.54011	+	20.4055i	−0.0215135	+	0.0671235i
$305$	−4.73304			−0.0155182
$306$	−118.238	+	101.190i	−0.386400	+	0.330685i
$307$			57.8430i			0.188414i	0.995553	+	0.0942068i	$0.0300315\pi$
$307$			57.8430i			0.188414i	−0.995553	+	0.0942068i	$0.969969\pi$
$308$		0			0
$309$	−51.2261			−0.165780
$310$	378.313	+	442.053i	1.22036	+	1.42598i
$311$		−	134.835i		−	0.433554i	−0.976221	−	0.216777i	$-0.930446\pi$
$311$		−	134.835i		−	0.433554i	0.976221	−	0.216777i	$-0.0695544\pi$
$312$	124.407	−	76.7506i	0.398740	−	0.245995i
$313$	122.113			0.390139			0.195069	−	0.980789i	$-0.437507\pi$
$313$	122.113			0.390139			0.195069	+	0.980789i	$0.437507\pi$
$314$	128.951	−	110.357i	0.410671	−	0.351456i
$315$		0			0
$316$	−132.075	−	20.6481i	−0.417958	−	0.0653420i
$317$	453.125			1.42942			0.714708	−	0.699423i	$-0.246559\pi$
$317$	453.125			1.42942			0.714708	+	0.699423i	$0.246559\pi$
$318$	167.681	+	195.932i	0.527298	+	0.616139i
$319$		−	230.751i		−	0.723359i
$320$	225.904	−	450.010i	0.705949	−	1.40628i
$321$	348.053			1.08428
$322$		0			0
$323$			34.7372i			0.107545i
$324$	5.56057	−	35.5680i	0.0171623	−	0.109778i
$325$	389.272			1.19776
$326$	164.652	+	192.394i	0.505069	+	0.590164i
$327$			6.66372i			0.0203784i
$328$	326.030	+	528.470i	0.993994	+	1.61119i
$329$		0			0
$330$	233.971	−	200.235i	0.709002	−	0.606771i
$331$		−	55.4245i		−	0.167446i	−0.996489	−	0.0837228i	$-0.973319\pi$
$331$		−	55.4245i		−	0.167446i	0.996489	−	0.0837228i	$-0.0266810\pi$
$332$	232.213	+	36.3033i	0.699436	+	0.109347i
$333$	−72.7446			−0.218452
$334$	23.2436	+	27.1597i	0.0695916	+	0.0813166i
$335$			395.755i			1.18136i
$336$		0			0
$337$	230.227			0.683167			0.341584	−	0.939851i	$-0.389037\pi$
$337$	230.227			0.683167			0.341584	+	0.939851i	$0.389037\pi$
$338$	87.6908	−	75.0467i	0.259440	−	0.222032i
$339$		−	116.874i		−	0.344761i
$340$	126.082	−	806.480i	0.370830	−	2.37200i
$341$	−417.808			−1.22524
$342$	−5.22474	−	6.10503i	−0.0152770	−	0.0178510i
$343$		0			0
$344$	529.196	−	326.478i	1.53836	−	0.949064i
$345$	150.526			0.436306
$346$	32.5120	−	27.8241i	0.0939654	−	0.0804166i
$347$		−	82.1713i		−	0.236805i	−0.992966	−	0.118402i	$-0.962223\pi$
$347$		−	82.1713i		−	0.236805i	0.992966	−	0.118402i	$-0.0377773\pi$
$348$	139.788	+	21.8540i	0.401689	+	0.0627987i
$349$	−211.150			−0.605015			−0.302508	−	0.953147i	$-0.597824\pi$
$349$	−211.150			−0.605015			−0.302508	+	0.953147i	$0.597824\pi$
$350$		0			0
$351$			54.8164i			0.156172i
$352$	140.037	+	333.359i	0.397833	+	0.947042i
$353$	72.9554			0.206673			0.103336	−	0.994646i	$-0.467048\pi$
$353$	72.9554			0.206673			0.103336	+	0.994646i	$0.467048\pi$
$354$	170.112	−	145.584i	0.480543	−	0.411253i
$355$			799.743i			2.25280i
$356$	33.3412	−	213.266i	0.0936551	−	0.599061i
$357$		0			0
$358$	45.3109	+	52.9451i	0.126567	+	0.147891i
$359$		−	273.505i		−	0.761852i	−0.924605	−	0.380926i	$-0.875605\pi$
$359$		−	273.505i		−	0.761852i	0.924605	−	0.380926i	$-0.124395\pi$
$360$	99.1422	+	160.702i	0.275395	+	0.446394i
$361$	359.206			0.995032
$362$	−69.3244	+	59.3285i	−0.191504	+	0.163891i
$363$			11.5602i			0.0318463i
$364$		0			0
$365$	−788.205			−2.15947
$366$	1.35500	+	1.58329i	0.00370217	+	0.00432593i
$367$			182.607i			0.497568i	0.968559	+	0.248784i	$0.0800308\pi$
$367$			182.607i			0.497568i	−0.968559	+	0.248784i	$0.919969\pi$
$368$	−53.9422	+	168.303i	−0.146582	+	0.457345i
$369$	−232.855			−0.631044
$370$	289.887	−	248.088i	0.783479	−	0.670509i
$371$		0			0
$372$	39.5697	−	253.106i	0.106370	−	0.680391i
$373$	−237.665			−0.637172			−0.318586	−	0.947894i	$-0.603208\pi$
$373$	−237.665			−0.637172			−0.318586	+	0.947894i	$0.603208\pi$
$374$	381.124	+	445.337i	1.01905	+	1.19074i
$375$			162.161i			0.432429i
$376$	−5.41848	+	3.34283i	−0.0144108	+	0.00889051i
$377$	−215.437			−0.571452
$378$		0			0
$379$			360.021i			0.949923i	0.880006	+	0.474962i	$0.157538\pi$
$379$			360.021i			0.949923i	−0.880006	+	0.474962i	$0.842462\pi$
$380$	41.6412	+	6.51004i	0.109582	+	0.0171317i
$381$	337.028			0.884587
$382$	36.8345	+	43.0405i	0.0964255	+	0.112672i
$383$		−	317.683i		−	0.829460i	−0.909945	−	0.414730i	$-0.863876\pi$
$383$		−	317.683i		−	0.829460i	0.909945	−	0.414730i	$-0.136124\pi$
$384$	−215.210	+	53.2620i	−0.560442	+	0.138703i
$385$		0			0
$386$	186.131	−	159.293i	0.482204	−	0.412676i
$387$			233.175i			0.602520i
$388$	24.7114	−	158.066i	0.0636893	−	0.407386i
$389$	−248.549			−0.638945			−0.319472	−	0.947596i	$-0.603506\pi$
$389$	−248.549			−0.638945			−0.319472	+	0.947596i	$0.603506\pi$
$390$	−186.946	−	218.443i	−0.479348	−	0.560111i
$391$			286.509i			0.732759i
$392$		0			0
$393$	−74.8740			−0.190519
$394$	−199.636	+	170.851i	−0.506691	+	0.433631i
$395$			262.934i			0.665657i
$396$	−133.964	−	20.9435i	−0.338294	−	0.0528877i
$397$	−356.666			−0.898402			−0.449201	−	0.893431i	$-0.648291\pi$
$397$	−356.666			−0.898402			−0.449201	+	0.893431i	$0.648291\pi$
$398$	−418.363	−	488.850i	−1.05116	−	1.22827i
$399$		0			0
$400$	−562.226	−	180.197i	−1.40556	−	0.450493i
$401$	−306.242			−0.763695			−0.381848	−	0.924225i	$-0.624712\pi$
$401$	−306.242			−0.763695			−0.381848	+	0.924225i	$0.624712\pi$
$402$	132.387	−	113.298i	0.329322	−	0.281837i
$403$			390.080i			0.967939i
$404$	−28.3144	+	181.112i	−0.0700850	+	0.448296i
$405$	−70.8088			−0.174837
$406$		0			0
$407$			273.988i			0.673189i
$408$	−305.878	+	188.706i	−0.749701	+	0.462515i
$409$	273.347			0.668331			0.334166	−	0.942514i	$-0.391546\pi$
$409$	273.347			0.668331			0.334166	+	0.942514i	$0.391546\pi$
$410$	927.928	−	794.130i	2.26324	−	1.93690i
$411$			111.385i			0.271009i
$412$	−116.882	−	18.2729i	−0.283694	−	0.0443517i
$413$		0			0
$414$	−43.0932	−	50.3537i	−0.104090	−	0.121627i
$415$		−	462.290i		−	1.11395i
$416$	311.235	−	130.743i	0.748162	−	0.314287i
$417$	−332.557			−0.797498
$418$	−22.9942	+	19.6787i	−0.0550100	+	0.0470781i
$419$		−	444.010i		−	1.05969i	−0.848094	−	0.529845i	$-0.822250\pi$
$419$		−	444.010i		−	1.05969i	0.848094	−	0.529845i	$-0.177750\pi$
$420$		0			0
$421$	−650.471			−1.54506			−0.772530	−	0.634978i	$-0.781009\pi$
$421$	−650.471			−1.54506			−0.772530	+	0.634978i	$0.781009\pi$
$422$	194.859	+	227.689i	0.461750	+	0.539547i
$423$		−	2.38750i		−	0.00564421i
$424$	312.704	+	506.869i	0.737509	+	1.19545i
$425$	−957.099			−2.25200
$426$	267.529	−	228.954i	0.628002	−	0.537451i
$427$		0			0
$428$	794.148	+	124.154i	1.85548	+	0.290080i
$429$	206.462			0.481264
$430$	−795.221	−	929.203i	−1.84935	−	2.16094i
$431$		−	624.972i		−	1.45005i	−0.688721	−	0.725026i	$-0.741828\pi$
$431$		−	624.972i		−	1.45005i	0.688721	−	0.725026i	$-0.258172\pi$
$432$	25.3750	−	79.1714i	0.0587383	−	0.183267i
$433$	440.222			1.01668			0.508339	−	0.861157i	$-0.330260\pi$
$433$	440.222			1.01668			0.508339	+	0.861157i	$0.330260\pi$
$434$		0			0
$435$		−	278.290i		−	0.639748i
$436$	−2.37702	+	15.2045i	−0.00545188	+	0.0348728i
$437$	−14.7934			−0.0338521
$438$	225.651	+	263.669i	0.515185	+	0.601985i
$439$			514.977i			1.17307i	0.809925	+	0.586534i	$0.199508\pi$
$439$			514.977i			1.17307i	−0.809925	+	0.586534i	$0.800492\pi$
$440$	605.274	−	373.412i	1.37562	−	0.848665i
$441$		0			0
$442$	415.782	−	355.830i	0.940683	−	0.805046i
$443$		−	457.342i		−	1.03237i	−0.856476	−	0.516187i	$-0.827351\pi$
$443$		−	457.342i		−	1.03237i	0.856476	−	0.516187i	$-0.172649\pi$
$444$	−165.980	−	25.9488i	−0.373830	−	0.0584432i
$445$	−424.570			−0.954090
$446$	−314.324	−	367.282i	−0.704762	−	0.823503i
$447$		−	144.361i		−	0.322955i
$448$		0			0
$449$	−188.955			−0.420835			−0.210417	−	0.977612i	$-0.567482\pi$
$449$	−188.955			−0.420835			−0.210417	+	0.977612i	$0.567482\pi$
$450$	168.209	−	143.955i	0.373798	−	0.319901i
$451$			877.035i			1.94464i
$452$	41.6902	−	266.670i	0.0922350	−	0.589977i
$453$	289.921			0.640003
$454$	505.297	+	590.431i	1.11299	+	1.30051i
$455$		0			0
$456$	−9.74350	−	15.7935i	−0.0213673	−	0.0346348i
$457$	789.509			1.72759			0.863796	−	0.503842i	$-0.168081\pi$
$457$	789.509			1.72759			0.863796	+	0.503842i	$0.168081\pi$
$458$	124.699	−	106.719i	0.272269	−	0.233011i
$459$		−	134.777i		−	0.293631i
$460$	343.452	+	53.6942i	0.746636	+	0.116726i
$461$	359.278			0.779344			0.389672	−	0.920954i	$-0.372588\pi$
$461$	359.278			0.779344			0.389672	+	0.920954i	$0.372588\pi$
$462$		0			0
$463$			865.525i			1.86939i	0.355457	+	0.934693i	$0.384325\pi$
$463$			865.525i			1.86939i	−0.355457	+	0.934693i	$0.615675\pi$
$464$	311.157	+	99.7278i	0.670596	+	0.214930i
$465$	−503.883			−1.08362
$466$	−343.847	+	294.268i	−0.737869	+	0.631476i
$467$		−	516.607i		−	1.10622i	−0.833107	−	0.553112i	$-0.813440\pi$
$467$		−	516.607i		−	1.10622i	0.833107	−	0.553112i	$-0.186560\pi$
$468$	−19.5536	+	125.074i	−0.0417812	+	0.267252i
$469$		0			0
$470$	8.14233	+	9.51417i	0.0173241	+	0.0202429i
$471$			146.987i			0.312075i
$472$	440.074	−	271.495i	0.932359	−	0.575202i
$473$	878.240			1.85674
$474$	87.9565	−	75.2741i	0.185562	−	0.158806i
$475$		−	49.4181i		−	0.104038i
$476$		0			0
$477$	−223.338			−0.468213
$478$	−226.846	−	265.065i	−0.474572	−	0.554530i
$479$		−	717.541i		−	1.49800i	−0.662572	−	0.748999i	$-0.730535\pi$
$479$		−	717.541i		−	1.49800i	0.662572	−	0.748999i	$-0.269465\pi$
$480$	168.887	+	402.037i	0.351848	+	0.837576i
$481$	255.805			0.531818
$482$	−525.839	+	450.019i	−1.09095	+	0.933649i
$483$		0			0
$484$	−4.12365	+	26.3768i	−0.00851994	+	0.0544974i
$485$	−314.678			−0.648820
$486$	20.2715	+	23.6869i	0.0417108	+	0.0487384i
$487$			901.181i			1.85047i	0.379389	+	0.925237i	$0.376134\pi$
$487$			901.181i			1.85047i	−0.379389	+	0.925237i	$0.623866\pi$
$488$	2.52690	+	4.09591i	0.00517807	+	0.00839326i
$489$	−219.304			−0.448474
$490$		0			0
$491$			475.042i			0.967499i	0.875206	+	0.483750i	$0.160725\pi$
$491$			475.042i			0.967499i	−0.875206	+	0.483750i	$0.839275\pi$
$492$	−531.303	−	83.0621i	−1.07988	−	0.168825i
$493$	529.694			1.07443
$494$	18.3727	+	21.4682i	0.0371916	+	0.0434578i
$495$			266.697i			0.538781i
$496$	180.571	−	563.393i	0.364055	−	1.13587i
$497$		0			0
$498$	−154.645	+	132.346i	−0.310531	+	0.265756i
$499$		−	45.6443i		−	0.0914715i	−0.998954	−	0.0457358i	$-0.985437\pi$
$499$		−	45.6443i		−	0.0914715i	0.998954	−	0.0457358i	$-0.0145632\pi$
$500$	−57.8445	+	370.000i	−0.115689	+	0.740000i
$501$	−30.9586			−0.0617937
$502$	141.468	+	165.303i	0.281809	+	0.329289i
$503$			621.019i			1.23463i	0.786716	+	0.617316i	$0.211780\pi$
$503$			621.019i			1.23463i	−0.786716	+	0.617316i	$0.788220\pi$
$504$		0			0
$505$	360.557			0.713975
$506$	−189.654	+	162.308i	−0.374810	+	0.320766i
$507$			99.9563i			0.197152i
$508$	768.991	+	120.221i	1.51376	+	0.236656i
$509$	298.051			0.585561			0.292781	−	0.956180i	$-0.405419\pi$
$509$	298.051			0.585561			0.292781	+	0.956180i	$0.405419\pi$
$510$	459.642	+	537.084i	0.901259	+	1.05311i
$511$		0			0
$512$	−510.040	+	44.7596i	−0.996171	+	0.0874210i
$513$	6.95895			0.0135652
$514$	−550.344	+	470.990i	−1.07071	+	0.916323i
$515$			232.689i			0.451823i
$516$	−83.1762	+	532.033i	−0.161194	+	1.03107i
$517$	−8.99236			−0.0173933
$518$		0			0
$519$			37.0596i			0.0714057i
$520$	−348.631	−	565.104i	−0.670444	−	1.08674i
$521$	−527.391			−1.01227			−0.506134	−	0.862455i	$-0.668926\pi$
$521$	−527.391			−1.01227			−0.506134	+	0.862455i	$0.668926\pi$
$522$	−93.0933	+	79.6702i	−0.178340	+	0.152625i
$523$		−	320.159i		−	0.612160i	−0.952006	−	0.306080i	$-0.900983\pi$
$523$		−	320.159i		−	0.612160i	0.952006	−	0.306080i	$-0.0990174\pi$
$524$	−170.839	−	26.7084i	−0.326029	−	0.0509702i
$525$		0			0
$526$	−341.325	−	398.832i	−0.648907	−	0.758236i
$527$		−	959.085i		−	1.81990i
$528$	−298.194	−	95.5731i	−0.564761	−	0.181010i
$529$	406.986			0.769349
$530$	890.000	−	761.671i	1.67924	−	1.43712i
$531$			193.906i			0.365171i
$532$		0			0
$533$	818.830			1.53627
$534$	121.548	+	142.027i	0.227618	+	0.265967i
$535$		−	1580.99i		−	2.95512i
$536$	342.481	−	211.287i	0.638957	−	0.394193i
$537$	−60.3506			−0.112385
$538$	−69.8243	+	59.7564i	−0.129785	+	0.111071i
$539$		0			0
$540$	−161.563	−	25.2583i	−0.299192	−	0.0467746i
$541$	−788.644			−1.45775			−0.728876	−	0.684646i	$-0.759957\pi$
$541$	−788.644			−1.45775			−0.728876	+	0.684646i	$0.759957\pi$
$542$	34.0924	+	39.8364i	0.0629011	+	0.0734989i
$543$		−	79.0209i		−	0.145527i
$544$	−765.231	+	321.458i	−1.40668	+	0.590915i
$545$	30.2692			0.0555398
$546$		0			0
$547$		−	920.537i		−	1.68288i	−0.540348	−	0.841441i	$-0.681708\pi$
$547$		−	920.537i		−	1.68288i	0.540348	−	0.841441i	$-0.318292\pi$
$548$	−39.7321	+	254.145i	−0.0725039	+	0.463768i
$549$	−1.80475			−0.00328734
$550$	−542.198	−	633.549i	−0.985815	−	1.15191i
$551$			27.3498i			0.0496367i
$552$	−80.3634	−	130.263i	−0.145586	−	0.235984i
$553$		0			0
$554$	−805.412	+	689.279i	−1.45381	+	1.24419i
$555$			330.434i			0.595377i
$556$	−758.790	−	118.627i	−1.36473	−	0.213357i
$557$	−119.959			−0.215367			−0.107683	−	0.994185i	$-0.534343\pi$
$557$	−119.959			−0.215367			−0.107683	+	0.994185i	$0.534343\pi$
$558$	144.254	+	168.558i	0.258520	+	0.302076i
$559$		−	819.955i		−	1.46682i
$560$		0			0
$561$	−507.627			−0.904861
$562$	408.709	−	349.777i	0.727240	−	0.622379i
$563$			40.0022i			0.0710518i	0.999369	+	0.0355259i	$0.0113106\pi$
$563$			40.0022i			0.0710518i	−0.999369	+	0.0355259i	$0.988689\pi$
$564$	0.851647	−	5.44752i	0.00151001	−	0.00965873i
$565$	−530.887			−0.939623
$566$	76.2396	+	89.0847i	0.134699	+	0.157393i
$567$		0			0
$568$	692.087	−	426.971i	1.21846	−	0.751709i
$569$	−916.184			−1.61016			−0.805082	−	0.593163i	$-0.797879\pi$
$569$	−916.184			−1.61016			−0.805082	+	0.593163i	$0.797879\pi$
$570$	−27.7314	+	23.7328i	−0.0486516	+	0.0416365i
$571$		−	673.478i		−	1.17947i	−0.807596	−	0.589736i	$-0.799232\pi$
$571$		−	673.478i		−	1.17947i	0.807596	−	0.589736i	$-0.200768\pi$
$572$	471.082	+	73.6474i	0.823570	+	0.128754i
$573$	−49.0607			−0.0856208
$574$		0			0
$575$		−	407.596i		−	0.708862i
$576$	86.1390	−	171.593i	0.149547	−	0.297904i
$577$	143.186			0.248157			0.124078	−	0.992272i	$-0.460403\pi$
$577$	143.186			0.248157			0.124078	+	0.992272i	$0.460403\pi$
$578$	−583.140	+	499.057i	−1.00889	+	0.863421i
$579$			212.165i			0.366434i
$580$	99.2691	−	634.971i	0.171154	−	1.09478i
$581$		0			0
$582$	90.0873	+	105.266i	0.154789	+	0.180869i
$583$			841.187i			1.44286i
$584$	420.811	+	682.103i	0.720566	+	1.16798i
$585$	248.997			0.425636
$586$	−306.944	+	262.686i	−0.523796	+	0.448270i
$587$			221.611i			0.377532i	0.982022	+	0.188766i	$0.0604487\pi$
$587$			221.611i			0.377532i	−0.982022	+	0.188766i	$0.939551\pi$
$588$		0			0
$589$	49.5207			0.0840758
$590$	−661.297	−	772.715i	−1.12084	−	1.30969i
$591$		−	227.560i		−	0.385042i
$592$	−369.459	−	118.414i	−0.624086	−	0.200024i
$593$	−207.246			−0.349488			−0.174744	−	0.984614i	$-0.555910\pi$
$593$	−207.246			−0.349488			−0.174744	+	0.984614i	$0.555910\pi$
$594$	89.2150	−	76.3512i	0.150194	−	0.128537i
$595$		0			0
$596$	51.4951	−	329.386i	0.0864012	−	0.552662i
$597$	557.226			0.933377
$598$	151.536	+	177.067i	0.253405	+	0.296099i
$599$		−	417.051i		−	0.696246i	−0.937449	−	0.348123i	$-0.886819\pi$
$599$		−	417.051i		−	0.696246i	0.937449	−	0.348123i	$-0.113181\pi$
$600$	435.151	−	268.459i	0.725252	−	0.447431i
$601$	−421.432			−0.701218			−0.350609	−	0.936522i	$-0.614025\pi$
$601$	−421.432			−0.701218			−0.350609	+	0.936522i	$0.614025\pi$
$602$		0			0
$603$			150.905i			0.250256i
$604$	661.509	+	103.418i	1.09521	+	0.171222i
$605$	52.5109			0.0867949
$606$	−103.222	−	120.613i	−0.170333	−	0.199032i
$607$		−	73.9674i		−	0.121857i	−0.998142	−	0.0609287i	$-0.980594\pi$
$607$		−	73.9674i		−	0.121857i	0.998142	−	0.0609287i	$-0.0194062\pi$
$608$	−16.5979	−	39.5114i	−0.0272992	−	0.0649858i
$609$		0			0
$610$	7.19192	−	6.15492i	0.0117900	−	0.0100900i
$611$			8.39557i			0.0137407i
$612$	48.0763	−	307.518i	0.0785560	−	0.502480i
$613$	−43.3126			−0.0706568			−0.0353284	−	0.999376i	$-0.511248\pi$
$613$	−43.3126			−0.0706568			−0.0353284	+	0.999376i	$0.511248\pi$
$614$	−75.2199	−	87.8932i	−0.122508	−	0.143149i
$615$			1057.72i			1.71987i
$616$		0			0
$617$	97.1444			0.157446			0.0787231	−	0.996897i	$-0.474916\pi$
$617$	97.1444			0.157446			0.0787231	+	0.996897i	$0.474916\pi$
$618$	77.8387	−	66.6152i	0.125953	−	0.107792i
$619$			802.809i			1.29695i	0.761238	+	0.648473i	$0.224592\pi$
$619$			802.809i			1.29695i	−0.761238	+	0.648473i	$0.775408\pi$
$620$	−1149.70	−	179.741i	−1.85436	−	0.289904i
$621$	57.3968			0.0924263
$622$	175.342	+	204.884i	0.281900	+	0.329395i
$623$		0			0
$624$	−89.2303	+	278.404i	−0.142997	+	0.446160i
$625$	−185.899			−0.297438
$626$	−185.553	+	158.798i	−0.296411	+	0.253671i
$627$		−	26.2104i		−	0.0418029i
$628$	−52.4319	+	335.379i	−0.0834903	+	0.534042i
$629$	−628.944			−0.999912
$630$		0			0
$631$		−	810.549i		−	1.28455i	−0.766475	−	0.642274i	$-0.777991\pi$
$631$		−	810.549i		−	1.28455i	0.766475	−	0.642274i	$-0.222009\pi$
$632$	227.540	−	140.377i	0.360032	−	0.222115i
$633$	−259.536			−0.410010
$634$	−688.530	+	589.251i	−1.08601	+	0.929417i
$635$		−	1530.91i		−	2.41088i
$636$	−509.586	−	79.6670i	−0.801236	−	0.125263i
$637$		0			0
$638$	300.073	+	350.630i	0.470333	+	0.549576i
$639$			304.949i			0.477228i
$640$	241.937	+	977.565i	0.378026	+	1.52745i
$641$	−622.415			−0.971006			−0.485503	−	0.874235i	$-0.661364\pi$
$641$	−622.415			−0.971006			−0.485503	+	0.874235i	$0.661364\pi$
$642$	−528.871	+	452.613i	−0.823787	+	0.705005i
$643$		−	867.679i		−	1.34942i	−0.738081	−	0.674712i	$-0.764268\pi$
$643$		−	867.679i		−	1.34942i	0.738081	−	0.674712i	$-0.235732\pi$
$644$		0			0
$645$	1059.17			1.64213
$646$	−45.1727	−	52.7836i	−0.0699268	−	0.0817083i
$647$		−	58.1580i		−	0.0898887i	−0.998989	−	0.0449443i	$-0.985689\pi$
$647$		−	58.1580i		−	0.0898887i	0.998989	−	0.0449443i	$-0.0143110\pi$
$648$	37.8038	+	61.2770i	0.0583391	+	0.0945633i
$649$	730.334			1.12532
$650$	−591.503	+	506.215i	−0.910005	+	0.778792i
$651$		0			0
$652$	−500.383	−	78.2281i	−0.767458	−	0.119982i
$653$	513.368			0.786169			0.393085	−	0.919502i	$-0.371408\pi$
$653$	513.368			0.786169			0.393085	+	0.919502i	$0.371408\pi$
$654$	−8.66560	−	10.1256i	−0.0132502	−	0.0154826i
$655$			340.107i			0.519247i
$656$	−1182.64	−	379.043i	−1.80280	−	0.577809i
$657$	−300.549			−0.457457
$658$		0			0
$659$		−	283.158i		−	0.429679i	−0.976649	−	0.214839i	$-0.931077\pi$
$659$		−	283.158i		−	0.429679i	0.976649	−	0.214839i	$-0.0689228\pi$
$660$	−95.1336	+	608.518i	−0.144142	+	0.921997i
$661$	−726.368			−1.09889			−0.549446	−	0.835529i	$-0.685161\pi$
$661$	−726.368			−1.09889			−0.549446	+	0.835529i	$0.685161\pi$
$662$	72.0748	+	84.2182i	0.108874	+	0.127218i
$663$			473.938i			0.714839i
$664$	−400.060	+	246.810i	−0.602500	+	0.371701i
$665$		0			0
$666$	110.536	−	94.5982i	0.165971	−	0.142039i
$667$			225.579i			0.338199i
$668$	−70.6379	−	11.0433i	−0.105745	−	0.0165319i
$669$	418.655			0.625792
$670$	−514.645	−	601.354i	−0.768127	−	0.897544i
$671$			6.79747i			0.0101304i
$672$		0			0
$673$	628.881			0.934444			0.467222	−	0.884140i	$-0.345255\pi$
$673$	628.881			0.934444			0.467222	+	0.884140i	$0.345255\pi$
$674$	−349.833	+	299.391i	−0.519041	+	0.444200i
$675$			191.737i			0.284055i
$676$	−35.6555	+	228.069i	−0.0527448	+	0.337380i
$677$	883.675			1.30528			0.652640	−	0.757668i	$-0.273661\pi$
$677$	883.675			1.30528			0.652640	+	0.757668i	$0.273661\pi$
$678$	151.985	+	177.592i	0.224166	+	0.261934i
$679$		0			0
$680$	857.175	+	1389.42i	1.26055	+	2.04326i
$681$	−673.015			−0.988275
$682$	634.864	−	543.323i	0.930886	−	0.796662i
$683$		−	115.751i		−	0.169474i	−0.996403	−	0.0847369i	$-0.972995\pi$
$683$		−	115.751i		−	0.169474i	0.996403	−	0.0847369i	$-0.0270050\pi$
$684$	15.8781	+	2.48233i	0.0232137	+	0.00362914i
$685$	505.952			0.738616
$686$		0			0
$687$			142.141i			0.206902i
$688$	−379.564	+	1184.26i	−0.551692	+	1.72131i
$689$	785.361			1.13986
$690$	−228.726	+	195.746i	−0.331487	+	0.283690i
$691$		−	301.211i		−	0.435906i	−0.975959	−	0.217953i	$-0.930062\pi$
$691$		−	301.211i		−	0.435906i	0.975959	−	0.217953i	$-0.0699380\pi$
$692$	−13.2195	+	84.5583i	−0.0191034	+	0.122194i
$693$		0			0
$694$	106.857	+	124.860i	0.153972	+	0.179914i
$695$			1510.60i			2.17353i
$696$	−240.829	+	148.575i	−0.346018	+	0.213470i
$697$	−2013.25			−2.88845
$698$	320.846	−	274.583i	0.459665	−	0.393386i
$699$		−	391.941i		−	0.560717i
$700$		0			0
$701$	−241.158			−0.344020			−0.172010	−	0.985095i	$-0.555026\pi$
$701$	−241.158			−0.344020			−0.172010	+	0.985095i	$0.555026\pi$
$702$	−71.2841	−	83.2942i	−0.101544	−	0.118653i
$703$		−	32.4744i		−	0.0461941i
$704$	−646.293	−	324.437i	−0.918030	−	0.460848i
$705$	−10.8449			−0.0153829
$706$	−110.857	+	94.8723i	−0.157021	+	0.134380i
$707$		0			0
$708$	−69.1684	+	442.433i	−0.0976955	+	0.624905i
$709$	720.401			1.01608			0.508040	−	0.861333i	$-0.330370\pi$
$709$	720.401			1.01608			0.508040	+	0.861333i	$0.330370\pi$
$710$	−1040.00	−	1215.22i	−1.46479	−	1.71158i
$711$			100.259i			0.141011i
$712$	226.672	+	367.418i	0.318359	+	0.516036i
$713$	408.442			0.572850
$714$		0			0
$715$		−	937.832i		−	1.31165i
$716$	−137.701	−	21.5277i	−0.192320	−	0.0300666i
$717$	302.140			0.421395
$718$	355.670	+	415.594i	0.495362	+	0.578822i
$719$			392.544i			0.545958i	0.962020	+	0.272979i	$0.0880089\pi$
$719$			392.544i			0.545958i	−0.962020	+	0.272979i	$0.911991\pi$
$720$	−359.627	−	115.263i	−0.499482	−	0.160087i
$721$		0			0
$722$	−545.819	+	467.117i	−0.755982	+	0.646977i
$723$		−	599.390i		−	0.829031i
$724$	28.1876	−	180.301i	0.0389332	−	0.249034i
$725$	−753.558			−1.03939
$726$	−15.0331	−	17.5659i	−0.0207067	−	0.0241954i
$727$			795.097i			1.09367i	0.837241	+	0.546835i	$0.184167\pi$
$727$			795.097i			1.09367i	−0.837241	+	0.546835i	$0.815833\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	1197.69	−	1024.99i	1.64067	−	1.40410i
$731$			2016.02i			2.75789i
$732$	−4.11787	−	0.643773i	−0.00562550	−	0.000879472i
$733$	1376.26			1.87757			0.938787	−	0.344499i	$-0.111951\pi$
$733$	1376.26			1.87757			0.938787	+	0.344499i	$0.111951\pi$
$734$	−237.465	−	277.474i	−0.323522	−	0.378030i
$735$		0			0
$736$	−136.898	−	325.886i	−0.186003	−	0.442780i
$737$	568.372			0.771197
$738$	353.827	−	302.809i	0.479440	−	0.410310i
$739$			723.760i			0.979378i	0.871897	+	0.489689i	$0.162890\pi$
$739$			723.760i			0.979378i	−0.871897	+	0.489689i	$0.837110\pi$
$740$	−117.869	+	753.947i	−0.159283	+	1.01885i
$741$	−24.4710			−0.0330242
$742$		0			0
$743$			863.433i			1.16209i	0.813871	+	0.581045i	$0.197356\pi$
$743$			863.433i			1.16209i	−0.813871	+	0.581045i	$0.802644\pi$
$744$	269.016	+	436.054i	0.361580	+	0.586095i
$745$	−655.743			−0.880192
$746$	361.136	−	309.064i	0.484096	−	0.414294i
$747$		−	176.275i		−	0.235977i
$748$	−1158.25	−	181.076i	−1.54846	−	0.242080i
$749$		0			0
$750$	−210.876	−	246.405i	−0.281168	−	0.328541i
$751$		−	316.065i		−	0.420859i	−0.977609	−	0.210429i	$-0.932514\pi$
$751$		−	316.065i		−	0.420859i	0.977609	−	0.210429i	$-0.0674862\pi$
$752$	3.88638	−	12.1257i	0.00516806	−	0.0161247i
$753$	−188.424			−0.250232
$754$	327.360	−	280.158i	0.434164	−	0.371562i
$755$		−	1316.93i		−	1.74428i
$756$		0			0
$757$	157.303			0.207798			0.103899	−	0.994588i	$-0.466868\pi$
$757$	157.303			0.207798			0.103899	+	0.994588i	$0.466868\pi$
$758$	−468.177	−	547.057i	−0.617647	−	0.721711i
$759$		−	216.181i		−	0.284824i
$760$	−71.7401	+	44.2587i	−0.0943948	+	0.0582352i
$761$	771.962			1.01440			0.507202	−	0.861827i	$-0.330680\pi$
$761$	771.962			1.01440			0.507202	+	0.861827i	$0.330680\pi$
$762$	−512.118	+	438.276i	−0.672071	+	0.575165i
$763$		0			0
$764$	−111.941	−	17.5005i	−0.146520	−	0.0229064i
$765$	−612.207			−0.800271
$766$	413.120	+	482.724i	0.539321	+	0.630188i
$767$		−	681.865i		−	0.889003i
$768$	257.751	−	360.794i	0.335613	−	0.469784i
$769$	351.638			0.457267			0.228634	−	0.973513i	$-0.426574\pi$
$769$	351.638			0.457267			0.228634	+	0.973513i	$0.426574\pi$
$770$		0			0
$771$		−	627.322i		−	0.813647i
$772$	−75.6817	+	484.095i	−0.0980333	+	0.627066i
$773$	−1463.97			−1.89389			−0.946943	−	0.321402i	$-0.895846\pi$
$773$	−1463.97			−1.89389			−0.946943	+	0.321402i	$0.895846\pi$
$774$	−303.225	−	354.313i	−0.391763	−	0.457769i
$775$			1364.42i			1.76055i
$776$	168.002	+	272.318i	0.216497	+	0.350925i
$777$		0			0
$778$	377.674	−	323.217i	0.485442	−	0.415447i
$779$		−	103.951i		−	0.133441i
$780$	568.133	+	88.8200i	0.728376	+	0.113872i
$781$	1148.57			1.47064
$782$	−372.580	−	435.354i	−0.476445	−	0.556719i
$783$		−	106.114i		−	0.135523i
$784$		0			0
$785$	667.673			0.850538
$786$	113.772	−	97.3673i	0.144748	−	0.123877i
$787$		−	244.329i		−	0.310457i	−0.987879	−	0.155228i	$-0.950389\pi$
$787$		−	244.329i		−	0.310457i	0.987879	−	0.155228i	$-0.0496113\pi$
$788$	81.1730	−	519.220i	0.103011	−	0.658908i
$789$	454.618			0.576195
$790$	−341.924	−	399.532i	−0.432815	−	0.505737i
$791$		0			0
$792$	230.796	−	142.385i	0.291409	−	0.179780i
$793$	6.34635			0.00800296
$794$	541.958	−	463.814i	0.682567	−	0.584148i
$795$			1014.49i			1.27608i
$796$	1271.41	+	198.769i	1.59725	+	0.249709i
$797$	−899.678			−1.12883			−0.564415	−	0.825491i	$-0.690898\pi$
$797$	−899.678			−1.12883			−0.564415	+	0.825491i	$0.690898\pi$
$798$		0			0
$799$		−	20.6421i		−	0.0258350i
$800$	1088.64	−	457.315i	1.36080	−	0.571644i
$801$	−161.892			−0.202113
$802$	465.338	−	398.241i	0.580222	−	0.496560i
$803$			1132.00i			1.40971i
$804$	−53.8293	+	344.317i	−0.0669519	+	0.428255i
$805$		0			0
$806$	−507.265	−	592.731i	−0.629361	−	0.735398i
$807$		−	79.5908i		−	0.0986255i
$808$	−192.496	−	312.022i	−0.238238	−	0.386166i
$809$	495.399			0.612359			0.306180	−	0.951974i	$-0.400949\pi$
$809$	495.399			0.612359			0.306180	+	0.951974i	$0.400949\pi$
$810$	107.595	−	92.0808i	0.132833	−	0.113680i
$811$			85.3185i			0.105202i	0.998616	+	0.0526008i	$0.0167511\pi$
$811$			85.3185i			0.105202i	−0.998616	+	0.0526008i	$0.983249\pi$
$812$		0			0
$813$	−45.4084			−0.0558529
$814$	−356.298	−	416.328i	−0.437713	−	0.511460i
$815$			996.163i			1.22229i
$816$	219.390	−	684.510i	0.268860	−	0.838860i
$817$	−104.093			−0.127409
$818$	−415.355	+	355.465i	−0.507769	+	0.434554i
$819$		0			0
$820$	−377.300	+	2413.38i	−0.460122	+	2.94315i
$821$	784.090			0.955043			0.477521	−	0.878620i	$-0.341535\pi$
$821$	784.090			0.955043			0.477521	+	0.878620i	$0.341535\pi$
$822$	−144.846	−	169.251i	−0.176212	−	0.205901i
$823$		−	1126.19i		−	1.36840i	−0.729295	−	0.684199i	$-0.760152\pi$
$823$		−	1126.19i		−	1.36840i	0.729295	−	0.684199i	$-0.239848\pi$
$824$	201.366	−	124.229i	0.244376	−	0.150763i
$825$	722.165			0.875352
$826$		0			0
$827$		−	1145.25i		−	1.38482i	−0.721502	−	0.692412i	$-0.756548\pi$
$827$		−	1145.25i		−	1.38482i	0.721502	−	0.692412i	$-0.243452\pi$
$828$	130.961	+	20.4740i	0.158166	+	0.0247271i
$829$	−984.596			−1.18769			−0.593846	−	0.804579i	$-0.702391\pi$
$829$	−984.596			−1.18769			−0.593846	+	0.804579i	$0.702391\pi$
$830$	601.168	+	702.455i	0.724299	+	0.846332i
$831$		−	918.066i		−	1.10477i
$832$	−302.905	+	603.401i	−0.364069	+	0.725242i
$833$		0			0
$834$	505.325	−	432.462i	0.605905	−	0.518539i
$835$			140.626i			0.168415i
$836$	9.34954	−	59.8040i	0.0111837	−	0.0715358i
$837$	−192.135			−0.229552
$838$	577.398	+	674.680i	0.689019	+	0.805107i
$839$			10.8022i			0.0128751i	0.999979	+	0.00643757i	$0.00204916\pi$
$839$			10.8022i			0.0128751i	−0.999979	+	0.00643757i	$0.997951\pi$
$840$		0			0
$841$	−423.953			−0.504106
$842$	988.399	−	845.882i	1.17387	−	1.00461i
$843$			465.876i			0.552640i
$844$	−592.180	−	92.5794i	−0.701635	−	0.109691i
$845$	454.040			0.537325
$846$	3.10474	+	3.62784i	0.00366990	+	0.00428822i
$847$		0			0
$848$	−1134.30	−	363.550i	−1.33762	−	0.428715i
$849$	−101.545			−0.119606
$850$	1454.32	−	1244.63i	1.71097	−	1.46427i
$851$		−	267.846i		−	0.314743i
$852$	−108.779	+	695.797i	−0.127674	+	0.816663i
$853$	1051.79			1.23305			0.616523	−	0.787337i	$-0.288541\pi$
$853$	1051.79			1.23305			0.616523	+	0.787337i	$0.288541\pi$
$854$		0			0
$855$		−	31.6102i		−	0.0369710i
$856$	−1368.17	+	844.067i	−1.59833	+	0.986060i
$857$	636.379			0.742566			0.371283	−	0.928520i	$-0.378918\pi$
$857$	636.379			0.742566			0.371283	+	0.928520i	$0.378918\pi$
$858$	−313.722	+	268.487i	−0.365644	+	0.312922i
$859$		−	1488.92i		−	1.73332i	−0.498896	−	0.866662i	$-0.666261\pi$
$859$		−	1488.92i		−	1.73332i	0.498896	−	0.866662i	$-0.333739\pi$
$860$	2416.70	+	377.818i	2.81011	+	0.439324i
$861$		0			0
$862$	812.724	+	949.654i	0.942835	+	1.10169i
$863$		−	567.795i		−	0.657932i	−0.944342	−	0.328966i	$-0.893300\pi$
$863$		−	567.795i		−	0.657932i	0.944342	−	0.328966i	$-0.106700\pi$
$864$	64.3981	+	153.300i	0.0745348	+	0.177431i
$865$	168.339			0.194611
$866$	−668.923	+	572.471i	−0.772428	+	0.661052i
$867$		−	664.705i		−	0.766673i
$868$		0			0
$869$	377.620			0.434545
$870$	361.893	+	422.866i	0.415969	+	0.486052i
$871$		−	530.652i		−	0.609245i
$872$	−16.1603	−	26.1946i	−0.0185324	−	0.0300397i
$873$	−119.989			−0.137445
$874$	22.4787	−	19.2375i	0.0257194	−	0.0220109i
$875$		0			0
$876$	−685.759	−	107.209i	−0.782830	−	0.122385i
$877$	−582.167			−0.663816			−0.331908	−	0.943312i	$-0.607692\pi$
$877$	−582.167			−0.663816			−0.331908	+	0.943312i	$0.607692\pi$
$878$	−669.683	−	782.514i	−0.762737	−	0.891246i
$879$		−	349.877i		−	0.398040i
$880$	−434.130	+	1354.51i	−0.493330	+	1.53922i
$881$	124.121			0.140886			0.0704431	−	0.997516i	$-0.477559\pi$
$881$	124.121			0.140886			0.0704431	+	0.997516i	$0.477559\pi$
$882$		0			0
$883$			486.901i			0.551417i	0.961241	+	0.275708i	$0.0889124\pi$
$883$			486.901i			0.551417i	−0.961241	+	0.275708i	$0.911088\pi$
$884$	−169.059	+	1081.38i	−0.191243	+	1.22328i
$885$	880.796			0.995250
$886$	594.734	+	694.937i	0.671258	+	0.784354i
$887$		−	1079.54i		−	1.21707i	−0.793525	−	0.608537i	$-0.791757\pi$
$887$		−	1079.54i		−	1.21707i	0.793525	−	0.608537i	$-0.208243\pi$
$888$	285.954	−	176.414i	0.322020	−	0.198664i
$889$		0			0
$890$	645.140	−	552.117i	0.724876	−	0.620356i
$891$			101.694i			0.114134i
$892$	955.238	+	149.339i	1.07090	+	0.167420i
$893$	1.06582			0.00119353
$894$	187.729	+	219.358i	0.209988	+	0.245367i
$895$			274.136i			0.306297i
$896$		0			0
$897$	−201.834			−0.225010
$898$	287.119	−	245.720i	0.319732	−	0.273630i
$899$		−	755.122i		−	0.839958i
$900$	−68.3947	+	437.484i	−0.0759941	+	0.486093i
$901$	−1930.96			−2.14313
$902$	−1140.51	−	1332.67i	−1.26442	−	1.47746i
$903$		0			0
$904$	283.432	+	459.423i	0.313531	+	0.508211i
$905$	−358.944			−0.396623
$906$	−440.539	+	377.018i	−0.486246	+	0.416135i
$907$		−	106.065i		−	0.116941i	−0.998289	−	0.0584704i	$-0.981378\pi$
$907$		−	106.065i		−	0.116941i	0.998289	−	0.0584704i	$-0.0186223\pi$
$908$	−1535.61	−	240.072i	−1.69120	−	0.264396i
$909$	137.484			0.151247
$910$		0			0
$911$			1291.42i			1.41758i	0.705419	+	0.708791i	$0.250759\pi$
$911$			1291.42i			1.41758i	−0.705419	+	0.708791i	$0.749241\pi$
$912$	35.3434	+	11.3278i	0.0387538	+	0.0124208i
$913$	−663.928			−0.727194
$914$	−1199.67	+	1026.69i	−1.31255	+	1.12329i
$915$			8.19786i			0.00895941i
$916$	−50.7034	+	324.322i	−0.0553530	+	0.354063i
$917$		0			0
$918$	175.265	+	204.795i	0.190921	+	0.223088i
$919$		−	1116.74i		−	1.21516i	−0.794257	−	0.607582i	$-0.792139\pi$
$919$		−	1116.74i		−	1.21516i	0.794257	−	0.607582i	$-0.207861\pi$
$920$	−591.705	+	365.042i	−0.643158	+	0.396785i
$921$	100.187			0.108781
$922$	−545.927	+	467.210i	−0.592112	+	0.506736i
$923$		−	1072.34i		−	1.16180i
$924$		0			0
$925$	894.755			0.967302
$926$	−1125.54	−	1315.18i	−1.21549	−	1.42028i
$927$			88.7262i			0.0957132i
$928$	−602.494	+	253.095i	−0.649239	+	0.272732i
$929$	−545.423			−0.587108			−0.293554	−	0.955942i	$-0.594838\pi$
$929$	−545.423			−0.587108			−0.293554	+	0.955942i	$0.594838\pi$
$930$	765.657	−	655.257i	0.823288	−	0.704578i
$931$		0			0
$932$	139.810	−	894.287i	0.150010	−	0.959535i
$933$	−233.542			−0.250312
$934$	671.803	+	784.990i	0.719275	+	0.840461i
$935$			2305.84i			2.46614i
$936$	−132.936	−	215.479i	−0.142026	−	0.230213i
$937$	−1292.02			−1.37889			−0.689443	−	0.724340i	$-0.742145\pi$
$937$	−1292.02			−1.37889			−0.689443	+	0.724340i	$0.742145\pi$
$938$		0			0
$939$		−	211.507i		−	0.225247i
$940$	−24.7448	−	3.86851i	−0.0263242	−	0.00411543i
$941$	−483.449			−0.513761			−0.256880	−	0.966443i	$-0.582695\pi$
$941$	−483.449			−0.513761			−0.256880	+	0.966443i	$0.582695\pi$
$942$	−191.144	−	223.349i	−0.202913	−	0.237101i
$943$		−	857.374i		−	0.909199i
$944$	−315.641	+	984.819i	−0.334366	+	1.04324i
$945$		0			0
$946$	−1334.50	+	1142.08i	−1.41067	+	1.20727i
$947$			1852.46i			1.95613i	0.208297	+	0.978066i	$0.433208\pi$
$947$			1852.46i			1.95613i	−0.208297	+	0.978066i	$0.566792\pi$
$948$	−35.7635	+	228.760i	−0.0377252	+	0.241308i
$949$	1056.87			1.11367
$950$	64.2640	+	75.0915i	0.0676464	+	0.0790436i
$951$		−	784.836i		−	0.825274i
$952$		0			0
$953$	1129.36			1.18506			0.592530	−	0.805549i	$-0.298129\pi$
$953$	1129.36			1.18506			0.592530	+	0.805549i	$0.298129\pi$
$954$	339.365	−	290.432i	0.355728	−	0.304436i
$955$			222.853i			0.233354i
$956$	689.390	+	107.777i	0.721119	+	0.112737i
$957$	−399.673			−0.417631
$958$	933.101	+	1090.31i	0.974009	+	1.13811i
$959$		0			0
$960$	−779.441	−	391.277i	−0.811917	−	0.407580i
$961$	−406.254			−0.422741
$962$	−388.698	+	332.652i	−0.404052	+	0.345792i
$963$		−	602.845i		−	0.626008i
$964$	213.809	−	1367.62i	0.221793	−	1.41869i
$965$	963.737			0.998692
$966$		0			0
$967$		−	1112.25i		−	1.15021i	−0.818080	−	0.575104i	$-0.804961\pi$
$967$		−	1112.25i		−	1.15021i	0.818080	−	0.575104i	$-0.195039\pi$
$968$	−28.0348	−	45.4423i	−0.0289616	−	0.0469445i
$969$	60.1665			0.0620914
$970$	478.157	−	409.211i	0.492945	−	0.421867i
$971$		−	181.497i		−	0.186917i	−0.995623	−	0.0934587i	$-0.970208\pi$
$971$		−	181.497i		−	0.186917i	0.995623	−	0.0934587i	$-0.0297923\pi$
$972$	−61.6055	−	9.63119i	−0.0633802	−	0.00990863i
$973$		0			0
$974$	−1171.91	−	1369.36i	−1.20319	−	1.40591i
$975$		−	674.238i		−	0.691526i
$976$	−9.16604	−	2.93778i	−0.00939144	−	0.00301002i
$977$	464.768			0.475710			0.237855	−	0.971301i	$-0.423556\pi$
$977$	464.768			0.475710			0.237855	+	0.971301i	$0.423556\pi$
$978$	333.235	−	285.186i	0.340731	−	0.291601i
$979$			609.756i			0.622836i
$980$		0			0
$981$	11.5419			0.0117654
$982$	−617.752	−	721.833i	−0.629075	−	0.735064i
$983$		−	638.900i		−	0.649950i	−0.945723	−	0.324975i	$-0.894644\pi$
$983$		−	638.900i		−	0.649950i	0.945723	−	0.324975i	$-0.105356\pi$
$984$	915.337	−	564.700i	0.930221	−	0.573883i
$985$	−1033.66			−1.04941
$986$	−804.877	+	688.822i	−0.816306	+	0.698603i
$987$		0			0
$988$	−55.8350	−	8.72906i	−0.0565132	−	0.00883508i
$989$	−858.552			−0.868101
$990$	−346.816	−	405.249i	−0.350320	−	0.409343i
$991$		−	562.410i		−	0.567518i	−0.958896	−	0.283759i	$-0.908418\pi$
$991$		−	562.410i		−	0.567518i	0.958896	−	0.283759i	$-0.0915816\pi$
$992$	458.264	+	1090.90i	0.461960	+	1.09970i
$993$	−95.9980			−0.0966748
$994$		0			0
$995$		−	2531.14i		−	2.54386i
$996$	62.8792	−	402.204i	0.0631317	−	0.403820i
$997$	116.774			0.117125			0.0585625	−	0.998284i	$-0.481348\pi$
$997$	116.774			0.117125			0.0585625	+	0.998284i	$0.481348\pi$
$998$	59.3565	+	69.3571i	0.0594755	+	0.0694961i
$999$			125.997i			0.126124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.d.295.4		12
4.3	odd	2	inner	588.3.g.d.295.3		12
7.6	odd	2		84.3.g.a.43.4	yes	12
21.20	even	2		252.3.g.b.127.9		12
28.27	even	2		84.3.g.a.43.3	✓	12
56.13	odd	2		1344.3.m.e.127.2		12
56.27	even	2		1344.3.m.e.127.8		12
84.83	odd	2		252.3.g.b.127.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.g.a.43.3	✓	12	28.27	even	2
84.3.g.a.43.4	yes	12	7.6	odd	2
252.3.g.b.127.9		12	21.20	even	2
252.3.g.b.127.10		12	84.83	odd	2
588.3.g.d.295.3		12	4.3	odd	2	inner
588.3.g.d.295.4		12	1.1	even	1	trivial
1344.3.m.e.127.2		12	56.13	odd	2
1344.3.m.e.127.8		12	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51951 + 1.30042i) q^{2} -1.73205i q^{3} +(0.617841 - 3.95200i) q^{4} -7.86764 q^{5} +(2.25238 + 2.63187i) q^{6} +(4.20042 + 6.80856i) q^{8} -3.00000 q^{9} +(11.9550 - 10.2312i) q^{10} +11.2993i q^{11} +(-6.84506 - 1.07013i) q^{12} +10.5494 q^{13} +13.6272i q^{15} +(-15.2365 - 4.88341i) q^{16} -25.9378 q^{17} +(4.55854 - 3.90125i) q^{18} -1.33925i q^{19} +(-4.86096 + 31.0929i) q^{20} +(-14.6938 - 17.1694i) q^{22} -11.0460i q^{23} +(11.7928 - 7.27534i) q^{24} +36.8998 q^{25} +(-16.0300 + 13.7186i) q^{26} +5.19615i q^{27} -20.4217 q^{29} +(-17.7210 - 20.7066i) q^{30} +36.9764i q^{31} +(29.5026 - 12.3934i) q^{32} +19.5710 q^{33} +(39.4128 - 33.7299i) q^{34} +(-1.85352 + 11.8560i) q^{36} +24.2482 q^{37} +(1.74158 + 2.03501i) q^{38} -18.2721i q^{39} +(-33.0474 - 53.5673i) q^{40} +77.6185 q^{41} -77.7251i q^{43} +(44.6548 + 6.98118i) q^{44} +23.6029 q^{45} +(14.3644 + 16.7846i) q^{46} +0.795833i q^{47} +(-8.45832 + 26.3905i) q^{48} +(-56.0698 + 47.9851i) q^{50} +44.9255i q^{51} +(6.51787 - 41.6913i) q^{52} +74.4459 q^{53} +(-6.75715 - 7.89562i) q^{54} -88.8989i q^{55} -2.31965 q^{57} +(31.0311 - 26.5567i) q^{58} -64.6353i q^{59} +(53.8545 + 8.41942i) q^{60} +0.601583 q^{61} +(-48.0847 - 56.1861i) q^{62} +(-28.7130 + 57.1976i) q^{64} -82.9991 q^{65} +(-29.7383 + 25.4504i) q^{66} -50.3015i q^{67} +(-16.0254 + 102.506i) q^{68} -19.1323 q^{69} -101.650i q^{71} +(-12.6013 - 20.4257i) q^{72} +100.183 q^{73} +(-36.8455 + 31.5327i) q^{74} -63.9124i q^{75} +(-5.29271 - 0.827444i) q^{76} +(23.7614 + 27.7647i) q^{78} -33.4197i q^{79} +(119.876 + 38.4210i) q^{80} +9.00000 q^{81} +(-117.942 + 100.936i) q^{82} +58.7583i q^{83} +204.069 q^{85} +(101.075 + 118.104i) q^{86} +35.3715i q^{87} +(-76.9320 + 47.4618i) q^{88} +53.9641 q^{89} +(-35.8650 + 30.6936i) q^{90} +(-43.6538 - 6.82468i) q^{92} +64.0450 q^{93} +(-1.03491 - 1.20928i) q^{94} +10.5367i q^{95} +(-21.4660 - 51.1000i) q^{96} +39.9964 q^{97} -33.8979i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{4} - 8 q^{5} + 12 q^{6} - 10 q^{8} - 36 q^{9} - 28 q^{10} - 24 q^{12} + 24 q^{13} - 14 q^{16} + 40 q^{17} - 6 q^{18} + 20 q^{20} - 88 q^{22} + 36 q^{24} + 180 q^{25} - 100 q^{26} + 72 q^{29}+ \cdots + 264 q^{97}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^4 - 8 * q^5 + 12 * q^6 - 10 * q^8 - 36 * q^9 - 28 * q^10 - 24 * q^12 + 24 * q^13 - 14 * q^16 + 40 * q^17 - 6 * q^18 + 20 * q^20 - 88 * q^22 + 36 * q^24 + 180 * q^25 - 100 * q^26 + 72 * q^29 + 72 * q^30 + 142 * q^32 + 100 * q^34 - 6 * q^36 - 88 * q^37 - 128 * q^38 + 28 * q^40 + 200 * q^41 - 40 * q^44 + 24 * q^45 - 24 * q^46 - 48 * q^48 - 346 * q^50 + 364 * q^52 + 104 * q^53 - 36 * q^54 + 148 * q^58 + 96 * q^60 - 104 * q^61 - 64 * q^62 - 70 * q^64 + 176 * q^65 - 24 * q^66 - 188 * q^68 + 192 * q^69 + 30 * q^72 - 312 * q^73 + 4 * q^74 - 432 * q^76 + 48 * q^78 + 564 * q^80 + 108 * q^81 - 332 * q^82 + 352 * q^85 + 160 * q^86 + 328 * q^88 + 552 * q^89 + 84 * q^90 + 232 * q^92 - 48 * q^93 + 144 * q^94 + 108 * q^96 + 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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