LMFDB - Embedded newform 504.3.g.c.379.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(379,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 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("504.379"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.9
Character	$\chi$	$=$	504.379
Dual form			504.3.g.c.379.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.550248 - 1.92282i) q^{2} +(-3.39445 + 2.11605i) q^{4} +2.10762i q^{5} -2.64575i q^{7} +(5.93658 + 5.36256i) q^{8} +(4.05258 - 1.15972i) q^{10} -5.49014 q^{11} -0.893817i q^{13} +(-5.08730 + 1.45582i) q^{14} +(7.04463 - 14.3657i) q^{16} -10.0306 q^{17} +25.3915 q^{19} +(-4.45985 - 7.15423i) q^{20} +(3.02094 + 10.5565i) q^{22} -15.9278i q^{23} +20.5579 q^{25} +(-1.71865 + 0.491821i) q^{26} +(5.59855 + 8.98088i) q^{28} -28.8363i q^{29} -41.5598i q^{31} +(-31.4989 - 5.64084i) q^{32} +(5.51933 + 19.2871i) q^{34} +5.57625 q^{35} -37.1910i q^{37} +(-13.9716 - 48.8233i) q^{38} +(-11.3023 + 12.5121i) q^{40} -70.6399 q^{41} +6.60609 q^{43} +(18.6360 - 11.6174i) q^{44} +(-30.6262 + 8.76424i) q^{46} -44.9902i q^{47} -7.00000 q^{49} +(-11.3120 - 39.5291i) q^{50} +(1.89136 + 3.03402i) q^{52} -27.8456i q^{53} -11.5711i q^{55} +(14.1880 - 15.7067i) q^{56} +(-55.4469 + 15.8671i) q^{58} +38.7342 q^{59} +7.21121i q^{61} +(-79.9120 + 22.8682i) q^{62} +(6.48592 + 63.6705i) q^{64} +1.88383 q^{65} -10.9281 q^{67} +(34.0485 - 21.2253i) q^{68} +(-3.06832 - 10.7221i) q^{70} +72.4872i q^{71} +26.0986 q^{73} +(-71.5114 + 20.4643i) q^{74} +(-86.1903 + 53.7298i) q^{76} +14.5255i q^{77} -96.8805i q^{79} +(30.2775 + 14.8474i) q^{80} +(38.8695 + 135.828i) q^{82} -26.3015 q^{83} -21.1408i q^{85} +(-3.63499 - 12.7023i) q^{86} +(-32.5926 - 29.4412i) q^{88} -41.8658 q^{89} -2.36482 q^{91} +(33.7041 + 54.0662i) q^{92} +(-86.5079 + 24.7558i) q^{94} +53.5158i q^{95} +74.6737 q^{97} +(3.85174 + 13.4597i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 12 q^{10} + 66 q^{16} - 64 q^{19} - 144 q^{22} - 168 q^{25} - 14 q^{28} + 12 q^{34} + 196 q^{40} + 224 q^{43} - 84 q^{46} - 168 q^{49} - 364 q^{52} + 348 q^{58} + 214 q^{64} - 32 q^{67}+ \cdots - 144 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 + 12 * q^10 + 66 * q^16 - 64 * q^19 - 144 * q^22 - 168 * q^25 - 14 * q^28 + 12 * q^34 + 196 * q^40 + 224 * q^43 - 84 * q^46 - 168 * q^49 - 364 * q^52 + 348 * q^58 + 214 * q^64 - 32 * q^67 - 84 * q^70 + 240 * q^73 + 416 * q^76 + 300 * q^82 - 120 * q^88 + 192 * q^94 - 144 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−0.550248	−	1.92282i	−0.275124	−	0.961409i
$2$	−0.550248	−	1.92282i	−0.275124	−	0.961409i
$3$		0			0
$3$		0			0
$4$	−3.39445	+	2.11605i	−0.848613	+	0.529014i
$5$			2.10762i			0.421525i	0.977537	+	0.210762i	$0.0675946\pi$
$5$			2.10762i			0.421525i	−0.977537	+	0.210762i	$0.932405\pi$
$6$		0			0
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	5.93658	+	5.36256i	0.742072	+	0.670320i
$9$		0			0
$10$	4.05258	−	1.15972i	0.405258	−	0.115972i
$11$	−5.49014			−0.499103			−0.249552	−	0.968361i	$-0.580283\pi$
$11$	−5.49014			−0.499103			−0.249552	+	0.968361i	$0.580283\pi$
$12$		0			0
$13$		−	0.893817i		−	0.0687551i	−0.999409	−	0.0343776i	$-0.989055\pi$
$13$		−	0.893817i		−	0.0687551i	0.999409	−	0.0343776i	$-0.0109449\pi$
$14$	−5.08730	+	1.45582i	−0.363378	+	0.103987i
$15$		0			0
$16$	7.04463	−	14.3657i	0.440289	−	0.897856i
$17$	−10.0306			−0.590037			−0.295018	−	0.955492i	$-0.595326\pi$
$17$	−10.0306			−0.590037			−0.295018	+	0.955492i	$0.595326\pi$
$18$		0			0
$19$	25.3915			1.33640			0.668198	−	0.743984i	$-0.267066\pi$
$19$	25.3915			1.33640			0.668198	+	0.743984i	$0.267066\pi$
$20$	−4.45985	−	7.15423i	−0.222992	−	0.357712i
$21$		0			0
$22$	3.02094	+	10.5565i	0.137315	+	0.479842i
$23$		−	15.9278i		−	0.692513i	−0.938140	−	0.346256i	$-0.887453\pi$
$23$		−	15.9278i		−	0.692513i	0.938140	−	0.346256i	$-0.112547\pi$
$24$		0			0
$25$	20.5579			0.822317
$26$	−1.71865	+	0.491821i	−0.0661018	+	0.0189162i
$27$		0			0
$28$	5.59855	+	8.98088i	0.199948	+	0.320746i
$29$		−	28.8363i		−	0.994354i	−0.867649	−	0.497177i	$-0.834370\pi$
$29$		−	28.8363i		−	0.994354i	0.867649	−	0.497177i	$-0.165630\pi$
$30$		0			0
$31$		−	41.5598i		−	1.34064i	−0.742072	−	0.670320i	$-0.766157\pi$
$31$		−	41.5598i		−	1.34064i	0.742072	−	0.670320i	$-0.233843\pi$
$32$	−31.4989	−	5.64084i	−0.984341	−	0.176276i
$33$		0			0
$34$	5.51933	+	19.2871i	0.162333	+	0.567266i
$35$	5.57625			0.159321
$36$		0			0
$37$		−	37.1910i		−	1.00516i	−0.864530	−	0.502580i	$-0.832384\pi$
$37$		−	37.1910i		−	1.00516i	0.864530	−	0.502580i	$-0.167616\pi$
$38$	−13.9716	−	48.8233i	−0.367675	−	1.28482i
$39$		0			0
$40$	−11.3023	+	12.5121i	−0.282556	+	0.312802i
$41$	−70.6399			−1.72292			−0.861462	−	0.507822i	$-0.830451\pi$
$41$	−70.6399			−1.72292			−0.861462	+	0.507822i	$0.830451\pi$
$42$		0			0
$43$	6.60609			0.153630			0.0768150	−	0.997045i	$-0.475525\pi$
$43$	6.60609			0.153630			0.0768150	+	0.997045i	$0.475525\pi$
$44$	18.6360	−	11.6174i	0.423546	−	0.264032i
$45$		0			0
$46$	−30.6262	+	8.76424i	−0.665788	+	0.190527i
$47$		−	44.9902i		−	0.957238i	−0.878023	−	0.478619i	$-0.841138\pi$
$47$		−	44.9902i		−	0.957238i	0.878023	−	0.478619i	$-0.158862\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−11.3120	−	39.5291i	−0.226239	−	0.790583i
$51$		0			0
$52$	1.89136	+	3.03402i	0.0363724	+	0.0583465i
$53$		−	27.8456i		−	0.525388i	−0.964879	−	0.262694i	$-0.915389\pi$
$53$		−	27.8456i		−	0.525388i	0.964879	−	0.262694i	$-0.0846110\pi$
$54$		0			0
$55$		−	11.5711i		−	0.210384i
$56$	14.1880	−	15.7067i	0.253357	−	0.280477i
$57$		0			0
$58$	−55.4469	+	15.8671i	−0.955981	+	0.273571i
$59$	38.7342			0.656512			0.328256	−	0.944589i	$-0.393539\pi$
$59$	38.7342			0.656512			0.328256	+	0.944589i	$0.393539\pi$
$60$		0			0
$61$			7.21121i			0.118216i	0.998252	+	0.0591082i	$0.0188257\pi$
$61$			7.21121i			0.118216i	−0.998252	+	0.0591082i	$0.981174\pi$
$62$	−79.9120	+	22.8682i	−1.28890	+	0.368842i
$63$		0			0
$64$	6.48592	+	63.6705i	0.101342	+	0.994852i
$65$	1.88383			0.0289820
$66$		0			0
$67$	−10.9281			−0.163106			−0.0815532	−	0.996669i	$-0.525988\pi$
$67$	−10.9281			−0.163106			−0.0815532	+	0.996669i	$0.525988\pi$
$68$	34.0485	−	21.2253i	0.500713	−	0.312137i
$69$		0			0
$70$	−3.06832	−	10.7221i	−0.0438332	−	0.153173i
$71$			72.4872i			1.02095i	0.859893	+	0.510474i	$0.170530\pi$
$71$			72.4872i			1.02095i	−0.859893	+	0.510474i	$0.829470\pi$
$72$		0			0
$73$	26.0986			0.357515			0.178757	−	0.983893i	$-0.442792\pi$
$73$	26.0986			0.357515			0.178757	+	0.983893i	$0.442792\pi$
$74$	−71.5114	+	20.4643i	−0.966370	+	0.276544i
$75$		0			0
$76$	−86.1903	+	53.7298i	−1.13408	+	0.706971i
$77$			14.5255i			0.188643i
$78$		0			0
$79$		−	96.8805i		−	1.22634i	−0.789953	−	0.613168i	$-0.789895\pi$
$79$		−	96.8805i		−	1.22634i	0.789953	−	0.613168i	$-0.210105\pi$
$80$	30.2775	+	14.8474i	0.378469	+	0.185593i
$81$		0			0
$82$	38.8695	+	135.828i	0.474018	+	1.65643i
$83$	−26.3015			−0.316886			−0.158443	−	0.987368i	$-0.550647\pi$
$83$	−26.3015			−0.316886			−0.158443	+	0.987368i	$0.550647\pi$
$84$		0			0
$85$		−	21.1408i		−	0.248715i
$86$	−3.63499	−	12.7023i	−0.0422674	−	0.147701i
$87$		0			0
$88$	−32.5926	−	29.4412i	−0.370371	−	0.334559i
$89$	−41.8658			−0.470402			−0.235201	−	0.971947i	$-0.575575\pi$
$89$	−41.8658			−0.470402			−0.235201	+	0.971947i	$0.575575\pi$
$90$		0			0
$91$	−2.36482			−0.0259870
$92$	33.7041	+	54.0662i	0.366349	+	0.587676i
$93$		0			0
$94$	−86.5079	+	24.7558i	−0.920297	+	0.263359i
$95$			53.5158i			0.563324i
$96$		0			0
$97$	74.6737			0.769832			0.384916	−	0.922952i	$-0.374230\pi$
$97$	74.6737			0.769832			0.384916	+	0.922952i	$0.374230\pi$
$98$	3.85174	+	13.4597i	0.0393035	+	0.137344i
$99$		0			0
$100$	−69.7829	+	43.5017i	−0.697829	+	0.435017i
$101$		−	82.1506i		−	0.813372i	−0.913568	−	0.406686i	$-0.866684\pi$
$101$		−	82.1506i		−	0.813372i	0.913568	−	0.406686i	$-0.133316\pi$
$102$		0			0
$103$			63.9274i			0.620654i	0.950630	+	0.310327i	$0.100439\pi$
$103$			63.9274i			0.620654i	−0.950630	+	0.310327i	$0.899561\pi$
$104$	4.79314	−	5.30621i	0.0460879	−	0.0510213i
$105$		0			0
$106$	−53.5420	+	15.3220i	−0.505113	+	0.144547i
$107$	176.996			1.65417			0.827086	−	0.562075i	$-0.189997\pi$
$107$	176.996			1.65417			0.827086	+	0.562075i	$0.189997\pi$
$108$		0			0
$109$		−	165.522i		−	1.51855i	−0.650771	−	0.759274i	$-0.725554\pi$
$109$		−	165.522i		−	1.51855i	0.650771	−	0.759274i	$-0.274446\pi$
$110$	−22.2492	+	6.36700i	−0.202265	+	0.0578818i
$111$		0			0
$112$	−38.0081	−	18.6383i	−0.339358	−	0.166414i
$113$	−100.006			−0.885010			−0.442505	−	0.896766i	$-0.645910\pi$
$113$	−100.006			−0.885010			−0.442505	+	0.896766i	$0.645910\pi$
$114$		0			0
$115$	33.5698			0.291911
$116$	61.0191	+	97.8834i	0.526027	+	0.843822i
$117$		0			0
$118$	−21.3134	−	74.4788i	−0.180622	−	0.631176i
$119$			26.5385i			0.223013i
$120$		0			0
$121$	−90.8584			−0.750896
$122$	13.8658	−	3.96795i	0.113654	−	0.0325242i
$123$		0			0
$124$	87.9429	+	141.073i	0.709217	+	1.13768i
$125$			96.0190i			0.768152i
$126$		0			0
$127$		−	16.1063i		−	0.126821i	−0.997988	−	0.0634104i	$-0.979802\pi$
$127$		−	16.1063i		−	0.126821i	0.997988	−	0.0634104i	$-0.0201977\pi$
$128$	118.858	−	47.5058i	0.928577	−	0.371139i
$129$		0			0
$130$	−1.03657	−	3.62226i	−0.00797365	−	0.0278635i
$131$	206.703			1.57789			0.788943	−	0.614467i	$-0.210629\pi$
$131$	206.703			1.57789			0.788943	+	0.614467i	$0.210629\pi$
$132$		0			0
$133$		−	67.1796i		−	0.505110i
$134$	6.01318	+	21.0128i	0.0448745	+	0.156812i
$135$		0			0
$136$	−59.5476	−	53.7898i	−0.437850	−	0.395513i
$137$	−174.265			−1.27201			−0.636005	−	0.771685i	$-0.719414\pi$
$137$	−174.265			−1.27201			−0.636005	+	0.771685i	$0.719414\pi$
$138$		0			0
$139$	186.676			1.34299			0.671496	−	0.741008i	$-0.265652\pi$
$139$	186.676			1.34299			0.671496	+	0.741008i	$0.265652\pi$
$140$	−18.9283	+	11.7996i	−0.135202	+	0.0842832i
$141$		0			0
$142$	139.380	−	39.8860i	0.981547	−	0.280887i
$143$			4.90718i			0.0343159i
$144$		0			0
$145$	60.7760			0.419145
$146$	−14.3607	−	50.1828i	−0.0983609	−	0.343718i
$147$		0			0
$148$	78.6981	+	126.243i	0.531744	+	0.852993i
$149$		−	138.373i		−	0.928678i	−0.885658	−	0.464339i	$-0.846292\pi$
$149$		−	138.373i		−	0.928678i	0.885658	−	0.464339i	$-0.153708\pi$
$150$		0			0
$151$		−	79.0738i		−	0.523668i	−0.965113	−	0.261834i	$-0.915673\pi$
$151$		−	79.0738i		−	0.523668i	0.965113	−	0.261834i	$-0.0843272\pi$
$152$	150.739	+	136.164i	0.991702	+	0.895813i
$153$		0			0
$154$	27.9300	−	7.99265i	0.181363	−	0.0519003i
$155$	87.5925			0.565113
$156$		0			0
$157$			10.4342i			0.0664596i	0.999448	+	0.0332298i	$0.0105793\pi$
$157$			10.4342i			0.0664596i	−0.999448	+	0.0332298i	$0.989421\pi$
$158$	−186.284	+	53.3083i	−1.17901	+	0.337394i
$159$		0			0
$160$	11.8888	−	66.3878i	0.0743048	−	0.414924i
$161$	−42.1410			−0.261745
$162$		0			0
$163$	−46.5311			−0.285467			−0.142734	−	0.989761i	$-0.545589\pi$
$163$	−46.5311			−0.285467			−0.142734	+	0.989761i	$0.545589\pi$
$164$	239.784	−	149.478i	1.46210	−	0.911450i
$165$		0			0
$166$	14.4724	+	50.5730i	0.0871829	+	0.304657i
$167$			128.113i			0.767147i	0.923510	+	0.383573i	$0.125307\pi$
$167$			128.113i			0.767147i	−0.923510	+	0.383573i	$0.874693\pi$
$168$		0			0
$169$	168.201			0.995273
$170$	−40.6499	+	11.6327i	−0.239117	+	0.0684275i
$171$		0			0
$172$	−22.4241	+	13.9789i	−0.130373	+	0.0812724i
$173$		−	18.9967i		−	0.109808i	−0.998492	−	0.0549038i	$-0.982515\pi$
$173$		−	18.9967i		−	0.109808i	0.998492	−	0.0549038i	$-0.0174852\pi$
$174$		0			0
$175$		−	54.3911i		−	0.310807i
$176$	−38.6760	+	78.8696i	−0.219750	+	0.448123i
$177$		0			0
$178$	23.0366	+	80.5003i	0.129419	+	0.452249i
$179$	142.472			0.795933			0.397966	−	0.917400i	$-0.369716\pi$
$179$	142.472			0.795933			0.397966	+	0.917400i	$0.369716\pi$
$180$		0			0
$181$			60.5041i			0.334277i	0.985933	+	0.167138i	$0.0534526\pi$
$181$			60.5041i			0.334277i	−0.985933	+	0.167138i	$0.946547\pi$
$182$	1.30124	+	4.54711i	0.00714965	+	0.0249841i
$183$		0			0
$184$	85.4137	−	94.5566i	0.464205	−	0.513895i
$185$	78.3845			0.423700
$186$		0			0
$187$	55.0695			0.294489
$188$	95.2016	+	152.717i	0.506392	+	0.812325i
$189$		0			0
$190$	102.901	−	29.4470i	0.541584	−	0.154984i
$191$			104.346i			0.546316i	0.961969	+	0.273158i	$0.0880681\pi$
$191$			104.346i			0.546316i	−0.961969	+	0.273158i	$0.911932\pi$
$192$		0			0
$193$	−5.66026			−0.0293278			−0.0146639	−	0.999892i	$-0.504668\pi$
$193$	−5.66026			−0.0293278			−0.0146639	+	0.999892i	$0.504668\pi$
$194$	−41.0891	−	143.584i	−0.211799	−	0.740123i
$195$		0			0
$196$	23.7612	−	14.8124i	0.121230	−	0.0755734i
$197$			335.617i			1.70364i	0.523836	+	0.851819i	$0.324501\pi$
$197$			335.617i			1.70364i	−0.523836	+	0.851819i	$0.675499\pi$
$198$		0			0
$199$		−	91.4717i		−	0.459657i	−0.973231	−	0.229829i	$-0.926183\pi$
$199$		−	91.4717i		−	0.459657i	0.973231	−	0.229829i	$-0.0738165\pi$
$200$	122.044	+	110.243i	0.610219	+	0.551215i
$201$		0			0
$202$	−157.961	+	45.2032i	−0.781983	+	0.223778i
$203$	−76.2936			−0.375831
$204$		0			0
$205$		−	148.882i		−	0.726255i
$206$	122.921	−	35.1759i	0.596702	−	0.170757i
$207$		0			0
$208$	−12.8403	−	6.29661i	−0.0617322	−	0.0302722i
$209$	−139.403			−0.667000
$210$		0			0
$211$	−280.360			−1.32872			−0.664359	−	0.747413i	$-0.731296\pi$
$211$	−280.360			−1.32872			−0.664359	+	0.747413i	$0.731296\pi$
$212$	58.9227	+	94.5205i	0.277937	+	0.445851i
$213$		0			0
$214$	−97.3920	−	340.332i	−0.455103	−	1.59034i
$215$			13.9232i			0.0647589i
$216$		0			0
$217$	−109.957			−0.506714
$218$	−318.268	+	91.0780i	−1.45994	+	0.417789i
$219$		0			0
$220$	24.4852	+	39.2777i	0.111296	+	0.178535i
$221$			8.96554i			0.0405680i
$222$		0			0
$223$			352.302i			1.57983i	0.613215	+	0.789916i	$0.289876\pi$
$223$			352.302i			1.57983i	−0.613215	+	0.789916i	$0.710124\pi$
$224$	−14.9243	+	83.3383i	−0.0666261	+	0.372046i
$225$		0			0
$226$	55.0282	+	192.293i	0.243488	+	0.850856i
$227$	427.232			1.88208			0.941041	−	0.338294i	$-0.109850\pi$
$227$	427.232			1.88208			0.941041	+	0.338294i	$0.109850\pi$
$228$		0			0
$229$			244.440i			1.06742i	0.845667	+	0.533711i	$0.179203\pi$
$229$			244.440i			1.06742i	−0.845667	+	0.533711i	$0.820797\pi$
$230$	−18.4717	−	64.5486i	−0.0803119	−	0.280646i
$231$		0			0
$232$	154.636	−	171.189i	0.666536	−	0.737883i
$233$	−65.9296			−0.282960			−0.141480	−	0.989941i	$-0.545186\pi$
$233$	−65.9296			−0.282960			−0.141480	+	0.989941i	$0.545186\pi$
$234$		0			0
$235$	94.8224			0.403499
$236$	−131.481	+	81.9637i	−0.557125	+	0.347304i
$237$		0			0
$238$	51.0287	−	14.6028i	0.214407	−	0.0613562i
$239$		−	117.973i		−	0.493613i	−0.969065	−	0.246806i	$-0.920619\pi$
$239$		−	117.973i		−	0.493613i	0.969065	−	0.246806i	$-0.0793811\pi$
$240$		0			0
$241$	−30.8746			−0.128110			−0.0640552	−	0.997946i	$-0.520403\pi$
$241$	−30.8746			−0.128110			−0.0640552	+	0.997946i	$0.520403\pi$
$242$	49.9947	+	174.704i	0.206590	+	0.721918i
$243$		0			0
$244$	−15.2593	−	24.4781i	−0.0625381	−	0.100320i
$245$		−	14.7534i		−	0.0602178i
$246$		0			0
$247$		−	22.6954i		−	0.0918841i
$248$	222.867	−	246.723i	0.898657	−	0.994852i
$249$		0			0
$250$	184.627	−	52.8343i	0.738508	−	0.211337i
$251$	292.824			1.16663			0.583314	−	0.812247i	$-0.301756\pi$
$251$	292.824			1.16663			0.583314	+	0.812247i	$0.301756\pi$
$252$		0			0
$253$			87.4458i			0.345635i
$254$	−30.9694	+	8.86244i	−0.121927	+	0.0348915i
$255$		0			0
$256$	−156.746	−	202.402i	−0.612291	−	0.790633i
$257$	−64.9208			−0.252610			−0.126305	−	0.991991i	$-0.540312\pi$
$257$	−64.9208			−0.252610			−0.126305	+	0.991991i	$0.540312\pi$
$258$		0			0
$259$	−98.3980			−0.379915
$260$	−6.39457	+	3.98628i	−0.0245945	+	0.0153319i
$261$		0			0
$262$	−113.738	−	397.452i	−0.434114	−	1.51699i
$263$			163.348i			0.621093i	0.950558	+	0.310547i	$0.100512\pi$
$263$			163.348i			0.621093i	−0.950558	+	0.310547i	$0.899488\pi$
$264$		0			0
$265$	58.6880			0.221464
$266$	−129.174	+	36.9655i	−0.485617	+	0.138968i
$267$		0			0
$268$	37.0950	−	23.1245i	0.138414	−	0.0862855i
$269$		−	337.337i		−	1.25404i	−0.779003	−	0.627020i	$-0.784275\pi$
$269$		−	337.337i		−	1.25404i	0.779003	−	0.627020i	$-0.215725\pi$
$270$		0			0
$271$			50.7068i			0.187110i	0.995614	+	0.0935550i	$0.0298231\pi$
$271$			50.7068i			0.187110i	−0.995614	+	0.0935550i	$0.970177\pi$
$272$	−70.6620	+	144.097i	−0.259787	+	0.529768i
$273$		0			0
$274$	95.8893	+	335.081i	0.349961	+	1.22292i
$275$	−112.866			−0.410421
$276$		0			0
$277$			507.625i			1.83258i	0.400514	+	0.916291i	$0.368832\pi$
$277$			507.625i			1.83258i	−0.400514	+	0.916291i	$0.631168\pi$
$278$	−102.718	−	358.944i	−0.369490	−	1.29116i
$279$		0			0
$280$	33.1038	+	29.9030i	0.118228	+	0.106796i
$281$	−517.785			−1.84265			−0.921325	−	0.388793i	$-0.872892\pi$
$281$	−517.785			−1.84265			−0.921325	+	0.388793i	$0.872892\pi$
$282$		0			0
$283$	−213.035			−0.752774			−0.376387	−	0.926463i	$-0.622834\pi$
$283$	−213.035			−0.752774			−0.376387	+	0.926463i	$0.622834\pi$
$284$	−153.387	−	246.055i	−0.540095	−	0.866389i
$285$		0			0
$286$	9.43560	−	2.70017i	0.0329916	−	0.00944114i
$287$			186.896i			0.651204i
$288$		0			0
$289$	−188.387			−0.651857
$290$	−33.4419	−	116.861i	−0.115317	−	0.402970i
$291$		0			0
$292$	−88.5904	+	55.2260i	−0.303392	+	0.189130i
$293$		−	183.590i		−	0.626586i	−0.949656	−	0.313293i	$-0.898568\pi$
$293$		−	183.590i		−	0.626586i	0.949656	−	0.313293i	$-0.101432\pi$
$294$		0			0
$295$			81.6371i			0.276736i
$296$	199.439	−	220.787i	0.673779	−	0.745902i
$297$		0			0
$298$	−266.066	+	76.1395i	−0.892839	+	0.255502i
$299$	−14.2365			−0.0476138
$300$		0			0
$301$		−	17.4781i		−	0.0580667i
$302$	−152.044	+	43.5102i	−0.503459	+	0.144074i
$303$		0			0
$304$	178.874	−	364.767i	0.588401	−	1.19989i
$305$	−15.1985			−0.0498312
$306$		0			0
$307$	289.386			0.942626			0.471313	−	0.881966i	$-0.343780\pi$
$307$	289.386			0.942626			0.471313	+	0.881966i	$0.343780\pi$
$308$	−30.7368	−	49.3063i	−0.0997949	−	0.160085i
$309$		0			0
$310$	−48.1976	−	168.424i	−0.155476	−	0.543304i
$311$		−	361.881i		−	1.16361i	−0.813330	−	0.581803i	$-0.802348\pi$
$311$		−	361.881i		−	1.16361i	0.813330	−	0.581803i	$-0.197652\pi$
$312$		0			0
$313$	−511.351			−1.63371			−0.816854	−	0.576845i	$-0.804284\pi$
$313$	−511.351			−1.63371			−0.816854	+	0.576845i	$0.804284\pi$
$314$	20.0630	−	5.74137i	0.0638948	−	0.0182846i
$315$		0			0
$316$	205.004	+	328.856i	0.648748	+	1.04068i
$317$		−	380.742i		−	1.20108i	−0.799596	−	0.600539i	$-0.794953\pi$
$317$		−	380.742i		−	1.20108i	0.799596	−	0.600539i	$-0.205047\pi$
$318$		0			0
$319$			158.315i			0.496286i
$320$	−134.193	+	13.6699i	−0.419355	+	0.0427184i
$321$		0			0
$322$	23.1880	+	81.0294i	0.0720124	+	0.251644i
$323$	−254.693			−0.788522
$324$		0			0
$325$		−	18.3750i		−	0.0565385i
$326$	25.6037	+	89.4709i	0.0785389	+	0.274451i
$327$		0			0
$328$	−419.359	−	378.811i	−1.27853	−	1.15491i
$329$	−119.033			−0.361802
$330$		0			0
$331$	−353.452			−1.06783			−0.533915	−	0.845538i	$-0.679280\pi$
$331$	−353.452			−1.06783			−0.533915	+	0.845538i	$0.679280\pi$
$332$	89.2792	−	55.6554i	0.268913	−	0.167637i
$333$		0			0
$334$	246.339	−	70.4942i	0.737541	−	0.211061i
$335$		−	23.0324i		−	0.0687534i
$336$		0			0
$337$	−549.243			−1.62980			−0.814901	−	0.579600i	$-0.803209\pi$
$337$	−549.243			−1.62980			−0.814901	+	0.579600i	$0.803209\pi$
$338$	−92.5524	−	323.420i	−0.273824	−	0.956864i
$339$		0			0
$340$	44.7350	+	71.7614i	0.131574	+	0.211063i
$341$			228.169i			0.669118i
$342$		0			0
$343$			18.5203i			0.0539949i
$344$	39.2176	+	35.4256i	0.114005	+	0.102981i
$345$		0			0
$346$	−36.5272	+	10.4529i	−0.105570	+	0.0302107i
$347$	−493.380			−1.42184			−0.710922	−	0.703271i	$-0.751722\pi$
$347$	−493.380			−1.42184			−0.710922	+	0.703271i	$0.751722\pi$
$348$		0			0
$349$			467.641i			1.33994i	0.742386	+	0.669972i	$0.233694\pi$
$349$			467.641i			1.33994i	−0.742386	+	0.669972i	$0.766306\pi$
$350$	−104.584	+	29.9286i	−0.298812	+	0.0855104i
$351$		0			0
$352$	172.933	+	30.9690i	0.491288	+	0.0879800i
$353$	226.374			0.641285			0.320643	−	0.947200i	$-0.396101\pi$
$353$	226.374			0.641285			0.320643	+	0.947200i	$0.396101\pi$
$354$		0			0
$355$	−152.776			−0.430354
$356$	142.112	−	88.5903i	0.399190	−	0.248849i
$357$		0			0
$358$	−78.3950	−	273.948i	−0.218980	−	0.765217i
$359$		−	118.269i		−	0.329440i	−0.986340	−	0.164720i	$-0.947328\pi$
$359$		−	118.269i		−	0.329440i	0.986340	−	0.164720i	$-0.0526720\pi$
$360$		0			0
$361$	283.729			0.785953
$362$	116.338	−	33.2923i	0.321376	−	0.0919676i
$363$		0			0
$364$	8.02726	−	5.00408i	0.0220529	−	0.0137475i
$365$			55.0060i			0.150701i
$366$		0			0
$367$			476.591i			1.29861i	0.760527	+	0.649306i	$0.224941\pi$
$367$			476.591i			1.29861i	−0.760527	+	0.649306i	$0.775059\pi$
$368$	−228.814	−	112.205i	−0.621777	−	0.304906i
$369$		0			0
$370$	−43.1310	−	150.719i	−0.116570	−	0.407349i
$371$	−73.6725			−0.198578
$372$		0			0
$373$			201.210i			0.539437i	0.962939	+	0.269718i	$0.0869306\pi$
$373$			201.210i			0.539437i	−0.962939	+	0.269718i	$0.913069\pi$
$374$	−30.3019	−	105.889i	−0.0810211	−	0.283124i
$375$		0			0
$376$	241.262	−	267.088i	0.641655	−	0.710339i
$377$	−25.7743			−0.0683670
$378$		0			0
$379$	−193.997			−0.511865			−0.255933	−	0.966695i	$-0.582383\pi$
$379$	−193.997			−0.511865			−0.255933	+	0.966695i	$0.582383\pi$
$380$	−113.242	−	181.657i	−0.298006	−	0.478044i
$381$		0			0
$382$	200.639	−	57.4164i	0.525233	−	0.150305i
$383$		−	733.165i		−	1.91427i	−0.289642	−	0.957135i	$-0.593536\pi$
$383$		−	733.165i		−	1.91427i	0.289642	−	0.957135i	$-0.406464\pi$
$384$		0			0
$385$	−30.6144			−0.0795178
$386$	3.11455	+	10.8837i	0.00806878	+	0.0281960i
$387$		0			0
$388$	−253.476	+	158.014i	−0.653290	+	0.407251i
$389$		−	116.310i		−	0.298997i	−0.988762	−	0.149498i	$-0.952234\pi$
$389$		−	116.310i		−	0.298997i	0.988762	−	0.149498i	$-0.0477659\pi$
$390$		0			0
$391$			159.766i			0.408608i
$392$	−41.5560	−	37.5379i	−0.106010	−	0.0957600i
$393$		0			0
$394$	645.330	−	184.673i	1.63789	−	0.468712i
$395$	204.188			0.516931
$396$		0			0
$397$		−	610.269i		−	1.53720i	−0.639729	−	0.768601i	$-0.720953\pi$
$397$		−	610.269i		−	1.53720i	0.639729	−	0.768601i	$-0.279047\pi$
$398$	−175.883	+	50.3322i	−0.441918	+	0.126463i
$399$		0			0
$400$	144.823	−	295.329i	0.362057	−	0.738322i
$401$	194.061			0.483943			0.241971	−	0.970283i	$-0.422206\pi$
$401$	194.061			0.483943			0.241971	+	0.970283i	$0.422206\pi$
$402$		0			0
$403$	−37.1469			−0.0921759
$404$	173.835	+	278.856i	0.430285	+	0.690239i
$405$		0			0
$406$	41.9804	+	146.699i	0.103400	+	0.361327i
$407$			204.183i			0.501679i
$408$		0			0
$409$	491.557			1.20185			0.600926	−	0.799305i	$-0.294799\pi$
$409$	491.557			1.20185			0.600926	+	0.799305i	$0.294799\pi$
$410$	−286.274	+	81.9223i	−0.698228	+	0.199810i
$411$		0			0
$412$	−135.274	−	216.999i	−0.328335	−	0.526696i
$413$		−	102.481i		−	0.248138i
$414$		0			0
$415$		−	55.4337i		−	0.133575i
$416$	−5.04187	+	28.1542i	−0.0121199	+	0.0676785i
$417$		0			0
$418$	76.7062	+	268.046i	0.183508	+	0.641259i
$419$	−408.661			−0.975325			−0.487663	−	0.873032i	$-0.662150\pi$
$419$	−408.661			−0.975325			−0.487663	+	0.873032i	$0.662150\pi$
$420$		0			0
$421$		−	6.98694i		−	0.0165961i	−0.999966	−	0.00829803i	$-0.997359\pi$
$421$		−	6.98694i		−	0.0165961i	0.999966	−	0.00829803i	$-0.00264138\pi$
$422$	154.267	+	539.080i	0.365563	+	1.27744i
$423$		0			0
$424$	149.324	−	165.307i	0.352178	−	0.389876i
$425$	−206.209			−0.485197
$426$		0			0
$427$	19.0791			0.0446816
$428$	−600.806	+	374.534i	−1.40375	+	0.875080i
$429$		0			0
$430$	26.7717	−	7.66120i	0.0622598	−	0.0178167i
$431$			736.266i			1.70827i	0.520048	+	0.854137i	$0.325914\pi$
$431$			736.266i			1.70827i	−0.520048	+	0.854137i	$0.674086\pi$
$432$		0			0
$433$	780.394			1.80230			0.901148	−	0.433511i	$-0.142725\pi$
$433$	780.394			1.80230			0.901148	+	0.433511i	$0.142725\pi$
$434$	60.5036	+	211.427i	0.139409	+	0.487159i
$435$		0			0
$436$	350.253	+	561.856i	0.803332	+	1.28866i
$437$		−	404.431i		−	0.925471i
$438$		0			0
$439$		−	125.408i		−	0.285667i	−0.989747	−	0.142834i	$-0.954379\pi$
$439$		−	125.408i		−	0.285667i	0.989747	−	0.142834i	$-0.0456214\pi$
$440$	62.0509	−	68.6930i	0.141025	−	0.156120i
$441$		0			0
$442$	17.2391	−	4.93327i	0.0390025	−	0.0111612i
$443$	166.914			0.376780			0.188390	−	0.982094i	$-0.439673\pi$
$443$	166.914			0.376780			0.188390	+	0.982094i	$0.439673\pi$
$444$		0			0
$445$		−	88.2374i		−	0.198286i
$446$	677.413	−	193.854i	1.51886	−	0.434650i
$447$		0			0
$448$	168.456	−	17.1601i	0.376019	−	0.0383039i
$449$	218.160			0.485881			0.242940	−	0.970041i	$-0.421888\pi$
$449$	218.160			0.485881			0.242940	+	0.970041i	$0.421888\pi$
$450$		0			0
$451$	387.823			0.859917
$452$	339.466	−	211.618i	0.751031	−	0.468182i
$453$		0			0
$454$	−235.084	−	821.490i	−0.517806	−	1.80945i
$455$		−	4.98414i		−	0.0109542i
$456$		0			0
$457$	−616.901			−1.34989			−0.674946	−	0.737867i	$-0.735833\pi$
$457$	−616.901			−1.34989			−0.674946	+	0.737867i	$0.735833\pi$
$458$	470.013	−	134.503i	1.02623	−	0.293674i
$459$		0			0
$460$	−113.951	+	71.0355i	−0.247720	+	0.154425i
$461$			616.614i			1.33756i	0.743462	+	0.668778i	$0.233182\pi$
$461$			616.614i			1.33756i	−0.743462	+	0.668778i	$0.766818\pi$
$462$		0			0
$463$		−	596.526i		−	1.28839i	−0.764860	−	0.644197i	$-0.777192\pi$
$463$		−	596.526i		−	1.28839i	0.764860	−	0.644197i	$-0.222808\pi$
$464$	−414.253	−	203.141i	−0.892787	−	0.437804i
$465$		0			0
$466$	36.2777	+	126.771i	0.0778490	+	0.272040i
$467$	175.892			0.376642			0.188321	−	0.982107i	$-0.439695\pi$
$467$	175.892			0.376642			0.188321	+	0.982107i	$0.439695\pi$
$468$		0			0
$469$			28.9131i			0.0616484i
$470$	−52.1758	−	182.326i	−0.111012	−	0.387928i
$471$		0			0
$472$	229.949	+	207.714i	0.487179	+	0.440073i
$473$	−36.2684			−0.0766773
$474$		0			0
$475$	521.997			1.09894
$476$	−56.1570	−	90.0838i	−0.117977	−	0.189252i
$477$		0			0
$478$	−226.841	+	64.9147i	−0.474563	+	0.135805i
$479$			37.6277i			0.0785548i	0.999228	+	0.0392774i	$0.0125056\pi$
$479$			37.6277i			0.0785548i	−0.999228	+	0.0392774i	$0.987494\pi$
$480$		0			0
$481$	−33.2419			−0.0691100
$482$	16.9887	+	59.3662i	0.0352463	+	0.123166i
$483$		0			0
$484$	308.415	−	192.261i	0.637220	−	0.397234i
$485$			157.384i			0.324503i
$486$		0			0
$487$			347.406i			0.713359i	0.934227	+	0.356680i	$0.116091\pi$
$487$			347.406i			0.713359i	−0.934227	+	0.356680i	$0.883909\pi$
$488$	−38.6705	+	42.8099i	−0.0792429	+	0.0877252i
$489$		0			0
$490$	−28.3680	+	8.11802i	−0.0578939	+	0.0165674i
$491$	−202.572			−0.412569			−0.206285	−	0.978492i	$-0.566137\pi$
$491$	−202.572			−0.412569			−0.206285	+	0.978492i	$0.566137\pi$
$492$		0			0
$493$			289.246i			0.586705i
$494$	−43.6390	+	12.4881i	−0.0883381	+	0.0252795i
$495$		0			0
$496$	−597.036	−	292.774i	−1.20370	−	0.590269i
$497$	191.783			0.385882
$498$		0			0
$499$	−46.0411			−0.0922666			−0.0461333	−	0.998935i	$-0.514690\pi$
$499$	−46.0411			−0.0922666			−0.0461333	+	0.998935i	$0.514690\pi$
$500$	−203.181	−	325.932i	−0.406363	−	0.651864i
$501$		0			0
$502$	−161.126	−	563.046i	−0.320968	−	1.12161i
$503$		−	515.894i		−	1.02563i	−0.858498	−	0.512817i	$-0.828602\pi$
$503$		−	515.894i		−	1.02563i	0.858498	−	0.512817i	$-0.171398\pi$
$504$		0			0
$505$	173.143			0.342857
$506$	168.142	−	48.1169i	0.332297	−	0.0950927i
$507$		0			0
$508$	34.0817	+	54.6719i	0.0670900	+	0.107622i
$509$			914.701i			1.79706i	0.438916	+	0.898528i	$0.355362\pi$
$509$			914.701i			1.79706i	−0.438916	+	0.898528i	$0.644638\pi$
$510$		0			0
$511$		−	69.0503i		−	0.135128i
$512$	−302.933	+	412.766i	−0.591665	+	0.806184i
$513$		0			0
$514$	35.7226	+	124.831i	0.0694992	+	0.242862i
$515$	−134.735			−0.261621
$516$		0			0
$517$			247.002i			0.477760i
$518$	54.1433	+	189.201i	0.104524	+	0.365254i
$519$		0			0
$520$	11.1835	+	10.1021i	0.0215067	+	0.0194272i
$521$	822.793			1.57926			0.789629	−	0.613585i	$-0.210273\pi$
$521$	822.793			1.57926			0.789629	+	0.613585i	$0.210273\pi$
$522$		0			0
$523$	−476.617			−0.911314			−0.455657	−	0.890155i	$-0.650596\pi$
$523$	−476.617			−0.911314			−0.455657	+	0.890155i	$0.650596\pi$
$524$	−701.644	+	437.395i	−1.33901	+	0.834723i
$525$		0			0
$526$	314.088	−	89.8817i	0.597125	−	0.170878i
$527$			416.871i			0.791026i
$528$		0			0
$529$	275.305			0.520426
$530$	−32.2930	−	112.846i	−0.0609301	−	0.212918i
$531$		0			0
$532$	142.156	+	228.038i	0.267210	+	0.428643i
$533$			63.1391i			0.118460i
$534$		0			0
$535$			373.042i			0.697275i
$536$	−64.8757	−	58.6027i	−0.121037	−	0.109333i
$537$		0			0
$538$	−648.637	+	185.619i	−1.20564	+	0.345017i
$539$	38.4310			0.0713005
$540$		0			0
$541$		−	804.561i		−	1.48717i	−0.668639	−	0.743587i	$-0.733123\pi$
$541$		−	804.561i		−	1.48717i	0.668639	−	0.743587i	$-0.266877\pi$
$542$	97.4999	−	27.9013i	0.179889	−	0.0514785i
$543$		0			0
$544$	315.954	+	56.5811i	0.580797	+	0.104009i
$545$	348.857			0.640105
$546$		0			0
$547$	−506.906			−0.926702			−0.463351	−	0.886175i	$-0.653353\pi$
$547$	−506.906			−0.926702			−0.463351	+	0.886175i	$0.653353\pi$
$548$	591.536	−	368.755i	1.07945	−	0.672911i
$549$		0			0
$550$	62.1042	+	217.020i	0.112917	+	0.394582i
$551$		−	732.197i		−	1.32885i
$552$		0			0
$553$	−256.322			−0.463511
$554$	976.070	−	279.320i	1.76186	−	0.504187i
$555$		0			0
$556$	−633.663	+	395.016i	−1.13968	+	0.710461i
$557$		−	95.4411i		−	0.171349i	−0.996323	−	0.0856743i	$-0.972696\pi$
$557$		−	95.4411i		−	0.171349i	0.996323	−	0.0856743i	$-0.0273044\pi$
$558$		0			0
$559$		−	5.90464i		−	0.0105629i
$560$	39.2826	−	80.1067i	0.0701475	−	0.143048i
$561$		0			0
$562$	284.910	+	995.605i	0.506958	+	1.77154i
$563$	−774.904			−1.37638			−0.688192	−	0.725529i	$-0.741595\pi$
$563$	−774.904			−1.37638			−0.688192	+	0.725529i	$0.741595\pi$
$564$		0			0
$565$		−	210.775i		−	0.373053i
$566$	117.222	+	409.627i	0.207106	+	0.723723i
$567$		0			0
$568$	−388.717	+	430.326i	−0.684361	+	0.757616i
$569$	878.255			1.54351			0.771753	−	0.635923i	$-0.219380\pi$
$569$	878.255			1.54351			0.771753	+	0.635923i	$0.219380\pi$
$570$		0			0
$571$	805.611			1.41088			0.705439	−	0.708771i	$-0.250750\pi$
$571$	805.611			1.41088			0.705439	+	0.708771i	$0.250750\pi$
$572$	−10.3838	−	16.6572i	−0.0181536	−	0.0291209i
$573$		0			0
$574$	359.366	−	102.839i	0.626073	−	0.179162i
$575$		−	327.442i		−	0.569465i
$576$		0			0
$577$	−176.390			−0.305701			−0.152851	−	0.988249i	$-0.548845\pi$
$577$	−176.390			−0.305701			−0.152851	+	0.988249i	$0.548845\pi$
$578$	103.659	+	362.233i	0.179342	+	0.626701i
$579$		0			0
$580$	−206.301	+	128.605i	−0.355692	+	0.221733i
$581$			69.5872i			0.119771i
$582$		0			0
$583$			152.876i			0.262223i
$584$	154.936	+	139.955i	0.265302	+	0.239649i
$585$		0			0
$586$	−353.010	+	101.020i	−0.602405	+	0.172389i
$587$	−453.137			−0.771954			−0.385977	−	0.922508i	$-0.626136\pi$
$587$	−453.137			−0.771954			−0.385977	+	0.922508i	$0.626136\pi$
$588$		0			0
$589$		−	1055.27i		−	1.79163i
$590$	156.973	−	44.9207i	0.266056	−	0.0761368i
$591$		0			0
$592$	−534.274	−	261.996i	−0.902490	−	0.442562i
$593$	182.436			0.307649			0.153824	−	0.988098i	$-0.450841\pi$
$593$	182.436			0.307649			0.153824	+	0.988098i	$0.450841\pi$
$594$		0			0
$595$	−55.9332			−0.0940054
$596$	292.805	+	469.701i	0.491283	+	0.788088i
$597$		0			0
$598$	7.83363	+	27.3742i	0.0130997	+	0.0457763i
$599$			362.698i			0.605505i	0.953069	+	0.302753i	$0.0979056\pi$
$599$			362.698i			0.605505i	−0.953069	+	0.302753i	$0.902094\pi$
$600$		0			0
$601$	221.633			0.368774			0.184387	−	0.982854i	$-0.440970\pi$
$601$	221.633			0.368774			0.184387	+	0.982854i	$0.440970\pi$
$602$	−33.6072	+	9.61729i	−0.0558258	+	0.0159756i
$603$		0			0
$604$	167.324	+	268.412i	0.277027	+	0.444391i
$605$		−	191.495i		−	0.316521i
$606$		0			0
$607$		−	895.470i		−	1.47524i	−0.675217	−	0.737619i	$-0.735950\pi$
$607$		−	895.470i		−	1.47524i	0.675217	−	0.737619i	$-0.264050\pi$
$608$	−799.805	−	143.229i	−1.31547	−	0.235575i
$609$		0			0
$610$	8.36295	+	29.2240i	0.0137098	+	0.0479081i
$611$	−40.2130			−0.0658150
$612$		0			0
$613$			570.870i			0.931273i	0.884976	+	0.465637i	$0.154175\pi$
$613$			570.870i			0.931273i	−0.884976	+	0.465637i	$0.845825\pi$
$614$	−159.234	−	556.436i	−0.259339	−	0.906248i
$615$		0			0
$616$	−77.8940	+	86.2320i	−0.126451	+	0.139987i
$617$	767.498			1.24392			0.621960	−	0.783049i	$-0.286337\pi$
$617$	767.498			1.24392			0.621960	+	0.783049i	$0.286337\pi$
$618$		0			0
$619$	152.660			0.246624			0.123312	−	0.992368i	$-0.460648\pi$
$619$	152.660			0.246624			0.123312	+	0.992368i	$0.460648\pi$
$620$	−297.329	+	185.350i	−0.479562	+	0.298952i
$621$		0			0
$622$	−695.831	+	199.125i	−1.11870	+	0.320136i
$623$			110.767i			0.177795i
$624$		0			0
$625$	311.576			0.498522
$626$	281.370	+	983.234i	0.449472	+	1.57066i
$627$		0			0
$628$	−22.0792	−	35.4182i	−0.0351580	−	0.0563985i
$629$			373.048i			0.593082i
$630$		0			0
$631$		−	734.766i		−	1.16445i	−0.813029	−	0.582224i	$-0.802183\pi$
$631$		−	734.766i		−	1.16445i	0.813029	−	0.582224i	$-0.197817\pi$
$632$	519.527	−	575.139i	0.822037	−	0.910029i
$633$		0			0
$634$	−732.097	+	209.502i	−1.15473	+	0.330446i
$635$	33.9459			0.0534581
$636$		0			0
$637$			6.25672i			0.00982216i
$638$	304.411	−	87.1126i	0.477133	−	0.136540i
$639$		0			0
$640$	100.124	+	250.508i	0.156444	+	0.391418i
$641$	333.294			0.519960			0.259980	−	0.965614i	$-0.416284\pi$
$641$	333.294			0.519960			0.259980	+	0.965614i	$0.416284\pi$
$642$		0			0
$643$	537.952			0.836628			0.418314	−	0.908302i	$-0.362621\pi$
$643$	537.952			0.836628			0.418314	+	0.908302i	$0.362621\pi$
$644$	143.046	−	89.1726i	0.222121	−	0.138467i
$645$		0			0
$646$	140.144	+	489.728i	0.216942	+	0.758092i
$647$			906.776i			1.40151i	0.713403	+	0.700754i	$0.247153\pi$
$647$			906.776i			1.40151i	−0.713403	+	0.700754i	$0.752847\pi$
$648$		0			0
$649$	−212.656			−0.327667
$650$	−35.3318	+	10.1108i	−0.0543566	+	0.0155551i
$651$		0			0
$652$	157.948	−	98.4624i	0.242251	−	0.151016i
$653$		−	586.718i		−	0.898495i	−0.893407	−	0.449248i	$-0.851692\pi$
$653$		−	586.718i		−	0.898495i	0.893407	−	0.449248i	$-0.148308\pi$
$654$		0			0
$655$			435.652i			0.665118i
$656$	−497.632	+	1014.79i	−0.758585	+	1.54694i
$657$		0			0
$658$	65.4976	+	228.878i	0.0995404	+	0.347839i
$659$	162.399			0.246433			0.123216	−	0.992380i	$-0.460679\pi$
$659$	162.399			0.246433			0.123216	+	0.992380i	$0.460679\pi$
$660$		0			0
$661$			477.664i			0.722638i	0.932442	+	0.361319i	$0.117674\pi$
$661$			477.664i			0.722638i	−0.932442	+	0.361319i	$0.882326\pi$
$662$	194.486	+	679.623i	0.293786	+	1.02662i
$663$		0			0
$664$	−156.141	−	141.043i	−0.235152	−	0.212415i
$665$	141.589			0.212916
$666$		0			0
$667$	−459.298			−0.688603
$668$	−271.095	−	434.875i	−0.405831	−	0.651011i
$669$		0			0
$670$	−44.2871	+	12.6735i	−0.0661001	+	0.0189157i
$671$		−	39.5905i		−	0.0590022i
$672$		0			0
$673$	−1088.73			−1.61773			−0.808864	−	0.587995i	$-0.799917\pi$
$673$	−1088.73			−1.61773			−0.808864	+	0.587995i	$0.799917\pi$
$674$	302.220	+	1056.09i	0.448398	+	1.56691i
$675$		0			0
$676$	−570.951	+	355.923i	−0.844602	+	0.526513i
$677$			1170.23i			1.72855i	0.503024	+	0.864273i	$0.332221\pi$
$677$			1170.23i			1.72855i	−0.503024	+	0.864273i	$0.667779\pi$
$678$		0			0
$679$		−	197.568i		−	0.290969i
$680$	113.369	−	125.504i	0.166719	−	0.184565i
$681$		0			0
$682$	438.728	−	125.550i	0.643296	−	0.184090i
$683$	−633.855			−0.928045			−0.464022	−	0.885823i	$-0.653594\pi$
$683$	−633.855			−0.928045			−0.464022	+	0.885823i	$0.653594\pi$
$684$		0			0
$685$		−	367.286i		−	0.536184i
$686$	35.6111	−	10.1907i	0.0519112	−	0.0148553i
$687$		0			0
$688$	46.5375	−	94.9011i	0.0676417	−	0.137938i
$689$	−24.8888			−0.0361231
$690$		0			0
$691$	−510.637			−0.738983			−0.369492	−	0.929234i	$-0.620468\pi$
$691$	−510.637			−0.738983			−0.369492	+	0.929234i	$0.620468\pi$
$692$	40.1981	+	64.4834i	0.0580897	+	0.0931842i
$693$		0			0
$694$	271.481	+	948.679i	0.391183	+	1.36697i
$695$			393.443i			0.566104i
$696$		0			0
$697$	708.562			1.01659
$698$	899.187	−	257.318i	1.28823	−	0.368651i
$699$		0			0
$700$	115.095	+	184.628i	0.164421	+	0.263755i
$701$			1057.09i			1.50797i	0.656892	+	0.753985i	$0.271871\pi$
$701$			1057.09i			1.50797i	−0.656892	+	0.753985i	$0.728129\pi$
$702$		0			0
$703$		−	944.335i		−	1.34329i
$704$	−35.6086	−	349.560i	−0.0505804	−	0.496534i
$705$		0			0
$706$	−124.562	−	435.275i	−0.176433	−	0.616537i
$707$	−217.350			−0.307426
$708$		0			0
$709$			352.280i			0.496869i	0.968649	+	0.248435i	$0.0799161\pi$
$709$			352.280i			0.496869i	−0.968649	+	0.248435i	$0.920084\pi$
$710$	84.0646	+	293.760i	0.118401	+	0.413747i
$711$		0			0
$712$	−248.540	−	224.508i	−0.349073	−	0.315320i
$713$	−661.957			−0.928410
$714$		0			0
$715$	−10.3425			−0.0144650
$716$	−483.614	+	301.478i	−0.675439	+	0.421059i
$717$		0			0
$718$	−227.409	+	65.0773i	−0.316726	+	0.0906368i
$719$		−	541.932i		−	0.753730i	−0.926268	−	0.376865i	$-0.877002\pi$
$719$		−	541.932i		−	0.753730i	0.926268	−	0.376865i	$-0.122998\pi$
$720$		0			0
$721$	169.136			0.234585
$722$	−156.121	−	545.559i	−0.216235	−	0.755622i
$723$		0			0
$724$	−128.030	−	205.378i	−0.176837	−	0.283672i
$725$		−	592.814i		−	0.817674i
$726$		0			0
$727$			324.113i			0.445823i	0.974839	+	0.222911i	$0.0715561\pi$
$727$			324.113i			0.445823i	−0.974839	+	0.222911i	$0.928444\pi$
$728$	−14.0389	−	12.6815i	−0.0192842	−	0.0174196i
$729$		0			0
$730$	105.766	−	30.2669i	0.144886	−	0.0414616i
$731$	−66.2632			−0.0906474
$732$		0			0
$733$		−	908.429i		−	1.23933i	−0.784866	−	0.619665i	$-0.787268\pi$
$733$		−	908.429i		−	1.23933i	0.784866	−	0.619665i	$-0.212732\pi$
$734$	916.397	−	262.243i	1.24850	−	0.357280i
$735$		0			0
$736$	−89.8461	+	501.708i	−0.122074	+	0.681669i
$737$	59.9969			0.0814069
$738$		0			0
$739$	953.149			1.28978			0.644891	−	0.764274i	$-0.276903\pi$
$739$	953.149			1.28978			0.644891	+	0.764274i	$0.276903\pi$
$740$	−266.073	+	165.866i	−0.359558	+	0.224143i
$741$		0			0
$742$	40.5382	+	141.659i	0.0546336	+	0.190915i
$743$		−	947.872i		−	1.27574i	−0.770146	−	0.637868i	$-0.779817\pi$
$743$		−	947.872i		−	1.27574i	0.770146	−	0.637868i	$-0.220183\pi$
$744$		0			0
$745$	291.638			0.391461
$746$	386.890	−	110.715i	0.518619	−	0.148412i
$747$		0			0
$748$	−186.931	+	116.530i	−0.249907	+	0.155789i
$749$		−	468.289i		−	0.625219i
$750$		0			0
$751$		−	635.979i		−	0.846843i	−0.905933	−	0.423421i	$-0.860829\pi$
$751$		−	635.979i		−	0.846843i	0.905933	−	0.423421i	$-0.139171\pi$
$752$	−646.315	−	316.939i	−0.859461	−	0.421462i
$753$		0			0
$754$	14.1823	+	49.5594i	0.0188094	+	0.0657286i
$755$	166.658			0.220739
$756$		0			0
$757$			162.283i			0.214376i	0.994239	+	0.107188i	$0.0341847\pi$
$757$			162.283i			0.214376i	−0.994239	+	0.107188i	$0.965815\pi$
$758$	106.747	+	373.021i	0.140827	+	0.492112i
$759$		0			0
$760$	−286.981	+	317.701i	−0.377607	+	0.418027i
$761$	925.684			1.21640			0.608202	−	0.793782i	$-0.291891\pi$
$761$	925.684			1.21640			0.608202	+	0.793782i	$0.291891\pi$
$762$		0			0
$763$	−437.929			−0.573957
$764$	−220.802	−	354.199i	−0.289008	−	0.463611i
$765$		0			0
$766$	−1409.74	+	403.423i	−1.84040	+	0.526662i
$767$		−	34.6213i		−	0.0451386i
$768$		0			0
$769$	1006.84			1.30929			0.654644	−	0.755938i	$-0.272819\pi$
$769$	1006.84			1.30929			0.654644	+	0.755938i	$0.272819\pi$
$770$	16.8455	+	58.8658i	0.0218773	+	0.0764491i
$771$		0			0
$772$	19.2135	−	11.9774i	0.0248880	−	0.0155148i
$773$		−	287.674i		−	0.372153i	−0.982535	−	0.186077i	$-0.940423\pi$
$773$		−	287.674i		−	0.372153i	0.982535	−	0.186077i	$-0.0595773\pi$
$774$		0			0
$775$		−	854.384i		−	1.10243i
$776$	443.306	+	400.442i	0.571271	+	0.516034i
$777$		0			0
$778$	−223.642	+	63.9992i	−0.287458	+	0.0822612i
$779$	−1793.65			−2.30251
$780$		0			0
$781$		−	397.965i		−	0.509558i
$782$	307.200	−	87.9108i	0.392839	−	0.112418i
$783$		0			0
$784$	−49.3124	+	100.560i	−0.0628985	+	0.128265i
$785$	−21.9913			−0.0280143
$786$		0			0
$787$	879.367			1.11737			0.558683	−	0.829381i	$-0.311307\pi$
$787$	879.367			1.11737			0.558683	+	0.829381i	$0.311307\pi$
$788$	−710.183	−	1139.24i	−0.901248	−	1.44573i
$789$		0			0
$790$	−112.354	−	392.616i	−0.142220	−	0.496982i
$791$			264.591i			0.334502i
$792$		0			0
$793$	6.44550			0.00812799
$794$	−1173.44	+	335.799i	−1.47788	+	0.422921i
$795$		0			0
$796$	193.559	+	310.497i	0.243165	+	0.390071i
$797$		−	209.433i		−	0.262777i	−0.991331	−	0.131388i	$-0.958056\pi$
$797$		−	209.433i		−	0.262777i	0.991331	−	0.131388i	$-0.0419435\pi$
$798$		0			0
$799$			451.279i			0.564805i
$800$	−647.552	−	115.964i	−0.809440	−	0.144955i
$801$		0			0
$802$	−106.782	−	373.144i	−0.133144	−	0.465267i
$803$	−143.285			−0.178437
$804$		0			0
$805$		−	88.8173i		−	0.110332i
$806$	20.4400	+	71.4266i	0.0253598	+	0.0886187i
$807$		0			0
$808$	440.538	−	487.694i	0.545220	−	0.603581i
$809$	914.728			1.13069			0.565345	−	0.824855i	$-0.308743\pi$
$809$	914.728			1.13069			0.565345	+	0.824855i	$0.308743\pi$
$810$		0			0
$811$	975.019			1.20224			0.601122	−	0.799158i	$-0.294721\pi$
$811$	975.019			1.20224			0.601122	+	0.799158i	$0.294721\pi$
$812$	258.975	−	161.441i	0.318935	−	0.198819i
$813$		0			0
$814$	392.607	−	112.352i	0.482319	−	0.138024i
$815$		−	98.0701i		−	0.120331i
$816$		0			0
$817$	167.739			0.205311
$818$	−270.479	−	945.175i	−0.330658	−	1.15547i
$819$		0			0
$820$	315.043	+	505.374i	0.384199	+	0.616310i
$821$		−	925.110i		−	1.12681i	−0.826181	−	0.563404i	$-0.809491\pi$
$821$		−	925.110i		−	1.12681i	0.826181	−	0.563404i	$-0.190509\pi$
$822$		0			0
$823$			124.493i			0.151267i	0.997136	+	0.0756335i	$0.0240979\pi$
$823$			124.493i			0.151267i	−0.997136	+	0.0756335i	$0.975902\pi$
$824$	−342.814	+	379.510i	−0.416037	+	0.460570i
$825$		0			0
$826$	−197.052	+	56.3900i	−0.238562	+	0.0682688i
$827$	261.133			0.315760			0.157880	−	0.987458i	$-0.449534\pi$
$827$	261.133			0.315760			0.157880	+	0.987458i	$0.449534\pi$
$828$		0			0
$829$		−	1464.65i		−	1.76677i	−0.468652	−	0.883383i	$-0.655260\pi$
$829$		−	1464.65i		−	1.76677i	0.468652	−	0.883383i	$-0.344740\pi$
$830$	−106.589	+	30.5023i	−0.128420	+	0.0367497i
$831$		0			0
$832$	56.9098	−	5.79722i	0.0684011	−	0.00696781i
$833$	70.2144			0.0842909
$834$		0			0
$835$	−270.015			−0.323371
$836$	473.197	−	294.984i	0.566025	−	0.352852i
$837$		0			0
$838$	224.865	+	785.781i	0.268336	+	0.937686i
$839$		−	57.9285i		−	0.0690447i	−0.999404	−	0.0345224i	$-0.989009\pi$
$839$		−	57.9285i		−	0.0690447i	0.999404	−	0.0345224i	$-0.0109910\pi$
$840$		0			0
$841$	9.46906			0.0112593
$842$	−13.4346	+	3.84455i	−0.0159556	+	0.00456598i
$843$		0			0
$844$	951.668	−	593.256i	1.12757	−	0.702910i
$845$			354.505i			0.419532i
$846$		0			0
$847$			240.389i			0.283812i
$848$	−400.021	−	196.162i	−0.471723	−	0.231323i
$849$		0			0
$850$	113.466	+	396.502i	0.133489	+	0.466473i
$851$	−592.370			−0.696087
$852$		0			0
$853$			1514.76i			1.77581i	0.460029	+	0.887904i	$0.347839\pi$
$853$			1514.76i			1.77581i	−0.460029	+	0.887904i	$0.652161\pi$
$854$	−10.4982	−	36.6855i	−0.0122930	−	0.0429573i
$855$		0			0
$856$	1050.75	+	949.154i	1.22752	+	1.10882i
$857$	−467.005			−0.544930			−0.272465	−	0.962166i	$-0.587839\pi$
$857$	−467.005			−0.544930			−0.272465	+	0.962166i	$0.587839\pi$
$858$		0			0
$859$	97.2971			0.113268			0.0566339	−	0.998395i	$-0.481963\pi$
$859$	97.2971			0.113268			0.0566339	+	0.998395i	$0.481963\pi$
$860$	−29.4622	−	47.2615i	−0.0342583	−	0.0549553i
$861$		0			0
$862$	1415.70	−	405.129i	1.64235	−	0.469987i
$863$			558.738i			0.647436i	0.946154	+	0.323718i	$0.104933\pi$
$863$			558.738i			0.647436i	−0.946154	+	0.323718i	$0.895067\pi$
$864$		0			0
$865$	40.0379			0.0462866
$866$	−429.411	−	1500.56i	−0.495855	−	1.73274i
$867$		0			0
$868$	373.244	−	232.675i	0.430004	−	0.268059i
$869$			531.887i			0.612068i
$870$		0			0
$871$			9.76774i			0.0112144i
$872$	887.620	−	982.632i	1.01791	−	1.12687i
$873$		0			0
$874$	−777.647	+	222.537i	−0.889756	+	0.254619i
$875$	254.042			0.290334
$876$		0			0
$877$			49.7086i			0.0566803i	0.999598	+	0.0283401i	$0.00902215\pi$
$877$			49.7086i			0.0566803i	−0.999598	+	0.0283401i	$0.990978\pi$
$878$	−241.137	+	69.0055i	−0.274643	+	0.0785940i
$879$		0			0
$880$	−166.228	−	81.5144i	−0.188895	−	0.0926300i
$881$	713.475			0.809846			0.404923	−	0.914351i	$-0.367298\pi$
$881$	713.475			0.809846			0.404923	+	0.914351i	$0.367298\pi$
$882$		0			0
$883$	405.709			0.459466			0.229733	−	0.973254i	$-0.426215\pi$
$883$	405.709			0.459466			0.229733	+	0.973254i	$0.426215\pi$
$884$	−18.9716	−	30.4331i	−0.0214610	−	0.0344266i
$885$		0			0
$886$	−91.8440	−	320.945i	−0.103661	−	0.362240i
$887$		−	1593.01i		−	1.79595i	−0.440045	−	0.897975i	$-0.645038\pi$
$887$		−	1593.01i		−	1.79595i	0.440045	−	0.897975i	$-0.354962\pi$
$888$		0			0
$889$	−42.6131			−0.0479338
$890$	−169.664	+	48.5525i	−0.190634	+	0.0545533i
$891$		0			0
$892$	−745.491	−	1195.87i	−0.835752	−	1.34067i
$893$		−	1142.37i		−	1.27925i
$894$		0			0
$895$			300.277i			0.335505i
$896$	−125.689	−	314.468i	−0.140277	−	0.350969i
$897$		0			0
$898$	−120.042	−	419.483i	−0.133678	−	0.467130i
$899$	−1198.43			−1.33307
$900$		0			0
$901$			279.308i			0.309998i
$902$	−213.399	−	745.712i	−0.236584	−	0.826732i
$903$		0			0
$904$	−593.694	−	536.289i	−0.656741	−	0.593240i
$905$	−127.520			−0.140906
$906$		0			0
$907$	−1138.55			−1.25530			−0.627648	−	0.778497i	$-0.715982\pi$
$907$	−1138.55			−1.25530			−0.627648	+	0.778497i	$0.715982\pi$
$908$	−1450.22	+	904.047i	−1.59716	+	0.995646i
$909$		0			0
$910$	−9.58360	+	2.74252i	−0.0105314	+	0.00301375i
$911$		−	1635.40i		−	1.79517i	−0.440837	−	0.897587i	$-0.645318\pi$
$911$		−	1635.40i		−	1.79517i	0.440837	−	0.897587i	$-0.354682\pi$
$912$		0			0
$913$	144.399			0.158159
$914$	339.449	+	1186.19i	0.371388	+	1.29780i
$915$		0			0
$916$	−517.248	−	829.739i	−0.564681	−	0.905829i
$917$		−	546.885i		−	0.596384i
$918$		0			0
$919$		−	1337.53i		−	1.45542i	−0.685887	−	0.727708i	$-0.740586\pi$
$919$		−	1337.53i		−	1.45542i	0.685887	−	0.727708i	$-0.259414\pi$
$920$	199.290	+	180.020i	0.216619	+	0.195674i
$921$		0			0
$922$	1185.64	−	339.291i	1.28594	−	0.367994i
$923$	64.7903			0.0701953
$924$		0			0
$925$		−	764.569i		−	0.826561i
$926$	−1147.01	+	328.238i	−1.23867	+	0.354468i
$927$		0			0
$928$	−162.661	+	908.311i	−0.175281	+	0.978784i
$929$	−1516.16			−1.63203			−0.816016	−	0.578029i	$-0.803822\pi$
$929$	−1516.16			−1.63203			−0.816016	+	0.578029i	$0.803822\pi$
$930$		0			0
$931$	−177.741			−0.190914
$932$	223.795	−	139.511i	0.240123	−	0.149689i
$933$		0			0
$934$	−96.7843	−	338.208i	−0.103623	−	0.362107i
$935$			116.066i			0.124134i
$936$		0			0
$937$	1012.59			1.08067			0.540335	−	0.841450i	$-0.318297\pi$
$937$	1012.59			1.08067			0.540335	+	0.841450i	$0.318297\pi$
$938$	55.5946	−	15.9094i	0.0592693	−	0.0169610i
$939$		0			0
$940$	−321.870	+	200.649i	−0.342415	+	0.213457i
$941$			1083.94i			1.15191i	0.817483	+	0.575953i	$0.195369\pi$
$941$			1083.94i			1.15191i	−0.817483	+	0.575953i	$0.804631\pi$
$942$		0			0
$943$			1125.14i			1.19315i
$944$	272.868	−	556.444i	0.289055	−	0.589453i
$945$		0			0
$946$	19.9566	+	69.7374i	0.0210958	+	0.0737182i
$947$	756.965			0.799329			0.399665	−	0.916661i	$-0.369127\pi$
$947$	756.965			0.799329			0.399665	+	0.916661i	$0.369127\pi$
$948$		0			0
$949$		−	23.3273i		−	0.0245810i
$950$	−287.228	−	1003.70i	−0.302345	−	1.05653i
$951$		0			0
$952$	−142.314	+	157.548i	−0.149490	+	0.165492i
$953$	−1345.87			−1.41225			−0.706123	−	0.708089i	$-0.749557\pi$
$953$	−1345.87			−1.41225			−0.706123	+	0.708089i	$0.749557\pi$
$954$		0			0
$955$	−219.923			−0.230286
$956$	249.638	+	400.455i	0.261128	+	0.418886i
$957$		0			0
$958$	72.3513	−	20.7046i	0.0755232	−	0.0216123i
$959$			461.063i			0.480775i
$960$		0			0
$961$	−766.220			−0.797315
$962$	18.2913	+	63.9181i	0.0190138	+	0.0664429i
$963$		0			0
$964$	104.802	−	65.3323i	0.108716	−	0.0677721i
$965$		−	11.9297i		−	0.0123624i
$966$		0			0
$967$			280.335i			0.289902i	0.989439	+	0.144951i	$0.0463024\pi$
$967$			280.335i			0.289902i	−0.989439	+	0.144951i	$0.953698\pi$
$968$	−539.388	−	487.234i	−0.557219	−	0.503340i
$969$		0			0
$970$	302.621	−	86.6003i	0.311980	−	0.0892787i
$971$	145.041			0.149372			0.0746862	−	0.997207i	$-0.476204\pi$
$971$	145.041			0.149372			0.0746862	+	0.997207i	$0.476204\pi$
$972$		0			0
$973$		−	493.898i		−	0.507603i
$974$	667.998	−	191.160i	0.685830	−	0.196262i
$975$		0			0
$976$	103.594	+	50.8003i	0.106141	+	0.0520495i
$977$	1083.72			1.10923			0.554617	−	0.832105i	$-0.312865\pi$
$977$	1083.72			1.10923			0.554617	+	0.832105i	$0.312865\pi$
$978$		0			0
$979$	229.849			0.234779
$980$	31.2189	+	50.0796i	0.0318560	+	0.0511017i
$981$		0			0
$982$	111.465	+	389.508i	0.113508	+	0.396648i
$983$			946.192i			0.962556i	0.876568	+	0.481278i	$0.159827\pi$
$983$			946.192i			0.962556i	−0.876568	+	0.481278i	$0.840173\pi$
$984$		0			0
$985$	−707.354			−0.718126
$986$	556.167	−	159.157i	0.564064	−	0.161417i
$987$		0			0
$988$	48.0246	+	77.0383i	0.0486079	+	0.0779740i
$989$		−	105.221i		−	0.106391i
$990$		0			0
$991$		−	736.299i		−	0.742986i	−0.928436	−	0.371493i	$-0.878846\pi$
$991$		−	736.299i		−	0.742986i	0.928436	−	0.371493i	$-0.121154\pi$
$992$	−234.432	+	1309.09i	−0.236323	+	1.31965i
$993$		0			0
$994$	−105.528	−	368.764i	−0.106165	−	0.370990i
$995$	192.788			0.193757
$996$		0			0
$997$			1821.57i			1.82705i	0.406783	+	0.913525i	$0.366651\pi$
$997$			1821.57i			1.82705i	−0.406783	+	0.913525i	$0.633349\pi$
$998$	25.3340	+	88.5285i	0.0253848	+	0.0887059i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.c.379.9	✓	24
3.2	odd	2	inner	504.3.g.c.379.16	yes	24
4.3	odd	2		2016.3.g.c.1135.14		24
8.3	odd	2	inner	504.3.g.c.379.10	yes	24
8.5	even	2		2016.3.g.c.1135.13		24
12.11	even	2		2016.3.g.c.1135.11		24
24.5	odd	2		2016.3.g.c.1135.12		24
24.11	even	2	inner	504.3.g.c.379.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.3.g.c.379.9	✓	24	1.1	even	1	trivial
504.3.g.c.379.10	yes	24	8.3	odd	2	inner
504.3.g.c.379.15	yes	24	24.11	even	2	inner
504.3.g.c.379.16	yes	24	3.2	odd	2	inner
2016.3.g.c.1135.11		24	12.11	even	2
2016.3.g.c.1135.12		24	24.5	odd	2
2016.3.g.c.1135.13		24	8.5	even	2
2016.3.g.c.1135.14		24	4.3	odd	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.550248 - 1.92282i) q^{2} +(-3.39445 + 2.11605i) q^{4} +2.10762i q^{5} -2.64575i q^{7} +(5.93658 + 5.36256i) q^{8} +(4.05258 - 1.15972i) q^{10} -5.49014 q^{11} -0.893817i q^{13} +(-5.08730 + 1.45582i) q^{14} +(7.04463 - 14.3657i) q^{16} -10.0306 q^{17} +25.3915 q^{19} +(-4.45985 - 7.15423i) q^{20} +(3.02094 + 10.5565i) q^{22} -15.9278i q^{23} +20.5579 q^{25} +(-1.71865 + 0.491821i) q^{26} +(5.59855 + 8.98088i) q^{28} -28.8363i q^{29} -41.5598i q^{31} +(-31.4989 - 5.64084i) q^{32} +(5.51933 + 19.2871i) q^{34} +5.57625 q^{35} -37.1910i q^{37} +(-13.9716 - 48.8233i) q^{38} +(-11.3023 + 12.5121i) q^{40} -70.6399 q^{41} +6.60609 q^{43} +(18.6360 - 11.6174i) q^{44} +(-30.6262 + 8.76424i) q^{46} -44.9902i q^{47} -7.00000 q^{49} +(-11.3120 - 39.5291i) q^{50} +(1.89136 + 3.03402i) q^{52} -27.8456i q^{53} -11.5711i q^{55} +(14.1880 - 15.7067i) q^{56} +(-55.4469 + 15.8671i) q^{58} +38.7342 q^{59} +7.21121i q^{61} +(-79.9120 + 22.8682i) q^{62} +(6.48592 + 63.6705i) q^{64} +1.88383 q^{65} -10.9281 q^{67} +(34.0485 - 21.2253i) q^{68} +(-3.06832 - 10.7221i) q^{70} +72.4872i q^{71} +26.0986 q^{73} +(-71.5114 + 20.4643i) q^{74} +(-86.1903 + 53.7298i) q^{76} +14.5255i q^{77} -96.8805i q^{79} +(30.2775 + 14.8474i) q^{80} +(38.8695 + 135.828i) q^{82} -26.3015 q^{83} -21.1408i q^{85} +(-3.63499 - 12.7023i) q^{86} +(-32.5926 - 29.4412i) q^{88} -41.8658 q^{89} -2.36482 q^{91} +(33.7041 + 54.0662i) q^{92} +(-86.5079 + 24.7558i) q^{94} +53.5158i q^{95} +74.6737 q^{97} +(3.85174 + 13.4597i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 12 q^{10} + 66 q^{16} - 64 q^{19} - 144 q^{22} - 168 q^{25} - 14 q^{28} + 12 q^{34} + 196 q^{40} + 224 q^{43} - 84 q^{46} - 168 q^{49} - 364 q^{52} + 348 q^{58} + 214 q^{64} - 32 q^{67}+ \cdots - 144 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 + 12 * q^10 + 66 * q^16 - 64 * q^19 - 144 * q^22 - 168 * q^25 - 14 * q^28 + 12 * q^34 + 196 * q^40 + 224 * q^43 - 84 * q^46 - 168 * q^49 - 364 * q^52 + 348 * q^58 + 214 * q^64 - 32 * q^67 - 84 * q^70 + 240 * q^73 + 416 * q^76 + 300 * q^82 - 120 * q^88 + 192 * q^94 - 144 * q^97

Introduction

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Database

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