LMFDB - Embedded newform 588.3.p.f.569.4

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1090537426944.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 4x^{6} - 44x^{5} + 71x^{4} + 196x^{3} + 28x^{2} + 294x + 441 $ x^8 - 2x^7 - 4x^6 - 44x^5 + 71x^4 + 196x^3 + 28x^2 + 294*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.4
Root			$-1.68211 - 3.07604i$ of defining polynomial
Character	$\chi$	$=$	588.569
Dual form			588.3.p.f.557.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50498 - 1.65078i) q^{3} +(-3.34957 - 1.93387i) q^{5} +(3.54987 - 8.27034i) q^{9} +O(q^{10})$	\(q+(2.50498 - 1.65078i) q^{3} +(-3.34957 - 1.93387i) q^{5} +(3.54987 - 8.27034i) q^{9} +(12.2117 - 7.05043i) q^{11} +20.2288 q^{13} +(-11.5830 + 0.685072i) q^{15} +(-18.9108 + 10.9182i) q^{17} +(-3.46863 + 6.00784i) q^{19} +(-6.69914 - 3.86775i) q^{23} +(-5.02026 - 8.69534i) q^{25} +(-4.76013 - 26.5771i) q^{27} -37.3073i q^{29} +(-7.64575 - 13.2428i) q^{31} +(18.9514 - 37.8200i) q^{33} +(6.06275 - 10.5010i) q^{37} +(50.6727 - 33.3932i) q^{39} -42.3026i q^{41} +16.1255 q^{43} +(-27.8843 + 20.8371i) q^{45} +(-62.2451 - 35.9372i) q^{47} +(-29.3478 + 58.5674i) q^{51} +(87.8550 - 50.7231i) q^{53} -54.5385 q^{55} +(1.22876 + 20.7755i) q^{57} +(-22.2604 + 12.8520i) q^{59} +(-39.0516 + 67.6394i) q^{61} +(-67.7576 - 39.1199i) q^{65} +(61.5830 + 106.665i) q^{67} +(-23.1660 + 1.37014i) q^{69} -34.5671i q^{71} +(50.2693 + 87.0689i) q^{73} +(-26.9297 - 13.4943i) q^{75} +(21.2915 - 36.8780i) q^{79} +(-55.7969 - 58.7172i) q^{81} -82.1075i q^{83} +84.4575 q^{85} +(-61.5861 - 93.4542i) q^{87} +(36.6351 + 21.1513i) q^{89} +(-41.0134 - 20.5516i) q^{93} +(23.2368 - 13.4158i) q^{95} +48.3320 q^{97} +(-14.9595 - 126.023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} + 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 + 4 * q^9	$ 8 q - 6 q^{3} + 4 q^{9} + 56 q^{13} - 8 q^{15} + 4 q^{19} + 108 q^{25} + 36 q^{27} - 40 q^{31} + 116 q^{33} + 112 q^{37} + 28 q^{39} + 256 q^{43} - 100 q^{45} - 124 q^{51} + 368 q^{55} - 96 q^{57} - 196 q^{61} + 408 q^{67} - 16 q^{69} + 358 q^{75} + 128 q^{79} - 188 q^{81} + 464 q^{85} - 140 q^{87} - 32 q^{93} + 48 q^{97} - 416 q^{99}+O(q^{100}) $ 8 * q - 6 * q^3 + 4 * q^9 + 56 * q^13 - 8 * q^15 + 4 * q^19 + 108 * q^25 + 36 * q^27 - 40 * q^31 + 116 * q^33 + 112 * q^37 + 28 * q^39 + 256 * q^43 - 100 * q^45 - 124 * q^51 + 368 * q^55 - 96 * q^57 - 196 * q^61 + 408 * q^67 - 16 * q^69 + 358 * q^75 + 128 * q^79 - 188 * q^81 + 464 * q^85 - 140 * q^87 - 32 * q^93 + 48 * q^97 - 416 * 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
$3$	2.50498	−	1.65078i	0.834994	−	0.550259i
$3$	2.50498	−	1.65078i	0.834994	−	0.550259i
$4$		0			0
$5$	−3.34957	−	1.93387i	−0.669914	−	0.386775i	0.126130	−	0.992014i	$-0.459744\pi$
$5$	−3.34957	−	1.93387i	−0.669914	−	0.386775i	−0.796044	+	0.605239i	$0.793078\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	3.54987	−	8.27034i	0.394430	−	0.918926i
$10$		0			0
$11$	12.2117	−	7.05043i	1.11015	−	0.640948i	0.171285	−	0.985222i	$-0.445208\pi$
$11$	12.2117	−	7.05043i	1.11015	−	0.640948i	0.938869	+	0.344274i	$0.111875\pi$
$12$		0			0
$13$	20.2288			1.55606			0.778029	−	0.628228i	$-0.216220\pi$
$13$	20.2288			1.55606			0.778029	+	0.628228i	$0.216220\pi$
$14$		0			0
$15$	−11.5830	+	0.685072i	−0.772200	+	0.0456715i
$16$		0			0
$17$	−18.9108	+	10.9182i	−1.11240	+	0.642246i	−0.939450	−	0.342685i	$-0.888664\pi$
$17$	−18.9108	+	10.9182i	−1.11240	+	0.642246i	−0.172951	+	0.984930i	$0.555330\pi$
$18$		0			0
$19$	−3.46863	+	6.00784i	−0.182559	+	0.316202i	−0.942751	−	0.333496i	$-0.891771\pi$
$19$	−3.46863	+	6.00784i	−0.182559	+	0.316202i	0.760192	+	0.649698i	$0.225105\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.69914	−	3.86775i	−0.291267	−	0.168163i	0.347246	−	0.937774i	$-0.387117\pi$
$23$	−6.69914	−	3.86775i	−0.291267	−	0.168163i	−0.638513	+	0.769611i	$0.720450\pi$
$24$		0			0
$25$	−5.02026	−	8.69534i	−0.200810	−	0.347814i
$26$		0			0
$27$	−4.76013	−	26.5771i	−0.176301	−	0.984336i
$28$		0			0
$29$		−	37.3073i		−	1.28646i	−0.765673	−	0.643230i	$-0.777594\pi$
$29$		−	37.3073i		−	1.28646i	0.765673	−	0.643230i	$-0.222406\pi$
$30$		0			0
$31$	−7.64575	−	13.2428i	−0.246637	−	0.427188i	0.715953	−	0.698148i	$-0.245992\pi$
$31$	−7.64575	−	13.2428i	−0.246637	−	0.427188i	−0.962591	+	0.270960i	$0.912659\pi$
$32$		0			0
$33$	18.9514	−	37.8200i	0.574285	−	1.14606i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.06275	−	10.5010i	0.163858	−	0.283810i	−0.772391	−	0.635147i	$-0.780939\pi$
$37$	6.06275	−	10.5010i	0.163858	−	0.283810i	0.936249	+	0.351337i	$0.114273\pi$
$38$		0			0
$39$	50.6727	−	33.3932i	1.29930	−	0.856235i
$40$		0			0
$41$		−	42.3026i		−	1.03177i	−0.856658	−	0.515885i	$-0.827463\pi$
$41$		−	42.3026i		−	1.03177i	0.856658	−	0.515885i	$-0.172537\pi$
$42$		0			0
$43$	16.1255			0.375011			0.187506	−	0.982264i	$-0.439960\pi$
$43$	16.1255			0.375011			0.187506	+	0.982264i	$0.439960\pi$
$44$		0			0
$45$	−27.8843	+	20.8371i	−0.619651	+	0.463046i
$46$		0			0
$47$	−62.2451	−	35.9372i	−1.32436	−	0.764621i	−0.339941	−	0.940447i	$-0.610407\pi$
$47$	−62.2451	−	35.9372i	−1.32436	−	0.764621i	−0.984421	+	0.175825i	$0.943741\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−29.3478	+	58.5674i	−0.575447	+	1.14838i
$52$		0			0
$53$	87.8550	−	50.7231i	1.65764	−	0.957040i	0.683843	−	0.729629i	$-0.260307\pi$
$53$	87.8550	−	50.7231i	1.65764	−	0.957040i	0.973799	−	0.227411i	$-0.0730261\pi$
$54$		0			0
$55$	−54.5385			−0.991610
$56$		0			0
$57$	1.22876	+	20.7755i	0.0215571	+	0.364482i
$58$		0			0
$59$	−22.2604	+	12.8520i	−0.377295	+	0.217831i	−0.676641	−	0.736313i	$-0.736565\pi$
$59$	−22.2604	+	12.8520i	−0.377295	+	0.217831i	0.299346	+	0.954145i	$0.403232\pi$
$60$		0			0
$61$	−39.0516	+	67.6394i	−0.640191	+	1.10884i	0.345199	+	0.938529i	$0.387811\pi$
$61$	−39.0516	+	67.6394i	−0.640191	+	1.10884i	−0.985390	+	0.170313i	$0.945522\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−67.7576	−	39.1199i	−1.04242	−	0.601844i
$66$		0			0
$67$	61.5830	+	106.665i	0.919149	+	1.59201i	0.800710	+	0.599052i	$0.204456\pi$
$67$	61.5830	+	106.665i	0.919149	+	1.59201i	0.118439	+	0.992961i	$0.462211\pi$
$68$		0			0
$69$	−23.1660	+	1.37014i	−0.335739	+	0.0198572i
$70$		0			0
$71$		−	34.5671i		−	0.486860i	−0.969918	−	0.243430i	$-0.921727\pi$
$71$		−	34.5671i		−	0.486860i	0.969918	−	0.243430i	$-0.0782726\pi$
$72$		0			0
$73$	50.2693	+	87.0689i	0.688620	+	1.19273i	0.972284	+	0.233801i	$0.0751166\pi$
$73$	50.2693	+	87.0689i	0.688620	+	1.19273i	−0.283664	+	0.958924i	$0.591550\pi$
$74$		0			0
$75$	−26.9297	−	13.4943i	−0.359063	−	0.179925i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	21.2915	−	36.8780i	0.269513	−	0.466810i	−0.699223	−	0.714903i	$-0.746471\pi$
$79$	21.2915	−	36.8780i	0.269513	−	0.466810i	0.968736	+	0.248094i	$0.0798040\pi$
$80$		0			0
$81$	−55.7969	−	58.7172i	−0.688850	−	0.724904i
$82$		0			0
$83$		−	82.1075i		−	0.989247i	−0.869107	−	0.494623i	$-0.835306\pi$
$83$		−	82.1075i		−	0.989247i	0.869107	−	0.494623i	$-0.164694\pi$
$84$		0			0
$85$	84.4575			0.993618
$86$		0			0
$87$	−61.5861	−	93.4542i	−0.707886	−	1.07419i
$88$		0			0
$89$	36.6351	+	21.1513i	0.411630	+	0.237655i	0.691490	−	0.722386i	$-0.256955\pi$
$89$	36.6351	+	21.1513i	0.411630	+	0.237655i	−0.279860	+	0.960041i	$0.590288\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−41.0134	−	20.5516i	−0.441005	−	0.220985i
$94$		0			0
$95$	23.2368	−	13.4158i	0.244598	−	0.141219i
$96$		0			0
$97$	48.3320			0.498268			0.249134	−	0.968469i	$-0.419854\pi$
$97$	48.3320			0.498268			0.249134	+	0.968469i	$0.419854\pi$
$98$		0			0
$99$	−14.9595	−	126.023i	−0.151106	−	1.27296i
$100$		0			0
$101$	−69.9206	+	40.3687i	−0.692283	+	0.399690i	−0.804467	−	0.593998i	$-0.797549\pi$
$101$	−69.9206	+	40.3687i	−0.692283	+	0.399690i	0.112184	+	0.993687i	$0.464216\pi$
$102$		0			0
$103$	−24.1255	+	41.7866i	−0.234228	+	0.405695i	−0.959048	−	0.283243i	$-0.908590\pi$
$103$	−24.1255	+	41.7866i	−0.234228	+	0.405695i	0.724820	+	0.688938i	$0.241923\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	170.197	+	98.2636i	1.59063	+	0.918351i	0.993199	+	0.116432i	$0.0371456\pi$
$107$	170.197	+	98.2636i	1.59063	+	0.918351i	0.597432	+	0.801920i	$0.296188\pi$
$108$		0			0
$109$	26.6458	+	46.1518i	0.244456	+	0.423411i	0.961979	−	0.273125i	$-0.0880572\pi$
$109$	26.6458	+	46.1518i	0.244456	+	0.423411i	−0.717522	+	0.696536i	$0.754724\pi$
$110$		0			0
$111$	−2.14772	−	36.3130i	−0.0193488	−	0.327144i
$112$		0			0
$113$			140.124i			1.24003i	0.784589	+	0.620017i	$0.212874\pi$
$113$			140.124i			1.24003i	−0.784589	+	0.620017i	$0.787126\pi$
$114$		0			0
$115$	14.9595	+	25.9106i	0.130082	+	0.225309i
$116$		0			0
$117$	71.8094	−	167.299i	0.613756	−	1.42990i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	38.9170	−	67.4062i	0.321628	−	0.557076i
$122$		0			0
$123$	−69.8321	−	105.967i	−0.567741	−	0.861521i
$124$		0			0
$125$			135.528i			1.08422i
$126$		0			0
$127$	−115.579			−0.910071			−0.455036	−	0.890473i	$-0.650374\pi$
$127$	−115.579			−0.910071			−0.455036	+	0.890473i	$0.650374\pi$
$128$		0			0
$129$	40.3941	−	26.6196i	0.313132	−	0.206353i
$130$		0			0
$131$	71.5275	+	41.2964i	0.546012	+	0.315240i	0.747512	−	0.664249i	$-0.231248\pi$
$131$	71.5275	+	41.2964i	0.546012	+	0.315240i	−0.201500	+	0.979488i	$0.564582\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−35.4524	+	98.2273i	−0.262610	+	0.727609i
$136$		0			0
$137$	−133.142	+	76.8696i	−0.971840	+	0.561092i	−0.899797	−	0.436309i	$-0.856285\pi$
$137$	−133.142	+	76.8696i	−0.971840	+	0.561092i	−0.0720432	+	0.997402i	$0.522952\pi$
$138$		0			0
$139$	220.516			1.58645			0.793224	−	0.608930i	$-0.208401\pi$
$139$	220.516			1.58645			0.793224	+	0.608930i	$0.208401\pi$
$140$		0			0
$141$	−215.247	+	12.7307i	−1.52657	+	0.0902887i
$142$		0			0
$143$	247.027	−	142.621i	1.72746	−	0.997352i
$144$		0			0
$145$	−72.1477	+	124.964i	−0.497570	+	0.861817i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−168.245	−	97.1361i	−1.12916	−	0.651920i	−0.185436	−	0.982656i	$-0.559370\pi$
$149$	−168.245	−	97.1361i	−1.12916	−	0.651920i	−0.943723	+	0.330736i	$0.892703\pi$
$150$		0			0
$151$	−64.0405	−	110.921i	−0.424109	−	0.734579i	0.572227	−	0.820095i	$-0.306079\pi$
$151$	−64.0405	−	110.921i	−0.424109	−	0.734579i	−0.996337	+	0.0855160i	$0.972746\pi$
$152$		0			0
$153$	23.1660	+	195.157i	0.151412	+	1.27554i
$154$		0			0
$155$			59.1437i			0.381572i
$156$		0			0
$157$	−73.8412	−	127.897i	−0.470326	−	0.814628i	0.529098	−	0.848561i	$-0.322530\pi$
$157$	−73.8412	−	127.897i	−0.470326	−	0.814628i	−0.999424	+	0.0339322i	$0.989197\pi$
$158$		0			0
$159$	136.343	−	272.090i	0.857501	−	1.71126i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	105.184	−	182.185i	0.645302	−	1.11770i	−0.338929	−	0.940812i	$-0.610065\pi$
$163$	105.184	−	182.185i	0.645302	−	1.11770i	0.984232	−	0.176885i	$-0.0566020\pi$
$164$		0			0
$165$	−136.618	+	90.0310i	−0.827988	+	0.545642i
$166$		0			0
$167$			85.0905i			0.509524i	0.967004	+	0.254762i	$0.0819971\pi$
$167$			85.0905i			0.509524i	−0.967004	+	0.254762i	$0.918003\pi$
$168$		0			0
$169$	240.203			1.42132
$170$		0			0
$171$	37.3737	+	50.0137i	0.218559	+	0.292478i
$172$		0			0
$173$	80.9457	+	46.7340i	0.467894	+	0.270139i	0.715358	−	0.698758i	$-0.246264\pi$
$173$	80.9457	+	46.7340i	0.467894	+	0.270139i	−0.247464	+	0.968897i	$0.579597\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−34.5460	+	68.9411i	−0.195175	+	0.389498i
$178$		0			0
$179$	−170.197	+	98.2636i	−0.950824	+	0.548958i	−0.893337	−	0.449388i	$-0.851642\pi$
$179$	−170.197	+	98.2636i	−0.950824	+	0.548958i	−0.0574872	+	0.998346i	$0.518309\pi$
$180$		0			0
$181$	−164.022			−0.906200			−0.453100	−	0.891460i	$-0.649682\pi$
$181$	−164.022			−0.906200			−0.453100	+	0.891460i	$0.649682\pi$
$182$		0			0
$183$	13.8340	+	233.901i	0.0755956	+	1.27815i
$184$		0			0
$185$	−40.6152	+	23.4492i	−0.219541	+	0.126752i
$186$		0			0
$187$	−153.956	+	266.659i	−0.823292	+	1.42598i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	199.367	+	115.105i	1.04381	+	0.602642i	0.920909	−	0.389777i	$-0.127448\pi$
$191$	199.367	+	115.105i	1.04381	+	0.602642i	0.122898	+	0.992419i	$0.460781\pi$
$192$		0			0
$193$	92.3098	+	159.885i	0.478289	+	0.828421i	0.999690	−	0.0248907i	$-0.00792378\pi$
$193$	92.3098	+	159.885i	0.478289	+	0.828421i	−0.521401	+	0.853312i	$0.674590\pi$
$194$		0			0
$195$	−234.310	+	13.8582i	−1.20159	+	0.0710675i
$196$		0			0
$197$		−	91.4558i		−	0.464243i	−0.972687	−	0.232121i	$-0.925433\pi$
$197$		−	91.4558i		−	0.464243i	0.972687	−	0.232121i	$-0.0745667\pi$
$198$		0			0
$199$	101.875	+	176.452i	0.511932	+	0.886693i	0.999904	+	0.0138334i	$0.00440344\pi$
$199$	101.875	+	176.452i	0.511932	+	0.886693i	−0.487972	+	0.872859i	$0.662263\pi$
$200$		0			0
$201$	330.344	+	165.534i	1.64350	+	0.823551i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−81.8078	+	141.695i	−0.399063	+	0.691197i
$206$		0			0
$207$	−55.7686	+	41.6741i	−0.269414	+	0.201324i
$208$		0			0
$209$			97.8212i			0.468044i
$210$		0			0
$211$	188.243			0.892147			0.446074	−	0.894996i	$-0.352822\pi$
$211$	188.243			0.892147			0.446074	+	0.894996i	$0.352822\pi$
$212$		0			0
$213$	−57.0625	−	86.5898i	−0.267899	−	0.406525i
$214$		0			0
$215$	−54.0134	−	31.1847i	−0.251225	−	0.145045i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	269.655	+	135.123i	1.23130	+	0.616999i
$220$		0			0
$221$	−382.543	+	220.861i	−1.73096	+	0.999371i
$222$		0			0
$223$	154.125			0.691146			0.345573	−	0.938392i	$-0.387685\pi$
$223$	154.125			0.691146			0.345573	+	0.938392i	$0.387685\pi$
$224$		0			0
$225$	−89.7347	+	10.6519i	−0.398821	+	0.0473418i
$226$		0			0
$227$	202.296	−	116.796i	0.891174	−	0.514519i	0.0168475	−	0.999858i	$-0.494637\pi$
$227$	202.296	−	116.796i	0.891174	−	0.514519i	0.874326	+	0.485339i	$0.161304\pi$
$228$		0			0
$229$	−137.635	+	238.390i	−0.601025	+	1.04101i	0.391642	+	0.920118i	$0.371907\pi$
$229$	−137.635	+	238.390i	−0.601025	+	1.04101i	−0.992666	+	0.120887i	$0.961426\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−30.7022	−	17.7259i	−0.131769	−	0.0760769i	0.432666	−	0.901554i	$-0.357573\pi$
$233$	−30.7022	−	17.7259i	−0.131769	−	0.0760769i	−0.564435	+	0.825477i	$0.690906\pi$
$234$		0			0
$235$	138.996	+	240.748i	0.591473	+	1.02446i
$236$		0			0
$237$	−7.54249	−	127.526i	−0.0318248	−	0.538085i
$238$		0			0
$239$		−	56.8888i		−	0.238028i	−0.992893	−	0.119014i	$-0.962027\pi$
$239$		−	56.8888i		−	0.238028i	0.992893	−	0.119014i	$-0.0379734\pi$
$240$		0			0
$241$	104.875	+	181.648i	0.435164	+	0.753726i	0.997309	−	0.0733126i	$-0.0233571\pi$
$241$	104.875	+	181.648i	0.435164	+	0.753726i	−0.562145	+	0.827039i	$0.690024\pi$
$242$		0			0
$243$	−236.699	−	54.9772i	−0.974071	−	0.226244i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−70.1660	+	121.531i	−0.284073	+	0.492029i
$248$		0			0
$249$	−135.541	−	205.678i	−0.544342	−	0.826015i
$250$		0			0
$251$			77.1123i			0.307220i	0.988132	+	0.153610i	$0.0490900\pi$
$251$			77.1123i			0.307220i	−0.988132	+	0.153610i	$0.950910\pi$
$252$		0			0
$253$	−109.077			−0.431135
$254$		0			0
$255$	211.565	−	139.421i	0.829665	−	0.546747i
$256$		0			0
$257$	137.122	+	79.1675i	0.533549	+	0.308045i	0.742461	−	0.669890i	$-0.233659\pi$
$257$	137.122	+	79.1675i	0.533549	+	0.308045i	−0.208911	+	0.977935i	$0.566992\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−308.544	−	132.436i	−1.18216	−	0.507418i
$262$		0			0
$263$	130.003	−	75.0571i	0.494307	−	0.285388i	−0.232053	−	0.972703i	$-0.574544\pi$
$263$	130.003	−	75.0571i	0.494307	−	0.285388i	0.726359	+	0.687315i	$0.241211\pi$
$264$		0			0
$265$	−392.369			−1.48064
$266$		0			0
$267$	126.686	−	7.49281i	0.474480	−	0.0280630i
$268$		0			0
$269$	−165.241	+	95.4019i	−0.614279	+	0.354654i	−0.774638	−	0.632405i	$-0.782068\pi$
$269$	−165.241	+	95.4019i	−0.614279	+	0.354654i	0.160359	+	0.987059i	$0.448735\pi$
$270$		0			0
$271$	171.225	−	296.570i	0.631826	−	1.09435i	−0.355352	−	0.934732i	$-0.615639\pi$
$271$	171.225	−	296.570i	0.631826	−	1.09435i	0.987178	−	0.159622i	$-0.0510276\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−122.612	−	70.7899i	−0.445861	−	0.257418i
$276$		0			0
$277$	46.6235	+	80.7543i	0.168316	+	0.291532i	0.937828	−	0.347101i	$-0.112834\pi$
$277$	46.6235	+	80.7543i	0.168316	+	0.291532i	−0.769512	+	0.638632i	$0.779500\pi$
$278$		0			0
$279$	−136.664	+	16.2226i	−0.489835	+	0.0581456i
$280$		0			0
$281$			251.075i			0.893505i	0.894657	+	0.446753i	$0.147420\pi$
$281$			251.075i			0.893505i	−0.894657	+	0.446753i	$0.852580\pi$
$282$		0			0
$283$	−8.32484	−	14.4191i	−0.0294164	−	0.0509507i	0.850942	−	0.525259i	$-0.176032\pi$
$283$	−8.32484	−	14.4191i	−0.0294164	−	0.0509507i	−0.880359	+	0.474308i	$0.842698\pi$
$284$		0			0
$285$	36.0613	−	71.9651i	0.126531	−	0.252509i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	93.9131	−	162.662i	0.324959	−	0.562845i
$290$		0			0
$291$	121.071	−	79.7854i	0.416051	−	0.274177i
$292$		0			0
$293$			307.322i			1.04888i	0.851448	+	0.524440i	$0.175725\pi$
$293$			307.322i			1.04888i	−0.851448	+	0.524440i	$0.824275\pi$
$294$		0			0
$295$	99.4170			0.337007
$296$		0			0
$297$	−245.509	−	290.990i	−0.826630	−	0.979765i
$298$		0			0
$299$	−135.515	−	78.2398i	−0.453228	−	0.261671i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−108.510	+	216.546i	−0.358119	+	0.714674i
$304$		0			0
$305$	261.612	−	151.042i	0.857745	−	0.495219i
$306$		0			0
$307$	126.775			0.412948			0.206474	−	0.978452i	$-0.433801\pi$
$307$	126.775			0.412948			0.206474	+	0.978452i	$0.433801\pi$
$308$		0			0
$309$	8.54642	+	144.500i	0.0276583	+	0.467639i
$310$		0			0
$311$	−284.849	+	164.458i	−0.915913	+	0.528803i	−0.882329	−	0.470633i	$-0.844026\pi$
$311$	−284.849	+	164.458i	−0.915913	+	0.528803i	−0.0335844	+	0.999436i	$0.510692\pi$
$312$		0			0
$313$	129.642	−	224.546i	0.414191	−	0.717400i	−0.581152	−	0.813795i	$-0.697398\pi$
$313$	129.642	−	224.546i	0.414191	−	0.717400i	0.995343	+	0.0963950i	$0.0307312\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.46537	−	4.31014i	−0.0235501	−	0.0135966i	0.488179	−	0.872744i	$-0.337661\pi$
$317$	−7.46537	−	4.31014i	−0.0235501	−	0.0135966i	−0.511729	+	0.859147i	$0.670995\pi$
$318$		0			0
$319$	−263.033	−	455.586i	−0.824554	−	1.42817i
$320$		0			0
$321$	588.553	−	34.8097i	1.83350	−	0.108442i
$322$		0			0
$323$		−	151.484i		−	0.468992i
$324$		0			0
$325$	−101.554	−	175.896i	−0.312473	−	0.541218i
$326$		0			0
$327$	142.933	+	71.6232i	0.437105	+	0.219031i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	237.184	−	410.815i	0.716569	−	1.24113i	−0.245782	−	0.969325i	$-0.579045\pi$
$331$	237.184	−	410.815i	0.716569	−	1.24113i	0.962351	−	0.271809i	$-0.0876218\pi$
$332$		0			0
$333$	−65.3247	−	87.4180i	−0.196170	−	0.262517i
$334$		0			0
$335$		−	476.375i		−	1.42202i
$336$		0			0
$337$	−609.195			−1.80770			−0.903850	−	0.427850i	$-0.859271\pi$
$337$	−609.195			−1.80770			−0.903850	+	0.427850i	$0.859271\pi$
$338$		0			0
$339$	231.313	+	351.007i	0.682340	+	1.03542i
$340$		0			0
$341$	−186.735	−	107.812i	−0.547610	−	0.316163i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	80.2458	+	40.2108i	0.232597	+	0.116553i
$346$		0			0
$347$	369.911	−	213.568i	1.06602	−	0.615470i	0.138932	−	0.990302i	$-0.455633\pi$
$347$	369.911	−	213.568i	1.06602	−	0.615470i	0.927093	+	0.374832i	$0.122300\pi$
$348$		0			0
$349$	316.759			0.907620			0.453810	−	0.891098i	$-0.350064\pi$
$349$	316.759			0.907620			0.453810	+	0.891098i	$0.350064\pi$
$350$		0			0
$351$	−96.2915	−	537.621i	−0.274335	−	1.53168i
$352$		0			0
$353$	74.8771	−	43.2303i	0.212116	−	0.122465i	−0.390178	−	0.920739i	$-0.627587\pi$
$353$	74.8771	−	43.2303i	0.212116	−	0.122465i	0.602295	+	0.798274i	$0.294253\pi$
$354$		0			0
$355$	−66.8483	+	115.785i	−0.188305	+	0.326154i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	247.868	+	143.107i	0.690440	+	0.398626i	0.803777	−	0.594931i	$-0.202821\pi$
$359$	247.868	+	143.107i	0.690440	+	0.398626i	−0.113337	+	0.993557i	$0.536154\pi$
$360$		0			0
$361$	156.437	+	270.957i	0.433344	+	0.750574i
$362$		0			0
$363$	−13.7863	−	233.095i	−0.0379788	−	0.642134i
$364$		0			0
$365$		−	388.858i		−	1.06536i
$366$		0			0
$367$	−55.8078	−	96.6620i	−0.152065	−	0.263384i	0.779922	−	0.625877i	$-0.215259\pi$
$367$	−55.8078	−	96.6620i	−0.152065	−	0.263384i	−0.931986	+	0.362493i	$0.881926\pi$
$368$		0			0
$369$	−349.856	−	150.168i	−0.948120	−	0.406961i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−42.5425	+	73.6857i	−0.114055	+	0.197549i	−0.917402	−	0.397963i	$-0.869717\pi$
$373$	−42.5425	+	73.6857i	−0.114055	+	0.197549i	0.803347	+	0.595512i	$0.203051\pi$
$374$		0			0
$375$	223.726	+	339.495i	0.596604	+	0.905320i
$376$		0			0
$377$		−	754.681i		−	2.00181i
$378$		0			0
$379$	−26.5464			−0.0700433			−0.0350217	−	0.999387i	$-0.511150\pi$
$379$	−26.5464			−0.0700433			−0.0350217	+	0.999387i	$0.511150\pi$
$380$		0			0
$381$	−289.523	+	190.795i	−0.759904	+	0.500775i
$382$		0			0
$383$	−100.067	−	57.7735i	−0.261271	−	0.150845i	0.363643	−	0.931538i	$-0.381533\pi$
$383$	−100.067	−	57.7735i	−0.261271	−	0.150845i	−0.624914	+	0.780693i	$0.714866\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	57.2434	−	133.363i	0.147916	−	0.344608i
$388$		0			0
$389$	334.042	−	192.859i	0.858719	−	0.495782i	−0.00486402	−	0.999988i	$-0.501548\pi$
$389$	334.042	−	192.859i	0.858719	−	0.495782i	0.863583	+	0.504206i	$0.168215\pi$
$390$		0			0
$391$	168.915			0.432008
$392$		0			0
$393$	247.346	−	14.6292i	0.629380	−	0.0372244i
$394$		0			0
$395$	−142.635	+	82.3502i	−0.361101	+	0.208481i
$396$		0			0
$397$	−23.7967	+	41.2171i	−0.0599413	+	0.103821i	−0.894439	−	0.447190i	$-0.852425\pi$
$397$	−23.7967	+	41.2171i	−0.0599413	+	0.103821i	0.834498	+	0.551012i	$0.185758\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−397.127	−	229.282i	−0.990343	−	0.571775i	−0.0849661	−	0.996384i	$-0.527078\pi$
$401$	−397.127	−	229.282i	−0.990343	−	0.571775i	−0.905377	+	0.424609i	$0.860412\pi$
$402$		0			0
$403$	−154.664	−	267.886i	−0.383782	−	0.664729i
$404$		0			0
$405$	73.3438	+	304.581i	0.181096	+	0.752053i
$406$		0			0
$407$		−	170.980i		−	0.420098i
$408$		0			0
$409$	28.9333	+	50.1140i	0.0707416	+	0.122528i	0.899227	−	0.437483i	$-0.144130\pi$
$409$	28.9333	+	50.1140i	0.0707416	+	0.122528i	−0.828485	+	0.560011i	$0.810797\pi$
$410$		0			0
$411$	−206.624	+	412.345i	−0.502734	+	1.00327i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−158.786	+	275.025i	−0.382616	+	0.662710i
$416$		0			0
$417$	552.389	−	364.023i	1.32467	−	0.872958i
$418$		0			0
$419$		−	115.304i		−	0.275190i	−0.990489	−	0.137595i	$-0.956063\pi$
$419$		−	115.304i		−	0.275190i	0.990489	−	0.137595i	$-0.0439372\pi$
$420$		0			0
$421$	622.664			1.47901			0.739506	−	0.673150i	$-0.235059\pi$
$421$	622.664			1.47901			0.739506	+	0.673150i	$0.235059\pi$
$422$		0			0
$423$	−518.174	+	387.215i	−1.22500	+	0.915402i
$424$		0			0
$425$	189.875	+	109.624i	0.446764	+	0.257939i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	383.363	−	765.051i	0.893620	−	1.78334i
$430$		0			0
$431$	147.801	−	85.3332i	0.342927	−	0.197989i	−0.318639	−	0.947876i	$-0.603226\pi$
$431$	147.801	−	85.3332i	0.342927	−	0.197989i	0.661565	+	0.749887i	$0.269892\pi$
$432$		0			0
$433$	−251.992			−0.581968			−0.290984	−	0.956728i	$-0.593983\pi$
$433$	−251.992			−0.581968			−0.290984	+	0.956728i	$0.593983\pi$
$434$		0			0
$435$	25.5582	+	432.131i	0.0587546	+	0.993405i
$436$		0			0
$437$	46.4736	−	26.8316i	0.106347	−	0.0613994i
$438$		0			0
$439$	226.044	−	391.520i	0.514908	−	0.891846i	−0.484943	−	0.874546i	$-0.661160\pi$
$439$	226.044	−	391.520i	0.514908	−	0.891846i	0.999850	−	0.0173003i	$-0.00550712\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−94.5542	−	54.5909i	−0.213441	−	0.123230i	0.389469	−	0.921040i	$-0.372659\pi$
$443$	−94.5542	−	54.5909i	−0.213441	−	0.123230i	−0.602909	+	0.797810i	$0.705992\pi$
$444$		0			0
$445$	−81.8078	−	141.695i	−0.183838	−	0.318416i
$446$		0			0
$447$	−581.800	+	34.4103i	−1.30157	+	0.0769806i
$448$		0			0
$449$			565.005i			1.25836i	0.777259	+	0.629181i	$0.216610\pi$
$449$			565.005i			1.25836i	−0.777259	+	0.629181i	$0.783390\pi$
$450$		0			0
$451$	−298.251	−	516.586i	−0.661310	−	1.14542i
$452$		0			0
$453$	−343.527	−	172.140i	−0.758338	−	0.379999i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−297.852	+	515.895i	−0.651756	+	1.12887i	0.330941	+	0.943651i	$0.392634\pi$
$457$	−297.852	+	515.895i	−0.651756	+	1.12887i	−0.982697	+	0.185222i	$0.940699\pi$
$458$		0			0
$459$	380.191	+	450.623i	0.828303	+	0.981749i
$460$		0			0
$461$			445.590i			0.966573i	0.875462	+	0.483286i	$0.160557\pi$
$461$			445.590i			0.966573i	−0.875462	+	0.483286i	$0.839443\pi$
$462$		0			0
$463$	−333.919			−0.721207			−0.360604	−	0.932719i	$-0.617429\pi$
$463$	−333.919			−0.721207			−0.360604	+	0.932719i	$0.617429\pi$
$464$		0			0
$465$	97.6331	+	148.154i	0.209964	+	0.318610i
$466$		0			0
$467$	−388.191	−	224.122i	−0.831244	−	0.479919i	0.0230345	−	0.999735i	$-0.492667\pi$
$467$	−388.191	−	224.122i	−0.831244	−	0.479919i	−0.854278	+	0.519816i	$0.826001\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−396.100	−	198.483i	−0.840976	−	0.421409i
$472$		0			0
$473$	196.920	−	113.692i	0.416320	−	0.240363i
$474$		0			0
$475$	69.6536			0.146639
$476$		0			0
$477$	−107.624	−	906.651i	−0.225626	−	1.90074i
$478$		0			0
$479$	11.8658	−	6.85072i	0.0247720	−	0.0143021i	−0.487563	−	0.873088i	$-0.662114\pi$
$479$	11.8658	−	6.85072i	0.0247720	−	0.0143021i	0.512335	+	0.858786i	$0.328781\pi$
$480$		0			0
$481$	122.642	−	212.422i	0.254973	−	0.441625i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−161.891	−	93.4681i	−0.333797	−	0.192718i
$486$		0			0
$487$	−5.62746	−	9.74705i	−0.0115554	−	0.0200145i	0.860190	−	0.509974i	$-0.170345\pi$
$487$	−5.62746	−	9.74705i	−0.0115554	−	0.0200145i	−0.871745	+	0.489959i	$0.837012\pi$
$488$		0			0
$489$	−37.2614	−	630.005i	−0.0761992	−	1.28835i
$490$		0			0
$491$			285.642i			0.581756i	0.956760	+	0.290878i	$0.0939473\pi$
$491$			285.642i			0.581756i	−0.956760	+	0.290878i	$0.906053\pi$
$492$		0			0
$493$	407.328	+	705.513i	0.826223	+	1.43106i
$494$		0			0
$495$	−193.605	+	451.052i	−0.391120	+	0.911216i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−390.409	+	676.208i	−0.782383	+	1.35513i	0.148167	+	0.988962i	$0.452663\pi$
$499$	−390.409	+	676.208i	−0.782383	+	1.35513i	−0.930550	+	0.366165i	$0.880671\pi$
$500$		0			0
$501$	140.465	+	213.150i	0.280370	+	0.425449i
$502$		0			0
$503$		−	420.771i		−	0.836522i	−0.908327	−	0.418261i	$-0.862640\pi$
$503$		−	420.771i		−	0.836522i	0.908327	−	0.418261i	$-0.137360\pi$
$504$		0			0
$505$	312.272			0.618360
$506$		0			0
$507$	601.703	−	396.521i	1.18679	−	0.782093i
$508$		0			0
$509$	−89.1773	−	51.4866i	−0.175201	−	0.101152i	0.409835	−	0.912160i	$-0.365586\pi$
$509$	−89.1773	−	51.4866i	−0.175201	−	0.101152i	−0.585036	+	0.811007i	$0.698920\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	176.182	+	63.5879i	0.343435	+	0.123953i
$514$		0			0
$515$	161.620	−	93.3113i	0.313825	−	0.181187i
$516$		0			0
$517$	−1013.49			−1.96033
$518$		0			0
$519$	279.915	−	16.5555i	0.539335	−	0.0318988i
$520$		0			0
$521$	−66.4966	+	38.3918i	−0.127633	+	0.0736887i	−0.562457	−	0.826827i	$-0.690144\pi$
$521$	−66.4966	+	38.3918i	−0.127633	+	0.0736887i	0.434824	+	0.900515i	$0.356810\pi$
$522$		0			0
$523$	202.280	−	350.360i	0.386769	−	0.669904i	−0.605244	−	0.796040i	$-0.706924\pi$
$523$	202.280	−	350.360i	0.386769	−	0.669904i	0.992013	+	0.126136i	$0.0402576\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	289.175	+	166.955i	0.548719	+	0.316803i
$528$		0			0
$529$	−234.581	−	406.306i	−0.443442	−	0.768065i
$530$		0			0
$531$	27.2693	+	229.724i	0.0513546	+	0.432625i
$532$		0			0
$533$		−	855.728i		−	1.60549i
$534$		0			0
$535$	−380.059	−	658.281i	−0.710390	−	1.23043i
$536$		0			0
$537$	−264.130	+	527.107i	−0.491863	+	0.981577i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−296.454	+	513.473i	−0.547973	+	0.949118i	0.450440	+	0.892807i	$0.351267\pi$
$541$	−296.454	+	513.473i	−0.547973	+	0.949118i	−0.998413	+	0.0563109i	$0.982066\pi$
$542$		0			0
$543$	−410.873	+	270.764i	−0.756672	+	0.498645i
$544$		0			0
$545$		−	206.118i		−	0.378198i
$546$		0			0
$547$	−793.689			−1.45099			−0.725493	−	0.688230i	$-0.758388\pi$
$547$	−793.689			−1.45099			−0.725493	+	0.688230i	$0.758388\pi$
$548$		0			0
$549$	420.772	+	563.081i	0.766434	+	1.02565i
$550$		0			0
$551$	224.136	+	129.405i	0.406781	+	0.234855i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−63.0309	+	125.786i	−0.113569	+	0.226642i
$556$		0			0
$557$	−319.531	+	184.482i	−0.573665	+	0.331206i	−0.758612	−	0.651543i	$-0.774122\pi$
$557$	−319.531	+	184.482i	−0.573665	+	0.331206i	0.184947	+	0.982749i	$0.440789\pi$
$558$		0			0
$559$	326.199			0.583540
$560$		0			0
$561$	54.5385	+	922.122i	0.0972167	+	1.64371i
$562$		0			0
$563$	−458.816	+	264.898i	−0.814949	+	0.470511i	−0.848672	−	0.528920i	$-0.822597\pi$
$563$	−458.816	+	264.898i	−0.814949	+	0.470511i	0.0337223	+	0.999431i	$0.489264\pi$
$564$		0			0
$565$	270.982	−	469.354i	0.479614	−	0.830715i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	924.949	+	534.020i	1.62557	+	0.938523i	0.985393	+	0.170296i	$0.0544724\pi$
$569$	924.949	+	534.020i	1.62557	+	0.938523i	0.640177	+	0.768227i	$0.278861\pi$
$570$		0			0
$571$	59.0954	+	102.356i	0.103495	+	0.179258i	0.913122	−	0.407686i	$-0.133664\pi$
$571$	59.0954	+	102.356i	0.103495	+	0.179258i	−0.809628	+	0.586944i	$0.800331\pi$
$572$		0			0
$573$	689.423	−	40.7757i	1.20318	−	0.0711618i
$574$		0			0
$575$			77.6684i			0.135075i
$576$		0			0
$577$	−293.280	−	507.975i	−0.508284	−	0.880373i	−0.999954	−	0.00959175i	$-0.996947\pi$
$577$	−293.280	−	507.975i	−0.508284	−	0.880373i	0.491670	−	0.870781i	$-0.336387\pi$
$578$		0			0
$579$	495.169	+	248.127i	0.855215	+	0.428544i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	715.239	−	1238.83i	1.22683	−	2.12492i
$584$		0			0
$585$	−564.065	+	421.508i	−0.964214	+	0.720526i
$586$		0			0
$587$			809.558i			1.37914i	0.724217	+	0.689572i	$0.242201\pi$
$587$			809.558i			1.37914i	−0.724217	+	0.689572i	$0.757799\pi$
$588$		0			0
$589$	106.081			0.180104
$590$		0			0
$591$	−150.973	−	229.095i	−0.255454	−	0.387640i
$592$		0			0
$593$	415.964	+	240.157i	0.701457	+	0.404986i	0.807890	−	0.589334i	$-0.200610\pi$
$593$	415.964	+	240.157i	0.701457	+	0.404986i	−0.106433	+	0.994320i	$0.533943\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	546.476	+	273.836i	0.915371	+	0.458688i
$598$		0			0
$599$	−334.882	+	193.344i	−0.559069	+	0.322779i	−0.752772	−	0.658282i	$-0.771284\pi$
$599$	−334.882	+	193.344i	−0.559069	+	0.322779i	0.193703	+	0.981060i	$0.437950\pi$
$600$		0			0
$601$	−474.369			−0.789299			−0.394649	−	0.918832i	$-0.629134\pi$
$601$	−474.369			−0.789299			−0.394649	+	0.918832i	$0.629134\pi$
$602$		0			0
$603$	1100.77	−	130.666i	1.82548	−	0.216693i
$604$		0			0
$605$	−260.710	+	150.521i	−0.430926	+	0.248795i
$606$		0			0
$607$	217.099	−	376.027i	0.357660	−	0.619484i	−0.629910	−	0.776668i	$-0.716908\pi$
$607$	217.099	−	376.027i	0.357660	−	0.619484i	0.987569	+	0.157184i	$0.0502415\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1259.14	−	726.965i	−2.06079	−	1.18980i
$612$		0			0
$613$	−307.391	−	532.417i	−0.501453	−	0.868542i	−0.999999	−	0.00167886i	$-0.999466\pi$
$613$	−307.391	−	532.417i	−0.501453	−	0.868542i	0.498545	−	0.866864i	$-0.333868\pi$
$614$		0			0
$615$	28.9803	+	489.991i	0.0471225	+	0.796733i
$616$		0			0
$617$			527.697i			0.855263i	0.903953	+	0.427632i	$0.140652\pi$
$617$			527.697i			0.855263i	−0.903953	+	0.427632i	$0.859348\pi$
$618$		0			0
$619$	339.985	+	588.871i	0.549249	+	0.951327i	0.998326	+	0.0578339i	$0.0184194\pi$
$619$	339.985	+	588.871i	0.549249	+	0.951327i	−0.449078	+	0.893493i	$0.648247\pi$
$620$		0			0
$621$	−70.9047	+	196.455i	−0.114178	+	0.316352i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	136.588	−	236.577i	0.218540	−	0.378522i
$626$		0			0
$627$	161.481	+	245.040i	0.257545	+	0.390814i
$628$		0			0
$629$			264.776i			0.420948i
$630$		0			0
$631$	−929.239			−1.47265			−0.736323	−	0.676631i	$-0.763439\pi$
$631$	−929.239			−1.47265			−0.736323	+	0.676631i	$0.763439\pi$
$632$		0			0
$633$	471.546	−	310.747i	0.744938	−	0.490912i
$634$		0			0
$635$	387.140	+	223.515i	0.609669	+	0.351993i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−285.881	−	122.708i	−0.447388	−	0.192032i
$640$		0			0
$641$	−691.890	+	399.463i	−1.07939	+	0.623187i	−0.930732	−	0.365702i	$-0.880829\pi$
$641$	−691.890	+	399.463i	−1.07939	+	0.623187i	−0.148659	+	0.988889i	$0.547496\pi$
$642$		0			0
$643$	306.051			0.475973			0.237987	−	0.971268i	$-0.423513\pi$
$643$	306.051			0.475973			0.237987	+	0.971268i	$0.423513\pi$
$644$		0			0
$645$	−186.782	+	11.0471i	−0.289584	+	0.0171273i
$646$		0			0
$647$	741.774	−	428.263i	1.14648	−	0.661922i	0.198455	−	0.980110i	$-0.436408\pi$
$647$	741.774	−	428.263i	1.14648	−	0.661922i	0.948028	+	0.318188i	$0.103074\pi$
$648$		0			0
$649$	−181.225	+	313.891i	−0.279237	+	0.483653i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	528.737	+	305.266i	0.809705	+	0.467483i	0.846853	−	0.531827i	$-0.178494\pi$
$653$	528.737	+	305.266i	0.809705	+	0.467483i	−0.0371487	+	0.999310i	$0.511828\pi$
$654$		0			0
$655$	−159.724	−	276.651i	−0.243854	−	0.422367i
$656$		0			0
$657$	898.539	−	106.661i	1.36764	−	0.162345i
$658$		0			0
$659$		−	41.3318i		−	0.0627190i	−0.999508	−	0.0313595i	$-0.990016\pi$
$659$		−	41.3318i		−	0.0627190i	0.999508	−	0.0313595i	$-0.00998367\pi$
$660$		0			0
$661$	−129.643	−	224.547i	−0.196131	−	0.339709i	0.751140	−	0.660143i	$-0.229504\pi$
$661$	−129.643	−	224.547i	−0.196131	−	0.339709i	−0.947271	+	0.320435i	$0.896171\pi$
$662$		0			0
$663$	−593.670	+	1184.75i	−0.895430	+	1.78695i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−144.295	+	249.927i	−0.216335	+	0.374703i
$668$		0			0
$669$	386.082	−	254.427i	0.577102	−	0.380309i
$670$		0			0
$671$			1101.32i			1.64132i
$672$		0			0
$673$	113.498			0.168645			0.0843225	−	0.996439i	$-0.473127\pi$
$673$	113.498			0.168645			0.0843225	+	0.996439i	$0.473127\pi$
$674$		0			0
$675$	−207.200	+	174.815i	−0.306963	+	0.258985i
$676$		0			0
$677$	−1073.38	−	619.717i	−1.58550	−	0.915387i	−0.994036	−	0.109053i	$-0.965218\pi$
$677$	−1073.38	−	619.717i	−1.58550	−	0.915387i	−0.591461	−	0.806334i	$-0.701449\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	313.945	−	626.518i	0.461006	−	0.919997i
$682$		0			0
$683$	−1114.21	+	643.288i	−1.63134	+	0.941856i	−0.647662	+	0.761927i	$0.724253\pi$
$683$	−1114.21	+	643.288i	−1.63134	+	0.941856i	−0.983680	+	0.179928i	$0.942413\pi$
$684$		0			0
$685$	594.625			0.868065
$686$		0			0
$687$	48.7569	+	824.367i	0.0709707	+	1.19995i
$688$		0			0
$689$	1777.20	−	1026.07i	2.57939	−	1.48921i
$690$		0			0
$691$	444.139	−	769.272i	0.642748	−	1.11327i	−0.342068	−	0.939675i	$-0.611127\pi$
$691$	444.139	−	769.272i	0.642748	−	1.11327i	0.984817	−	0.173598i	$-0.0555393\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−738.635	−	426.451i	−1.06278	−	0.613598i
$696$		0			0
$697$	461.867	+	799.976i	0.662649	+	1.14774i
$698$		0			0
$699$	−106.170	+	6.27938i	−0.151888	+	0.00898338i
$700$		0			0
$701$		−	270.171i		−	0.385408i	−0.981257	−	0.192704i	$-0.938274\pi$
$701$		−	270.171i		−	0.385408i	0.981257	−	0.192704i	$-0.0617257\pi$
$702$		0			0
$703$	42.0588	+	72.8480i	0.0598276	+	0.103624i
$704$		0			0
$705$	745.604	+	373.618i	1.05759	+	0.529955i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−40.9412	+	70.9122i	−0.0577450	+	0.100017i	−0.893453	−	0.449157i	$-0.851724\pi$
$709$	−40.9412	+	70.9122i	−0.0577450	+	0.100017i	0.835708	+	0.549174i	$0.185058\pi$
$710$		0			0
$711$	−229.411	−	307.000i	−0.322660	−	0.431786i
$712$		0			0
$713$			118.287i			0.165901i
$714$		0			0
$715$	−1103.25			−1.54300
$716$		0			0
$717$	−93.9107	−	142.505i	−0.130977	−	0.198752i
$718$		0			0
$719$	589.375	+	340.276i	0.819715	+	0.473263i	0.850318	−	0.526269i	$-0.176409\pi$
$719$	589.375	+	340.276i	0.819715	+	0.473263i	−0.0306031	+	0.999532i	$0.509743\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	562.569	+	281.900i	0.778104	+	0.389904i
$724$		0			0
$725$	−324.400	+	187.293i	−0.447449	+	0.258335i
$726$		0			0
$727$	333.344			0.458520			0.229260	−	0.973365i	$-0.426369\pi$
$727$	333.344			0.458520			0.229260	+	0.973365i	$0.426369\pi$
$728$		0			0
$729$	−683.682	+	253.021i	−0.937836	+	0.347079i
$730$		0			0
$731$	−304.946	+	176.061i	−0.417163	+	0.240849i
$732$		0			0
$733$	412.631	−	714.697i	0.562934	−	0.975030i	−0.434304	−	0.900766i	$-0.643006\pi$
$733$	412.631	−	714.697i	0.562934	−	0.975030i	0.997239	−	0.0742643i	$-0.0236609\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1504.07	+	868.373i	2.04079	+	1.17825i
$738$		0			0
$739$	−537.383	−	930.775i	−0.727176	−	1.25951i	−0.958072	−	0.286527i	$-0.907499\pi$
$739$	−537.383	−	930.775i	−0.727176	−	1.25951i	0.230896	−	0.972978i	$-0.425834\pi$
$740$		0			0
$741$	24.8562	+	420.262i	0.0335442	+	0.567155i
$742$		0			0
$743$			171.465i			0.230774i	0.993321	+	0.115387i	$0.0368108\pi$
$743$			171.465i			0.230774i	−0.993321	+	0.115387i	$0.963189\pi$
$744$		0			0
$745$	375.698	+	650.728i	0.504293	+	0.873461i
$746$		0			0
$747$	−679.057	−	291.471i	−0.909045	−	0.390188i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−176.320	+	305.396i	−0.234781	+	0.406652i	−0.959209	−	0.282698i	$-0.908770\pi$
$751$	−176.320	+	305.396i	−0.234781	+	0.406652i	0.724428	+	0.689350i	$0.242104\pi$
$752$		0			0
$753$	127.295	+	193.165i	0.169051	+	0.256527i
$754$		0			0
$755$			495.385i			0.656139i
$756$		0			0
$757$	624.790			0.825349			0.412675	−	0.910878i	$-0.364595\pi$
$757$	624.790			0.825349			0.412675	+	0.910878i	$0.364595\pi$
$758$		0			0
$759$	−273.236	+	180.062i	−0.359995	+	0.237236i
$760$		0			0
$761$	466.912	+	269.572i	0.613551	+	0.354234i	0.774354	−	0.632753i	$-0.218075\pi$
$761$	466.912	+	269.572i	0.613551	+	0.354234i	−0.160803	+	0.986987i	$0.551408\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	299.813	−	698.492i	0.391912	−	0.913061i
$766$		0			0
$767$	−450.300	+	259.981i	−0.587093	+	0.338958i
$768$		0			0
$769$	−357.409			−0.464771			−0.232386	−	0.972624i	$-0.574653\pi$
$769$	−357.409			−0.464771			−0.232386	+	0.972624i	$0.574653\pi$
$770$		0			0
$771$	474.176	−	28.0450i	0.615015	−	0.0363748i
$772$		0			0
$773$	−201.530	+	116.354i	−0.260712	+	0.150522i	−0.624659	−	0.780897i	$-0.714762\pi$
$773$	−201.530	+	116.354i	−0.260712	+	0.150522i	0.363947	+	0.931419i	$0.381429\pi$
$774$		0			0
$775$	−76.7673	+	132.965i	−0.0990546	+	0.171568i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	254.147	+	146.732i	0.326248	+	0.188359i
$780$		0			0
$781$	−243.712	−	422.122i	−0.312052	−	0.540490i
$782$		0			0
$783$	−991.520	+	177.588i	−1.26631	+	0.226804i
$784$		0			0
$785$			571.198i			0.727641i
$786$		0			0
$787$	−601.357	−	1041.58i	−0.764114	−	1.32348i	−0.940714	−	0.339201i	$-0.889843\pi$
$787$	−601.357	−	1041.58i	−0.764114	−	1.32348i	0.176600	−	0.984283i	$-0.443490\pi$
$788$		0			0
$789$	201.752	−	402.622i	0.255706	−	0.510294i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−789.966	+	1368.26i	−0.996174	+	1.72542i
$794$		0			0
$795$	−982.876	+	647.713i	−1.23632	+	0.814734i
$796$		0			0
$797$		−	1108.42i		−	1.39074i	−0.718654	−	0.695368i	$-0.755242\pi$
$797$		−	1108.42i		−	1.39074i	0.718654	−	0.695368i	$-0.244758\pi$
$798$		0			0
$799$	1569.47			1.96430
$800$		0			0
$801$	304.978	−	227.900i	0.380746	−	0.284520i
$802$		0			0
$803$	1227.75	+	708.840i	1.52895	+	0.882739i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−256.438	+	511.756i	−0.317767	+	0.634147i
$808$		0			0
$809$	750.921	−	433.544i	0.928209	−	0.535901i	0.0419640	−	0.999119i	$-0.486639\pi$
$809$	750.921	−	433.544i	0.928209	−	0.535901i	0.886245	+	0.463218i	$0.153305\pi$
$810$		0			0
$811$	−1008.35			−1.24335			−0.621673	−	0.783277i	$-0.713547\pi$
$811$	−1008.35			−1.24335			−0.621673	+	0.783277i	$0.713547\pi$
$812$		0			0
$813$	−60.6562	−	1025.56i	−0.0746078	−	1.26145i
$814$		0			0
$815$	−704.644	+	406.826i	−0.864594	+	0.499174i
$816$		0			0
$817$	−55.9333	+	96.8793i	−0.0684618	+	0.118579i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1139.74	−	658.030i	−1.38824	−	0.801499i	−0.395120	−	0.918630i	$-0.629297\pi$
$821$	−1139.74	−	658.030i	−1.38824	−	0.801499i	−0.993116	+	0.117131i	$0.962630\pi$
$822$		0			0
$823$	496.073	+	859.224i	0.602762	+	1.04401i	0.992401	+	0.123047i	$0.0392665\pi$
$823$	496.073	+	859.224i	0.602762	+	1.04401i	−0.389639	+	0.920968i	$0.627400\pi$
$824$		0			0
$825$	−423.999	+	25.0772i	−0.513938	+	0.0303967i
$826$		0			0
$827$			39.2488i			0.0474593i	0.999718	+	0.0237296i	$0.00755409\pi$
$827$			39.2488i			0.0474593i	−0.999718	+	0.0237296i	$0.992446\pi$
$828$		0			0
$829$	−541.870	−	938.546i	−0.653643	−	1.13214i	−0.982232	−	0.187670i	$-0.939907\pi$
$829$	−541.870	−	938.546i	−0.653643	−	1.13214i	0.328589	−	0.944473i	$-0.393427\pi$
$830$		0			0
$831$	250.098	+	125.323i	0.300961	+	0.150810i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	164.554	−	285.016i	0.197071	−	0.341337i
$836$		0			0
$837$	−315.561	+	266.239i	−0.377014	+	0.318088i
$838$		0			0
$839$		−	570.971i		−	0.680537i	−0.940328	−	0.340269i	$-0.889482\pi$
$839$		−	570.971i		−	0.680537i	0.940328	−	0.340269i	$-0.110518\pi$
$840$		0			0
$841$	−550.838			−0.654980
$842$		0			0
$843$	414.469	+	628.938i	0.491660	+	0.746072i
$844$		0			0
$845$	−804.575	−	464.522i	−0.952160	−	0.549730i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−44.6562	−	22.3770i	−0.0525986	−	0.0263569i
$850$		0			0
$851$	−81.2303	+	46.8984i	−0.0954528	+	0.0551097i
$852$		0			0
$853$	−381.290			−0.446999			−0.223499	−	0.974704i	$-0.571748\pi$
$853$	−381.290			−0.446999			−0.223499	+	0.974704i	$0.571748\pi$
$854$		0			0
$855$	−28.4654	−	239.800i	−0.0332929	−	0.280468i
$856$		0			0
$857$	296.640	−	171.265i	0.346138	−	0.199843i	−0.316845	−	0.948477i	$-0.602623\pi$
$857$	296.640	−	171.265i	0.346138	−	0.199843i	0.662983	+	0.748634i	$0.269290\pi$
$858$		0			0
$859$	−261.025	+	452.109i	−0.303871	+	0.526321i	−0.977009	−	0.213196i	$-0.931613\pi$
$859$	−261.025	+	452.109i	−0.303871	+	0.526321i	0.673138	+	0.739517i	$0.264946\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−102.514	−	59.1867i	−0.118788	−	0.0685825i	0.439429	−	0.898278i	$-0.355181\pi$
$863$	−102.514	−	59.1867i	−0.118788	−	0.0685825i	−0.558217	+	0.829695i	$0.688514\pi$
$864$		0			0
$865$	−180.755	−	313.078i	−0.208966	−	0.361940i
$866$		0			0
$867$	−33.2686	−	562.495i	−0.0383721	−	0.648784i
$868$		0			0
$869$		−	600.457i		−	0.690974i
$870$		0			0
$871$	1245.75	+	2157.70i	1.43025	+	2.47727i
$872$		0			0
$873$	171.572	−	399.722i	0.196532	−	0.457872i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−30.3661	+	52.5956i	−0.0346249	+	0.0599721i	−0.882819	−	0.469714i	$-0.844357\pi$
$877$	−30.3661	+	52.5956i	−0.0346249	+	0.0599721i	0.848194	+	0.529686i	$0.177690\pi$
$878$		0			0
$879$	507.320	+	769.835i	0.577156	+	0.875808i
$880$		0			0
$881$			817.935i			0.928417i	0.885726	+	0.464208i	$0.153661\pi$
$881$			817.935i			0.928417i	−0.885726	+	0.464208i	$0.846339\pi$
$882$		0			0
$883$	19.9764			0.0226233			0.0113117	−	0.999936i	$-0.496399\pi$
$883$	19.9764			0.0226233			0.0113117	+	0.999936i	$0.496399\pi$
$884$		0			0
$885$	249.038	−	164.115i	0.281399	−	0.185441i
$886$		0			0
$887$	−590.636	−	341.004i	−0.665881	−	0.384446i	0.128633	−	0.991692i	$-0.458941\pi$
$887$	−590.636	−	341.004i	−0.665881	−	0.384446i	−0.794514	+	0.607246i	$0.792274\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1095.36	−	323.645i	−1.22936	−	0.363237i
$892$		0			0
$893$	431.810	−	249.305i	0.483550	−	0.279177i
$894$		0			0
$895$	760.118			0.849293
$896$		0			0
$897$	−468.620	+	27.7163i	−0.522430	+	0.0308989i
$898$		0			0
$899$	−494.055	+	285.243i	−0.549560	+	0.317289i
$900$		0			0
$901$	−1107.61	+	1918.43i	−1.22931	+	2.12923i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	549.404	+	317.198i	0.607076	+	0.350495i
$906$		0			0
$907$	−324.948	−	562.826i	−0.358266	−	0.620536i	0.629405	−	0.777078i	$-0.283299\pi$
$907$	−324.948	−	562.826i	−0.358266	−	0.620536i	−0.987671	+	0.156542i	$0.949965\pi$
$908$		0			0
$909$	85.6536	+	721.570i	0.0942284	+	0.793807i
$910$		0			0
$911$			1522.75i			1.67152i	0.549099	+	0.835758i	$0.314971\pi$
$911$			1522.75i			1.67152i	−0.549099	+	0.835758i	$0.685029\pi$
$912$		0			0
$913$	−578.893	−	1002.67i	−0.634056	−	1.09822i
$914$		0			0
$915$	405.997	−	810.221i	0.443713	−	0.885487i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	376.826	−	652.682i	0.410039	−	0.710209i	−0.584854	−	0.811138i	$-0.698848\pi$
$919$	376.826	−	652.682i	0.410039	−	0.710209i	0.994894	+	0.100929i	$0.0321816\pi$
$920$		0			0
$921$	317.570	−	209.278i	0.344809	−	0.227229i
$922$		0			0
$923$		−	699.249i		−	0.757582i
$924$		0			0
$925$	−121.746			−0.131618
$926$		0			0
$927$	259.947	+	347.863i	0.280417	+	0.375256i
$928$		0			0
$929$	−480.731	−	277.550i	−0.517471	−	0.298762i	0.218428	−	0.975853i	$-0.429907\pi$
$929$	−480.731	−	277.550i	−0.517471	−	0.298762i	−0.735900	+	0.677091i	$0.763240\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−442.059	+	882.186i	−0.473804	+	0.945537i
$934$		0			0
$935$	1031.37	−	595.461i	1.10307	−	0.636857i
$936$		0			0
$937$	−231.357			−0.246912			−0.123456	−	0.992350i	$-0.539398\pi$
$937$	−231.357			−0.246912			−0.123456	+	0.992350i	$0.539398\pi$
$938$		0			0
$939$	−45.9254	−	776.494i	−0.0489089	−	0.826937i
$940$		0			0
$941$	−455.108	+	262.757i	−0.483643	+	0.279231i	−0.721933	−	0.691963i	$-0.756746\pi$
$941$	−455.108	+	262.757i	−0.483643	+	0.279231i	0.238291	+	0.971194i	$0.423413\pi$
$942$		0			0
$943$	−163.616	+	283.391i	−0.173505	+	0.300520i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	495.241	+	285.928i	0.522958	+	0.301930i	0.738144	−	0.674643i	$-0.235702\pi$
$947$	495.241	+	285.928i	0.522958	+	0.301930i	−0.215186	+	0.976573i	$0.569036\pi$
$948$		0			0
$949$	1016.88	+	1761.30i	1.07153	+	1.85595i
$950$		0			0
$951$	−25.8157	+	1.52686i	−0.0271458	+	0.00160553i
$952$		0			0
$953$			596.119i			0.625518i	0.949833	+	0.312759i	$0.101253\pi$
$953$			596.119i			0.625518i	−0.949833	+	0.312759i	$0.898747\pi$
$954$		0			0
$955$	−445.196	−	771.102i	−0.466174	−	0.807437i
$956$		0			0
$957$	−1410.96	−	707.026i	−1.47436	−	0.738794i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	363.585	−	629.748i	0.378340	−	0.655305i
$962$		0			0
$963$	1416.85	−	1058.77i	1.47129	−	1.09945i
$964$		0			0
$965$		−	714.062i		−	0.739961i
$966$		0			0
$967$	1519.98			1.57185			0.785924	−	0.618324i	$-0.212188\pi$
$967$	1519.98			1.57185			0.785924	+	0.618324i	$0.212188\pi$
$968$		0			0
$969$	−250.067	−	379.465i	−0.258067	−	0.391605i
$970$		0			0
$971$	933.045	+	538.694i	0.960912	+	0.554783i	0.896454	−	0.443138i	$-0.146135\pi$
$971$	933.045	+	538.694i	0.960912	+	0.554783i	0.0644582	+	0.997920i	$0.479468\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−544.755	−	272.974i	−0.558723	−	0.279973i
$976$		0			0
$977$	1559.34	−	900.285i	1.59605	−	0.921480i	0.603811	−	0.797127i	$-0.293648\pi$
$977$	1559.34	−	900.285i	1.59605	−	0.921480i	0.992238	−	0.124352i	$-0.0396853\pi$
$978$		0			0
$979$	596.502			0.609297
$980$		0			0
$981$	476.280	−	56.5365i	0.485504	−	0.0576315i
$982$		0			0
$983$	444.096	−	256.399i	0.451776	−	0.260833i	−0.256804	−	0.966464i	$-0.582669\pi$
$983$	444.096	−	256.399i	0.451776	−	0.260833i	0.708580	+	0.705630i	$0.249336\pi$
$984$		0			0
$985$	−176.864	+	306.338i	−0.179557	+	0.311003i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−108.027	−	62.3694i	−0.109228	−	0.0630630i
$990$		0			0
$991$	95.8745	+	166.060i	0.0967452	+	0.167568i	0.910336	−	0.413871i	$-0.135823\pi$
$991$	95.8745	+	166.060i	0.0967452	+	0.167568i	−0.813590	+	0.581438i	$0.802490\pi$
$992$		0			0
$993$	−84.0222	−	1420.62i	−0.0846145	−	1.43064i
$994$		0			0
$995$		−	788.050i		−	0.792010i
$996$		0			0
$997$	838.778	+	1452.81i	0.841302	+	1.45718i	0.888794	+	0.458307i	$0.151544\pi$
$997$	838.778	+	1452.81i	0.841302	+	1.45718i	−0.0474918	+	0.998872i	$0.515123\pi$
$998$		0			0
$999$	−307.945	−	111.144i	−0.308253	−	0.111255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.p.f.569.4		8
3.2	odd	2	inner	588.3.p.f.569.1		8
7.2	even	3		84.3.c.a.29.2	yes	4
7.3	odd	6		588.3.p.h.557.4		8
7.4	even	3	inner	588.3.p.f.557.1		8
7.5	odd	6		588.3.c.h.197.3		4
7.6	odd	2		588.3.p.h.569.1		8
21.2	odd	6		84.3.c.a.29.1	✓	4
21.5	even	6		588.3.c.h.197.4		4
21.11	odd	6	inner	588.3.p.f.557.4		8
21.17	even	6		588.3.p.h.557.1		8
21.20	even	2		588.3.p.h.569.4		8
28.23	odd	6		336.3.d.a.113.3		4
35.2	odd	12		2100.3.e.a.449.7		8
35.9	even	6		2100.3.g.a.701.3		4
35.23	odd	12		2100.3.e.a.449.2		8
56.37	even	6		1344.3.d.a.449.3		4
56.51	odd	6		1344.3.d.g.449.2		4
63.2	odd	6		2268.3.bg.a.701.3		8
63.16	even	3		2268.3.bg.a.701.2		8
63.23	odd	6		2268.3.bg.a.2213.2		8
63.58	even	3		2268.3.bg.a.2213.3		8
84.23	even	6		336.3.d.a.113.4		4
105.2	even	12		2100.3.e.a.449.1		8
105.23	even	12		2100.3.e.a.449.8		8
105.44	odd	6		2100.3.g.a.701.4		4
168.107	even	6		1344.3.d.g.449.1		4
168.149	odd	6		1344.3.d.a.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.c.a.29.1	✓	4	21.2	odd	6
84.3.c.a.29.2	yes	4	7.2	even	3
336.3.d.a.113.3		4	28.23	odd	6
336.3.d.a.113.4		4	84.23	even	6
588.3.c.h.197.3		4	7.5	odd	6
588.3.c.h.197.4		4	21.5	even	6
588.3.p.f.557.1		8	7.4	even	3	inner
588.3.p.f.557.4		8	21.11	odd	6	inner
588.3.p.f.569.1		8	3.2	odd	2	inner
588.3.p.f.569.4		8	1.1	even	1	trivial
588.3.p.h.557.1		8	21.17	even	6
588.3.p.h.557.4		8	7.3	odd	6
588.3.p.h.569.1		8	7.6	odd	2
588.3.p.h.569.4		8	21.20	even	2
1344.3.d.a.449.3		4	56.37	even	6
1344.3.d.a.449.4		4	168.149	odd	6
1344.3.d.g.449.1		4	168.107	even	6
1344.3.d.g.449.2		4	56.51	odd	6
2100.3.e.a.449.1		8	105.2	even	12
2100.3.e.a.449.2		8	35.23	odd	12
2100.3.e.a.449.7		8	35.2	odd	12
2100.3.e.a.449.8		8	105.23	even	12
2100.3.g.a.701.3		4	35.9	even	6
2100.3.g.a.701.4		4	105.44	odd	6
2268.3.bg.a.701.2		8	63.16	even	3
2268.3.bg.a.701.3		8	63.2	odd	6
2268.3.bg.a.2213.2		8	63.23	odd	6
2268.3.bg.a.2213.3		8	63.58	even	3

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)

\(f(q)\)	\(=\)	\(q+(2.50498 - 1.65078i) q^{3} +(-3.34957 - 1.93387i) q^{5} +(3.54987 - 8.27034i) q^{9} +O(q^{10})\)	\(q+(2.50498 - 1.65078i) q^{3} +(-3.34957 - 1.93387i) q^{5} +(3.54987 - 8.27034i) q^{9} +(12.2117 - 7.05043i) q^{11} +20.2288 q^{13} +(-11.5830 + 0.685072i) q^{15} +(-18.9108 + 10.9182i) q^{17} +(-3.46863 + 6.00784i) q^{19} +(-6.69914 - 3.86775i) q^{23} +(-5.02026 - 8.69534i) q^{25} +(-4.76013 - 26.5771i) q^{27} -37.3073i q^{29} +(-7.64575 - 13.2428i) q^{31} +(18.9514 - 37.8200i) q^{33} +(6.06275 - 10.5010i) q^{37} +(50.6727 - 33.3932i) q^{39} -42.3026i q^{41} +16.1255 q^{43} +(-27.8843 + 20.8371i) q^{45} +(-62.2451 - 35.9372i) q^{47} +(-29.3478 + 58.5674i) q^{51} +(87.8550 - 50.7231i) q^{53} -54.5385 q^{55} +(1.22876 + 20.7755i) q^{57} +(-22.2604 + 12.8520i) q^{59} +(-39.0516 + 67.6394i) q^{61} +(-67.7576 - 39.1199i) q^{65} +(61.5830 + 106.665i) q^{67} +(-23.1660 + 1.37014i) q^{69} -34.5671i q^{71} +(50.2693 + 87.0689i) q^{73} +(-26.9297 - 13.4943i) q^{75} +(21.2915 - 36.8780i) q^{79} +(-55.7969 - 58.7172i) q^{81} -82.1075i q^{83} +84.4575 q^{85} +(-61.5861 - 93.4542i) q^{87} +(36.6351 + 21.1513i) q^{89} +(-41.0134 - 20.5516i) q^{93} +(23.2368 - 13.4158i) q^{95} +48.3320 q^{97} +(-14.9595 - 126.023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} + 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 + 4 * q^9	\( 8 q - 6 q^{3} + 4 q^{9} + 56 q^{13} - 8 q^{15} + 4 q^{19} + 108 q^{25} + 36 q^{27} - 40 q^{31} + 116 q^{33} + 112 q^{37} + 28 q^{39} + 256 q^{43} - 100 q^{45} - 124 q^{51} + 368 q^{55} - 96 q^{57} - 196 q^{61} + 408 q^{67} - 16 q^{69} + 358 q^{75} + 128 q^{79} - 188 q^{81} + 464 q^{85} - 140 q^{87} - 32 q^{93} + 48 q^{97} - 416 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 + 4 * q^9 + 56 * q^13 - 8 * q^15 + 4 * q^19 + 108 * q^25 + 36 * q^27 - 40 * q^31 + 116 * q^33 + 112 * q^37 + 28 * q^39 + 256 * q^43 - 100 * q^45 - 124 * q^51 + 368 * q^55 - 96 * q^57 - 196 * q^61 + 408 * q^67 - 16 * q^69 + 358 * q^75 + 128 * q^79 - 188 * q^81 + 464 * q^85 - 140 * q^87 - 32 * q^93 + 48 * q^97 - 416 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more