LMFDB - Embedded newform 504.3.l.h.181.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(181,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.181"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 3, names="a")

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

Newform invariants

comment:select newform

sage:traces = [32,2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.32
Character	$\chi$	$=$	504.181
Dual form			504.3.l.h.181.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.84891 + 0.762588i) q^{2} +(2.83692 + 2.81991i) q^{4} +2.18588 q^{5} +(-5.50290 - 4.32644i) q^{7} +(3.09477 + 7.37715i) q^{8} +(4.04149 + 1.66693i) q^{10} +13.7904i q^{11} +7.07900 q^{13} +(-6.87506 - 12.1956i) q^{14} +(0.0962226 + 15.9997i) q^{16} +27.5636i q^{17} +30.2138 q^{19} +(6.20116 + 6.16398i) q^{20} +(-10.5164 + 25.4972i) q^{22} +29.0258 q^{23} -20.2219 q^{25} +(13.0884 + 5.39836i) q^{26} +(-3.41110 - 27.7914i) q^{28} +21.2655i q^{29} -45.7050i q^{31} +(-12.0233 + 29.6554i) q^{32} +(-21.0196 + 50.9625i) q^{34} +(-12.0287 - 9.45708i) q^{35} +41.0047i q^{37} +(55.8626 + 23.0407i) q^{38} +(6.76480 + 16.1256i) q^{40} -60.4609i q^{41} -33.6925i q^{43} +(-38.8876 + 39.1222i) q^{44} +(53.6660 + 22.1347i) q^{46} -9.53009i q^{47} +(11.5638 + 47.6160i) q^{49} +(-37.3885 - 15.4210i) q^{50} +(20.0826 + 19.9621i) q^{52} -46.9181i q^{53} +30.1441i q^{55} +(14.8866 - 53.9851i) q^{56} +(-16.2168 + 39.3179i) q^{58} -95.6189 q^{59} -45.4040 q^{61} +(34.8540 - 84.5042i) q^{62} +(-44.8448 + 45.6612i) q^{64} +15.4738 q^{65} -19.4310i q^{67} +(-77.7268 + 78.1956i) q^{68} +(-15.0280 - 26.6582i) q^{70} -4.84963 q^{71} +5.02093i q^{73} +(-31.2697 + 75.8140i) q^{74} +(85.7142 + 85.2003i) q^{76} +(59.6633 - 75.8871i) q^{77} +110.666 q^{79} +(0.210331 + 34.9734i) q^{80} +(46.1067 - 111.787i) q^{82} +17.9504 q^{83} +60.2506i q^{85} +(25.6935 - 62.2944i) q^{86} +(-101.734 + 42.6781i) q^{88} -10.6492i q^{89} +(-38.9550 - 30.6269i) q^{91} +(82.3437 + 81.8500i) q^{92} +(7.26753 - 17.6203i) q^{94} +66.0438 q^{95} +8.67407i q^{97} +(-14.9310 + 96.8559i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

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 $

$2$	1.84891	+	0.762588i	0.924454	+	0.381294i
$2$	1.84891	+	0.762588i	0.924454	+	0.381294i
$3$		0			0
$3$		0			0
$4$	2.83692	+	2.81991i	0.709230	+	0.704977i
$5$	2.18588			0.437176			0.218588	−	0.975817i	$-0.429855\pi$
$5$	2.18588			0.437176			0.218588	+	0.975817i	$0.429855\pi$
$6$		0			0
$7$	−5.50290	−	4.32644i	−0.786128	−	0.618063i
$7$	−5.50290	−	4.32644i	−0.786128	−	0.618063i
$8$	3.09477	+	7.37715i	0.386847	+	0.922144i
$9$		0			0
$10$	4.04149	+	1.66693i	0.404149	+	0.166693i
$11$			13.7904i			1.25367i	0.779151	+	0.626836i	$0.215650\pi$
$11$			13.7904i			1.25367i	−0.779151	+	0.626836i	$0.784350\pi$
$12$		0			0
$13$	7.07900			0.544539			0.272269	−	0.962221i	$-0.412226\pi$
$13$	7.07900			0.544539			0.272269	+	0.962221i	$0.412226\pi$
$14$	−6.87506	−	12.1956i	−0.491076	−	0.871117i
$15$		0			0
$16$	0.0962226	+	15.9997i	0.00601391	+	0.999982i
$17$			27.5636i			1.62139i	0.585471	+	0.810693i	$0.300910\pi$
$17$			27.5636i			1.62139i	−0.585471	+	0.810693i	$0.699090\pi$
$18$		0			0
$19$	30.2138			1.59020			0.795101	−	0.606477i	$-0.207418\pi$
$19$	30.2138			1.59020			0.795101	+	0.606477i	$0.207418\pi$
$20$	6.20116	+	6.16398i	0.310058	+	0.308199i
$21$		0			0
$22$	−10.5164	+	25.4972i	−0.478017	+	1.15896i
$23$	29.0258			1.26199			0.630995	−	0.775787i	$-0.282647\pi$
$23$	29.0258			1.26199			0.630995	+	0.775787i	$0.282647\pi$
$24$		0			0
$25$	−20.2219			−0.808877
$26$	13.0884	+	5.39836i	0.503401	+	0.207629i
$27$		0			0
$28$	−3.41110	−	27.7914i	−0.121825	−	0.992552i
$29$			21.2655i			0.733292i	0.930361	+	0.366646i	$0.119494\pi$
$29$			21.2655i			0.733292i	−0.930361	+	0.366646i	$0.880506\pi$
$30$		0			0
$31$		−	45.7050i		−	1.47435i	−0.675700	−	0.737177i	$-0.736159\pi$
$31$		−	45.7050i		−	1.47435i	0.675700	−	0.737177i	$-0.263841\pi$
$32$	−12.0233	+	29.6554i	−0.375727	+	0.926730i
$33$		0			0
$34$	−21.0196	+	50.9625i	−0.618225	+	1.49890i
$35$	−12.0287	−	9.45708i	−0.343676	−	0.270202i
$36$		0			0
$37$			41.0047i			1.10824i	0.832438	+	0.554118i	$0.186944\pi$
$37$			41.0047i			1.10824i	−0.832438	+	0.554118i	$0.813056\pi$
$38$	55.8626	+	23.0407i	1.47007	+	0.606334i
$39$		0			0
$40$	6.76480	+	16.1256i	0.169120	+	0.403139i
$41$		−	60.4609i		−	1.47465i	−0.675535	−	0.737327i	$-0.736087\pi$
$41$		−	60.4609i		−	1.47465i	0.675535	−	0.737327i	$-0.263913\pi$
$42$		0			0
$43$		−	33.6925i		−	0.783547i	−0.920062	−	0.391774i	$-0.871862\pi$
$43$		−	33.6925i		−	0.783547i	0.920062	−	0.391774i	$-0.128138\pi$
$44$	−38.8876	+	39.1222i	−0.883810	+	0.889141i
$45$		0			0
$46$	53.6660	+	22.1347i	1.16665	+	0.481189i
$47$		−	9.53009i		−	0.202768i	−0.994847	−	0.101384i	$-0.967673\pi$
$47$		−	9.53009i		−	0.202768i	0.994847	−	0.101384i	$-0.0323271\pi$
$48$		0			0
$49$	11.5638	+	47.6160i	0.235996	+	0.971754i
$50$	−37.3885	−	15.4210i	−0.747770	−	0.308420i
$51$		0			0
$52$	20.0826	+	19.9621i	0.386203	+	0.383887i
$53$		−	46.9181i		−	0.885247i	−0.896708	−	0.442624i	$-0.854048\pi$
$53$		−	46.9181i		−	0.885247i	0.896708	−	0.442624i	$-0.145952\pi$
$54$		0			0
$55$			30.1441i			0.548075i
$56$	14.8866	−	53.9851i	0.265832	−	0.964019i
$57$		0			0
$58$	−16.2168	+	39.3179i	−0.279600	+	0.677895i
$59$	−95.6189			−1.62066			−0.810329	−	0.585975i	$-0.800712\pi$
$59$	−95.6189			−1.62066			−0.810329	+	0.585975i	$0.800712\pi$
$60$		0			0
$61$	−45.4040			−0.744327			−0.372164	−	0.928167i	$-0.621384\pi$
$61$	−45.4040			−0.744327			−0.372164	+	0.928167i	$0.621384\pi$
$62$	34.8540	−	84.5042i	0.562162	−	1.36297i
$63$		0			0
$64$	−44.8448	+	45.6612i	−0.700699	+	0.713457i
$65$	15.4738			0.238059
$66$		0			0
$67$		−	19.4310i		−	0.290014i	−0.989431	−	0.145007i	$-0.953679\pi$
$67$		−	19.4310i		−	0.290014i	0.989431	−	0.145007i	$-0.0463205\pi$
$68$	−77.7268	+	78.1956i	−1.14304	+	1.14994i
$69$		0			0
$70$	−15.0280	−	26.6582i	−0.214686	−	0.380831i
$71$	−4.84963			−0.0683047			−0.0341523	−	0.999417i	$-0.510873\pi$
$71$	−4.84963			−0.0683047			−0.0341523	+	0.999417i	$0.510873\pi$
$72$		0			0
$73$			5.02093i			0.0687799i	0.999408	+	0.0343899i	$0.0109488\pi$
$73$			5.02093i			0.0687799i	−0.999408	+	0.0343899i	$0.989051\pi$
$74$	−31.2697	+	75.8140i	−0.422564	+	1.02451i
$75$		0			0
$76$	85.7142	+	85.2003i	1.12782	+	1.12106i
$77$	59.6633	−	75.8871i	0.774848	−	0.985547i
$78$		0			0
$79$	110.666			1.40083			0.700416	−	0.713735i	$-0.252998\pi$
$79$	110.666			1.40083			0.700416	+	0.713735i	$0.252998\pi$
$80$	0.210331	+	34.9734i	0.00262914	+	0.437168i
$81$		0			0
$82$	46.1067	−	111.787i	0.562277	−	1.36325i
$83$	17.9504			0.216270			0.108135	−	0.994136i	$-0.465512\pi$
$83$	17.9504			0.216270			0.108135	+	0.994136i	$0.465512\pi$
$84$		0			0
$85$			60.2506i			0.708831i
$86$	25.6935	−	62.2944i	0.298762	−	0.724353i
$87$		0			0
$88$	−101.734	+	42.6781i	−1.15607	+	0.484979i
$89$		−	10.6492i		−	0.119654i	−0.998209	−	0.0598272i	$-0.980945\pi$
$89$		−	10.6492i		−	0.119654i	0.998209	−	0.0598272i	$-0.0190550\pi$
$90$		0			0
$91$	−38.9550	−	30.6269i	−0.428077	−	0.336559i
$92$	82.3437	+	81.8500i	0.895041	+	0.889674i
$93$		0			0
$94$	7.26753	−	17.6203i	0.0773142	−	0.187450i
$95$	66.0438			0.695198
$96$		0			0
$97$			8.67407i			0.0894234i	0.999000	+	0.0447117i	$0.0142369\pi$
$97$			8.67407i			0.0894234i	−0.999000	+	0.0447117i	$0.985763\pi$
$98$	−14.9310	+	96.8559i	−0.152357	+	0.988326i
$99$		0			0
$100$	−57.3680	−	57.0240i	−0.573680	−	0.570240i
$101$	2.51811			0.0249318			0.0124659	−	0.999922i	$-0.496032\pi$
$101$	2.51811			0.0249318			0.0124659	+	0.999922i	$0.496032\pi$
$102$		0			0
$103$		−	123.863i		−	1.20255i	−0.799041	−	0.601277i	$-0.794659\pi$
$103$		−	123.863i		−	1.20255i	0.799041	−	0.601277i	$-0.205341\pi$
$104$	21.9079	+	52.2229i	0.210653	+	0.502143i
$105$		0			0
$106$	35.7792	−	86.7472i	0.337539	−	0.818370i
$107$		−	101.168i		−	0.945494i	−0.881198	−	0.472747i	$-0.843263\pi$
$107$		−	101.168i		−	0.945494i	0.881198	−	0.472747i	$-0.156737\pi$
$108$		0			0
$109$			8.84786i			0.0811730i	0.999176	+	0.0405865i	$0.0129226\pi$
$109$			8.84786i			0.0811730i	−0.999176	+	0.0405865i	$0.987077\pi$
$110$	−22.9875	+	55.7337i	−0.208978	+	0.506670i
$111$		0			0
$112$	68.6923	−	88.4611i	0.613324	−	0.789831i
$113$	−52.4755			−0.464385			−0.232192	−	0.972670i	$-0.574590\pi$
$113$	−52.4755			−0.464385			−0.232192	+	0.972670i	$0.574590\pi$
$114$		0			0
$115$	63.4468			0.551711
$116$	−59.9667	+	60.3284i	−0.516954	+	0.520072i
$117$		0			0
$118$	−176.790	−	72.9178i	−1.49822	−	0.617947i
$119$	119.252	−	151.680i	1.00212	−	1.27462i
$120$		0			0
$121$	−69.1748			−0.571692
$122$	−83.9478	−	34.6245i	−0.688096	−	0.283808i
$123$		0			0
$124$	128.884	−	129.661i	1.03939	−	1.04566i
$125$	−98.8497			−0.790797
$126$		0			0
$127$	−12.5367			−0.0987140			−0.0493570	−	0.998781i	$-0.515717\pi$
$127$	−12.5367			−0.0987140			−0.0493570	+	0.998781i	$0.515717\pi$
$128$	−117.735	+	50.2253i	−0.919801	+	0.392385i
$129$		0			0
$130$	28.6097	+	11.8002i	0.220075	+	0.0907705i
$131$	−17.4890			−0.133504			−0.0667519	−	0.997770i	$-0.521264\pi$
$131$	−17.4890			−0.133504			−0.0667519	+	0.997770i	$0.521264\pi$
$132$		0			0
$133$	−166.264	−	130.718i	−1.25010	−	0.982845i
$134$	14.8178	−	35.9260i	0.110581	−	0.268105i
$135$		0			0
$136$	−203.341	+	85.3030i	−1.49515	+	0.627228i
$137$	66.3588			0.484371			0.242186	−	0.970230i	$-0.422136\pi$
$137$	66.3588			0.484371			0.242186	+	0.970230i	$0.422136\pi$
$138$		0			0
$139$	−136.556			−0.982416			−0.491208	−	0.871042i	$-0.663444\pi$
$139$	−136.556			−0.982416			−0.491208	+	0.871042i	$0.663444\pi$
$140$	−7.45626	−	60.7487i	−0.0532590	−	0.433920i
$141$		0			0
$142$	−8.96652	−	3.69827i	−0.0631445	−	0.0260442i
$143$			97.6222i			0.682672i
$144$		0			0
$145$			46.4837i			0.320578i
$146$	−3.82890	+	9.28324i	−0.0262254	+	0.0635838i
$147$		0			0
$148$	−115.630	+	116.327i	−0.781281	+	0.785994i
$149$		−	143.761i		−	0.964841i	−0.875940	−	0.482420i	$-0.839758\pi$
$149$		−	143.761i		−	0.964841i	0.875940	−	0.482420i	$-0.160242\pi$
$150$		0			0
$151$	213.192			1.41186			0.705932	−	0.708279i	$-0.250528\pi$
$151$	213.192			1.41186			0.705932	+	0.708279i	$0.250528\pi$
$152$	93.5050	+	222.892i	0.615164	+	1.46640i
$153$		0			0
$154$	168.183	−	94.8097i	1.09209	−	0.615648i
$155$		−	99.9055i		−	0.644552i
$156$		0			0
$157$	91.0134			0.579703			0.289851	−	0.957072i	$-0.406394\pi$
$157$	91.0134			0.579703			0.289851	+	0.957072i	$0.406394\pi$
$158$	204.611	+	84.3923i	1.29500	+	0.534129i
$159$		0			0
$160$	−26.2814	+	64.8231i	−0.164259	+	0.405144i
$161$	−159.726	−	125.578i	−0.992086	−	0.779989i
$162$		0			0
$163$		−	201.585i		−	1.23672i	−0.785895	−	0.618360i	$-0.787797\pi$
$163$		−	201.585i		−	1.23672i	0.785895	−	0.618360i	$-0.212203\pi$
$164$	170.494	−	171.523i	1.03960	−	1.04587i
$165$		0			0
$166$	33.1886	+	13.6887i	0.199931	+	0.0824623i
$167$		−	196.271i		−	1.17527i	−0.809125	−	0.587637i	$-0.800059\pi$
$167$		−	196.271i		−	1.17527i	0.809125	−	0.587637i	$-0.199941\pi$
$168$		0			0
$169$	−118.888			−0.703478
$170$	−45.9464	+	111.398i	−0.270273	+	0.655282i
$171$		0			0
$172$	95.0099	−	95.5830i	0.552383	−	0.555715i
$173$	10.8740			0.0628556			0.0314278	−	0.999506i	$-0.489995\pi$
$173$	10.8740			0.0628556			0.0314278	+	0.999506i	$0.489995\pi$
$174$		0			0
$175$	111.279	+	87.4890i	0.635881	+	0.499937i
$176$	−220.642	+	1.32695i	−1.25365	+	0.00753947i
$177$		0			0
$178$	8.12098	−	19.6895i	0.0456235	−	0.110615i
$179$			113.741i			0.635422i	0.948188	+	0.317711i	$0.102914\pi$
$179$			113.741i			0.635422i	−0.948188	+	0.317711i	$0.897086\pi$
$180$		0			0
$181$	249.908			1.38071			0.690354	−	0.723471i	$-0.257455\pi$
$181$	249.908			1.38071			0.690354	+	0.723471i	$0.257455\pi$
$182$	−48.6685	−	86.3329i	−0.267410	−	0.474357i
$183$		0			0
$184$	89.8281	+	214.127i	0.488196	+	1.16374i
$185$			89.6314i			0.484494i
$186$		0			0
$187$	−380.112			−2.03269
$188$	26.8740	−	27.0361i	0.142947	−	0.143809i
$189$		0			0
$190$	122.109	+	50.3642i	0.642678	+	0.265075i
$191$	29.4966			0.154433			0.0772163	−	0.997014i	$-0.475397\pi$
$191$	29.4966			0.154433			0.0772163	+	0.997014i	$0.475397\pi$
$192$		0			0
$193$	4.76565			0.0246925			0.0123462	−	0.999924i	$-0.496070\pi$
$193$	4.76565			0.0246925			0.0123462	+	0.999924i	$0.496070\pi$
$194$	−6.61474	+	16.0376i	−0.0340966	+	0.0826678i
$195$		0			0
$196$	−101.467	+	167.691i	−0.517689	+	0.855569i
$197$			371.925i			1.88794i	0.330028	+	0.943971i	$0.392942\pi$
$197$			371.925i			1.88794i	−0.330028	+	0.943971i	$0.607058\pi$
$198$		0			0
$199$		−	245.194i		−	1.23213i	−0.787695	−	0.616065i	$-0.788726\pi$
$199$		−	245.194i		−	1.23213i	0.787695	−	0.616065i	$-0.211274\pi$
$200$	−62.5823	−	149.180i	−0.312911	−	0.745901i
$201$		0			0
$202$	4.65575	+	1.92028i	0.0230483	+	0.00950634i
$203$	92.0038	−	117.022i	0.453221	−	0.576462i
$204$		0			0
$205$		−	132.160i		−	0.644684i
$206$	94.4564	−	229.011i	0.458526	−	1.11170i
$207$		0			0
$208$	0.681160	+	113.262i	0.00327481	+	0.544529i
$209$			416.660i			1.99359i
$210$		0			0
$211$			303.979i			1.44066i	0.693633	+	0.720328i	$0.256009\pi$
$211$			303.979i			1.44066i	−0.693633	+	0.720328i	$0.743991\pi$
$212$	132.305	−	133.103i	0.624079	−	0.627844i
$213$		0			0
$214$	77.1494	−	187.050i	0.360511	−	0.874065i
$215$		−	73.6478i		−	0.342548i
$216$		0			0
$217$	−197.740	+	251.510i	−0.911244	+	1.15903i
$218$	−6.74727	+	16.3589i	−0.0309508	+	0.0750407i
$219$		0			0
$220$	−85.0037	+	85.5164i	−0.386380	+	0.388711i
$221$			195.123i			0.882907i
$222$		0			0
$223$		−	342.621i		−	1.53642i	−0.640200	−	0.768208i	$-0.721149\pi$
$223$		−	342.621i		−	1.53642i	0.640200	−	0.768208i	$-0.278851\pi$
$224$	194.465	−	111.172i	0.868148	−	0.496306i
$225$		0			0
$226$	−97.0223	−	40.0172i	−0.429302	−	0.177067i
$227$	−337.680			−1.48758			−0.743788	−	0.668416i	$-0.766973\pi$
$227$	−337.680			−1.48758			−0.743788	+	0.668416i	$0.766973\pi$
$228$		0			0
$229$	327.787			1.43138			0.715692	−	0.698416i	$-0.246111\pi$
$229$	327.787			1.43138			0.715692	+	0.698416i	$0.246111\pi$
$230$	117.307	+	48.3838i	0.510032	+	0.210364i
$231$		0			0
$232$	−156.879	+	65.8118i	−0.676201	+	0.283672i
$233$	226.032			0.970093			0.485047	−	0.874488i	$-0.338803\pi$
$233$	226.032			0.970093			0.485047	+	0.874488i	$0.338803\pi$
$234$		0			0
$235$		−	20.8316i		−	0.0886452i
$236$	−271.263	−	269.637i	−1.14942	−	1.14253i
$237$		0			0
$238$	336.155	−	189.501i	1.41242	−	0.796224i
$239$	13.0451			0.0545818			0.0272909	−	0.999628i	$-0.491312\pi$
$239$	13.0451			0.0545818			0.0272909	+	0.999628i	$0.491312\pi$
$240$		0			0
$241$		−	36.2348i		−	0.150352i	−0.997170	−	0.0751759i	$-0.976048\pi$
$241$		−	36.2348i		−	0.150352i	0.997170	−	0.0751759i	$-0.0239518\pi$
$242$	−127.898	−	52.7518i	−0.528503	−	0.217983i
$243$		0			0
$244$	−128.807	−	128.035i	−0.527899	−	0.524734i
$245$	25.2770	+	104.083i	0.103172	+	0.424827i
$246$		0			0
$247$	213.884			0.865926
$248$	337.172	−	141.446i	1.35957	−	0.570349i
$249$		0			0
$250$	−182.764	−	75.3816i	−0.731056	−	0.301526i
$251$	489.836			1.95154			0.975769	−	0.218805i	$-0.0702158\pi$
$251$	489.836			1.95154			0.975769	+	0.218805i	$0.0702158\pi$
$252$		0			0
$253$			400.276i			1.58212i
$254$	−23.1791	−	9.56031i	−0.0912565	−	0.0376390i
$255$		0			0
$256$	−255.981	+	3.07907i	−0.999928	+	0.0120276i
$257$			76.9880i			0.299564i	0.988719	+	0.149782i	$0.0478572\pi$
$257$			76.9880i			0.299564i	−0.988719	+	0.149782i	$0.952143\pi$
$258$		0			0
$259$	177.405	−	225.645i	0.684960	−	0.871216i
$260$	43.8980	+	43.6348i	0.168839	+	0.167826i
$261$		0			0
$262$	−32.3355	−	13.3369i	−0.123418	−	0.0509042i
$263$	−36.4215			−0.138485			−0.0692424	−	0.997600i	$-0.522058\pi$
$263$	−36.4215			−0.138485			−0.0692424	+	0.997600i	$0.522058\pi$
$264$		0			0
$265$		−	102.557i		−	0.387009i
$266$	−207.722	−	368.477i	−0.780909	−	1.38525i
$267$		0			0
$268$	54.7935	−	55.1240i	0.204453	−	0.205687i
$269$	−64.2746			−0.238939			−0.119470	−	0.992838i	$-0.538119\pi$
$269$	−64.2746			−0.238939			−0.119470	+	0.992838i	$0.538119\pi$
$270$		0			0
$271$			477.989i			1.76380i	0.471441	+	0.881898i	$0.343734\pi$
$271$			477.989i			1.76380i	−0.471441	+	0.881898i	$0.656266\pi$
$272$	−441.009	+	2.65224i	−1.62136	+	0.00975087i
$273$		0			0
$274$	122.691	+	50.6044i	0.447779	+	0.184688i
$275$		−	278.868i		−	1.01407i
$276$		0			0
$277$		−	320.075i		−	1.15551i	−0.816211	−	0.577753i	$-0.803930\pi$
$277$		−	320.075i		−	1.15551i	0.816211	−	0.577753i	$-0.196070\pi$
$278$	−252.479	−	104.136i	−0.908198	−	0.374589i
$279$		0			0
$280$	32.5403	−	118.005i	0.116215	−	0.421446i
$281$	−292.624			−1.04137			−0.520683	−	0.853750i	$-0.674323\pi$
$281$	−292.624			−1.04137			−0.520683	+	0.853750i	$0.674323\pi$
$282$		0			0
$283$	262.188			0.926458			0.463229	−	0.886239i	$-0.346691\pi$
$283$	262.188			0.926458			0.463229	+	0.886239i	$0.346691\pi$
$284$	−13.7580	−	13.6755i	−0.0484437	−	0.0481532i
$285$		0			0
$286$	−74.4455	+	180.494i	−0.260299	+	0.631099i
$287$	−261.580	+	332.710i	−0.911430	+	1.15927i
$288$		0			0
$289$	−470.751			−1.62889
$290$	−35.4479	+	85.9441i	−0.122234	+	0.296359i
$291$		0			0
$292$	−14.1586	+	14.2440i	−0.0484883	+	0.0487807i
$293$	−533.907			−1.82221			−0.911104	−	0.412175i	$-0.864769\pi$
$293$	−533.907			−1.82221			−0.911104	+	0.412175i	$0.864769\pi$
$294$		0			0
$295$	−209.011			−0.708513
$296$	−302.498	+	126.900i	−1.02195	+	0.428717i
$297$		0			0
$298$	109.631	−	265.801i	0.367888	−	0.891951i
$299$	205.473			0.687202
$300$		0			0
$301$	−145.769	+	185.407i	−0.484282	+	0.615969i
$302$	394.171	+	162.577i	1.30520	+	0.538335i
$303$		0			0
$304$	2.90725	+	483.413i	0.00956333	+	1.59017i
$305$	−99.2476			−0.325402
$306$		0			0
$307$	−72.1659			−0.235068			−0.117534	−	0.993069i	$-0.537499\pi$
$307$	−72.1659			−0.235068			−0.117534	+	0.993069i	$0.537499\pi$
$308$	383.255	−	47.0404i	1.24433	−	0.152729i
$309$		0			0
$310$	76.1867	−	184.716i	0.245764	−	0.595858i
$311$			243.116i			0.781725i	0.920449	+	0.390862i	$0.127823\pi$
$311$			243.116i			0.781725i	−0.920449	+	0.390862i	$0.872177\pi$
$312$		0			0
$313$			170.316i			0.544142i	0.962277	+	0.272071i	$0.0877085\pi$
$313$			170.316i			0.544142i	−0.962277	+	0.272071i	$0.912292\pi$
$314$	168.275	+	69.4057i	0.535909	+	0.221037i
$315$		0			0
$316$	313.950	+	312.067i	0.993512	+	0.987555i
$317$		−	70.0039i		−	0.220832i	−0.993885	−	0.110416i	$-0.964782\pi$
$317$		−	70.0039i		−	0.220832i	0.993885	−	0.110416i	$-0.0352184\pi$
$318$		0			0
$319$	−293.259			−0.919307
$320$	−98.0252	+	99.8099i	−0.306329	+	0.311906i
$321$		0			0
$322$	−199.554	−	353.988i	−0.619732	−	1.09934i
$323$			832.801i			2.57833i
$324$		0			0
$325$	−143.151			−0.440465
$326$	153.726	−	372.713i	0.471554	−	1.14329i
$327$		0			0
$328$	446.029	−	187.113i	1.35984	−	0.570465i
$329$	−41.2314	+	52.4431i	−0.125323	+	0.159402i
$330$		0			0
$331$			138.345i			0.417960i	0.977920	+	0.208980i	$0.0670143\pi$
$331$			138.345i			0.417960i	−0.977920	+	0.208980i	$0.932986\pi$
$332$	50.9238	+	50.6184i	0.153385	+	0.152465i
$333$		0			0
$334$	149.674	−	362.886i	0.448125	−	1.08649i
$335$		−	42.4737i		−	0.126787i
$336$		0			0
$337$	−306.172			−0.908521			−0.454261	−	0.890869i	$-0.650097\pi$
$337$	−306.172			−0.908521			−0.454261	+	0.890869i	$0.650097\pi$
$338$	−219.812	−	90.6624i	−0.650333	−	0.268232i
$339$		0			0
$340$	−169.901	+	170.926i	−0.499710	+	0.502724i
$341$	630.289			1.84835
$342$		0			0
$343$	142.373	−	312.056i	0.415083	−	0.909784i
$344$	248.555	−	104.271i	0.722543	−	0.303113i
$345$		0			0
$346$	20.1050	+	8.29239i	0.0581071	+	0.0239665i
$347$		−	350.108i		−	1.00896i	−0.863424	−	0.504478i	$-0.831685\pi$
$347$		−	350.108i		−	1.00896i	0.863424	−	0.504478i	$-0.168315\pi$
$348$		0			0
$349$	331.132			0.948803			0.474402	−	0.880308i	$-0.342664\pi$
$349$	331.132			0.948803			0.474402	+	0.880308i	$0.342664\pi$
$350$	139.027	+	246.619i	0.397220	+	0.704627i
$351$		0			0
$352$	−408.959	−	165.806i	−1.16182	−	0.471039i
$353$		−	94.0398i		−	0.266402i	−0.991089	−	0.133201i	$-0.957474\pi$
$353$		−	94.0398i		−	0.266402i	0.991089	−	0.133201i	$-0.0425256\pi$
$354$		0			0
$355$	−10.6007			−0.0298612
$356$	30.0299	−	30.2110i	0.0843536	−	0.0848625i
$357$		0			0
$358$	−86.7372	+	210.296i	−0.242283	+	0.587418i
$359$	273.140			0.760835			0.380417	−	0.924815i	$-0.375780\pi$
$359$	273.140			0.760835			0.380417	+	0.924815i	$0.375780\pi$
$360$		0			0
$361$	551.876			1.52874
$362$	462.057	+	190.577i	1.27640	+	0.526456i
$363$		0			0
$364$	−24.1472	−	196.736i	−0.0663385	−	0.540483i
$365$			10.9752i			0.0300689i
$366$		0			0
$367$		−	17.5525i		−	0.0478270i	−0.999714	−	0.0239135i	$-0.992387\pi$
$367$		−	17.5525i		−	0.0478270i	0.999714	−	0.0239135i	$-0.00761263\pi$
$368$	2.79293	+	464.404i	0.00758949	+	1.26197i
$369$		0			0
$370$	−68.3518	+	165.720i	−0.184735	+	0.447892i
$371$	−202.988	+	258.186i	−0.547139	+	0.695918i
$372$		0			0
$373$			282.579i			0.757584i	0.925482	+	0.378792i	$0.123660\pi$
$373$			282.579i			0.757584i	−0.925482	+	0.378792i	$0.876340\pi$
$374$	−702.793	−	289.869i	−1.87912	−	0.775051i
$375$		0			0
$376$	70.3049	−	29.4935i	0.186981	−	0.0784401i
$377$			150.538i			0.399306i
$378$		0			0
$379$			712.398i			1.87968i	0.341618	+	0.939839i	$0.389025\pi$
$379$			712.398i			1.87968i	−0.341618	+	0.939839i	$0.610975\pi$
$380$	187.361	+	186.237i	0.493055	+	0.490099i
$381$		0			0
$382$	54.5366	+	22.4938i	0.142766	+	0.0588842i
$383$		−	394.452i		−	1.02990i	−0.857220	−	0.514950i	$-0.827810\pi$
$383$		−	394.452i		−	1.02990i	0.857220	−	0.514950i	$-0.172190\pi$
$384$		0			0
$385$	130.417	−	165.880i	0.338745	−	0.430857i
$386$	8.81125	+	3.63423i	0.0228271	+	0.00941510i
$387$		0			0
$388$	−24.4601	+	24.6076i	−0.0630415	+	0.0634217i
$389$		−	365.323i		−	0.939133i	−0.882897	−	0.469567i	$-0.844410\pi$
$389$		−	365.323i		−	0.939133i	0.882897	−	0.469567i	$-0.155590\pi$
$390$		0			0
$391$			800.054i			2.04617i
$392$	−315.483	+	232.668i	−0.804803	+	0.593542i
$393$		0			0
$394$	−283.625	+	687.654i	−0.719861	+	1.74532i
$395$	241.902			0.612410
$396$		0			0
$397$	−326.289			−0.821886			−0.410943	−	0.911661i	$-0.634800\pi$
$397$	−326.289			−0.821886			−0.410943	+	0.911661i	$0.634800\pi$
$398$	186.982	−	453.341i	0.469804	−	1.13905i
$399$		0			0
$400$	−1.94581	−	323.545i	−0.00486451	−	0.808863i
$401$	−554.438			−1.38264			−0.691319	−	0.722550i	$-0.742970\pi$
$401$	−554.438			−1.38264			−0.691319	+	0.722550i	$0.742970\pi$
$402$		0			0
$403$		−	323.545i		−	0.802842i
$404$	7.14368	+	7.10084i	0.0176824	+	0.0175763i
$405$		0			0
$406$	259.346	−	146.201i	0.638783	−	0.360102i
$407$	−565.471			−1.38936
$408$		0			0
$409$			149.560i			0.365671i	0.983143	+	0.182836i	$0.0585277\pi$
$409$			149.560i			0.365671i	−0.983143	+	0.182836i	$0.941472\pi$
$410$	100.784	−	244.352i	0.245814	−	0.595980i
$411$		0			0
$412$	349.282	−	351.389i	0.847773	−	0.852887i
$413$	526.181	+	413.689i	1.27405	+	1.00167i
$414$		0			0
$415$	39.2374			0.0945478
$416$	−85.1128	+	209.930i	−0.204598	+	0.504640i
$417$		0			0
$418$	−317.740	+	770.367i	−0.760144	+	1.84298i
$419$	−88.8842			−0.212134			−0.106067	−	0.994359i	$-0.533826\pi$
$419$	−88.8842			−0.212134			−0.106067	+	0.994359i	$0.533826\pi$
$420$		0			0
$421$			426.991i			1.01423i	0.861879	+	0.507115i	$0.169288\pi$
$421$			426.991i			1.01423i	−0.861879	+	0.507115i	$0.830712\pi$
$422$	−231.810	+	562.028i	−0.549314	+	1.33182i
$423$		0			0
$424$	346.122	−	145.201i	0.816325	−	0.342455i
$425$		−	557.389i		−	1.31150i
$426$		0			0
$427$	249.853	+	196.438i	0.585137	+	0.460041i
$428$	285.284	−	287.005i	0.666552	−	0.670572i
$429$		0			0
$430$	56.1629	−	136.168i	0.130611	−	0.316670i
$431$	−230.518			−0.534846			−0.267423	−	0.963579i	$-0.586172\pi$
$431$	−230.518			−0.534846			−0.267423	+	0.963579i	$0.586172\pi$
$432$		0			0
$433$			104.206i			0.240661i	0.992734	+	0.120331i	$0.0383955\pi$
$433$			104.206i			0.240661i	−0.992734	+	0.120331i	$0.961605\pi$
$434$	−557.401	+	314.224i	−1.28433	+	0.724019i
$435$		0			0
$436$	−24.9502	+	25.1007i	−0.0572252	+	0.0575703i
$437$	876.979			2.00682
$438$		0			0
$439$		−	23.9344i		−	0.0545203i	−0.999628	−	0.0272601i	$-0.991322\pi$
$439$		−	23.9344i		−	0.0545203i	0.999628	−	0.0272601i	$-0.00867825\pi$
$440$	−222.378	+	93.2892i	−0.505404	+	0.212021i
$441$		0			0
$442$	−148.798	+	360.764i	−0.336647	+	0.816207i
$443$			145.095i			0.327528i	0.986500	+	0.163764i	$0.0523635\pi$
$443$			145.095i			0.327528i	−0.986500	+	0.163764i	$0.947637\pi$
$444$		0			0
$445$		−	23.2780i		−	0.0523100i
$446$	261.278	−	633.474i	0.585826	−	1.42035i
$447$		0			0
$448$	444.327	−	57.2508i	0.991801	−	0.127792i
$449$	−188.122			−0.418981			−0.209490	−	0.977811i	$-0.567181\pi$
$449$	−188.122			−0.418981			−0.209490	+	0.977811i	$0.567181\pi$
$450$		0			0
$451$	833.779			1.84873
$452$	−148.869	−	147.976i	−0.329355	−	0.327381i
$453$		0			0
$454$	−624.339	−	257.511i	−1.37520	−	0.567204i
$455$	−85.1510	−	66.9467i	−0.187145	−	0.147136i
$456$		0			0
$457$	725.123			1.58670			0.793351	−	0.608765i	$-0.208335\pi$
$457$	725.123			1.58670			0.793351	+	0.608765i	$0.208335\pi$
$458$	606.048	+	249.966i	1.32325	+	0.545778i
$459$		0			0
$460$	179.993	+	178.914i	0.391290	+	0.388944i
$461$	104.422			0.226511			0.113256	−	0.993566i	$-0.463872\pi$
$461$	104.422			0.226511			0.113256	+	0.993566i	$0.463872\pi$
$462$		0			0
$463$	−68.1610			−0.147216			−0.0736080	−	0.997287i	$-0.523451\pi$
$463$	−68.1610			−0.147216			−0.0736080	+	0.997287i	$0.523451\pi$
$464$	−340.241	+	2.04622i	−0.733279	+	0.00440995i
$465$		0			0
$466$	417.912	+	172.369i	0.896806	+	0.369891i
$467$	−8.55407			−0.0183171			−0.00915853	−	0.999958i	$-0.502915\pi$
$467$	−8.55407			−0.0183171			−0.00915853	+	0.999958i	$0.502915\pi$
$468$		0			0
$469$	−84.0669	+	106.927i	−0.179247	+	0.227988i
$470$	15.8860	−	38.5158i	0.0337999	−	0.0819484i
$471$		0			0
$472$	−295.919	−	705.395i	−0.626946	−	1.49448i
$473$	464.633			0.982311
$474$		0			0
$475$	−610.982			−1.28628
$476$	766.032	−	94.0222i	1.60931	−	0.197526i
$477$		0			0
$478$	24.1191	+	9.94800i	0.0504584	+	0.0208117i
$479$			210.356i			0.439156i	0.975595	+	0.219578i	$0.0704681\pi$
$479$			210.356i			0.439156i	−0.975595	+	0.219578i	$0.929532\pi$
$480$		0			0
$481$			290.273i			0.603477i
$482$	27.6322	−	66.9948i	0.0573283	−	0.138993i
$483$		0			0
$484$	−196.243	−	195.067i	−0.405461	−	0.403030i
$485$			18.9605i			0.0390937i
$486$		0			0
$487$	−844.714			−1.73453			−0.867263	−	0.497850i	$-0.834123\pi$
$487$	−844.714			−1.73453			−0.867263	+	0.497850i	$0.834123\pi$
$488$	−140.515	−	334.952i	−0.287941	−	0.686377i
$489$		0			0
$490$	−32.6373	+	211.715i	−0.0666067	+	0.432072i
$491$			399.255i			0.813146i	0.913618	+	0.406573i	$0.133276\pi$
$491$			399.255i			0.813146i	−0.913618	+	0.406573i	$0.866724\pi$
$492$		0			0
$493$	−586.152			−1.18895
$494$	395.451	+	163.105i	0.800509	+	0.330172i
$495$		0			0
$496$	731.266	−	4.39785i	1.47433	−	0.00886663i
$497$	26.6870	+	20.9817i	0.0536962	+	0.0422166i
$498$		0			0
$499$		−	453.416i		−	0.908650i	−0.890836	−	0.454325i	$-0.849881\pi$
$499$		−	453.416i		−	0.908650i	0.890836	−	0.454325i	$-0.150119\pi$
$500$	−280.429	−	278.747i	−0.560857	−	0.557494i
$501$		0			0
$502$	905.661	+	373.543i	1.80411	+	0.744109i
$503$			424.590i			0.844116i	0.906569	+	0.422058i	$0.138692\pi$
$503$			424.590i			0.844116i	−0.906569	+	0.422058i	$0.861308\pi$
$504$		0			0
$505$	5.50429			0.0108996
$506$	−305.246	+	740.074i	−0.603253	+	1.46260i
$507$		0			0
$508$	−35.5655	−	35.3523i	−0.0700109	−	0.0695911i
$509$	−869.875			−1.70899			−0.854495	−	0.519460i	$-0.826133\pi$
$509$	−869.875			−1.70899			−0.854495	+	0.519460i	$0.826133\pi$
$510$		0			0
$511$	21.7228	−	27.6297i	0.0425103	−	0.0540698i
$512$	−475.634	−	189.515i	−0.928973	−	0.370147i
$513$		0			0
$514$	−58.7101	+	142.344i	−0.114222	+	0.276933i
$515$		−	270.750i		−	0.525727i
$516$		0			0
$517$	131.424			0.254204
$518$	500.079	−	281.910i	0.965403	−	0.544228i
$519$		0			0
$520$	47.8880	+	114.153i	0.0920924	+	0.219525i
$521$		−	216.686i		−	0.415905i	−0.978139	−	0.207952i	$-0.933320\pi$
$521$		−	216.686i		−	0.415905i	0.978139	−	0.207952i	$-0.0666799\pi$
$522$		0			0
$523$	96.1102			0.183767			0.0918836	−	0.995770i	$-0.470711\pi$
$523$	96.1102			0.183767			0.0918836	+	0.995770i	$0.470711\pi$
$524$	−49.6148	−	49.3174i	−0.0946848	−	0.0941171i
$525$		0			0
$526$	−67.3400	−	27.7746i	−0.128023	−	0.0528034i
$527$	1259.79			2.39050
$528$		0			0
$529$	313.495			0.592618
$530$	78.2090	−	189.619i	0.147564	−	0.357772i
$531$		0			0
$532$	−103.063	−	839.686i	−0.193727	−	1.57836i
$533$		−	428.002i		−	0.803006i
$534$		0			0
$535$		−	221.141i		−	0.413347i
$536$	143.345	−	60.1344i	0.267435	−	0.112191i
$537$		0			0
$538$	−118.838	−	49.0150i	−0.220888	−	0.0911060i
$539$	−656.642	+	159.469i	−1.21826	+	0.295861i
$540$		0			0
$541$			34.2281i			0.0632681i	0.999500	+	0.0316341i	$0.0100711\pi$
$541$			34.2281i			0.0632681i	−0.999500	+	0.0316341i	$0.989929\pi$
$542$	−364.508	+	883.757i	−0.672525	+	1.63055i
$543$		0			0
$544$	−817.408	−	331.405i	−1.50259	−	0.609200i
$545$			19.3404i			0.0354869i
$546$		0			0
$547$		−	642.135i		−	1.17392i	−0.809616	−	0.586960i	$-0.800324\pi$
$547$		−	642.135i		−	1.17392i	0.809616	−	0.586960i	$-0.199676\pi$
$548$	188.255	+	187.126i	0.343530	+	0.341471i
$549$		0			0
$550$	212.662	−	515.602i	0.386657	−	0.937458i
$551$			642.511i			1.16608i
$552$		0			0
$553$	−608.982	−	478.789i	−1.10123	−	0.865803i
$554$	244.086	−	591.790i	0.440588	−	1.06821i
$555$		0			0
$556$	−387.398	−	385.075i	−0.696759	−	0.692581i
$557$		−	656.595i		−	1.17881i	−0.807839	−	0.589403i	$-0.799363\pi$
$557$		−	656.595i		−	1.17881i	0.807839	−	0.589403i	$-0.200637\pi$
$558$		0			0
$559$		−	238.509i		−	0.426672i
$560$	150.153	−	193.365i	0.268131	−	0.345295i
$561$		0			0
$562$	−541.034	−	223.151i	−0.962694	−	0.397066i
$563$	−1031.16			−1.83154			−0.915771	−	0.401701i	$-0.868419\pi$
$563$	−1031.16			−1.83154			−0.915771	+	0.401701i	$0.868419\pi$
$564$		0			0
$565$	−114.705			−0.203018
$566$	484.761	+	199.941i	0.856468	+	0.353253i
$567$		0			0
$568$	−15.0085	−	35.7765i	−0.0264234	−	0.0629867i
$569$	909.436			1.59831			0.799153	−	0.601128i	$-0.205282\pi$
$569$	909.436			1.59831			0.799153	+	0.601128i	$0.205282\pi$
$570$		0			0
$571$		−	9.05964i		−	0.0158663i	−0.999969	−	0.00793314i	$-0.997475\pi$
$571$		−	9.05964i		−	0.0158663i	0.999969	−	0.00793314i	$-0.00252522\pi$
$572$	−275.286	+	276.946i	−0.481269	+	0.484172i
$573$		0			0
$574$	−737.359	+	415.672i	−1.28460	+	0.724167i
$575$	−586.957			−1.02079
$576$		0			0
$577$			283.128i			0.490691i	0.969436	+	0.245345i	$0.0789013\pi$
$577$			283.128i			0.490691i	−0.969436	+	0.245345i	$0.921099\pi$
$578$	−870.374	−	358.989i	−1.50584	−	0.621088i
$579$		0			0
$580$	−131.080	+	131.871i	−0.226000	+	0.227363i
$581$	−98.7791	−	77.6613i	−0.170016	−	0.133668i
$582$		0			0
$583$	647.019			1.10981
$584$	−37.0402	+	15.5386i	−0.0634250	+	0.0266073i
$585$		0			0
$586$	−987.145	−	407.151i	−1.68455	−	0.694797i
$587$	540.935			0.921525			0.460762	−	0.887524i	$-0.347576\pi$
$587$	540.935			0.921525			0.460762	+	0.887524i	$0.347576\pi$
$588$		0			0
$589$		−	1380.92i		−	2.34452i
$590$	−386.443	−	159.389i	−0.654987	−	0.270152i
$591$		0			0
$592$	−656.064	+	3.94558i	−1.10822	+	0.00666483i
$593$			292.924i			0.493969i	0.969019	+	0.246984i	$0.0794397\pi$
$593$			292.924i			0.493969i	−0.969019	+	0.246984i	$0.920560\pi$
$594$		0			0
$595$	260.671	−	331.553i	0.438102	−	0.557232i
$596$	405.394	−	407.839i	0.680191	−	0.684294i
$597$		0			0
$598$	379.901	+	156.692i	0.635286	+	0.262026i
$599$	155.121			0.258966			0.129483	−	0.991582i	$-0.458668\pi$
$599$	155.121			0.258966			0.129483	+	0.991582i	$0.458668\pi$
$600$		0			0
$601$		−	1073.77i		−	1.78665i	−0.449415	−	0.893323i	$-0.648368\pi$
$601$		−	1073.77i		−	1.78665i	0.449415	−	0.893323i	$-0.351632\pi$
$602$	−410.902	+	231.638i	−0.682561	+	0.384781i
$603$		0			0
$604$	604.807	+	601.181i	1.00134	+	0.995332i
$605$	−151.208			−0.249930
$606$		0			0
$607$		−	547.872i		−	0.902590i	−0.892375	−	0.451295i	$-0.850962\pi$
$607$		−	547.872i		−	0.902590i	0.892375	−	0.451295i	$-0.149038\pi$
$608$	−363.269	+	896.002i	−0.597482	+	1.47369i
$609$		0			0
$610$	−183.500	−	75.6850i	−0.300819	−	0.124074i
$611$		−	67.4635i		−	0.110415i
$612$		0			0
$613$		−	1015.32i		−	1.65632i	−0.560495	−	0.828158i	$-0.689389\pi$
$613$		−	1015.32i		−	1.65632i	0.560495	−	0.828158i	$-0.310611\pi$
$614$	−133.428	−	55.0329i	−0.217310	−	0.0896301i
$615$		0			0
$616$	744.475	+	205.292i	1.20856	+	0.333266i
$617$	172.568			0.279688			0.139844	−	0.990174i	$-0.455340\pi$
$617$	172.568			0.279688			0.139844	+	0.990174i	$0.455340\pi$
$618$		0			0
$619$	−699.885			−1.13067			−0.565335	−	0.824862i	$-0.691253\pi$
$619$	−699.885			−1.13067			−0.565335	+	0.824862i	$0.691253\pi$
$620$	281.724	−	283.424i	0.454394	−	0.457135i
$621$		0			0
$622$	−185.398	+	449.500i	−0.298067	+	0.722669i
$623$	−46.0733	+	58.6017i	−0.0739540	+	0.0940637i
$624$		0			0
$625$	289.475			0.463160
$626$	−129.881	+	314.899i	−0.207478	+	0.503034i
$627$		0			0
$628$	258.198	+	256.649i	0.411143	+	0.408677i
$629$	−1130.24			−1.79688
$630$		0			0
$631$	−948.786			−1.50362			−0.751811	−	0.659378i	$-0.770820\pi$
$631$	−948.786			−1.50362			−0.751811	+	0.659378i	$0.770820\pi$
$632$	342.485	+	816.398i	0.541907	+	1.29177i
$633$		0			0
$634$	53.3841	−	129.431i	0.0842021	−	0.204149i
$635$	−27.4037			−0.0431554
$636$		0			0
$637$	81.8601	+	337.073i	0.128509	+	0.529158i
$638$	−542.209	−	223.636i	−0.849857	−	0.350526i
$639$		0			0
$640$	−257.353	+	109.786i	−0.402115	+	0.171541i
$641$	1059.07			1.65222			0.826111	−	0.563508i	$-0.190549\pi$
$641$	1059.07			1.65222			0.826111	+	0.563508i	$0.190549\pi$
$642$		0			0
$643$	−303.428			−0.471894			−0.235947	−	0.971766i	$-0.575819\pi$
$643$	−303.428			−0.471894			−0.235947	+	0.971766i	$0.575819\pi$
$644$	−99.0099	−	806.668i	−0.153742	−	1.25259i
$645$		0			0
$646$	−635.084	+	1539.77i	−0.983102	+	2.38355i
$647$		−	845.076i		−	1.30615i	−0.757295	−	0.653073i	$-0.773480\pi$
$647$		−	845.076i		−	1.30615i	0.757295	−	0.653073i	$-0.226520\pi$
$648$		0			0
$649$		−	1318.62i		−	2.03177i
$650$	−264.673	−	109.165i	−0.407189	−	0.167947i
$651$		0			0
$652$	568.452	−	571.881i	0.871859	−	0.877118i
$653$		−	513.012i		−	0.785623i	−0.919619	−	0.392811i	$-0.871503\pi$
$653$		−	513.012i		−	0.785623i	0.919619	−	0.392811i	$-0.128497\pi$
$654$		0			0
$655$	−38.2288			−0.0583646
$656$	967.356	−	5.81770i	1.47463	−	0.00886844i
$657$		0			0
$658$	−116.226	+	65.5199i	−0.176635	+	0.0995744i
$659$		−	369.080i		−	0.560061i	−0.959991	−	0.280030i	$-0.909655\pi$
$659$		−	369.080i		−	0.560061i	0.959991	−	0.280030i	$-0.0903445\pi$
$660$		0			0
$661$	−705.924			−1.06796			−0.533982	−	0.845496i	$-0.679305\pi$
$661$	−705.924			−1.06796			−0.533982	+	0.845496i	$0.679305\pi$
$662$	−105.500	+	255.786i	−0.159365	+	0.386384i
$663$		0			0
$664$	55.5523	+	132.423i	0.0836632	+	0.199432i
$665$	−363.432	−	285.735i	−0.546515	−	0.429676i
$666$		0			0
$667$			617.246i			0.925407i
$668$	553.465	−	556.804i	0.828541	−	0.833539i
$669$		0			0
$670$	32.3899	−	78.5300i	0.0483432	−	0.117209i
$671$		−	626.138i		−	0.933142i
$672$		0			0
$673$	767.660			1.14065			0.570327	−	0.821418i	$-0.306817\pi$
$673$	767.660			1.14065			0.570327	+	0.821418i	$0.306817\pi$
$674$	−566.083	−	233.483i	−0.839886	−	0.346414i
$675$		0			0
$676$	−337.275	−	335.253i	−0.498927	−	0.495936i
$677$	−797.530			−1.17804			−0.589018	−	0.808120i	$-0.700485\pi$
$677$	−797.530			−1.17804			−0.589018	+	0.808120i	$0.700485\pi$
$678$		0			0
$679$	37.5279	−	47.7325i	0.0552693	−	0.0702983i
$680$	−444.478	+	186.462i	−0.653644	+	0.274209i
$681$		0			0
$682$	1165.35	+	480.651i	1.70872	+	0.704766i
$683$		−	538.501i		−	0.788435i	−0.919017	−	0.394217i	$-0.871016\pi$
$683$		−	538.501i		−	0.788435i	0.919017	−	0.394217i	$-0.128984\pi$
$684$		0			0
$685$	145.052			0.211755
$686$	501.205	−	468.390i	0.730620	−	0.682785i
$687$		0			0
$688$	539.071	−	3.24198i	0.783533	−	0.00471218i
$689$		−	332.133i		−	0.482051i
$690$		0			0
$691$	833.516			1.20625			0.603123	−	0.797648i	$-0.293923\pi$
$691$	833.516			1.20625			0.603123	+	0.797648i	$0.293923\pi$
$692$	30.8487	+	30.6637i	0.0445791	+	0.0443118i
$693$		0			0
$694$	266.988	−	647.317i	0.384709	−	0.932734i
$695$	−298.494			−0.429488
$696$		0			0
$697$	1666.52			2.39099
$698$	612.233	+	252.518i	0.877125	+	0.361773i
$699$		0			0
$700$	68.9791	+	561.997i	0.0985416	+	0.802852i
$701$			375.441i			0.535578i	0.963478	+	0.267789i	$0.0862931\pi$
$701$			375.441i			0.535578i	−0.963478	+	0.267789i	$0.913707\pi$
$702$		0			0
$703$			1238.91i			1.76232i
$704$	−629.686	−	618.427i	−0.894440	−	0.878447i
$705$		0			0
$706$	71.7136	−	173.871i	0.101577	−	0.246276i
$707$	−13.8569	−	10.8945i	−0.0195996	−	0.0154094i
$708$		0			0
$709$		−	1106.91i		−	1.56123i	−0.625013	−	0.780614i	$-0.714906\pi$
$709$		−	1106.91i		−	1.56123i	0.625013	−	0.780614i	$-0.285094\pi$
$710$	−19.5997	−	8.08397i	−0.0276053	−	0.0113859i
$711$		0			0
$712$	78.5611	−	32.9570i	0.110339	−	0.0462879i
$713$		−	1326.62i		−	1.86062i
$714$		0			0
$715$			213.390i			0.298448i
$716$	−320.738	+	322.673i	−0.447958	+	0.450660i
$717$		0			0
$718$	505.010	+	208.293i	0.703357	+	0.290102i
$719$			257.047i			0.357506i	0.983894	+	0.178753i	$0.0572063\pi$
$719$			257.047i			0.357506i	−0.983894	+	0.178753i	$0.942794\pi$
$720$		0			0
$721$	−535.886	+	681.605i	−0.743254	+	0.945361i
$722$	1020.37	+	420.854i	1.41325	+	0.582900i
$723$		0			0
$724$	708.970	+	704.719i	0.979240	+	0.973368i
$725$		−	430.029i		−	0.593143i
$726$		0			0
$727$			849.134i			1.16800i	0.811755	+	0.583998i	$0.198513\pi$
$727$			849.134i			1.16800i	−0.811755	+	0.583998i	$0.801487\pi$
$728$	105.382	−	382.160i	0.144756	−	0.524946i
$729$		0			0
$730$	−8.36952	+	20.2920i	−0.0114651	+	0.0277973i
$731$	928.687			1.27043
$732$		0			0
$733$	329.912			0.450085			0.225042	−	0.974349i	$-0.427748\pi$
$733$	329.912			0.450085			0.225042	+	0.974349i	$0.427748\pi$
$734$	13.3853	−	32.4530i	0.0182361	−	0.0442138i
$735$		0			0
$736$	−348.985	+	860.770i	−0.474164	+	1.16952i
$737$	267.960			0.363583
$738$		0			0
$739$			623.097i			0.843162i	0.906791	+	0.421581i	$0.138525\pi$
$739$			623.097i			0.843162i	−0.906791	+	0.421581i	$0.861475\pi$
$740$	−252.752	+	254.277i	−0.341557	+	0.343618i
$741$		0			0
$742$	−572.196	+	322.565i	−0.771154	+	0.434723i
$743$	226.053			0.304244			0.152122	−	0.988362i	$-0.451389\pi$
$743$	226.053			0.304244			0.152122	+	0.988362i	$0.451389\pi$
$744$		0			0
$745$		−	314.245i		−	0.421805i
$746$	−215.491	+	522.462i	−0.288862	+	0.700352i
$747$		0			0
$748$	−1078.35	−	1071.88i	−1.44164	−	1.43300i
$749$	−437.697	+	556.716i	−0.584375	+	0.743279i
$750$		0			0
$751$	−580.772			−0.773331			−0.386666	−	0.922220i	$-0.626373\pi$
$751$	−580.772			−0.773331			−0.386666	+	0.922220i	$0.626373\pi$
$752$	152.479	−	0.917010i	0.202764	−	0.00121943i
$753$		0			0
$754$	−114.799	+	278.331i	−0.152253	+	0.369140i
$755$	466.011			0.617233
$756$		0			0
$757$			1280.71i			1.69182i	0.533323	+	0.845911i	$0.320943\pi$
$757$			1280.71i			1.69182i	−0.533323	+	0.845911i	$0.679057\pi$
$758$	−543.266	+	1317.16i	−0.716710	+	1.73768i
$759$		0			0
$760$	204.391	+	487.215i	0.268935	+	0.641073i
$761$			1072.13i			1.40884i	0.709785	+	0.704419i	$0.248792\pi$
$761$			1072.13i			1.40884i	−0.709785	+	0.704419i	$0.751208\pi$
$762$		0			0
$763$	38.2798	−	48.6889i	0.0501701	−	0.0638124i
$764$	83.6796	+	83.1778i	0.109528	+	0.108872i
$765$		0			0
$766$	300.804	−	729.305i	0.392695	−	0.952095i
$767$	−676.886			−0.882511
$768$		0			0
$769$		−	143.146i		−	0.186145i	−0.995659	−	0.0930725i	$-0.970331\pi$
$769$		−	143.146i		−	0.186145i	0.995659	−	0.0930725i	$-0.0296688\pi$
$770$	367.627	−	207.243i	0.477437	−	0.269146i
$771$		0			0
$772$	13.5198	+	13.4387i	0.0175127	+	0.0174076i
$773$	159.665			0.206553			0.103276	−	0.994653i	$-0.467067\pi$
$773$	159.665			0.206553			0.103276	+	0.994653i	$0.467067\pi$
$774$		0			0
$775$			924.242i			1.19257i
$776$	−63.9899	+	26.8443i	−0.0824612	+	0.0345931i
$777$		0			0
$778$	278.591	−	675.448i	0.358086	−	0.868185i
$779$		−	1826.75i		−	2.34500i
$780$		0			0
$781$		−	66.8783i		−	0.0856316i
$782$	−610.111	+	1479.23i	−0.780193	+	1.89159i
$783$		0			0
$784$	−760.729	+	189.599i	−0.970317	+	0.241835i
$785$	198.944			0.253432
$786$		0			0
$787$	−794.871			−1.01000			−0.505000	−	0.863119i	$-0.668508\pi$
$787$	−794.871			−1.01000			−0.505000	+	0.863119i	$0.668508\pi$
$788$	−1048.79	+	1055.12i	−1.33096	+	1.33899i
$789$		0			0
$790$	447.254	+	184.471i	0.566145	+	0.233508i
$791$	288.767	+	227.032i	0.365066	+	0.287019i
$792$		0			0
$793$	−321.415			−0.405315
$794$	−603.278	−	248.824i	−0.759796	−	0.313380i
$795$		0			0
$796$	691.424	−	695.595i	0.868624	−	0.873863i
$797$	999.284			1.25381			0.626903	−	0.779097i	$-0.284322\pi$
$797$	999.284			1.25381			0.626903	+	0.779097i	$0.284322\pi$
$798$		0			0
$799$	262.683			0.328765
$800$	243.134	−	599.689i	0.303917	−	0.749611i
$801$		0			0
$802$	−1025.10	−	422.807i	−1.27818	−	0.527191i
$803$	−69.2406			−0.0862274
$804$		0			0
$805$	−349.141	−	274.499i	−0.433716	−	0.340993i
$806$	246.732	−	598.206i	0.306119	−	0.742191i
$807$		0			0
$808$	7.79298	+	18.5765i	0.00964478	+	0.0229907i
$809$	578.890			0.715562			0.357781	−	0.933805i	$-0.383533\pi$
$809$	578.890			0.715562			0.357781	+	0.933805i	$0.383533\pi$
$810$		0			0
$811$	−88.8234			−0.109523			−0.0547617	−	0.998499i	$-0.517440\pi$
$811$	−88.8234			−0.109523			−0.0547617	+	0.998499i	$0.517440\pi$
$812$	590.998	−	72.5387i	0.727830	−	0.0893334i
$813$		0			0
$814$	−1045.50	−	431.221i	−1.28440	−	0.529756i
$815$		−	440.641i		−	0.540664i
$816$		0			0
$817$		−	1017.98i		−	1.24600i
$818$	−114.052	+	276.522i	−0.139428	+	0.338046i
$819$		0			0
$820$	372.680	−	374.928i	0.454487	−	0.457229i
$821$			165.701i			0.201828i	0.994895	+	0.100914i	$0.0321767\pi$
$821$			165.701i			0.201828i	−0.994895	+	0.100914i	$0.967823\pi$
$822$		0			0
$823$	−565.754			−0.687430			−0.343715	−	0.939074i	$-0.611685\pi$
$823$	−565.754			−0.687430			−0.343715	+	0.939074i	$0.611685\pi$
$824$	913.756	−	383.328i	1.10893	−	0.465204i
$825$		0			0
$826$	657.385	+	1166.13i	0.795866	+	1.41178i
$827$		−	287.050i		−	0.347098i	−0.984825	−	0.173549i	$-0.944476\pi$
$827$		−	287.050i		−	0.347098i	0.984825	−	0.173549i	$-0.0555236\pi$
$828$		0			0
$829$	409.212			0.493622			0.246811	−	0.969064i	$-0.420617\pi$
$829$	409.212			0.493622			0.246811	+	0.969064i	$0.420617\pi$
$830$	72.5462	+	29.9219i	0.0874051	+	0.0360505i
$831$		0			0
$832$	−317.456	+	323.236i	−0.381558	+	0.388505i
$833$	−1312.47	+	318.739i	−1.57559	+	0.382640i
$834$		0			0
$835$		−	429.024i		−	0.513801i
$836$	−1174.94	+	1182.03i	−1.40544	+	1.41391i
$837$		0			0
$838$	−164.339	−	67.7820i	−0.196108	−	0.0808855i
$839$			276.923i			0.330064i	0.986288	+	0.165032i	$0.0527727\pi$
$839$			276.923i			0.330064i	−0.986288	+	0.165032i	$0.947227\pi$
$840$		0			0
$841$	388.780			0.462283
$842$	−325.618	+	789.466i	−0.386720	+	0.937608i
$843$		0			0
$844$	−857.192	+	862.363i	−1.01563	+	1.02176i
$845$	−259.874			−0.307544
$846$		0			0
$847$	380.662	+	299.281i	0.449423	+	0.353342i
$848$	750.676	−	4.51458i	0.885231	−	0.00532380i
$849$		0			0
$850$	425.058	−	1030.56i	0.500068	−	1.21242i
$851$			1190.19i			1.39858i
$852$		0			0
$853$	−301.813			−0.353825			−0.176913	−	0.984227i	$-0.556611\pi$
$853$	−301.813			−0.353825			−0.176913	+	0.984227i	$0.556611\pi$
$854$	312.155	+	553.730i	0.365521	+	0.648396i
$855$		0			0
$856$	746.330	−	313.091i	0.871881	−	0.365761i
$857$		−	1401.15i		−	1.63495i	−0.575967	−	0.817473i	$-0.695374\pi$
$857$		−	1401.15i		−	1.63495i	0.575967	−	0.817473i	$-0.304626\pi$
$858$		0			0
$859$	−632.275			−0.736059			−0.368029	−	0.929814i	$-0.619967\pi$
$859$	−632.275			−0.736059			−0.368029	+	0.929814i	$0.619967\pi$
$860$	207.680	−	208.933i	0.241489	−	0.242945i
$861$		0			0
$862$	−426.207	−	175.791i	−0.494440	−	0.203933i
$863$	460.776			0.533924			0.266962	−	0.963707i	$-0.413980\pi$
$863$	460.776			0.533924			0.266962	+	0.963707i	$0.413980\pi$
$864$		0			0
$865$	23.7693			0.0274789
$866$	−79.4665	+	192.668i	−0.0917627	+	0.222480i
$867$		0			0
$868$	−1270.21	+	155.904i	−1.46337	+	0.179613i
$869$			1526.12i			1.75618i
$870$		0			0
$871$		−	137.552i		−	0.157924i
$872$	−65.2720	+	27.3821i	−0.0748532	+	0.0314015i
$873$		0			0
$874$	1621.45	+	668.774i	1.85521	+	0.765188i
$875$	543.960	+	427.667i	0.621668	+	0.488763i
$876$		0			0
$877$			800.621i			0.912909i	0.889747	+	0.456455i	$0.150881\pi$
$877$			800.621i			0.912909i	−0.889747	+	0.456455i	$0.849119\pi$
$878$	18.2521	−	44.2525i	0.0207883	−	0.0504015i
$879$		0			0
$880$	−482.297	+	2.90054i	−0.548065	+	0.00329607i
$881$			467.366i			0.530495i	0.964180	+	0.265247i	$0.0854537\pi$
$881$			467.366i			0.530495i	−0.964180	+	0.265247i	$0.914546\pi$
$882$		0			0
$883$			798.280i			0.904054i	0.892004	+	0.452027i	$0.149299\pi$
$883$			798.280i			0.904054i	−0.892004	+	0.452027i	$0.850701\pi$
$884$	−550.228	+	553.547i	−0.622430	+	0.626184i
$885$		0			0
$886$	−110.647	+	268.267i	−0.124884	+	0.302784i
$887$		−	51.5357i		−	0.0581011i	−0.999578	−	0.0290505i	$-0.990752\pi$
$887$		−	51.5357i		−	0.0581011i	0.999578	−	0.0290505i	$-0.00924838\pi$
$888$		0			0
$889$	68.9880	+	54.2392i	0.0776018	+	0.0610115i
$890$	17.7515	−	43.0388i	0.0199455	−	0.0483582i
$891$		0			0
$892$	966.160	−	971.988i	1.08314	−	1.08967i
$893$		−	287.941i		−	0.322442i
$894$		0			0
$895$			248.623i			0.277791i
$896$	865.178	+	232.987i	0.965601	+	0.260030i
$897$		0			0
$898$	−347.821	−	143.460i	−0.387328	−	0.159755i
$899$	971.937			1.08113
$900$		0			0
$901$	1293.23			1.43533
$902$	1541.58	+	635.829i	1.70907	+	0.704911i
$903$		0			0
$904$	−162.400	−	387.120i	−0.179646	−	0.428230i
$905$	546.269			0.603613
$906$		0			0
$907$			1539.21i			1.69703i	0.529168	+	0.848517i	$0.322504\pi$
$907$			1539.21i			1.69703i	−0.529168	+	0.848517i	$0.677496\pi$
$908$	−957.970	−	952.226i	−1.05503	−	1.04871i
$909$		0			0
$910$	−106.384	−	188.713i	−0.116905	−	0.207377i
$911$	−750.377			−0.823685			−0.411842	−	0.911255i	$-0.635115\pi$
$911$	−750.377			−0.823685			−0.411842	+	0.911255i	$0.635115\pi$
$912$		0			0
$913$			247.543i			0.271131i
$914$	1340.68	+	552.970i	1.46683	+	0.605000i
$915$		0			0
$916$	929.905	+	924.330i	1.01518	+	1.00909i
$917$	96.2401	+	75.6651i	0.104951	+	0.0825137i
$918$		0			0
$919$	1526.32			1.66085			0.830423	−	0.557134i	$-0.188099\pi$
$919$	1526.32			1.66085			0.830423	+	0.557134i	$0.188099\pi$
$920$	196.353	+	468.057i	0.213428	+	0.508757i
$921$		0			0
$922$	193.066	+	79.6308i	0.209399	+	0.0863675i
$923$	−34.3305			−0.0371945
$924$		0			0
$925$		−	829.195i		−	0.896427i
$926$	−126.023	−	51.9788i	−0.136094	−	0.0561326i
$927$		0			0
$928$	−630.635	−	255.681i	−0.679564	−	0.275518i
$929$			610.738i			0.657414i	0.944432	+	0.328707i	$0.106613\pi$
$929$			610.738i			0.657414i	−0.944432	+	0.328707i	$0.893387\pi$
$930$		0			0
$931$	349.386	+	1438.66i	0.375281	+	1.54528i
$932$	641.234	+	637.389i	0.688019	+	0.683894i
$933$		0			0
$934$	−15.8157	−	6.52323i	−0.0169333	−	0.00698418i
$935$	−830.880			−0.888641
$936$		0			0
$937$			1670.35i			1.78266i	0.453354	+	0.891330i	$0.350227\pi$
$937$			1670.35i			1.78266i	−0.453354	+	0.891330i	$0.649773\pi$
$938$	−236.973	+	133.589i	−0.252636	+	0.142419i
$939$		0			0
$940$	58.7433	−	59.0977i	0.0624929	−	0.0628698i
$941$	114.242			0.121405			0.0607026	−	0.998156i	$-0.480666\pi$
$941$	114.242			0.121405			0.0607026	+	0.998156i	$0.480666\pi$
$942$		0			0
$943$		−	1754.92i		−	1.86100i
$944$	−9.20069	−	1529.87i	−0.00974649	−	1.62063i
$945$		0			0
$946$	859.064	+	354.324i	0.908101	+	0.374549i
$947$			450.692i			0.475915i	0.971276	+	0.237958i	$0.0764779\pi$
$947$			450.692i			0.475915i	−0.971276	+	0.237958i	$0.923522\pi$
$948$		0			0
$949$			35.5432i			0.0374533i
$950$	−1129.65	−	465.928i	−1.18910	−	0.490450i
$951$		0			0
$952$	1488.02	+	410.328i	1.56305	+	0.431017i
$953$	1045.92			1.09750			0.548750	−	0.835987i	$-0.315104\pi$
$953$	1045.92			1.09750			0.548750	+	0.835987i	$0.315104\pi$
$954$		0			0
$955$	64.4761			0.0675142
$956$	37.0078	+	36.7859i	0.0387111	+	0.0384789i
$957$		0			0
$958$	−160.415	+	388.929i	−0.167448	+	0.405980i
$959$	−365.166	−	287.098i	−0.380778	−	0.299372i
$960$		0			0
$961$	−1127.94			−1.17372
$962$	−221.358	+	536.687i	−0.230102	+	0.557887i
$963$		0			0
$964$	102.179	−	102.795i	0.105995	−	0.106634i
$965$	10.4171			0.0107950
$966$		0			0
$967$	−315.609			−0.326379			−0.163190	−	0.986595i	$-0.552178\pi$
$967$	−315.609			−0.326379			−0.163190	+	0.986595i	$0.552178\pi$
$968$	−214.080	−	510.313i	−0.221157	−	0.527183i
$969$		0			0
$970$	−14.4590	+	35.0562i	−0.0149062	+	0.0361404i
$971$	−499.109			−0.514015			−0.257008	−	0.966409i	$-0.582737\pi$
$971$	−499.109			−0.514015			−0.257008	+	0.966409i	$0.582737\pi$
$972$		0			0
$973$	751.453	+	590.801i	0.772305	+	0.607195i
$974$	−1561.80	−	644.169i	−1.60349	−	0.661364i
$975$		0			0
$976$	−4.36889	−	726.450i	−0.00447632	−	0.744314i
$977$	−1071.53			−1.09676			−0.548379	−	0.836230i	$-0.684755\pi$
$977$	−1071.53			−1.09676			−0.548379	+	0.836230i	$0.684755\pi$
$978$		0			0
$979$	146.857			0.150007
$980$	−221.795	+	366.553i	−0.226321	+	0.374034i
$981$		0			0
$982$	−304.467	+	738.186i	−0.310048	+	0.751716i
$983$			808.263i			0.822241i	0.911581	+	0.411121i	$0.134863\pi$
$983$			808.263i			0.822241i	−0.911581	+	0.411121i	$0.865137\pi$
$984$		0			0
$985$			812.982i			0.825363i
$986$	−1083.74	−	446.993i	−1.09913	−	0.453339i
$987$		0			0
$988$	606.771	+	603.133i	0.614141	+	0.610458i
$989$		−	977.951i		−	0.988828i
$990$		0			0
$991$	−1848.16			−1.86494			−0.932470	−	0.361247i	$-0.882351\pi$
$991$	−1848.16			−1.86494			−0.932470	+	0.361247i	$0.882351\pi$
$992$	1355.40	+	549.523i	1.36633	+	0.553955i
$993$		0			0
$994$	33.3415	+	59.1443i	0.0335428	+	0.0595014i
$995$		−	535.964i		−	0.538657i
$996$		0			0
$997$	238.170			0.238886			0.119443	−	0.992841i	$-0.461889\pi$
$997$	238.170			0.238886			0.119443	+	0.992841i	$0.461889\pi$
$998$	345.770	−	838.325i	0.346463	−	0.840005i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.l.h.181.32		32
3.2	odd	2		168.3.l.a.13.2	yes	32
4.3	odd	2		2016.3.l.h.433.21		32
7.6	odd	2	inner	504.3.l.h.181.31		32
8.3	odd	2		2016.3.l.h.433.12		32
8.5	even	2	inner	504.3.l.h.181.29		32
12.11	even	2		672.3.l.a.433.4		32
21.20	even	2		168.3.l.a.13.1	✓	32
24.5	odd	2		168.3.l.a.13.3	yes	32
24.11	even	2		672.3.l.a.433.29		32
28.27	even	2		2016.3.l.h.433.11		32
56.13	odd	2	inner	504.3.l.h.181.30		32
56.27	even	2		2016.3.l.h.433.22		32
84.83	odd	2		672.3.l.a.433.20		32
168.83	odd	2		672.3.l.a.433.13		32
168.125	even	2		168.3.l.a.13.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.l.a.13.1	✓	32	21.20	even	2
168.3.l.a.13.2	yes	32	3.2	odd	2
168.3.l.a.13.3	yes	32	24.5	odd	2
168.3.l.a.13.4	yes	32	168.125	even	2
504.3.l.h.181.29		32	8.5	even	2	inner
504.3.l.h.181.30		32	56.13	odd	2	inner
504.3.l.h.181.31		32	7.6	odd	2	inner
504.3.l.h.181.32		32	1.1	even	1	trivial
672.3.l.a.433.4		32	12.11	even	2
672.3.l.a.433.13		32	168.83	odd	2
672.3.l.a.433.20		32	84.83	odd	2
672.3.l.a.433.29		32	24.11	even	2
2016.3.l.h.433.11		32	28.27	even	2
2016.3.l.h.433.12		32	8.3	odd	2
2016.3.l.h.433.21		32	4.3	odd	2
2016.3.l.h.433.22		32	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.84891 + 0.762588i) q^{2} +(2.83692 + 2.81991i) q^{4} +2.18588 q^{5} +(-5.50290 - 4.32644i) q^{7} +(3.09477 + 7.37715i) q^{8} +(4.04149 + 1.66693i) q^{10} +13.7904i q^{11} +7.07900 q^{13} +(-6.87506 - 12.1956i) q^{14} +(0.0962226 + 15.9997i) q^{16} +27.5636i q^{17} +30.2138 q^{19} +(6.20116 + 6.16398i) q^{20} +(-10.5164 + 25.4972i) q^{22} +29.0258 q^{23} -20.2219 q^{25} +(13.0884 + 5.39836i) q^{26} +(-3.41110 - 27.7914i) q^{28} +21.2655i q^{29} -45.7050i q^{31} +(-12.0233 + 29.6554i) q^{32} +(-21.0196 + 50.9625i) q^{34} +(-12.0287 - 9.45708i) q^{35} +41.0047i q^{37} +(55.8626 + 23.0407i) q^{38} +(6.76480 + 16.1256i) q^{40} -60.4609i q^{41} -33.6925i q^{43} +(-38.8876 + 39.1222i) q^{44} +(53.6660 + 22.1347i) q^{46} -9.53009i q^{47} +(11.5638 + 47.6160i) q^{49} +(-37.3885 - 15.4210i) q^{50} +(20.0826 + 19.9621i) q^{52} -46.9181i q^{53} +30.1441i q^{55} +(14.8866 - 53.9851i) q^{56} +(-16.2168 + 39.3179i) q^{58} -95.6189 q^{59} -45.4040 q^{61} +(34.8540 - 84.5042i) q^{62} +(-44.8448 + 45.6612i) q^{64} +15.4738 q^{65} -19.4310i q^{67} +(-77.7268 + 78.1956i) q^{68} +(-15.0280 - 26.6582i) q^{70} -4.84963 q^{71} +5.02093i q^{73} +(-31.2697 + 75.8140i) q^{74} +(85.7142 + 85.2003i) q^{76} +(59.6633 - 75.8871i) q^{77} +110.666 q^{79} +(0.210331 + 34.9734i) q^{80} +(46.1067 - 111.787i) q^{82} +17.9504 q^{83} +60.2506i q^{85} +(25.6935 - 62.2944i) q^{86} +(-101.734 + 42.6781i) q^{88} -10.6492i q^{89} +(-38.9550 - 30.6269i) q^{91} +(82.3437 + 81.8500i) q^{92} +(7.26753 - 17.6203i) q^{94} +66.0438 q^{95} +8.67407i q^{97} +(-14.9310 + 96.8559i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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