LMFDB - Embedded newform 504.3.e.c.251.46

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(251,504)] 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, 1, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.251"); S:= CuspForms(chi, 3); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.46
Character	$\chi$	$=$	504.251
Dual form			504.3.e.c.251.48

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.96086 - 0.393720i) q^{2} +(3.68997 - 1.54406i) q^{4} +6.99549i q^{5} +(-6.66208 - 2.14866i) q^{7} +(6.62759 - 4.48051i) q^{8} +(2.75427 + 13.7172i) q^{10} +18.1971i q^{11} -6.68252 q^{13} +(-13.9094 - 1.59024i) q^{14} +(11.2317 - 11.3951i) q^{16} +16.6136 q^{17} +31.7713i q^{19} +(10.8015 + 25.8131i) q^{20} +(7.16455 + 35.6819i) q^{22} +28.2125 q^{23} -23.9368 q^{25} +(-13.1035 + 2.63105i) q^{26} +(-27.9005 + 2.35817i) q^{28} -55.3335 q^{29} +18.6829 q^{31} +(17.5374 - 26.7664i) q^{32} +(32.5770 - 6.54112i) q^{34} +(15.0309 - 46.6045i) q^{35} +18.8501i q^{37} +(12.5090 + 62.2991i) q^{38} +(31.3434 + 46.3632i) q^{40} -33.6389 q^{41} +14.3177 q^{43} +(28.0974 + 67.1466i) q^{44} +(55.3208 - 11.1078i) q^{46} -57.3785i q^{47} +(39.7665 + 28.6291i) q^{49} +(-46.9368 + 9.42441i) q^{50} +(-24.6583 + 10.3182i) q^{52} +5.13773 q^{53} -127.297 q^{55} +(-53.7806 + 15.6091i) q^{56} +(-108.501 + 21.7859i) q^{58} +83.0383 q^{59} -75.6870 q^{61} +(36.6347 - 7.35585i) q^{62} +(23.8500 - 59.3900i) q^{64} -46.7475i q^{65} +17.6649 q^{67} +(61.3037 - 25.6525i) q^{68} +(11.1245 - 97.3029i) q^{70} +75.8131 q^{71} -103.904i q^{73} +(7.42167 + 36.9625i) q^{74} +(49.0568 + 117.235i) q^{76} +(39.0993 - 121.230i) q^{77} +33.8548i q^{79} +(79.7142 + 78.5714i) q^{80} +(-65.9613 + 13.2443i) q^{82} +127.193 q^{83} +116.220i q^{85} +(28.0751 - 5.63718i) q^{86} +(81.5321 + 120.603i) q^{88} +31.6907 q^{89} +(44.5195 + 14.3585i) q^{91} +(104.103 - 43.5619i) q^{92} +(-22.5911 - 112.511i) q^{94} -222.255 q^{95} -97.7829i q^{97} +(89.2485 + 40.4809i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) $ 48 * q + 144 * q^22 - 336 * q^25 - 232 * q^28 - 384 * q^43 + 736 * q^46 + 368 * q^49 - 432 * q^58 + 480 * q^64 - 896 * q^67 + 264 * q^70 - 48 * q^88 - 576 * q^91

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 $

$2$	1.96086	−	0.393720i	0.980432	−	0.196860i
$2$	1.96086	−	0.393720i	0.980432	−	0.196860i
$3$		0			0
$3$		0			0
$4$	3.68997	−	1.54406i	0.922492	−	0.386016i
$5$			6.99549i			1.39910i	0.714585	+	0.699549i	$0.246616\pi$
$5$			6.99549i			1.39910i	−0.714585	+	0.699549i	$0.753384\pi$
$6$		0			0
$7$	−6.66208	−	2.14866i	−0.951725	−	0.306952i
$7$	−6.66208	−	2.14866i	−0.951725	−	0.306952i
$8$	6.62759	−	4.48051i	0.828449	−	0.560064i
$9$		0			0
$10$	2.75427	+	13.7172i	0.275427	+	1.37172i
$11$			18.1971i			1.65428i	0.561998	+	0.827139i	$0.310033\pi$
$11$			18.1971i			1.65428i	−0.561998	+	0.827139i	$0.689967\pi$
$12$		0			0
$13$	−6.68252			−0.514040			−0.257020	−	0.966406i	$-0.582741\pi$
$13$	−6.68252			−0.514040			−0.257020	+	0.966406i	$0.582741\pi$
$14$	−13.9094	−	1.59024i	−0.993528	−	0.113588i
$15$		0			0
$16$	11.2317	−	11.3951i	0.701983	−	0.712193i
$17$	16.6136			0.977271			0.488635	−	0.872488i	$-0.337495\pi$
$17$	16.6136			0.977271			0.488635	+	0.872488i	$0.337495\pi$
$18$		0			0
$19$			31.7713i			1.67217i	0.548599	+	0.836086i	$0.315162\pi$
$19$			31.7713i			1.67217i	−0.548599	+	0.836086i	$0.684838\pi$
$20$	10.8015	+	25.8131i	0.540074	+	1.29066i
$21$		0			0
$22$	7.16455	+	35.6819i	0.325661	+	1.62191i
$23$	28.2125			1.22663			0.613315	−	0.789838i	$-0.289836\pi$
$23$	28.2125			1.22663			0.613315	+	0.789838i	$0.289836\pi$
$24$		0			0
$25$	−23.9368			−0.957473
$26$	−13.1035	+	2.63105i	−0.503981	+	0.101194i
$27$		0			0
$28$	−27.9005	+	2.35817i	−0.996447	+	0.0842205i
$29$	−55.3335			−1.90805			−0.954026	−	0.299723i	$-0.903106\pi$
$29$	−55.3335			−1.90805			−0.954026	+	0.299723i	$0.903106\pi$
$30$		0			0
$31$	18.6829			0.602675			0.301338	−	0.953518i	$-0.402567\pi$
$31$	18.6829			0.602675			0.301338	+	0.953518i	$0.402567\pi$
$32$	17.5374	−	26.7664i	0.548044	−	0.836449i
$33$		0			0
$34$	32.5770	−	6.54112i	0.958147	−	0.192386i
$35$	15.0309	−	46.6045i	0.429455	−	1.33156i
$36$		0			0
$37$			18.8501i			0.509462i	0.967012	+	0.254731i	$0.0819870\pi$
$37$			18.8501i			0.509462i	−0.967012	+	0.254731i	$0.918013\pi$
$38$	12.5090	+	62.2991i	0.329184	+	1.63945i
$39$		0			0
$40$	31.3434	+	46.3632i	0.783584	+	1.15908i
$41$	−33.6389			−0.820461			−0.410231	−	0.911982i	$-0.634552\pi$
$41$	−33.6389			−0.820461			−0.410231	+	0.911982i	$0.634552\pi$
$42$		0			0
$43$	14.3177			0.332970			0.166485	−	0.986044i	$-0.446758\pi$
$43$	14.3177			0.332970			0.166485	+	0.986044i	$0.446758\pi$
$44$	28.0974	+	67.1466i	0.638577	+	1.52606i
$45$		0			0
$46$	55.3208	−	11.1078i	1.20263	−	0.241475i
$47$		−	57.3785i		−	1.22082i	−0.792086	−	0.610410i	$-0.791005\pi$
$47$		−	57.3785i		−	1.22082i	0.792086	−	0.610410i	$-0.208995\pi$
$48$		0			0
$49$	39.7665	+	28.6291i	0.811561	+	0.584267i
$50$	−46.9368	+	9.42441i	−0.938737	+	0.188488i
$51$		0			0
$52$	−24.6583	+	10.3182i	−0.474198	+	0.198428i
$53$	5.13773			0.0969383			0.0484691	−	0.998825i	$-0.484566\pi$
$53$	5.13773			0.0969383			0.0484691	+	0.998825i	$0.484566\pi$
$54$		0			0
$55$	−127.297			−2.31450
$56$	−53.7806	+	15.6091i	−0.960369	+	0.278733i
$57$		0			0
$58$	−108.501	+	21.7859i	−1.87071	+	0.375620i
$59$	83.0383			1.40743			0.703715	−	0.710483i	$-0.251523\pi$
$59$	83.0383			1.40743			0.703715	+	0.710483i	$0.251523\pi$
$60$		0			0
$61$	−75.6870			−1.24077			−0.620385	−	0.784297i	$-0.713024\pi$
$61$	−75.6870			−1.24077			−0.620385	+	0.784297i	$0.713024\pi$
$62$	36.6347	−	7.35585i	0.590882	−	0.118643i
$63$		0			0
$64$	23.8500	−	59.3900i	0.372656	−	0.927969i
$65$		−	46.7475i		−	0.719192i
$66$		0			0
$67$	17.6649			0.263655			0.131827	−	0.991273i	$-0.457916\pi$
$67$	17.6649			0.263655			0.131827	+	0.991273i	$0.457916\pi$
$68$	61.3037	−	25.6525i	0.901525	−	0.377242i
$69$		0			0
$70$	11.1245	−	97.3029i	0.158921	−	1.39004i
$71$	75.8131			1.06779			0.533895	−	0.845551i	$-0.320728\pi$
$71$	75.8131			1.06779			0.533895	+	0.845551i	$0.320728\pi$
$72$		0			0
$73$		−	103.904i		−	1.42335i	−0.702511	−	0.711673i	$-0.747938\pi$
$73$		−	103.904i		−	1.42335i	0.702511	−	0.711673i	$-0.252062\pi$
$74$	7.42167	+	36.9625i	0.100293	+	0.499493i
$75$		0			0
$76$	49.0568	+	117.235i	0.645485	+	1.54257i
$77$	39.0993	−	121.230i	0.507783	−	1.57442i
$78$		0			0
$79$			33.8548i			0.428541i	0.976774	+	0.214271i	$0.0687375\pi$
$79$			33.8548i			0.428541i	−0.976774	+	0.214271i	$0.931263\pi$
$80$	79.7142	+	78.5714i	0.996427	+	0.982143i
$81$		0			0
$82$	−65.9613	+	13.2443i	−0.804406	+	0.161516i
$83$	127.193			1.53245			0.766226	−	0.642572i	$-0.222132\pi$
$83$	127.193			1.53245			0.766226	+	0.642572i	$0.222132\pi$
$84$		0			0
$85$			116.220i			1.36730i
$86$	28.0751	−	5.63718i	0.326454	−	0.0655486i
$87$		0			0
$88$	81.5321	+	120.603i	0.926502	+	1.37049i
$89$	31.6907			0.356075			0.178038	−	0.984024i	$-0.443025\pi$
$89$	31.6907			0.356075			0.178038	+	0.984024i	$0.443025\pi$
$90$		0			0
$91$	44.5195	+	14.3585i	0.489225	+	0.157786i
$92$	104.103	−	43.5619i	1.13156	−	0.473499i
$93$		0			0
$94$	−22.5911	−	112.511i	−0.240331	−	1.19693i
$95$	−222.255			−2.33953
$96$		0			0
$97$		−	97.7829i		−	1.00807i	−0.863683	−	0.504036i	$-0.831848\pi$
$97$		−	97.7829i		−	1.00807i	0.863683	−	0.504036i	$-0.168152\pi$
$98$	89.2485	+	40.4809i	0.910699	+	0.413070i
$99$		0			0
$100$	−88.3261	+	36.9600i	−0.883261	+	0.369600i
$101$		−	127.765i		−	1.26500i	−0.774560	−	0.632501i	$-0.782029\pi$
$101$		−	127.765i		−	1.26500i	0.774560	−	0.632501i	$-0.217971\pi$
$102$		0			0
$103$	−63.9717			−0.621084			−0.310542	−	0.950560i	$-0.600511\pi$
$103$	−63.9717			−0.621084			−0.310542	+	0.950560i	$0.600511\pi$
$104$	−44.2891	+	29.9411i	−0.425856	+	0.287896i
$105$		0			0
$106$	10.0744	−	2.02283i	0.0950413	−	0.0190833i
$107$		−	79.5953i		−	0.743882i	−0.928256	−	0.371941i	$-0.878692\pi$
$107$		−	79.5953i		−	0.743882i	0.928256	−	0.371941i	$-0.121308\pi$
$108$		0			0
$109$		−	38.8557i		−	0.356474i	−0.983988	−	0.178237i	$-0.942961\pi$
$109$		−	38.8557i		−	0.356474i	0.983988	−	0.178237i	$-0.0570394\pi$
$110$	−249.612	+	50.1195i	−2.26920	+	0.455632i
$111$		0			0
$112$	−99.3109	+	51.7818i	−0.886704	+	0.462337i
$113$			76.4605i			0.676641i	0.941031	+	0.338321i	$0.109859\pi$
$113$			76.4605i			0.676641i	−0.941031	+	0.338321i	$0.890141\pi$
$114$		0			0
$115$			197.360i			1.71617i
$116$	−204.179	+	85.4385i	−1.76016	+	0.736539i
$117$		0			0
$118$	162.827	−	32.6939i	1.37989	−	0.277067i
$119$	−110.681	−	35.6970i	−0.930093	−	0.299975i
$120$		0			0
$121$	−210.133			−1.73663
$122$	−148.412	+	29.7995i	−1.21649	+	0.244258i
$123$		0			0
$124$	68.9394	−	28.8476i	0.555963	−	0.232642i
$125$			7.43746i			0.0594997i
$126$		0			0
$127$		−	11.8617i		−	0.0933989i	−0.998909	−	0.0466994i	$-0.985130\pi$
$127$		−	11.8617i		−	0.0933989i	0.998909	−	0.0466994i	$-0.0148703\pi$
$128$	23.3835	−	125.846i	0.182684	−	0.983172i
$129$		0			0
$130$	−18.4054	−	91.6655i	−0.141580	−	0.705119i
$131$	−108.198			−0.825938			−0.412969	−	0.910745i	$-0.635508\pi$
$131$	−108.198			−0.825938			−0.412969	+	0.910745i	$0.635508\pi$
$132$		0			0
$133$	68.2657	−	211.663i	0.513276	−	1.59145i
$134$	34.6384	−	6.95502i	0.258496	−	0.0519032i
$135$		0			0
$136$	110.108	−	74.4375i	0.809619	−	0.547334i
$137$			165.973i			1.21148i	0.795661	+	0.605742i	$0.207124\pi$
$137$			165.973i			1.21148i	−0.795661	+	0.605742i	$0.792876\pi$
$138$		0			0
$139$		−	70.0346i		−	0.503846i	−0.967747	−	0.251923i	$-0.918937\pi$
$139$		−	70.0346i		−	0.503846i	0.967747	−	0.251923i	$-0.0810629\pi$
$140$	−16.4966	−	195.178i	−0.117833	−	1.39413i
$141$		0			0
$142$	148.659	−	29.8492i	1.04690	−	0.210205i
$143$		−	121.602i		−	0.850365i
$144$		0			0
$145$		−	387.085i		−	2.66955i
$146$	−40.9092	−	203.742i	−0.280200	−	1.39549i
$147$		0			0
$148$	29.1058	+	69.5563i	0.196661	+	0.469975i
$149$	83.2376			0.558642			0.279321	−	0.960198i	$-0.409891\pi$
$149$	83.2376			0.558642			0.279321	+	0.960198i	$0.409891\pi$
$150$		0			0
$151$			99.0522i			0.655975i	0.944682	+	0.327988i	$0.106370\pi$
$151$			99.0522i			0.655975i	−0.944682	+	0.327988i	$0.893630\pi$
$152$	142.352	+	210.567i	0.936523	+	1.38531i
$153$		0			0
$154$	28.9376	−	253.110i	0.187907	−	1.64357i
$155$			130.696i			0.843201i
$156$		0			0
$157$	114.893			0.731804			0.365902	−	0.930653i	$-0.380760\pi$
$157$	114.893			0.731804			0.365902	+	0.930653i	$0.380760\pi$
$158$	13.3293	+	66.3846i	0.0843627	+	0.420156i
$159$		0			0
$160$	187.244	+	122.683i	1.17027	+	0.766767i
$161$	−187.954	−	60.6191i	−1.16741	−	0.376516i
$162$		0			0
$163$	−181.136			−1.11126			−0.555630	−	0.831429i	$-0.687523\pi$
$163$	−181.136			−1.11126			−0.555630	+	0.831429i	$0.687523\pi$
$164$	−124.127	+	51.9406i	−0.756869	+	0.316711i
$165$		0			0
$166$	249.409	−	50.0787i	1.50246	−	0.301679i
$167$			127.590i			0.764014i	0.924159	+	0.382007i	$0.124767\pi$
$167$			127.590i			0.764014i	−0.924159	+	0.382007i	$0.875233\pi$
$168$		0			0
$169$	−124.344			−0.735763
$170$	45.7583	+	227.892i	0.269166	+	1.34054i
$171$		0			0
$172$	52.8319	−	22.1075i	0.307162	−	0.128532i
$173$		−	47.7694i		−	0.276124i	−0.990424	−	0.138062i	$-0.955913\pi$
$173$		−	47.7694i		−	0.276124i	0.990424	−	0.138062i	$-0.0440873\pi$
$174$		0			0
$175$	159.469	+	51.4321i	0.911251	+	0.293898i
$176$	207.357	+	204.385i	1.17817	+	1.16128i
$177$		0			0
$178$	62.1411	−	12.4773i	0.349107	−	0.0700970i
$179$		−	189.834i		−	1.06053i	−0.847833	−	0.530264i	$-0.822093\pi$
$179$		−	189.834i		−	1.06053i	0.847833	−	0.530264i	$-0.177907\pi$
$180$		0			0
$181$	−223.560			−1.23514			−0.617569	−	0.786517i	$-0.711882\pi$
$181$	−223.560			−1.23514			−0.617569	+	0.786517i	$0.711882\pi$
$182$	92.9498	+	10.6268i	0.510713	+	0.0583890i
$183$		0			0
$184$	186.981	−	126.406i	1.01620	−	0.686991i
$185$	−131.866			−0.712787
$186$		0			0
$187$			302.319i			1.61668i
$188$	−88.5961	−	211.725i	−0.471256	−	1.12620i
$189$		0			0
$190$	−435.812	+	87.5065i	−2.29375	+	0.460560i
$191$	261.590			1.36958			0.684790	−	0.728740i	$-0.259894\pi$
$191$	261.590			1.36958			0.684790	+	0.728740i	$0.259894\pi$
$192$		0			0
$193$	298.207			1.54511			0.772556	−	0.634947i	$-0.218978\pi$
$193$	298.207			1.54511			0.772556	+	0.634947i	$0.218978\pi$
$194$	−38.4991	−	191.739i	−0.198449	−	0.988345i
$195$		0			0
$196$	190.942	+	44.2385i	0.974195	+	0.225706i
$197$	−14.7389			−0.0748168			−0.0374084	−	0.999300i	$-0.511910\pi$
$197$	−14.7389			−0.0748168			−0.0374084	+	0.999300i	$0.511910\pi$
$198$		0			0
$199$	−5.15270			−0.0258930			−0.0129465	−	0.999916i	$-0.504121\pi$
$199$	−5.15270			−0.0258930			−0.0129465	+	0.999916i	$0.504121\pi$
$200$	−158.644	+	107.249i	−0.793218	+	0.536246i
$201$		0			0
$202$	−50.3037	−	250.530i	−0.249028	−	1.24025i
$203$	368.636	+	118.893i	1.81594	+	0.585680i
$204$		0			0
$205$		−	235.321i		−	1.14791i
$206$	−125.440	+	25.1870i	−0.608931	+	0.122267i
$207$		0			0
$208$	−75.0563	+	76.1480i	−0.360848	+	0.366096i
$209$	−578.143			−2.76624
$210$		0			0
$211$	108.422			0.513847			0.256924	−	0.966432i	$-0.417291\pi$
$211$	108.422			0.513847			0.256924	+	0.966432i	$0.417291\pi$
$212$	18.9581	−	7.93298i	0.0894248	−	0.0374197i
$213$		0			0
$214$	−31.3383	−	156.076i	−0.146441	−	0.729325i
$215$			100.159i			0.465857i
$216$		0			0
$217$	−124.467	−	40.1433i	−0.573581	−	0.184992i
$218$	−15.2983	−	76.1907i	−0.0701756	−	0.349498i
$219$		0			0
$220$	−469.723	+	196.555i	−2.13510	+	0.893432i
$221$	−111.021			−0.502357
$222$		0			0
$223$	132.822			0.595613			0.297806	−	0.954626i	$-0.403745\pi$
$223$	132.822			0.595613			0.297806	+	0.954626i	$0.403745\pi$
$224$	−174.347	+	140.638i	−0.778337	+	0.627847i
$225$		0			0
$226$	30.1040	+	149.929i	0.133204	+	0.663400i
$227$	−93.0732			−0.410014			−0.205007	−	0.978761i	$-0.565722\pi$
$227$	−93.0732			−0.410014			−0.205007	+	0.978761i	$0.565722\pi$
$228$		0			0
$229$	404.588			1.76676			0.883379	−	0.468659i	$-0.155263\pi$
$229$	404.588			1.76676			0.883379	+	0.468659i	$0.155263\pi$
$230$	77.7047	+	386.996i	0.337846	+	1.68259i
$231$		0			0
$232$	−366.728	+	247.923i	−1.58072	+	1.06863i
$233$		−	122.179i		−	0.524374i	−0.965017	−	0.262187i	$-0.915556\pi$
$233$		−	122.179i		−	0.524374i	0.965017	−	0.262187i	$-0.0844437\pi$
$234$		0			0
$235$	401.391			1.70805
$236$	306.409	−	128.216i	1.29834	−	0.543290i
$237$		0			0
$238$	−231.085	−	26.4196i	−0.970946	−	0.111007i
$239$	95.7941			0.400812			0.200406	−	0.979713i	$-0.435774\pi$
$239$	95.7941			0.400812			0.200406	+	0.979713i	$0.435774\pi$
$240$		0			0
$241$		−	155.437i		−	0.644966i	−0.946575	−	0.322483i	$-0.895482\pi$
$241$		−	155.437i		−	0.644966i	0.946575	−	0.322483i	$-0.104518\pi$
$242$	−412.042	+	82.7336i	−1.70265	+	0.341874i
$243$		0			0
$244$	−279.283	+	116.866i	−1.14460	+	0.478957i
$245$	−200.274	+	278.186i	−0.817447	+	1.13545i
$246$		0			0
$247$		−	212.312i		−	0.859564i
$248$	123.823	−	83.7091i	0.499286	−	0.337537i
$249$		0			0
$250$	2.92828	+	14.5838i	0.0117131	+	0.0583353i
$251$	223.183			0.889177			0.444588	−	0.895735i	$-0.353350\pi$
$251$	223.183			0.889177			0.444588	+	0.895735i	$0.353350\pi$
$252$		0			0
$253$			513.384i			2.02919i
$254$	−4.67018	−	23.2591i	−0.0183865	−	0.0915712i
$255$		0			0
$256$	−3.69622	−	255.973i	−0.0144384	−	0.999896i
$257$	434.336			1.69002			0.845011	−	0.534748i	$-0.179594\pi$
$257$	434.336			1.69002			0.845011	+	0.534748i	$0.179594\pi$
$258$		0			0
$259$	40.5025	−	125.581i	0.156380	−	0.484868i
$260$	−72.1811	−	172.497i	−0.277620	−	0.663449i
$261$		0			0
$262$	−212.161	+	42.5997i	−0.809776	+	0.162594i
$263$	0.872408			0.00331714			0.00165857	−	0.999999i	$-0.499472\pi$
$263$	0.872408			0.00331714			0.00165857	+	0.999999i	$0.499472\pi$
$264$		0			0
$265$			35.9409i			0.135626i
$266$	50.5238	−	441.919i	0.189939	−	1.66135i
$267$		0			0
$268$	65.1829	−	27.2757i	0.243220	−	0.101775i
$269$			114.052i			0.423986i	0.977271	+	0.211993i	$0.0679954\pi$
$269$			114.052i			0.423986i	−0.977271	+	0.211993i	$0.932005\pi$
$270$		0			0
$271$	−212.581			−0.784431			−0.392216	−	0.919873i	$-0.628291\pi$
$271$	−212.581			−0.784431			−0.392216	+	0.919873i	$0.628291\pi$
$272$	186.600	−	189.314i	0.686028	−	0.696006i
$273$		0			0
$274$	65.3471	+	325.451i	0.238493	+	1.18778i
$275$		−	435.580i		−	1.58393i
$276$		0			0
$277$			105.878i			0.382231i	0.981568	+	0.191115i	$0.0612105\pi$
$277$			105.878i			0.382231i	−0.981568	+	0.191115i	$0.938790\pi$
$278$	−27.5740	−	137.328i	−0.0991872	−	0.493986i
$279$		0			0
$280$	−109.193	−	376.222i	−0.389975	−	1.34365i
$281$			431.952i			1.53720i	0.639732	+	0.768598i	$0.279045\pi$
$281$			431.952i			1.53720i	−0.639732	+	0.768598i	$0.720955\pi$
$282$		0			0
$283$			186.571i			0.659262i	0.944110	+	0.329631i	$0.106924\pi$
$283$			186.571i			0.659262i	−0.944110	+	0.329631i	$0.893076\pi$
$284$	279.748	−	117.060i	0.985028	−	0.412184i
$285$		0			0
$286$	−47.8773	−	238.445i	−0.167403	−	0.833725i
$287$	224.105	+	72.2786i	0.780854	+	0.251842i
$288$		0			0
$289$	−12.9881			−0.0449415
$290$	−152.403	−	759.020i	−0.525528	−	2.61731i
$291$		0			0
$292$	−160.435	−	383.403i	−0.549434	−	1.31302i
$293$			5.13791i			0.0175355i	0.999962	+	0.00876777i	$0.00279090\pi$
$293$			5.13791i			0.0175355i	−0.999962	+	0.00876777i	$0.997209\pi$
$294$		0			0
$295$			580.894i			1.96913i
$296$	84.4582	+	124.931i	0.285332	+	0.422064i
$297$		0			0
$298$	163.218	−	32.7723i	0.547710	−	0.109974i
$299$	−188.531			−0.630537
$300$		0			0
$301$	−95.3857	−	30.7639i	−0.316896	−	0.102206i
$302$	38.9989	+	194.228i	0.129135	+	0.643139i
$303$		0			0
$304$	362.036	+	356.846i	1.19091	+	1.17384i
$305$		−	529.468i		−	1.73596i
$306$		0			0
$307$			323.370i			1.05332i	0.850075	+	0.526661i	$0.176556\pi$
$307$			323.370i			1.05332i	−0.850075	+	0.526661i	$0.823444\pi$
$308$	−42.9118	−	507.707i	−0.139324	−	1.64840i
$309$		0			0
$310$	51.4578	+	256.277i	0.165993	+	0.826701i
$311$			191.354i			0.615286i	0.951502	+	0.307643i	$0.0995403\pi$
$311$			191.354i			0.615286i	−0.951502	+	0.307643i	$0.900460\pi$
$312$		0			0
$313$		−	55.8314i		−	0.178375i	−0.996015	−	0.0891875i	$-0.971573\pi$
$313$		−	55.8314i		−	0.178375i	0.996015	−	0.0891875i	$-0.0284270\pi$
$314$	225.290	−	45.2358i	0.717484	−	0.144063i
$315$		0			0
$316$	52.2739	+	124.923i	0.165424	+	0.395326i
$317$	−100.839			−0.318103			−0.159051	−	0.987270i	$-0.550844\pi$
$317$	−100.839			−0.318103			−0.159051	+	0.987270i	$0.550844\pi$
$318$		0			0
$319$		−	1006.91i		−	3.15645i
$320$	415.462	+	166.842i	1.29832	+	0.521382i
$321$		0			0
$322$	−392.419	−	44.8645i	−1.21869	−	0.139331i
$323$			527.835i			1.63416i
$324$		0			0
$325$	159.958			0.492180
$326$	−355.182	+	71.3167i	−1.08952	+	0.218763i
$327$		0			0
$328$	−222.945	+	150.720i	−0.679711	+	0.459511i
$329$	−123.287	+	382.260i	−0.374733	+	1.16189i
$330$		0			0
$331$	−138.740			−0.419155			−0.209577	−	0.977792i	$-0.567209\pi$
$331$	−138.740			−0.419155			−0.209577	+	0.977792i	$0.567209\pi$
$332$	469.340	−	196.395i	1.41367	−	0.591551i
$333$		0			0
$334$	50.2349	+	250.187i	0.150404	+	0.749063i
$335$			123.574i			0.368879i
$336$		0			0
$337$	−118.399			−0.351334			−0.175667	−	0.984450i	$-0.556208\pi$
$337$	−118.399			−0.351334			−0.175667	+	0.984450i	$0.556208\pi$
$338$	−243.821	+	48.9567i	−0.721365	+	0.144842i
$339$		0			0
$340$	179.451	+	428.849i	0.527798	+	1.26132i
$341$			339.974i			0.996992i
$342$		0			0
$343$	−203.413	−	276.174i	−0.593041	−	0.805172i
$344$	94.8920	−	64.1507i	0.275849	−	0.186485i
$345$		0			0
$346$	−18.8078	−	93.6692i	−0.0543577	−	0.270720i
$347$			69.4367i			0.200106i	0.994982	+	0.100053i	$0.0319012\pi$
$347$			69.4367i			0.200106i	−0.994982	+	0.100053i	$0.968099\pi$
$348$		0			0
$349$	263.144			0.753994			0.376997	−	0.926214i	$-0.376957\pi$
$349$	263.144			0.753994			0.376997	+	0.926214i	$0.376957\pi$
$350$	332.947	+	38.0652i	0.951276	+	0.108758i
$351$		0			0
$352$	487.069	+	319.129i	1.38372	+	0.906617i
$353$	72.4623			0.205276			0.102638	−	0.994719i	$-0.467272\pi$
$353$	72.4623			0.205276			0.102638	+	0.994719i	$0.467272\pi$
$354$		0			0
$355$			530.349i			1.49394i
$356$	116.938	−	48.9324i	0.328476	−	0.137451i
$357$		0			0
$358$	−74.7417	−	372.239i	−0.208776	−	1.03977i
$359$	178.507			0.497234			0.248617	−	0.968602i	$-0.420024\pi$
$359$	178.507			0.497234			0.248617	+	0.968602i	$0.420024\pi$
$360$		0			0
$361$	−648.413			−1.79616
$362$	−438.370	+	88.0201i	−1.21097	+	0.243149i
$363$		0			0
$364$	186.446	−	15.7585i	0.512214	−	0.0432927i
$365$	726.860			1.99140
$366$		0			0
$367$	−275.630			−0.751036			−0.375518	−	0.926815i	$-0.622535\pi$
$367$	−275.630			−0.751036			−0.375518	+	0.926815i	$0.622535\pi$
$368$	316.875	−	321.484i	0.861074	−	0.873598i
$369$		0			0
$370$	−258.571	+	51.9182i	−0.698839	+	0.140319i
$371$	−34.2279	−	11.0392i	−0.0922586	−	0.0297554i
$372$		0			0
$373$		−	162.322i		−	0.435180i	−0.976040	−	0.217590i	$-0.930180\pi$
$373$		−	162.322i		−	0.435180i	0.976040	−	0.217590i	$-0.0698195\pi$
$374$	119.029	+	592.806i	0.318259	+	1.58504i
$375$		0			0
$376$	−257.085	−	380.282i	−0.683737	−	1.01139i
$377$	369.768			0.980816
$378$		0			0
$379$	−294.419			−0.776830			−0.388415	−	0.921484i	$-0.626977\pi$
$379$	−294.419			−0.776830			−0.388415	+	0.921484i	$0.626977\pi$
$380$	−820.116	+	343.176i	−2.15820	+	0.903096i
$381$		0			0
$382$	512.942	−	102.993i	1.34278	−	0.269616i
$383$			422.380i			1.10282i	0.834235	+	0.551410i	$0.185910\pi$
$383$			422.380i			1.10282i	−0.834235	+	0.551410i	$0.814090\pi$
$384$		0			0
$385$	848.064	+	273.519i	2.20276	+	0.710438i
$386$	584.742	−	117.410i	1.51488	−	0.304171i
$387$		0			0
$388$	−150.983	−	360.816i	−0.389132	−	0.929938i
$389$	219.542			0.564376			0.282188	−	0.959359i	$-0.408940\pi$
$389$	219.542			0.564376			0.282188	+	0.959359i	$0.408940\pi$
$390$		0			0
$391$	468.711			1.19875
$392$	391.829	+	11.5677i	0.999565	+	0.0295094i
$393$		0			0
$394$	−28.9010	+	5.80301i	−0.0733528	+	0.0147285i
$395$	−236.831			−0.599571
$396$		0			0
$397$	−163.460			−0.411737			−0.205868	−	0.978580i	$-0.566002\pi$
$397$	−163.460			−0.411737			−0.205868	+	0.978580i	$0.566002\pi$
$398$	−10.1037	+	2.02872i	−0.0253863	+	0.00509730i
$399$		0			0
$400$	−268.852	+	272.762i	−0.672130	+	0.681906i
$401$		−	673.216i		−	1.67884i	−0.543482	−	0.839421i	$-0.682894\pi$
$401$		−	673.216i		−	1.67884i	0.543482	−	0.839421i	$-0.317106\pi$
$402$		0			0
$403$	−124.849			−0.309799
$404$	−197.277	−	471.449i	−0.488311	−	1.16695i
$405$		0			0
$406$	769.656	+	87.9934i	1.89570	+	0.216733i
$407$	−343.016			−0.842792
$408$		0			0
$409$			416.822i			1.01912i	0.860434	+	0.509562i	$0.170193\pi$
$409$			416.822i			1.01912i	−0.860434	+	0.509562i	$0.829807\pi$
$410$	−92.6505	−	461.431i	−0.225977	−	1.12544i
$411$		0			0
$412$	−236.053	+	98.7763i	−0.572945	+	0.239748i
$413$	−553.208	−	178.421i	−1.33949	−	0.432013i
$414$		0			0
$415$			889.780i			2.14405i
$416$	−117.194	+	178.867i	−0.281717	+	0.429969i
$417$		0			0
$418$	−1133.66	+	227.627i	−2.71211	+	0.544562i
$419$	354.382			0.845781			0.422890	−	0.906181i	$-0.361016\pi$
$419$	354.382			0.845781			0.422890	+	0.906181i	$0.361016\pi$
$420$		0			0
$421$		−	497.096i		−	1.18075i	−0.807129	−	0.590376i	$-0.798980\pi$
$421$		−	497.096i		−	1.18075i	0.807129	−	0.590376i	$-0.201020\pi$
$422$	212.600	−	42.6878i	0.503792	−	0.101156i
$423$		0			0
$424$	34.0508	−	23.0197i	0.0803084	−	0.0542916i
$425$	−397.677			−0.935710
$426$		0			0
$427$	504.233	+	162.626i	1.18087	+	0.380857i
$428$	−122.900	−	293.704i	−0.287150	−	0.686225i
$429$		0			0
$430$	39.4348	+	196.399i	0.0917088	+	0.456741i
$431$	−266.414			−0.618129			−0.309065	−	0.951041i	$-0.600016\pi$
$431$	−266.414			−0.618129			−0.309065	+	0.951041i	$0.600016\pi$
$432$		0			0
$433$			748.445i			1.72851i	0.503053	+	0.864255i	$0.332210\pi$
$433$			748.445i			1.72851i	−0.503053	+	0.864255i	$0.667790\pi$
$434$	−259.868	−	29.7103i	−0.598775	−	0.0684569i
$435$		0			0
$436$	−59.9956	−	143.376i	−0.137605	−	0.328845i
$437$			896.346i			2.05114i
$438$		0			0
$439$	665.040			1.51490			0.757448	−	0.652895i	$-0.226446\pi$
$439$	665.040			1.51490			0.757448	+	0.652895i	$0.226446\pi$
$440$	−843.674	+	570.357i	−1.91744	+	1.29627i
$441$		0			0
$442$	−217.697	+	43.7112i	−0.492526	+	0.0988940i
$443$		−	202.672i		−	0.457500i	−0.973485	−	0.228750i	$-0.926536\pi$
$443$		−	202.672i		−	0.457500i	0.973485	−	0.228750i	$-0.0734638\pi$
$444$		0			0
$445$			221.692i			0.498184i
$446$	260.445	−	52.2946i	0.583957	−	0.117252i
$447$		0			0
$448$	−286.500	+	344.415i	−0.639508	+	0.768784i
$449$			759.051i			1.69054i	0.534342	+	0.845268i	$0.320559\pi$
$449$			759.051i			1.69054i	−0.534342	+	0.845268i	$0.679441\pi$
$450$		0			0
$451$		−	612.129i		−	1.35727i
$452$	118.060	+	282.137i	0.261194	+	0.624196i
$453$		0			0
$454$	−182.504	+	36.6448i	−0.401991	+	0.0807154i
$455$	−100.445	+	311.435i	−0.220757	+	0.684473i
$456$		0			0
$457$	−219.847			−0.481066			−0.240533	−	0.970641i	$-0.577322\pi$
$457$	−219.847			−0.481066			−0.240533	+	0.970641i	$0.577322\pi$
$458$	793.341	−	159.294i	1.73219	−	0.347804i
$459$		0			0
$460$	304.736	+	728.252i	0.662471	+	1.58316i
$461$		−	394.153i		−	0.854996i	−0.904016	−	0.427498i	$-0.859395\pi$
$461$		−	394.153i		−	0.854996i	0.904016	−	0.427498i	$-0.140605\pi$
$462$		0			0
$463$			411.620i			0.889028i	0.895772	+	0.444514i	$0.146624\pi$
$463$			411.620i			0.889028i	−0.895772	+	0.444514i	$0.853376\pi$
$464$	−621.491	+	630.531i	−1.33942	+	1.35890i
$465$		0			0
$466$	−48.1044	−	239.577i	−0.103228	−	0.514113i
$467$	−448.091			−0.959510			−0.479755	−	0.877402i	$-0.659274\pi$
$467$	−448.091			−0.959510			−0.479755	+	0.877402i	$0.659274\pi$
$468$		0			0
$469$	−117.685	−	37.9559i	−0.250927	−	0.0809293i
$470$	787.072	−	158.036i	1.67462	−	0.336246i
$471$		0			0
$472$	550.344	−	372.054i	1.16598	−	0.788251i
$473$			260.540i			0.550825i
$474$		0			0
$475$		−	760.503i		−	1.60106i
$476$	−463.528	+	39.1778i	−0.973799	+	0.0823062i
$477$		0			0
$478$	187.839	−	37.7161i	0.392969	−	0.0789040i
$479$			415.331i			0.867079i	0.901134	+	0.433540i	$0.142736\pi$
$479$			415.331i			0.867079i	−0.901134	+	0.433540i	$0.857264\pi$
$480$		0			0
$481$		−	125.966i		−	0.261884i
$482$	−61.1987	−	304.790i	−0.126968	−	0.632345i
$483$		0			0
$484$	−775.384	+	324.458i	−1.60203	+	0.670369i
$485$	684.039			1.41039
$486$		0			0
$487$		−	641.626i		−	1.31751i	−0.752359	−	0.658754i	$-0.771084\pi$
$487$		−	641.626i		−	1.31751i	0.752359	−	0.658754i	$-0.228916\pi$
$488$	−501.623	+	339.117i	−1.02792	+	0.694911i
$489$		0			0
$490$	−283.183	+	624.337i	−0.577925	+	1.27416i
$491$		−	183.492i		−	0.373712i	−0.982387	−	0.186856i	$-0.940170\pi$
$491$		−	183.492i		−	0.373712i	0.982387	−	0.186856i	$-0.0598297\pi$
$492$		0			0
$493$	−919.289			−1.86468
$494$	−83.5917	−	416.315i	−0.169214	−	0.842743i
$495$		0			0
$496$	209.842	−	212.894i	0.423068	−	0.429221i
$497$	−505.073	−	162.897i	−1.01624	−	0.327760i
$498$		0			0
$499$	−177.302			−0.355314			−0.177657	−	0.984092i	$-0.556852\pi$
$499$	−177.302			−0.355314			−0.177657	+	0.984092i	$0.556852\pi$
$500$	11.4839	+	27.4440i	0.0229678	+	0.0548880i
$501$		0			0
$502$	437.632	−	87.8718i	0.871777	−	0.175043i
$503$		−	237.590i		−	0.472346i	−0.971711	−	0.236173i	$-0.924107\pi$
$503$		−	237.590i		−	0.472346i	0.971711	−	0.236173i	$-0.0758932\pi$
$504$		0			0
$505$	893.779			1.76986
$506$	202.130	+	1006.68i	0.399466	+	1.98948i
$507$		0			0
$508$	−18.3151	−	43.7691i	−0.0360534	−	0.0861597i
$509$		−	162.377i		−	0.319011i	−0.987197	−	0.159506i	$-0.949010\pi$
$509$		−	162.377i		−	0.319011i	0.987197	−	0.159506i	$-0.0509900\pi$
$510$		0			0
$511$	−223.255	+	692.218i	−0.436898	+	1.35463i
$512$	−108.030	−	500.473i	−0.210995	−	0.977487i
$513$		0			0
$514$	851.673	−	171.007i	1.65695	−	0.332698i
$515$		−	447.513i		−	0.868957i
$516$		0			0
$517$	1044.12			2.01958
$518$	29.9761	−	262.194i	0.0578690	−	0.506165i
$519$		0			0
$520$	−209.453	−	309.823i	−0.402794	−	0.595814i
$521$	534.282			1.02549			0.512747	−	0.858540i	$-0.328628\pi$
$521$	534.282			1.02549			0.512747	+	0.858540i	$0.328628\pi$
$522$		0			0
$523$		−	632.352i		−	1.20909i	−0.796572	−	0.604543i	$-0.793356\pi$
$523$		−	632.352i		−	1.20909i	0.796572	−	0.604543i	$-0.206644\pi$
$524$	−399.247	+	167.064i	−0.761921	+	0.318825i
$525$		0			0
$526$	1.71067	−	0.343485i	0.00325223	−	0.000653013i
$527$	310.391			0.588977
$528$		0			0
$529$	266.944			0.504621
$530$	14.1507	+	70.4752i	0.0266994	+	0.132972i
$531$		0			0
$532$	−74.9221	−	886.435i	−0.140831	−	1.66623i
$533$	224.793			0.421750
$534$		0			0
$535$	556.808			1.04076
$536$	117.076	−	79.1477i	0.218425	−	0.147664i
$537$		0			0
$538$	44.9047	+	223.641i	0.0834659	+	0.415689i
$539$	−520.965	+	723.633i	−0.966540	+	1.34255i
$540$		0			0
$541$		−	816.142i		−	1.50858i	−0.656541	−	0.754290i	$-0.727981\pi$
$541$		−	816.142i		−	1.50858i	0.656541	−	0.754290i	$-0.272019\pi$
$542$	−416.842	+	83.6974i	−0.769081	+	0.154423i
$543$		0			0
$544$	291.360	−	444.686i	0.535588	−	0.817438i
$545$	271.814			0.498742
$546$		0			0
$547$	115.353			0.210883			0.105441	−	0.994426i	$-0.466374\pi$
$547$	115.353			0.210883			0.105441	+	0.994426i	$0.466374\pi$
$548$	256.273	+	612.436i	0.467652	+	1.11758i
$549$		0			0
$550$	−171.497	−	854.112i	−0.311812	−	1.55293i
$551$		−	1758.02i		−	3.19059i
$552$		0			0
$553$	72.7425	−	225.543i	0.131542	−	0.407854i
$554$	41.6863	+	207.612i	0.0752461	+	0.374751i
$555$		0			0
$556$	−108.138	−	258.425i	−0.194492	−	0.464794i
$557$	301.385			0.541087			0.270543	−	0.962708i	$-0.412797\pi$
$557$	301.385			0.541087			0.270543	+	0.962708i	$0.412797\pi$
$558$		0			0
$559$	−95.6785			−0.171160
$560$	−362.239	−	694.728i	−0.646855	−	1.24059i
$561$		0			0
$562$	170.068	+	846.999i	0.302613	+	1.50712i
$563$	20.5662			0.0365296			0.0182648	−	0.999833i	$-0.494186\pi$
$563$	20.5662			0.0365296			0.0182648	+	0.999833i	$0.494186\pi$
$564$		0			0
$565$	−534.878			−0.946687
$566$	73.4569	+	365.841i	0.129782	+	0.646361i
$567$		0			0
$568$	502.458	−	339.682i	0.884610	−	0.598031i
$569$		−	521.456i		−	0.916442i	−0.888838	−	0.458221i	$-0.848487\pi$
$569$		−	521.456i		−	0.916442i	0.888838	−	0.458221i	$-0.151513\pi$
$570$		0			0
$571$	−873.461			−1.52970			−0.764852	−	0.644206i	$-0.777188\pi$
$571$	−873.461			−1.52970			−0.764852	+	0.644206i	$0.777188\pi$
$572$	−187.762	−	448.709i	−0.328255	−	0.784455i
$573$		0			0
$574$	467.897	+	53.4938i	0.815151	+	0.0931949i
$575$	−675.317			−1.17446
$576$		0			0
$577$		−	564.551i		−	0.978425i	−0.872165	−	0.489213i	$-0.837284\pi$
$577$		−	564.551i		−	0.978425i	0.872165	−	0.489213i	$-0.162716\pi$
$578$	−25.4679	+	5.11367i	−0.0440620	+	0.00884718i
$579$		0			0
$580$	−597.684	−	1428.33i	−1.03049	−	2.46264i
$581$	−847.372	−	273.296i	−1.45847	−	0.470389i
$582$		0			0
$583$			93.4915i			0.160363i
$584$	−465.544	−	688.635i	−0.797165	−	1.17917i
$585$		0			0
$586$	2.02290	+	10.0747i	0.00345205	+	0.0171924i
$587$	−862.091			−1.46864			−0.734319	−	0.678804i	$-0.762498\pi$
$587$	−862.091			−1.46864			−0.734319	+	0.678804i	$0.762498\pi$
$588$		0			0
$589$			593.580i			1.00778i
$590$	228.710	+	1139.05i	0.387643	+	1.93060i
$591$		0			0
$592$	214.799	+	211.719i	0.362836	+	0.357634i
$593$	797.530			1.34491			0.672454	−	0.740139i	$-0.265240\pi$
$593$	797.530			1.34491			0.672454	+	0.740139i	$0.265240\pi$
$594$		0			0
$595$	249.718	−	774.268i	0.419694	−	1.30129i
$596$	307.144	−	128.524i	0.515343	−	0.215645i
$597$		0			0
$598$	−369.683	+	74.2284i	−0.618199	+	0.124128i
$599$	183.557			0.306438			0.153219	−	0.988192i	$-0.451036\pi$
$599$	183.557			0.306438			0.153219	+	0.988192i	$0.451036\pi$
$600$		0			0
$601$		−	253.057i		−	0.421060i	−0.977587	−	0.210530i	$-0.932481\pi$
$601$		−	253.057i		−	0.421060i	0.977587	−	0.210530i	$-0.0675189\pi$
$602$	−199.151	−	22.7686i	−0.330815	−	0.0378215i
$603$		0			0
$604$	152.943	+	365.500i	0.253217	+	0.605132i
$605$		−	1469.98i		−	2.42972i
$606$		0			0
$607$	−98.9064			−0.162943			−0.0814715	−	0.996676i	$-0.525962\pi$
$607$	−98.9064			−0.162943			−0.0814715	+	0.996676i	$0.525962\pi$
$608$	850.402	+	557.186i	1.39869	+	0.916424i
$609$		0			0
$610$	−208.462	−	1038.21i	−0.341741	−	1.70199i
$611$			383.433i			0.627551i
$612$		0			0
$613$			453.259i			0.739411i	0.929149	+	0.369705i	$0.120541\pi$
$613$			453.259i			0.739411i	−0.929149	+	0.369705i	$0.879459\pi$
$614$	127.317	+	634.084i	0.207357	+	1.03271i
$615$		0			0
$616$	−284.039	−	978.649i	−0.461102	−	1.58872i
$617$		−	639.880i		−	1.03708i	−0.855053	−	0.518541i	$-0.826475\pi$
$617$		−	639.880i		−	1.03708i	0.855053	−	0.518541i	$-0.173525\pi$
$618$		0			0
$619$		−	258.190i		−	0.417109i	−0.978011	−	0.208554i	$-0.933124\pi$
$619$		−	258.190i		−	0.417109i	0.978011	−	0.208554i	$-0.0668758\pi$
$620$	201.803	+	482.265i	0.325489	+	0.777846i
$621$		0			0
$622$	75.3400	+	375.219i	0.121125	+	0.603246i
$623$	−211.126	−	68.0925i	−0.338886	−	0.109298i
$624$		0			0
$625$	−650.449			−1.04072
$626$	−21.9819	−	109.478i	−0.0351149	−	0.174884i
$627$		0			0
$628$	423.953	−	177.403i	0.675084	−	0.282488i
$629$			313.168i			0.497883i
$630$		0			0
$631$		−	785.936i		−	1.24554i	−0.782405	−	0.622770i	$-0.786007\pi$
$631$		−	785.936i		−	1.24554i	0.782405	−	0.622770i	$-0.213993\pi$
$632$	151.687	+	224.376i	0.240011	+	0.355025i
$633$		0			0
$634$	−197.731	+	39.7022i	−0.311878	+	0.0626218i
$635$	82.9780			0.130674
$636$		0			0
$637$	−265.741	−	191.315i	−0.417175	−	0.300337i
$638$	−396.440	−	1974.41i	−0.621379	−	3.09468i
$639$		0			0
$640$	880.354	+	163.579i	1.37555	+	0.255592i
$641$		−	571.627i		−	0.891774i	−0.895089	−	0.445887i	$-0.852888\pi$
$641$		−	571.627i		−	0.891774i	0.895089	−	0.445887i	$-0.147112\pi$
$642$		0			0
$643$		−	45.6671i		−	0.0710220i	−0.999369	−	0.0355110i	$-0.988694\pi$
$643$		−	45.6671i		−	0.0710220i	0.999369	−	0.0355110i	$-0.0113059\pi$
$644$	−787.143	+	66.5299i	−1.22227	+	0.103307i
$645$		0			0
$646$	207.819	+	1035.01i	0.321702	+	1.60219i
$647$		−	344.503i		−	0.532462i	−0.963909	−	0.266231i	$-0.914222\pi$
$647$		−	344.503i		−	0.532462i	0.963909	−	0.266231i	$-0.0857785\pi$
$648$		0			0
$649$			1511.05i			2.32828i
$650$	313.656	−	62.9789i	0.482548	−	0.0968906i
$651$		0			0
$652$	−668.384	+	279.685i	−1.02513	+	0.428964i
$653$	−1179.22			−1.80585			−0.902927	−	0.429793i	$-0.858586\pi$
$653$	−1179.22			−1.80585			−0.902927	+	0.429793i	$0.858586\pi$
$654$		0			0
$655$		−	756.897i		−	1.15557i
$656$	−377.823	+	383.318i	−0.575950	+	0.584327i
$657$		0			0
$658$	−91.2455	+	798.101i	−0.138671	+	1.21292i
$659$			770.505i			1.16920i	0.811321	+	0.584601i	$0.198749\pi$
$659$			770.505i			1.16920i	−0.811321	+	0.584601i	$0.801251\pi$
$660$		0			0
$661$	406.214			0.614544			0.307272	−	0.951622i	$-0.400584\pi$
$661$	406.214			0.614544			0.307272	+	0.951622i	$0.400584\pi$
$662$	−272.050	+	54.6248i	−0.410952	+	0.0825148i
$663$		0			0
$664$	842.987	−	569.892i	1.26956	−	0.858271i
$665$	1480.68	+	477.552i	2.22659	+	0.718123i
$666$		0			0
$667$	−1561.10			−2.34047
$668$	197.008	+	470.804i	0.294921	+	0.704797i
$669$		0			0
$670$	48.6538	+	242.313i	0.0726176	+	0.361661i
$671$		−	1377.28i		−	2.05258i
$672$		0			0
$673$	−809.941			−1.20348			−0.601739	−	0.798692i	$-0.705525\pi$
$673$	−809.941			−1.20348			−0.601739	+	0.798692i	$0.705525\pi$
$674$	−232.165	+	46.6163i	−0.344459	+	0.0691636i
$675$		0			0
$676$	−458.825	+	191.995i	−0.678735	+	0.284016i
$677$		−	259.621i		−	0.383488i	−0.981445	−	0.191744i	$-0.938586\pi$
$677$		−	259.621i		−	0.383488i	0.981445	−	0.191744i	$-0.0614143\pi$
$678$		0			0
$679$	−210.102	+	651.437i	−0.309429	+	0.959407i
$680$	520.726	+	770.261i	0.765774	+	1.13274i
$681$		0			0
$682$	133.855	+	666.643i	0.196268	+	0.977483i
$683$		−	1047.64i		−	1.53387i	−0.641722	−	0.766937i	$-0.721780\pi$
$683$		−	1047.64i		−	1.53387i	0.641722	−	0.766937i	$-0.278220\pi$
$684$		0			0
$685$	−1161.06			−1.69498
$686$	−507.601	−	461.451i	−0.739943	−	0.672670i
$687$		0			0
$688$	160.813	−	163.152i	0.233740	−	0.237139i
$689$	−34.3330			−0.0498302
$690$		0			0
$691$		−	1372.76i		−	1.98663i	−0.115454	−	0.993313i	$-0.536832\pi$
$691$		−	1372.76i		−	1.98663i	0.115454	−	0.993313i	$-0.463168\pi$
$692$	−73.7589	−	176.267i	−0.106588	−	0.254722i
$693$		0			0
$694$	27.3387	+	136.156i	0.0393929	+	0.196190i
$695$	489.926			0.704929
$696$		0			0
$697$	−558.864			−0.801813
$698$	515.989	−	103.605i	0.739240	−	0.148431i
$699$		0			0
$700$	667.850	−	56.4472i	0.954071	−	0.0806388i
$701$	−1073.92			−1.53199			−0.765994	−	0.642848i	$-0.777753\pi$
$701$	−1073.92			−1.53199			−0.765994	+	0.642848i	$0.777753\pi$
$702$		0			0
$703$	−598.892			−0.851909
$704$	1080.72	+	434.000i	1.53512	+	0.616477i
$705$		0			0
$706$	142.089	−	28.5299i	0.201259	−	0.0404106i
$707$	−274.524	+	851.181i	−0.388294	+	1.20393i
$708$		0			0
$709$			437.716i			0.617371i	0.951164	+	0.308685i	$0.0998890\pi$
$709$			437.716i			0.617371i	−0.951164	+	0.308685i	$0.900111\pi$
$710$	208.809	+	1039.94i	0.294098	+	1.46471i
$711$		0			0
$712$	210.033	−	141.990i	0.294990	−	0.199425i
$713$	527.092			0.739259
$714$		0			0
$715$	850.667			1.18974
$716$	−293.116	−	700.483i	−0.409380	−	0.978328i
$717$		0			0
$718$	350.028	−	70.2818i	0.487504	−	0.0978855i
$719$			872.944i			1.21411i	0.794660	+	0.607055i	$0.207649\pi$
$719$			872.944i			1.21411i	−0.794660	+	0.607055i	$0.792351\pi$
$720$		0			0
$721$	426.184	+	137.454i	0.591101	+	0.190643i
$722$	−1271.45	+	255.293i	−1.76101	+	0.353592i
$723$		0			0
$724$	−824.929	+	345.191i	−1.13940	+	0.476783i
$725$	1324.51			1.82691
$726$		0			0
$727$	−1102.49			−1.51649			−0.758244	−	0.651970i	$-0.773943\pi$
$727$	−1102.49			−1.51649			−0.758244	+	0.651970i	$0.773943\pi$
$728$	359.390	−	104.308i	0.493668	−	0.143280i
$729$		0			0
$730$	1425.27	−	286.180i	1.95243	−	0.392027i
$731$	237.869			0.325402
$732$		0			0
$733$	185.173			0.252624			0.126312	−	0.991991i	$-0.459686\pi$
$733$	185.173			0.252624			0.126312	+	0.991991i	$0.459686\pi$
$734$	−540.473	+	108.521i	−0.736340	+	0.147849i
$735$		0			0
$736$	494.774	−	755.146i	0.672248	−	1.02601i
$737$			321.449i			0.436159i
$738$		0			0
$739$	418.919			0.566873			0.283436	−	0.958991i	$-0.408526\pi$
$739$	418.919			0.566873			0.283436	+	0.958991i	$0.408526\pi$
$740$	−486.580	+	203.609i	−0.657541	+	0.275147i
$741$		0			0
$742$	−71.4627	−	8.17021i	−0.0963109	−	0.0110111i
$743$	268.321			0.361131			0.180566	−	0.983563i	$-0.442207\pi$
$743$	268.321			0.361131			0.180566	+	0.983563i	$0.442207\pi$
$744$		0			0
$745$			582.288i			0.781594i
$746$	−63.9095	−	318.291i	−0.0856696	−	0.426664i
$747$		0			0
$748$	466.799	+	1115.55i	0.624063	+	1.49137i
$749$	−171.023	+	530.270i	−0.228336	+	0.707971i
$750$		0			0
$751$		−	113.223i		−	0.150764i	−0.997155	−	0.0753818i	$-0.975982\pi$
$751$		−	113.223i		−	0.150764i	0.997155	−	0.0753818i	$-0.0240175\pi$
$752$	−653.834	−	644.461i	−0.869460	−	0.856996i
$753$		0			0
$754$	725.064	−	145.585i	0.961623	−	0.193084i
$755$	−692.919			−0.917773
$756$		0			0
$757$			1322.83i			1.74746i	0.486412	+	0.873730i	$0.338305\pi$
$757$			1322.83i			1.74746i	−0.486412	+	0.873730i	$0.661695\pi$
$758$	−577.315	+	115.919i	−0.761629	+	0.152927i
$759$		0			0
$760$	−1473.02	+	995.818i	−1.93818	+	1.31029i
$761$	−897.995			−1.18002			−0.590010	−	0.807396i	$-0.700876\pi$
$761$	−897.995			−1.18002			−0.590010	+	0.807396i	$0.700876\pi$
$762$		0			0
$763$	−83.4877	+	258.859i	−0.109420	+	0.339265i
$764$	965.258	−	403.911i	1.26343	−	0.528680i
$765$		0			0
$766$	166.300	+	828.229i	0.217101	+	1.08124i
$767$	−554.906			−0.723476
$768$		0			0
$769$			228.027i			0.296524i	0.988948	+	0.148262i	$0.0473680\pi$
$769$			228.027i			0.296524i	−0.988948	+	0.148262i	$0.952632\pi$
$770$	1770.63	+	202.433i	2.29952	+	0.262900i
$771$		0			0
$772$	1100.37	−	460.450i	1.42535	−	0.596438i
$773$			529.260i			0.684683i	0.939576	+	0.342342i	$0.111220\pi$
$773$			529.260i			0.684683i	−0.939576	+	0.342342i	$0.888780\pi$
$774$		0			0
$775$	−447.210			−0.577045
$776$	−438.118	−	648.066i	−0.564585	−	0.835136i
$777$		0			0
$778$	430.493	−	86.4383i	0.553332	−	0.111103i
$779$		−	1068.75i		−	1.37195i
$780$		0			0
$781$			1379.57i			1.76642i
$782$	919.078	−	184.541i	1.17529	−	0.235986i
$783$		0			0
$784$	772.878	−	131.589i	0.985814	−	0.167842i
$785$			803.734i			1.02387i
$786$		0			0
$787$		−	954.787i		−	1.21320i	−0.795008	−	0.606599i	$-0.792533\pi$
$787$		−	954.787i		−	1.21320i	0.795008	−	0.606599i	$-0.207467\pi$
$788$	−54.3861	+	22.7578i	−0.0690179	+	0.0288805i
$789$		0			0
$790$	−464.392	+	93.2450i	−0.587838	+	0.118032i
$791$	164.288	−	509.385i	0.207696	−	0.643976i
$792$		0			0
$793$	505.780			0.637806
$794$	−320.522	+	64.3573i	−0.403680	+	0.0810546i
$795$		0			0
$796$	−19.0133	+	7.95610i	−0.0238861	+	0.00999510i
$797$		−	460.317i		−	0.577562i	−0.957395	−	0.288781i	$-0.906750\pi$
$797$		−	460.317i		−	0.577562i	0.957395	−	0.288781i	$-0.0932499\pi$
$798$		0			0
$799$		−	953.265i		−	1.19307i
$800$	−419.790	+	640.702i	−0.524738	+	0.800877i
$801$		0			0
$802$	−265.059	−	1320.08i	−0.330497	−	1.64599i
$803$	1890.75			2.35461
$804$		0			0
$805$	424.060	−	1314.83i	0.526783	−	1.63333i
$806$	−244.812	+	49.1557i	−0.303737	+	0.0609872i
$807$		0			0
$808$	−572.453	−	846.776i	−0.708482	−	1.04799i
$809$		−	801.362i		−	0.990559i	−0.868734	−	0.495279i	$-0.835066\pi$
$809$		−	801.362i		−	0.990559i	0.868734	−	0.495279i	$-0.164934\pi$
$810$		0			0
$811$			280.177i			0.345471i	0.984968	+	0.172736i	$0.0552607\pi$
$811$			280.177i			0.345471i	−0.984968	+	0.172736i	$0.944739\pi$
$812$	1543.83	−	130.486i	1.90127	−	0.160697i
$813$		0			0
$814$	−672.608	+	135.053i	−0.826300	+	0.165912i
$815$		−	1267.13i		−	1.55476i
$816$		0			0
$817$			454.892i			0.556783i
$818$	164.111	+	817.330i	0.200625	+	0.999181i
$819$		0			0
$820$	−363.350	−	868.325i	−0.443110	−	1.05893i
$821$	−766.775			−0.933953			−0.466976	−	0.884270i	$-0.654657\pi$
$821$	−766.775			−0.933953			−0.466976	+	0.884270i	$0.654657\pi$
$822$		0			0
$823$		−	534.131i		−	0.649005i	−0.945885	−	0.324503i	$-0.894803\pi$
$823$		−	534.131i		−	0.649005i	0.945885	−	0.324503i	$-0.105197\pi$
$824$	−423.978	+	286.626i	−0.514537	+	0.347847i
$825$		0			0
$826$	−1155.01	−	132.051i	−1.39832	−	0.159868i
$827$			558.663i			0.675529i	0.941231	+	0.337765i	$0.109671\pi$
$827$			558.663i			0.675529i	−0.941231	+	0.337765i	$0.890329\pi$
$828$		0			0
$829$	−343.185			−0.413974			−0.206987	−	0.978344i	$-0.566366\pi$
$829$	−343.185			−0.413974			−0.206987	+	0.978344i	$0.566366\pi$
$830$	350.325	+	1744.74i	0.422078	+	2.10209i
$831$		0			0
$832$	−159.378	+	396.875i	−0.191560	+	0.477014i
$833$	660.665	+	475.633i	0.793115	+	0.570987i
$834$		0			0
$835$	−892.556			−1.06893
$836$	−2133.33	+	892.690i	−2.55183	+	1.06781i
$837$		0			0
$838$	694.895	−	139.527i	0.829230	−	0.166501i
$839$			1321.98i			1.57566i	0.615890	+	0.787832i	$0.288797\pi$
$839$			1321.98i			1.57566i	−0.615890	+	0.787832i	$0.711203\pi$
$840$		0			0
$841$	2220.80			2.64066
$842$	−195.717	−	974.738i	−0.232443	−	1.15765i
$843$		0			0
$844$	400.073	−	167.410i	0.474020	−	0.198353i
$845$		−	869.846i		−	1.02940i
$846$		0			0
$847$	1399.92	+	451.504i	1.65280	+	0.533063i
$848$	57.7056	−	58.5449i	0.0680491	−	0.0690388i
$849$		0			0
$850$	−779.790	+	156.573i	−0.917400	+	0.184204i
$851$			531.808i			0.624922i
$852$		0			0
$853$	−521.818			−0.611744			−0.305872	−	0.952073i	$-0.598948\pi$
$853$	−521.818			−0.611744			−0.305872	+	0.952073i	$0.598948\pi$
$854$	1052.76	+	120.360i	1.23274	+	0.140937i
$855$		0			0
$856$	−356.628	−	527.526i	−0.416621	−	0.616268i
$857$	−891.115			−1.03981			−0.519904	−	0.854225i	$-0.674032\pi$
$857$	−891.115			−1.03981			−0.519904	+	0.854225i	$0.674032\pi$
$858$		0			0
$859$		−	730.878i		−	0.850847i	−0.904994	−	0.425424i	$-0.860125\pi$
$859$		−	730.878i		−	0.850847i	0.904994	−	0.425424i	$-0.139875\pi$
$860$	154.652	+	369.585i	0.179828	+	0.429750i
$861$		0			0
$862$	−522.401	+	104.893i	−0.606034	+	0.121685i
$863$	1079.58			1.25096			0.625480	−	0.780241i	$-0.284903\pi$
$863$	1079.58			1.25096			0.625480	+	0.780241i	$0.284903\pi$
$864$		0			0
$865$	334.170			0.386324
$866$	294.678	+	1467.60i	0.340275	+	1.69469i
$867$		0			0
$868$	−521.264	+	44.0576i	−0.600534	+	0.0507576i
$869$	−616.057			−0.708926
$870$		0			0
$871$	−118.046			−0.135529
$872$	−174.093	−	257.520i	−0.199648	−	0.295321i
$873$		0			0
$874$	352.910	+	1757.61i	0.403787	+	2.01100i
$875$	15.9806	−	49.5489i	0.0182635	−	0.0566273i
$876$		0			0
$877$		−	923.092i		−	1.05256i	−0.850312	−	0.526278i	$-0.823587\pi$
$877$		−	923.092i		−	1.05256i	0.850312	−	0.526278i	$-0.176413\pi$
$878$	1304.05	−	261.840i	1.48525	−	0.298223i
$879$		0			0
$880$	−1429.77	+	1450.56i	−1.62474	+	1.64837i
$881$	941.627			1.06882			0.534408	−	0.845227i	$-0.320535\pi$
$881$	941.627			1.06882			0.534408	+	0.845227i	$0.320535\pi$
$882$		0			0
$883$	1197.51			1.35618			0.678089	−	0.734980i	$-0.262808\pi$
$883$	1197.51			1.35618			0.678089	+	0.734980i	$0.262808\pi$
$884$	−409.663	+	171.423i	−0.463420	+	0.193918i
$885$		0			0
$886$	−79.7962	−	397.413i	−0.0900634	−	0.448547i
$887$			1387.04i			1.56375i	0.623437	+	0.781874i	$0.285736\pi$
$887$			1387.04i			1.56375i	−0.623437	+	0.781874i	$0.714264\pi$
$888$		0			0
$889$	−25.4867	+	79.0232i	−0.0286689	+	0.0888900i
$890$	87.2845	+	434.707i	0.0980725	+	0.488435i
$891$		0			0
$892$	490.108	−	205.085i	0.549448	−	0.229916i
$893$	1822.99			2.04142
$894$		0			0
$895$	1327.98			1.48378
$896$	−426.183	+	788.152i	−0.475651	+	0.879634i
$897$		0			0
$898$	298.854	+	1488.39i	0.332799	+	1.65746i
$899$	−1033.79			−1.14994
$900$		0			0
$901$	85.3562			0.0947350
$902$	−241.008	−	1200.30i	−0.267193	−	1.33071i
$903$		0			0
$904$	342.582	+	506.749i	0.378962	+	0.560563i
$905$		−	1563.91i		−	1.72808i
$906$		0			0
$907$	661.502			0.729329			0.364665	−	0.931139i	$-0.381184\pi$
$907$	661.502			0.729329			0.364665	+	0.931139i	$0.381184\pi$
$908$	−343.437	+	143.711i	−0.378235	+	0.158272i
$909$		0			0
$910$	−74.3396	+	650.229i	−0.0816919	+	0.714538i
$911$	256.300			0.281339			0.140669	−	0.990057i	$-0.455075\pi$
$911$	256.300			0.281339			0.140669	+	0.990057i	$0.455075\pi$
$912$		0			0
$913$			2314.55i			2.53510i
$914$	−431.090	+	86.5583i	−0.471652	+	0.0947027i
$915$		0			0
$916$	1492.92	−	624.709i	1.62982	−	0.681997i
$917$	720.823	+	232.481i	0.786066	+	0.253523i
$918$		0			0
$919$			1526.69i			1.66125i	0.556834	+	0.830624i	$0.312016\pi$
$919$			1526.69i			1.66125i	−0.556834	+	0.830624i	$0.687984\pi$
$920$	884.274	+	1308.02i	0.961168	+	1.42176i
$921$		0			0
$922$	−155.186	−	772.880i	−0.168315	−	0.838265i
$923$	−506.623			−0.548887
$924$		0			0
$925$		−	451.212i		−	0.487796i
$926$	162.063	+	807.130i	0.175014	+	0.871631i
$927$		0			0
$928$	−970.407	+	1481.08i	−1.04570	+	1.59599i
$929$	−181.855			−0.195753			−0.0978765	−	0.995199i	$-0.531205\pi$
$929$	−181.855			−0.195753			−0.0978765	+	0.995199i	$0.531205\pi$
$930$		0			0
$931$	−909.583	+	1263.43i	−0.976995	+	1.35707i
$932$	−188.652	−	450.837i	−0.202417	−	0.483731i
$933$		0			0
$934$	−878.646	+	176.423i	−0.940734	+	0.188889i
$935$	−2114.87			−2.26189
$936$		0			0
$937$		−	1347.05i		−	1.43763i	−0.695204	−	0.718813i	$-0.744686\pi$
$937$		−	1347.05i		−	1.43763i	0.695204	−	0.718813i	$-0.255314\pi$
$938$	−245.708	−	28.0914i	−0.261949	−	0.0299481i
$939$		0			0
$940$	1481.12	−	619.773i	1.57566	−	0.659333i
$941$		−	742.050i		−	0.788576i	−0.918987	−	0.394288i	$-0.870991\pi$
$941$		−	742.050i		−	0.788576i	0.918987	−	0.394288i	$-0.129009\pi$
$942$		0			0
$943$	−949.037			−1.00640
$944$	932.665	−	946.230i	0.987992	−	1.00236i
$945$		0			0
$946$	102.580	+	510.884i	0.108436	+	0.540046i
$947$		−	1393.76i		−	1.47176i	−0.677112	−	0.735880i	$-0.736769\pi$
$947$		−	1393.76i		−	1.47176i	0.677112	−	0.735880i	$-0.263231\pi$
$948$		0			0
$949$			694.342i			0.731657i
$950$	−299.426	−	1491.24i	−0.315185	−	1.56973i
$951$		0			0
$952$	−893.490	+	259.323i	−0.938540	+	0.272398i
$953$		−	1353.08i		−	1.41981i	−0.704295	−	0.709907i	$-0.748737\pi$
$953$		−	1353.08i		−	1.41981i	0.704295	−	0.709907i	$-0.251263\pi$
$954$		0			0
$955$			1829.95i			1.91618i
$956$	353.477	−	147.912i	0.369746	−	0.154720i
$957$		0			0
$958$	163.524	+	814.407i	0.170693	+	0.850112i
$959$	356.620	−	1105.73i	0.371867	−	1.15300i
$960$		0			0
$961$	−611.948			−0.636783
$962$	−49.5955	−	247.003i	−0.0515546	−	0.256760i
$963$		0			0
$964$	−240.004	−	573.557i	−0.248967	−	0.594976i
$965$			2086.10i			2.16176i
$966$		0			0
$967$		−	249.421i		−	0.257932i	−0.991649	−	0.128966i	$-0.958834\pi$
$967$		−	249.421i		−	0.257932i	0.991649	−	0.128966i	$-0.0411659\pi$
$968$	−1392.68	+	941.503i	−1.43871	+	0.972627i
$969$		0			0
$970$	1341.31	−	269.320i	1.38279	−	0.277650i
$971$	−462.662			−0.476480			−0.238240	−	0.971206i	$-0.576570\pi$
$971$	−462.662			−0.476480			−0.238240	+	0.971206i	$0.576570\pi$
$972$		0			0
$973$	−150.481	+	466.575i	−0.154656	+	0.479523i
$974$	−252.621	−	1258.14i	−0.259365	−	1.29173i
$975$		0			0
$976$	−850.097	+	862.461i	−0.871001	+	0.883669i
$977$			920.090i			0.941751i	0.882200	+	0.470875i	$0.156062\pi$
$977$			920.090i			0.941751i	−0.882200	+	0.470875i	$0.843938\pi$
$978$		0			0
$979$			576.677i			0.589047i
$980$	−309.469	+	1335.73i	−0.315785	+	1.36299i
$981$		0			0
$982$	−72.2447	−	359.804i	−0.0735690	−	0.366399i
$983$			529.109i			0.538259i	0.963104	+	0.269130i	$0.0867360\pi$
$983$			529.109i			0.538259i	−0.963104	+	0.269130i	$0.913264\pi$
$984$		0			0
$985$		−	103.106i		−	0.104676i
$986$	−1802.60	+	361.943i	−1.82820	+	0.367082i
$987$		0			0
$988$	−327.824	−	783.425i	−0.331805	−	0.792941i
$989$	403.938			0.408431
$990$		0			0
$991$			880.886i			0.888886i	0.895807	+	0.444443i	$0.146598\pi$
$991$			880.886i			0.888886i	−0.895807	+	0.444443i	$0.853402\pi$
$992$	327.650	−	500.074i	0.330293	−	0.504107i
$993$		0			0
$994$	−1054.51	−	120.561i	−1.06088	−	0.121289i
$995$		−	36.0457i		−	0.0362268i
$996$		0			0
$997$	1063.46			1.06666			0.533330	−	0.845907i	$-0.320940\pi$
$997$	1063.46			1.06666			0.533330	+	0.845907i	$0.320940\pi$
$998$	−347.665	+	69.8073i	−0.348361	+	0.0699472i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.e.c.251.46	yes	48
3.2	odd	2	inner	504.3.e.c.251.3	yes	48
4.3	odd	2		2016.3.e.c.1007.32		48
7.6	odd	2	inner	504.3.e.c.251.45	yes	48
8.3	odd	2	inner	504.3.e.c.251.2	yes	48
8.5	even	2		2016.3.e.c.1007.37		48
12.11	even	2		2016.3.e.c.1007.21		48
21.20	even	2	inner	504.3.e.c.251.4	yes	48
24.5	odd	2		2016.3.e.c.1007.2		48
24.11	even	2	inner	504.3.e.c.251.47	yes	48
28.27	even	2		2016.3.e.c.1007.1		48
56.13	odd	2		2016.3.e.c.1007.22		48
56.27	even	2	inner	504.3.e.c.251.1	✓	48
84.83	odd	2		2016.3.e.c.1007.38		48
168.83	odd	2	inner	504.3.e.c.251.48	yes	48
168.125	even	2		2016.3.e.c.1007.31		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.3.e.c.251.1	✓	48	56.27	even	2	inner
504.3.e.c.251.2	yes	48	8.3	odd	2	inner
504.3.e.c.251.3	yes	48	3.2	odd	2	inner
504.3.e.c.251.4	yes	48	21.20	even	2	inner
504.3.e.c.251.45	yes	48	7.6	odd	2	inner
504.3.e.c.251.46	yes	48	1.1	even	1	trivial
504.3.e.c.251.47	yes	48	24.11	even	2	inner
504.3.e.c.251.48	yes	48	168.83	odd	2	inner
2016.3.e.c.1007.1		48	28.27	even	2
2016.3.e.c.1007.2		48	24.5	odd	2
2016.3.e.c.1007.21		48	12.11	even	2
2016.3.e.c.1007.22		48	56.13	odd	2
2016.3.e.c.1007.31		48	168.125	even	2
2016.3.e.c.1007.32		48	4.3	odd	2
2016.3.e.c.1007.37		48	8.5	even	2
2016.3.e.c.1007.38		48	84.83	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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.96086 - 0.393720i) q^{2} +(3.68997 - 1.54406i) q^{4} +6.99549i q^{5} +(-6.66208 - 2.14866i) q^{7} +(6.62759 - 4.48051i) q^{8} +(2.75427 + 13.7172i) q^{10} +18.1971i q^{11} -6.68252 q^{13} +(-13.9094 - 1.59024i) q^{14} +(11.2317 - 11.3951i) q^{16} +16.6136 q^{17} +31.7713i q^{19} +(10.8015 + 25.8131i) q^{20} +(7.16455 + 35.6819i) q^{22} +28.2125 q^{23} -23.9368 q^{25} +(-13.1035 + 2.63105i) q^{26} +(-27.9005 + 2.35817i) q^{28} -55.3335 q^{29} +18.6829 q^{31} +(17.5374 - 26.7664i) q^{32} +(32.5770 - 6.54112i) q^{34} +(15.0309 - 46.6045i) q^{35} +18.8501i q^{37} +(12.5090 + 62.2991i) q^{38} +(31.3434 + 46.3632i) q^{40} -33.6389 q^{41} +14.3177 q^{43} +(28.0974 + 67.1466i) q^{44} +(55.3208 - 11.1078i) q^{46} -57.3785i q^{47} +(39.7665 + 28.6291i) q^{49} +(-46.9368 + 9.42441i) q^{50} +(-24.6583 + 10.3182i) q^{52} +5.13773 q^{53} -127.297 q^{55} +(-53.7806 + 15.6091i) q^{56} +(-108.501 + 21.7859i) q^{58} +83.0383 q^{59} -75.6870 q^{61} +(36.6347 - 7.35585i) q^{62} +(23.8500 - 59.3900i) q^{64} -46.7475i q^{65} +17.6649 q^{67} +(61.3037 - 25.6525i) q^{68} +(11.1245 - 97.3029i) q^{70} +75.8131 q^{71} -103.904i q^{73} +(7.42167 + 36.9625i) q^{74} +(49.0568 + 117.235i) q^{76} +(39.0993 - 121.230i) q^{77} +33.8548i q^{79} +(79.7142 + 78.5714i) q^{80} +(-65.9613 + 13.2443i) q^{82} +127.193 q^{83} +116.220i q^{85} +(28.0751 - 5.63718i) q^{86} +(81.5321 + 120.603i) q^{88} +31.6907 q^{89} +(44.5195 + 14.3585i) q^{91} +(104.103 - 43.5619i) q^{92} +(-22.5911 - 112.511i) q^{94} -222.255 q^{95} -97.7829i q^{97} +(89.2485 + 40.4809i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) \) 48 * q + 144 * q^22 - 336 * q^25 - 232 * q^28 - 384 * q^43 + 736 * q^46 + 368 * q^49 - 432 * q^58 + 480 * q^64 - 896 * q^67 + 264 * q^70 - 48 * q^88 - 576 * q^91

Introduction

L-functions

Modular forms

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Database

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