LMFDB - Embedded newform 560.3.v.b.223.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,3,Mod(223,560)] 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("560.223"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	560.v (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$15.2588948042$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.5
Character	$\chi$	$=$	560.223
Dual form			560.3.v.b.447.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.71375 - 2.71375i) q^{3} +(-4.98103 + 0.435186i) q^{5} +(4.64182 + 5.23961i) q^{7} +5.72885i q^{9} +8.05423i q^{11} +(12.1277 - 12.1277i) q^{13} +(14.6982 + 12.3363i) q^{15} +(4.68539 + 4.68539i) q^{17} -3.49526i q^{19} +(1.62225 - 26.8157i) q^{21} +(-4.14599 + 4.14599i) q^{23} +(24.6212 - 4.33534i) q^{25} +(-8.87708 + 8.87708i) q^{27} -42.7116i q^{29} -7.32494 q^{31} +(21.8572 - 21.8572i) q^{33} +(-25.4012 - 24.0786i) q^{35} +(-10.4184 + 10.4184i) q^{37} -65.8231 q^{39} -51.4638i q^{41} +(37.8696 - 37.8696i) q^{43} +(-2.49311 - 28.5355i) q^{45} +(-49.4674 + 49.4674i) q^{47} +(-5.90700 + 48.6426i) q^{49} -25.4299i q^{51} +(-49.7603 - 49.7603i) q^{53} +(-3.50509 - 40.1183i) q^{55} +(-9.48526 + 9.48526i) q^{57} -74.7661i q^{59} -43.1770i q^{61} +(-30.0169 + 26.5923i) q^{63} +(-55.1306 + 65.6862i) q^{65} +(-57.2502 - 57.2502i) q^{67} +22.5023 q^{69} -45.6576i q^{71} +(53.0254 - 53.0254i) q^{73} +(-78.5808 - 55.0508i) q^{75} +(-42.2010 + 37.3863i) q^{77} +96.4300 q^{79} +99.7399 q^{81} +(52.7822 + 52.7822i) q^{83} +(-25.3771 - 21.2990i) q^{85} +(-115.909 + 115.909i) q^{87} +31.9308 q^{89} +(119.839 + 7.24980i) q^{91} +(19.8780 + 19.8780i) q^{93} +(1.52109 + 17.4100i) q^{95} +(-19.5610 - 19.5610i) q^{97} -46.1415 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) $ 64 * q + 16 * q^21 - 72 * q^25 + 72 * q^37 + 272 * q^53 - 376 * q^57 - 88 * q^65 + 24 * q^77 - 432 * q^81 + 384 * q^85 + 840 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.71375	−	2.71375i	−0.904582	−	0.904582i	0.0912459	−	0.995828i	$-0.470915\pi$
$3$	−2.71375	−	2.71375i	−0.904582	−	0.904582i	−0.995828	+	0.0912459i	$0.970915\pi$
$4$		0			0
$5$	−4.98103	+	0.435186i	−0.996205	+	0.0870372i
$5$	−4.98103	+	0.435186i	−0.996205	+	0.0870372i
$6$		0			0
$7$	4.64182	+	5.23961i	0.663117	+	0.748516i
$7$	4.64182	+	5.23961i	0.663117	+	0.748516i
$8$		0			0
$9$			5.72885i			0.636539i
$10$		0			0
$11$			8.05423i			0.732203i	0.930575	+	0.366102i	$0.119308\pi$
$11$			8.05423i			0.732203i	−0.930575	+	0.366102i	$0.880692\pi$
$12$		0			0
$13$	12.1277	−	12.1277i	0.932901	−	0.932901i	−0.0649853	−	0.997886i	$-0.520700\pi$
$13$	12.1277	−	12.1277i	0.932901	−	0.932901i	0.997886	+	0.0649853i	$0.0207001\pi$
$14$		0			0
$15$	14.6982	+	12.3363i	0.979882	+	0.822417i
$16$		0			0
$17$	4.68539	+	4.68539i	0.275611	+	0.275611i	0.831354	−	0.555743i	$-0.187566\pi$
$17$	4.68539	+	4.68539i	0.275611	+	0.275611i	−0.555743	+	0.831354i	$0.687566\pi$
$18$		0			0
$19$		−	3.49526i		−	0.183961i	−0.995761	−	0.0919806i	$-0.970680\pi$
$19$		−	3.49526i		−	0.183961i	0.995761	−	0.0919806i	$-0.0293198\pi$
$20$		0			0
$21$	1.62225	−	26.8157i	0.0772498	−	1.27694i
$22$		0			0
$23$	−4.14599	+	4.14599i	−0.180260	+	0.180260i	−0.791469	−	0.611209i	$-0.790683\pi$
$23$	−4.14599	+	4.14599i	−0.180260	+	0.180260i	0.611209	+	0.791469i	$0.290683\pi$
$24$		0			0
$25$	24.6212	−	4.33534i	0.984849	−	0.173414i
$26$		0			0
$27$	−8.87708	+	8.87708i	−0.328781	+	0.328781i
$28$		0			0
$29$		−	42.7116i		−	1.47281i	−0.676539	−	0.736407i	$-0.736521\pi$
$29$		−	42.7116i		−	1.47281i	0.676539	−	0.736407i	$-0.263479\pi$
$30$		0			0
$31$	−7.32494			−0.236288			−0.118144	−	0.992996i	$-0.537694\pi$
$31$	−7.32494			−0.236288			−0.118144	+	0.992996i	$0.537694\pi$
$32$		0			0
$33$	21.8572	−	21.8572i	0.662338	−	0.662338i
$34$		0			0
$35$	−25.4012	−	24.0786i	−0.725749	−	0.687959i
$36$		0			0
$37$	−10.4184	+	10.4184i	−0.281579	+	0.281579i	−0.833739	−	0.552159i	$-0.813804\pi$
$37$	−10.4184	+	10.4184i	−0.281579	+	0.281579i	0.552159	+	0.833739i	$0.313804\pi$
$38$		0			0
$39$	−65.8231			−1.68777
$40$		0			0
$41$		−	51.4638i		−	1.25522i	−0.778530	−	0.627608i	$-0.784034\pi$
$41$		−	51.4638i		−	1.25522i	0.778530	−	0.627608i	$-0.215966\pi$
$42$		0			0
$43$	37.8696	−	37.8696i	0.880689	−	0.880689i	−0.112915	−	0.993605i	$-0.536019\pi$
$43$	37.8696	−	37.8696i	0.880689	−	0.880689i	0.993605	+	0.112915i	$0.0360188\pi$
$44$		0			0
$45$	−2.49311	−	28.5355i	−0.0554025	−	0.634123i
$46$		0			0
$47$	−49.4674	+	49.4674i	−1.05250	+	1.05250i	−0.0539550	+	0.998543i	$0.517183\pi$
$47$	−49.4674	+	49.4674i	−1.05250	+	1.05250i	−0.998543	+	0.0539550i	$0.982817\pi$
$48$		0			0
$49$	−5.90700	+	48.6426i	−0.120551	+	0.992707i
$50$		0			0
$51$		−	25.4299i		−	0.498626i
$52$		0			0
$53$	−49.7603	−	49.7603i	−0.938873	−	0.938873i	0.0593637	−	0.998236i	$-0.481093\pi$
$53$	−49.7603	−	49.7603i	−0.938873	−	0.938873i	−0.998236	+	0.0593637i	$0.981093\pi$
$54$		0			0
$55$	−3.50509	−	40.1183i	−0.0637289	−	0.729424i
$56$		0			0
$57$	−9.48526	+	9.48526i	−0.166408	+	0.166408i
$58$		0			0
$59$		−	74.7661i		−	1.26722i	−0.773652	−	0.633611i	$-0.781572\pi$
$59$		−	74.7661i		−	1.26722i	0.773652	−	0.633611i	$-0.218428\pi$
$60$		0			0
$61$		−	43.1770i		−	0.707820i	−0.935279	−	0.353910i	$-0.884852\pi$
$61$		−	43.1770i		−	0.707820i	0.935279	−	0.353910i	$-0.115148\pi$
$62$		0			0
$63$	−30.0169	+	26.5923i	−0.476459	+	0.422100i
$64$		0			0
$65$	−55.1306	+	65.6862i	−0.848164	+	1.01056i
$66$		0			0
$67$	−57.2502	−	57.2502i	−0.854481	−	0.854481i	0.136200	−	0.990681i	$-0.456511\pi$
$67$	−57.2502	−	57.2502i	−0.854481	−	0.854481i	−0.990681	+	0.136200i	$0.956511\pi$
$68$		0			0
$69$	22.5023			0.326121
$70$		0			0
$71$		−	45.6576i		−	0.643065i	−0.946899	−	0.321533i	$-0.895802\pi$
$71$		−	45.6576i		−	0.643065i	0.946899	−	0.321533i	$-0.104198\pi$
$72$		0			0
$73$	53.0254	−	53.0254i	0.726375	−	0.726375i	−0.243521	−	0.969896i	$-0.578302\pi$
$73$	53.0254	−	53.0254i	0.726375	−	0.726375i	0.969896	+	0.243521i	$0.0783024\pi$
$74$		0			0
$75$	−78.5808	−	55.0508i	−1.04774	−	0.734010i
$76$		0			0
$77$	−42.2010	+	37.3863i	−0.548065	+	0.485536i
$78$		0			0
$79$	96.4300			1.22063			0.610316	−	0.792158i	$-0.291042\pi$
$79$	96.4300			1.22063			0.610316	+	0.792158i	$0.291042\pi$
$80$		0			0
$81$	99.7399			1.23136
$82$		0			0
$83$	52.7822	+	52.7822i	0.635930	+	0.635930i	0.949549	−	0.313619i	$-0.101542\pi$
$83$	52.7822	+	52.7822i	0.635930	+	0.635930i	−0.313619	+	0.949549i	$0.601542\pi$
$84$		0			0
$85$	−25.3771	−	21.2990i	−0.298554	−	0.250577i
$86$		0			0
$87$	−115.909	+	115.909i	−1.33228	+	1.33228i
$88$		0			0
$89$	31.9308			0.358773			0.179387	−	0.983779i	$-0.442589\pi$
$89$	31.9308			0.358773			0.179387	+	0.983779i	$0.442589\pi$
$90$		0			0
$91$	119.839	+	7.24980i	1.31691	+	0.0796682i
$92$		0			0
$93$	19.8780	+	19.8780i	0.213742	+	0.213742i
$94$		0			0
$95$	1.52109	+	17.4100i	0.0160115	+	0.183263i
$96$		0			0
$97$	−19.5610	−	19.5610i	−0.201660	−	0.201660i	0.599051	−	0.800711i	$-0.295545\pi$
$97$	−19.5610	−	19.5610i	−0.201660	−	0.201660i	−0.800711	+	0.599051i	$0.795545\pi$
$98$		0			0
$99$	−46.1415			−0.466076
$100$		0			0
$101$			14.0986i			0.139591i	0.997561	+	0.0697953i	$0.0222346\pi$
$101$			14.0986i			0.139591i	−0.997561	+	0.0697953i	$0.977765\pi$
$102$		0			0
$103$	−2.99656	−	2.99656i	−0.0290928	−	0.0290928i	0.692411	−	0.721504i	$-0.256549\pi$
$103$	−2.99656	−	2.99656i	−0.0290928	−	0.0290928i	−0.721504	+	0.692411i	$0.756549\pi$
$104$		0			0
$105$	3.58937	+	134.276i	0.0341844	+	1.27882i
$106$		0			0
$107$	137.258	+	137.258i	1.28279	+	1.28279i	0.939074	+	0.343714i	$0.111685\pi$
$107$	137.258	+	137.258i	1.28279	+	1.28279i	0.343714	+	0.939074i	$0.388315\pi$
$108$		0			0
$109$		−	179.722i		−	1.64883i	−0.565988	−	0.824413i	$-0.691505\pi$
$109$		−	179.722i		−	1.64883i	0.565988	−	0.824413i	$-0.308495\pi$
$110$		0			0
$111$	56.5460			0.509424
$112$		0			0
$113$	−82.1352	−	82.1352i	−0.726860	−	0.726860i	0.243133	−	0.969993i	$-0.421825\pi$
$113$	−82.1352	−	82.1352i	−0.726860	−	0.726860i	−0.969993	+	0.243133i	$0.921825\pi$
$114$		0			0
$115$	18.8470	−	22.4555i	0.163887	−	0.195266i
$116$		0			0
$117$	69.4778	+	69.4778i	0.593828	+	0.593828i
$118$		0			0
$119$	−2.80087	+	46.2984i	−0.0235367	+	0.389062i
$120$		0			0
$121$	56.1293			0.463879
$122$		0			0
$123$	−139.660	+	139.660i	−1.13545	+	1.13545i
$124$		0			0
$125$	−120.752	+	32.3093i	−0.966018	+	0.258474i
$126$		0			0
$127$	44.7994	+	44.7994i	0.352751	+	0.352751i	0.861132	−	0.508381i	$-0.169756\pi$
$127$	44.7994	+	44.7994i	0.352751	+	0.352751i	−0.508381	+	0.861132i	$0.669756\pi$
$128$		0			0
$129$	−205.537			−1.59331
$130$		0			0
$131$	−60.1169			−0.458908			−0.229454	−	0.973320i	$-0.573694\pi$
$131$	−60.1169			−0.458908			−0.229454	+	0.973320i	$0.573694\pi$
$132$		0			0
$133$	18.3138	−	16.2244i	0.137698	−	0.121988i
$134$		0			0
$135$	40.3538	−	48.0801i	0.298917	−	0.356149i
$136$		0			0
$137$	173.938	−	173.938i	1.26962	−	1.26962i	0.323340	−	0.946283i	$-0.395194\pi$
$137$	173.938	−	173.938i	1.26962	−	1.26962i	0.946283	−	0.323340i	$-0.104806\pi$
$138$		0			0
$139$		−	232.112i		−	1.66987i	−0.550350	−	0.834934i	$-0.685506\pi$
$139$		−	232.112i		−	1.66987i	0.550350	−	0.834934i	$-0.314494\pi$
$140$		0			0
$141$	268.484			1.90414
$142$		0			0
$143$	97.6794	+	97.6794i	0.683073	+	0.683073i
$144$		0			0
$145$	18.5875	+	212.748i	0.128190	+	1.46723i
$146$		0			0
$147$	148.034	−	115.974i	1.00703	−	0.788937i
$148$		0			0
$149$		−	3.10175i		−	0.0208171i	−0.999946	−	0.0104085i	$-0.996687\pi$
$149$		−	3.10175i		−	0.0208171i	0.999946	−	0.0104085i	$-0.00331320\pi$
$150$		0			0
$151$		−	146.600i		−	0.970859i	−0.874276	−	0.485429i	$-0.838663\pi$
$151$		−	146.600i		−	0.970859i	0.874276	−	0.485429i	$-0.161337\pi$
$152$		0			0
$153$	−26.8419	+	26.8419i	−0.175437	+	0.175437i
$154$		0			0
$155$	36.4857	−	3.18771i	0.235392	−	0.0205659i
$156$		0			0
$157$	202.634	+	202.634i	1.29066	+	1.29066i	0.934378	+	0.356284i	$0.115956\pi$
$157$	202.634	+	202.634i	1.29066	+	1.29066i	0.356284	+	0.934378i	$0.384044\pi$
$158$		0			0
$159$			270.074i			1.69858i
$160$		0			0
$161$	−40.9683	−	2.47842i	−0.254461	−	0.0153939i
$162$		0			0
$163$	−92.8155	+	92.8155i	−0.569420	+	0.569420i	−0.931966	−	0.362546i	$-0.881908\pi$
$163$	−92.8155	+	92.8155i	−0.569420	+	0.569420i	0.362546	+	0.931966i	$0.381908\pi$
$164$		0			0
$165$	−99.3591	+	118.383i	−0.602176	+	0.717473i
$166$		0			0
$167$	25.5085	−	25.5085i	0.152745	−	0.152745i	−0.626598	−	0.779343i	$-0.715553\pi$
$167$	25.5085	−	25.5085i	0.152745	−	0.152745i	0.779343	+	0.626598i	$0.215553\pi$
$168$		0			0
$169$		−	125.163i		−	0.740608i
$170$		0			0
$171$	20.0238			0.117098
$172$		0			0
$173$	−204.836	+	204.836i	−1.18402	+	1.18402i	−0.205331	+	0.978693i	$0.565827\pi$
$173$	−204.836	+	204.836i	−1.18402	+	1.18402i	−0.978693	+	0.205331i	$0.934173\pi$
$174$		0			0
$175$	137.003	+	108.882i	0.782873	+	0.622181i
$176$		0			0
$177$	−202.896	+	202.896i	−1.14631	+	1.14631i
$178$		0			0
$179$	−8.40197			−0.0469384			−0.0234692	−	0.999725i	$-0.507471\pi$
$179$	−8.40197			−0.0469384			−0.0234692	+	0.999725i	$0.507471\pi$
$180$		0			0
$181$		−	15.1006i		−	0.0834286i	−0.999130	−	0.0417143i	$-0.986718\pi$
$181$		−	15.1006i		−	0.0834286i	0.999130	−	0.0417143i	$-0.0132819\pi$
$182$		0			0
$183$	−117.172	+	117.172i	−0.640282	+	0.640282i
$184$		0			0
$185$	47.3605	−	56.4285i	0.256003	−	0.305019i
$186$		0			0
$187$	−37.7372	+	37.7372i	−0.201803	+	0.201803i
$188$		0			0
$189$	−87.7182	−	5.30661i	−0.464117	−	0.0280773i
$190$		0			0
$191$		−	245.069i		−	1.28308i	−0.767089	−	0.641541i	$-0.778295\pi$
$191$		−	245.069i		−	1.28308i	0.767089	−	0.641541i	$-0.221705\pi$
$192$		0			0
$193$	−90.6786	−	90.6786i	−0.469837	−	0.469837i	0.432025	−	0.901862i	$-0.357799\pi$
$193$	−90.6786	−	90.6786i	−0.469837	−	0.469837i	−0.901862	+	0.432025i	$0.857799\pi$
$194$		0			0
$195$	327.866	−	28.6453i	1.68137	−	0.146899i
$196$		0			0
$197$	−203.386	+	203.386i	−1.03242	+	1.03242i	−0.0329592	+	0.999457i	$0.510493\pi$
$197$	−203.386	+	203.386i	−1.03242	+	1.03242i	−0.999457	+	0.0329592i	$0.989507\pi$
$198$		0			0
$199$			73.2624i			0.368153i	0.982912	+	0.184076i	$0.0589294\pi$
$199$			73.2624i			0.368153i	−0.982912	+	0.184076i	$0.941071\pi$
$200$		0			0
$201$			310.725i			1.54590i
$202$		0			0
$203$	223.792	−	198.260i	1.10242	−	0.976649i
$204$		0			0
$205$	22.3963	+	256.343i	0.109250	+	1.25045i
$206$		0			0
$207$	−23.7517	−	23.7517i	−0.114743	−	0.114743i
$208$		0			0
$209$	28.1517			0.134697
$210$		0			0
$211$		−	138.457i		−	0.656193i	−0.944644	−	0.328096i	$-0.893593\pi$
$211$		−	138.457i		−	0.656193i	0.944644	−	0.328096i	$-0.106407\pi$
$212$		0			0
$213$	−123.903	+	123.903i	−0.581705	+	0.581705i
$214$		0			0
$215$	−172.149	+	205.110i	−0.800695	+	0.954000i
$216$		0			0
$217$	−34.0010	−	38.3798i	−0.156687	−	0.176865i
$218$		0			0
$219$	−287.795			−1.31413
$220$		0			0
$221$	113.646			0.514236
$222$		0			0
$223$	138.952	+	138.952i	0.623102	+	0.623102i	0.946323	−	0.323222i	$-0.104766\pi$
$223$	138.952	+	138.952i	0.623102	+	0.623102i	−0.323222	+	0.946323i	$0.604766\pi$
$224$		0			0
$225$	24.8365	+	141.051i	0.110385	+	0.626895i
$226$		0			0
$227$	106.358	−	106.358i	0.468539	−	0.468539i	−0.432902	−	0.901441i	$-0.642510\pi$
$227$	106.358	−	106.358i	0.468539	−	0.468539i	0.901441	+	0.432902i	$0.142510\pi$
$228$		0			0
$229$	262.879			1.14794			0.573971	−	0.818875i	$-0.305402\pi$
$229$	262.879			1.14794			0.573971	+	0.818875i	$0.305402\pi$
$230$		0			0
$231$	215.980	+	13.0659i	0.934978	+	0.0565625i
$232$		0			0
$233$	−99.0110	−	99.0110i	−0.424940	−	0.424940i	0.461960	−	0.886901i	$-0.347146\pi$
$233$	−99.0110	−	99.0110i	−0.424940	−	0.424940i	−0.886901	+	0.461960i	$0.847146\pi$
$234$		0			0
$235$	224.871	−	267.926i	0.956898	−	1.14011i
$236$		0			0
$237$	−261.687	−	261.687i	−1.10416	−	1.10416i
$238$		0			0
$239$	−238.546			−0.998101			−0.499050	−	0.866573i	$-0.666318\pi$
$239$	−238.546			−0.998101			−0.499050	+	0.866573i	$0.666318\pi$
$240$		0			0
$241$			407.926i			1.69264i	0.532675	+	0.846320i	$0.321187\pi$
$241$			407.926i			1.69264i	−0.532675	+	0.846320i	$0.678813\pi$
$242$		0			0
$243$	−190.775	−	190.775i	−0.785083	−	0.785083i
$244$		0			0
$245$	8.25433	−	244.861i	0.0336911	−	0.999432i
$246$		0			0
$247$	−42.3896	−	42.3896i	−0.171618	−	0.171618i
$248$		0			0
$249$		−	286.475i		−	1.15050i
$250$		0			0
$251$	85.4034			0.340253			0.170126	−	0.985422i	$-0.445582\pi$
$251$	85.4034			0.340253			0.170126	+	0.985422i	$0.445582\pi$
$252$		0			0
$253$	−33.3927	−	33.3927i	−0.131987	−	0.131987i
$254$		0			0
$255$	11.0667	+	126.667i	0.0433990	+	0.496734i
$256$		0			0
$257$	−66.5808	−	66.5808i	−0.259069	−	0.259069i	0.565606	−	0.824675i	$-0.308642\pi$
$257$	−66.5808	−	66.5808i	−0.259069	−	0.259069i	−0.824675	+	0.565606i	$0.808642\pi$
$258$		0			0
$259$	−102.949	−	6.22802i	−0.397487	−	0.0240464i
$260$		0			0
$261$	244.688			0.937503
$262$		0			0
$263$	−16.8482	+	16.8482i	−0.0640617	+	0.0640617i	−0.738412	−	0.674350i	$-0.764424\pi$
$263$	−16.8482	+	16.8482i	−0.0640617	+	0.0640617i	0.674350	+	0.738412i	$0.264424\pi$
$264$		0			0
$265$	269.512	+	226.202i	1.01703	+	0.853593i
$266$		0			0
$267$	−86.6521	−	86.6521i	−0.324540	−	0.324540i
$268$		0			0
$269$	4.72680			0.0175717			0.00878587	−	0.999961i	$-0.497203\pi$
$269$	4.72680			0.0175717			0.00878587	+	0.999961i	$0.497203\pi$
$270$		0			0
$271$	−487.131			−1.79753			−0.898766	−	0.438429i	$-0.855535\pi$
$271$	−487.131			−1.79753			−0.898766	+	0.438429i	$0.855535\pi$
$272$		0			0
$273$	−305.539	−	344.887i	−1.11919	−	1.26332i
$274$		0			0
$275$	34.9179	+	198.305i	0.126974	+	0.721109i
$276$		0			0
$277$	−318.759	+	318.759i	−1.15076	+	1.15076i	−0.164355	+	0.986401i	$0.552554\pi$
$277$	−318.759	+	318.759i	−1.15076	+	1.15076i	−0.986401	+	0.164355i	$0.947446\pi$
$278$		0			0
$279$		−	41.9635i		−	0.150407i
$280$		0			0
$281$	318.579			1.13373			0.566866	−	0.823810i	$-0.308156\pi$
$281$	318.579			1.13373			0.566866	+	0.823810i	$0.308156\pi$
$282$		0			0
$283$	−273.197	−	273.197i	−0.965362	−	0.965362i	0.0340583	−	0.999420i	$-0.489157\pi$
$283$	−273.197	−	273.197i	−0.965362	−	0.965362i	−0.999420	+	0.0340583i	$0.989157\pi$
$284$		0			0
$285$	43.1185	−	51.3742i	0.151293	−	0.180260i
$286$		0			0
$287$	269.650	−	238.886i	0.939548	−	0.832355i
$288$		0			0
$289$		−	245.094i		−	0.848077i
$290$		0			0
$291$			106.167i			0.364836i
$292$		0			0
$293$	−232.872	+	232.872i	−0.794784	+	0.794784i	−0.982268	−	0.187484i	$-0.939967\pi$
$293$	−232.872	+	232.872i	−0.794784	+	0.794784i	0.187484	+	0.982268i	$0.439967\pi$
$294$		0			0
$295$	32.5371	+	372.412i	0.110295	+	1.26241i
$296$		0			0
$297$	−71.4980	−	71.4980i	−0.240734	−	0.240734i
$298$		0			0
$299$			100.563i			0.336330i
$300$		0			0
$301$	374.206	+	22.6380i	1.24321	+	0.0752094i
$302$		0			0
$303$	38.2602	−	38.2602i	0.126271	−	0.126271i
$304$		0			0
$305$	18.7900	+	215.066i	0.0616067	+	0.705134i
$306$		0			0
$307$	359.855	−	359.855i	1.17217	−	1.17217i	0.190475	−	0.981692i	$-0.438997\pi$
$307$	359.855	−	359.855i	1.17217	−	1.17217i	0.981692	−	0.190475i	$-0.0610030\pi$
$308$		0			0
$309$			16.2638i			0.0526337i
$310$		0			0
$311$	−478.684			−1.53918			−0.769588	−	0.638541i	$-0.779538\pi$
$311$	−478.684			−1.53918			−0.769588	+	0.638541i	$0.779538\pi$
$312$		0			0
$313$	199.146	−	199.146i	0.636248	−	0.636248i	−0.313380	−	0.949628i	$-0.601461\pi$
$313$	199.146	−	199.146i	0.636248	−	0.636248i	0.949628	+	0.313380i	$0.101461\pi$
$314$		0			0
$315$	137.942	−	145.520i	0.437913	−	0.461968i
$316$		0			0
$317$	356.804	−	356.804i	1.12556	−	1.12556i	0.134675	−	0.990890i	$-0.457001\pi$
$317$	356.804	−	356.804i	1.12556	−	1.12556i	0.990890	−	0.134675i	$-0.0429990\pi$
$318$		0			0
$319$	344.009			1.07840
$320$		0			0
$321$		−	744.969i		−	2.32078i
$322$		0			0
$323$	16.3767	−	16.3767i	0.0507018	−	0.0507018i
$324$		0			0
$325$	246.021	−	351.177i	0.756989	−	1.08054i
$326$		0			0
$327$	−487.720	+	487.720i	−1.49150	+	1.49150i
$328$		0			0
$329$	−488.809	−	29.5710i	−1.48574	−	0.0898816i
$330$		0			0
$331$			138.262i			0.417711i	0.977946	+	0.208856i	$0.0669739\pi$
$331$			138.262i			0.417711i	−0.977946	+	0.208856i	$0.933026\pi$
$332$		0			0
$333$	−59.6857	−	59.6857i	−0.179236	−	0.179236i
$334$		0			0
$335$	310.079	+	260.250i	0.925610	+	0.776867i
$336$		0			0
$337$	−64.3676	+	64.3676i	−0.191002	+	0.191002i	−0.796129	−	0.605127i	$-0.793122\pi$
$337$	−64.3676	+	64.3676i	−0.191002	+	0.191002i	0.605127	+	0.796129i	$0.293122\pi$
$338$		0			0
$339$			445.788i			1.31501i
$340$		0			0
$341$		−	58.9968i		−	0.173011i
$342$		0			0
$343$	−282.288	+	194.840i	−0.822996	+	0.568047i
$344$		0			0
$345$	−112.085	+	9.79269i	−0.324883	+	0.0283846i
$346$		0			0
$347$	250.905	+	250.905i	0.723070	+	0.723070i	0.969229	−	0.246160i	$-0.0791688\pi$
$347$	250.905	+	250.905i	0.723070	+	0.723070i	−0.246160	+	0.969229i	$0.579169\pi$
$348$		0			0
$349$	638.808			1.83040			0.915198	−	0.403006i	$-0.132034\pi$
$349$	638.808			1.83040			0.915198	+	0.403006i	$0.132034\pi$
$350$		0			0
$351$			215.317i			0.613439i
$352$		0			0
$353$	233.730	−	233.730i	0.662125	−	0.662125i	−0.293756	−	0.955881i	$-0.594905\pi$
$353$	233.730	−	233.730i	0.662125	−	0.662125i	0.955881	+	0.293756i	$0.0949052\pi$
$354$		0			0
$355$	19.8695	+	227.422i	0.0559706	+	0.640625i
$356$		0			0
$357$	133.243	−	118.041i	0.373229	−	0.330648i
$358$		0			0
$359$	182.850			0.509330			0.254665	−	0.967029i	$-0.418035\pi$
$359$	182.850			0.509330			0.254665	+	0.967029i	$0.418035\pi$
$360$		0			0
$361$	348.783			0.966158
$362$		0			0
$363$	−152.321	−	152.321i	−0.419617	−	0.419617i
$364$		0			0
$365$	−241.045	+	287.197i	−0.660397	+	0.786840i
$366$		0			0
$367$	342.311	−	342.311i	0.932728	−	0.932728i	−0.0651473	−	0.997876i	$-0.520752\pi$
$367$	342.311	−	342.311i	0.932728	−	0.932728i	0.997876	+	0.0651473i	$0.0207517\pi$
$368$		0			0
$369$	294.829			0.798993
$370$		0			0
$371$	29.7461	−	491.702i	0.0801781	−	1.32534i
$372$		0			0
$373$	−270.236	−	270.236i	−0.724492	−	0.724492i	0.245025	−	0.969517i	$-0.421204\pi$
$373$	−270.236	−	270.236i	−0.724492	−	0.724492i	−0.969517	+	0.245025i	$0.921204\pi$
$374$		0			0
$375$	415.370	+	240.012i	1.10765	+	0.640032i
$376$		0			0
$377$	−517.994	−	517.994i	−1.37399	−	1.37399i
$378$		0			0
$379$	−210.014			−0.554126			−0.277063	−	0.960852i	$-0.589361\pi$
$379$	−210.014			−0.554126			−0.277063	+	0.960852i	$0.589361\pi$
$380$		0			0
$381$		−	243.148i		−	0.638185i
$382$		0			0
$383$	−88.6754	−	88.6754i	−0.231529	−	0.231529i	0.581802	−	0.813330i	$-0.302348\pi$
$383$	−88.6754	−	88.6754i	−0.231529	−	0.231529i	−0.813330	+	0.581802i	$0.802348\pi$
$384$		0			0
$385$	193.934	−	204.587i	0.503726	−	0.531396i
$386$		0			0
$387$	216.949	+	216.949i	0.560593	+	0.560593i
$388$		0			0
$389$			536.468i			1.37909i	0.724241	+	0.689547i	$0.242191\pi$
$389$			536.468i			1.37909i	−0.724241	+	0.689547i	$0.757809\pi$
$390$		0			0
$391$	−38.8511			−0.0993635
$392$		0			0
$393$	163.142	+	163.142i	0.415120	+	0.415120i
$394$		0			0
$395$	−480.320	+	41.9650i	−1.21600	+	0.106240i
$396$		0			0
$397$	417.941	+	417.941i	1.05275	+	1.05275i	0.998529	+	0.0542180i	$0.0172666\pi$
$397$	417.941	+	417.941i	1.05275	+	1.05275i	0.0542180	+	0.998529i	$0.482733\pi$
$398$		0			0
$399$	−93.7280	−	5.67018i	−0.234907	−	0.0142110i
$400$		0			0
$401$	192.581			0.480252			0.240126	−	0.970742i	$-0.422811\pi$
$401$	192.581			0.480252			0.240126	+	0.970742i	$0.422811\pi$
$402$		0			0
$403$	−88.8347	+	88.8347i	−0.220434	+	0.220434i
$404$		0			0
$405$	−496.807	+	43.4054i	−1.22668	+	0.107174i
$406$		0			0
$407$	−83.9125	−	83.9125i	−0.206173	−	0.206173i
$408$		0			0
$409$	−339.059			−0.828994			−0.414497	−	0.910051i	$-0.636042\pi$
$409$	−339.059			−0.828994			−0.414497	+	0.910051i	$0.636042\pi$
$410$		0			0
$411$	−944.049			−2.29696
$412$		0			0
$413$	391.745	−	347.051i	0.948535	−	0.840317i
$414$		0			0
$415$	−285.879	−	239.939i	−0.688866	−	0.578167i
$416$		0			0
$417$	−629.892	+	629.892i	−1.51053	+	1.51053i
$418$		0			0
$419$		−	498.049i		−	1.18866i	−0.804221	−	0.594330i	$-0.797417\pi$
$419$		−	498.049i		−	1.18866i	0.804221	−	0.594330i	$-0.202583\pi$
$420$		0			0
$421$	−397.097			−0.943223			−0.471611	−	0.881807i	$-0.656327\pi$
$421$	−397.097			−0.943223			−0.471611	+	0.881807i	$0.656327\pi$
$422$		0			0
$423$	−283.391	−	283.391i	−0.669956	−	0.669956i
$424$		0			0
$425$	135.673	+	95.0473i	0.319230	+	0.223641i
$426$		0			0
$427$	226.231	−	200.420i	0.529815	−	0.469368i
$428$		0			0
$429$		−	530.155i		−	1.23579i
$430$		0			0
$431$			40.8156i			0.0946998i	0.998878	+	0.0473499i	$0.0150776\pi$
$431$			40.8156i			0.0946998i	−0.998878	+	0.0473499i	$0.984922\pi$
$432$		0			0
$433$	298.631	−	298.631i	0.689679	−	0.689679i	−0.272482	−	0.962161i	$-0.587845\pi$
$433$	298.631	−	298.631i	0.689679	−	0.689679i	0.962161	+	0.272482i	$0.0878445\pi$
$434$		0			0
$435$	526.902	−	627.785i	1.21127	−	1.44318i
$436$		0			0
$437$	14.4913	+	14.4913i	0.0331609	+	0.0331609i
$438$		0			0
$439$		−	522.507i		−	1.19022i	−0.803644	−	0.595111i	$-0.797108\pi$
$439$		−	522.507i		−	1.19022i	0.803644	−	0.595111i	$-0.202892\pi$
$440$		0			0
$441$	−278.666	−	33.8403i	−0.631897	−	0.0767354i
$442$		0			0
$443$	−254.833	+	254.833i	−0.575245	+	0.575245i	−0.933589	−	0.358345i	$-0.883341\pi$
$443$	−254.833	+	254.833i	−0.575245	+	0.575245i	0.358345	+	0.933589i	$0.383341\pi$
$444$		0			0
$445$	−159.048	+	13.8958i	−0.357412	+	0.0312266i
$446$		0			0
$447$	−8.41736	+	8.41736i	−0.0188308	+	0.0188308i
$448$		0			0
$449$		−	15.4094i		−	0.0343194i	−0.999853	−	0.0171597i	$-0.994538\pi$
$449$		−	15.4094i		−	0.0343194i	0.999853	−	0.0171597i	$-0.00546237\pi$
$450$		0			0
$451$	414.502			0.919073
$452$		0			0
$453$	−397.835	+	397.835i	−0.878222	+	0.878222i
$454$		0			0
$455$	−600.077	+	16.0408i	−1.31885	+	0.0352546i
$456$		0			0
$457$	89.3021	−	89.3021i	0.195409	−	0.195409i	−0.602619	−	0.798029i	$-0.705876\pi$
$457$	89.3021	−	89.3021i	0.195409	−	0.195409i	0.798029	+	0.602619i	$0.205876\pi$
$458$		0			0
$459$	−83.1851			−0.181231
$460$		0			0
$461$		−	519.204i		−	1.12626i	−0.826370	−	0.563128i	$-0.809598\pi$
$461$		−	519.204i		−	1.12626i	0.826370	−	0.563128i	$-0.190402\pi$
$462$		0			0
$463$	−123.120	+	123.120i	−0.265918	+	0.265918i	−0.827453	−	0.561535i	$-0.810211\pi$
$463$	−123.120	+	123.120i	−0.265918	+	0.265918i	0.561535	+	0.827453i	$0.310211\pi$
$464$		0			0
$465$	−107.664	−	90.3623i	−0.231535	−	0.194328i
$466$		0			0
$467$	−398.255	+	398.255i	−0.852795	+	0.852795i	−0.990477	−	0.137681i	$-0.956035\pi$
$467$	−398.255	+	398.255i	−0.852795	+	0.852795i	0.137681	+	0.990477i	$0.456035\pi$
$468$		0			0
$469$	34.2235	−	565.714i	0.0729712	−	1.20621i
$470$		0			0
$471$		−	1099.79i		−	2.33502i
$472$		0			0
$473$	305.011	+	305.011i	0.644843	+	0.644843i
$474$		0			0
$475$	−15.1532	−	86.0577i	−0.0319014	−	0.181174i
$476$		0			0
$477$	285.069	−	285.069i	0.597629	−	0.597629i
$478$		0			0
$479$			838.869i			1.75129i	0.482954	+	0.875646i	$0.339564\pi$
$479$			838.869i			1.75129i	−0.482954	+	0.875646i	$0.660436\pi$
$480$		0			0
$481$			252.704i			0.525371i
$482$		0			0
$483$	104.452	+	117.903i	0.216256	+	0.244106i
$484$		0			0
$485$	105.947	+	88.9212i	0.218447	+	0.183343i
$486$		0			0
$487$	−612.108	−	612.108i	−1.25690	−	1.25690i	−0.952567	−	0.304329i	$-0.901568\pi$
$487$	−612.108	−	612.108i	−1.25690	−	1.25690i	−0.304329	−	0.952567i	$-0.598432\pi$
$488$		0			0
$489$	503.755			1.03017
$490$		0			0
$491$		−	301.186i		−	0.613413i	−0.951804	−	0.306707i	$-0.900773\pi$
$491$		−	301.186i		−	0.613413i	0.951804	−	0.306707i	$-0.0992270\pi$
$492$		0			0
$493$	200.121	−	200.121i	0.405924	−	0.405924i
$494$		0			0
$495$	229.832	−	20.0801i	0.464307	−	0.0405659i
$496$		0			0
$497$	239.228	−	211.934i	0.481344	−	0.426428i
$498$		0			0
$499$	−717.539			−1.43795			−0.718977	−	0.695034i	$-0.755389\pi$
$499$	−717.539			−1.43795			−0.718977	+	0.695034i	$0.755389\pi$
$500$		0			0
$501$	−138.447			−0.276341
$502$		0			0
$503$	126.415	+	126.415i	0.251322	+	0.251322i	0.821513	−	0.570190i	$-0.193131\pi$
$503$	126.415	+	126.415i	0.251322	+	0.251322i	−0.570190	+	0.821513i	$0.693131\pi$
$504$		0			0
$505$	−6.13553	−	70.2257i	−0.0121496	−	0.139061i
$506$		0			0
$507$	−339.660	+	339.660i	−0.669941	+	0.669941i
$508$		0			0
$509$	−530.977			−1.04318			−0.521588	−	0.853197i	$-0.674660\pi$
$509$	−530.977			−1.04318			−0.521588	+	0.853197i	$0.674660\pi$
$510$		0			0
$511$	523.966	+	31.6979i	1.02537	+	0.0620312i
$512$		0			0
$513$	31.0277	+	31.0277i	0.0604829	+	0.0604829i
$514$		0			0
$515$	16.2300	+	13.6219i	0.0315146	+	0.0264502i
$516$		0			0
$517$	−398.422	−	398.422i	−0.770642	−	0.770642i
$518$		0			0
$519$	1111.75			2.14209
$520$		0			0
$521$			510.712i			0.980252i	0.871651	+	0.490126i	$0.163049\pi$
$521$			510.712i			0.980252i	−0.871651	+	0.490126i	$0.836951\pi$
$522$		0			0
$523$	396.043	+	396.043i	0.757253	+	0.757253i	0.975822	−	0.218569i	$-0.0701387\pi$
$523$	396.043	+	396.043i	0.757253	+	0.757253i	−0.218569	+	0.975822i	$0.570139\pi$
$524$		0			0
$525$	−76.3136	−	667.268i	−0.145359	−	1.27099i
$526$		0			0
$527$	−34.3202	−	34.3202i	−0.0651237	−	0.0651237i
$528$		0			0
$529$			494.622i			0.935012i
$530$		0			0
$531$	428.324			0.806636
$532$		0			0
$533$	−624.139	−	624.139i	−1.17099	−	1.17099i
$534$		0			0
$535$	−743.420	−	623.954i	−1.38957	−	1.16627i
$536$		0			0
$537$	22.8008	+	22.8008i	0.0424596	+	0.0424596i
$538$		0			0
$539$	−391.779	−	47.5764i	−0.726863	−	0.0882678i
$540$		0			0
$541$	−444.659			−0.821920			−0.410960	−	0.911653i	$-0.634806\pi$
$541$	−444.659			−0.821920			−0.410960	+	0.911653i	$0.634806\pi$
$542$		0			0
$543$	−40.9792	+	40.9792i	−0.0754681	+	0.0754681i
$544$		0			0
$545$	78.2125	+	895.200i	0.143509	+	1.64257i
$546$		0			0
$547$	472.552	+	472.552i	0.863898	+	0.863898i	0.991788	−	0.127890i	$-0.0408206\pi$
$547$	472.552	+	472.552i	0.863898	+	0.863898i	−0.127890	+	0.991788i	$0.540821\pi$
$548$		0			0
$549$	247.355			0.450555
$550$		0			0
$551$	−149.288			−0.270941
$552$		0			0
$553$	447.611	+	505.255i	0.809423	+	0.913663i
$554$		0			0
$555$	−281.657	+	24.6080i	−0.507490	+	0.0443388i
$556$		0			0
$557$	−160.293	+	160.293i	−0.287779	+	0.287779i	−0.836201	−	0.548422i	$-0.815229\pi$
$557$	−160.293	+	160.293i	−0.287779	+	0.287779i	0.548422	+	0.836201i	$0.315229\pi$
$558$		0			0
$559$		−	918.544i		−	1.64319i
$560$		0			0
$561$	204.819			0.365096
$562$		0			0
$563$	389.168	+	389.168i	0.691240	+	0.691240i	0.962505	−	0.271265i	$-0.0874418\pi$
$563$	389.168	+	389.168i	0.691240	+	0.691240i	−0.271265	+	0.962505i	$0.587442\pi$
$564$		0			0
$565$	444.861	+	373.373i	0.787365	+	0.660838i
$566$		0			0
$567$	462.975	+	522.598i	0.816534	+	0.921690i
$568$		0			0
$569$			282.418i			0.496342i	0.968716	+	0.248171i	$0.0798294\pi$
$569$			282.418i			0.496342i	−0.968716	+	0.248171i	$0.920171\pi$
$570$		0			0
$571$			820.860i			1.43758i	0.695225	+	0.718792i	$0.255305\pi$
$571$			820.860i			1.43758i	−0.695225	+	0.718792i	$0.744695\pi$
$572$		0			0
$573$	−665.055	+	665.055i	−1.16065	+	1.16065i
$574$		0			0
$575$	−84.1050	+	120.054i	−0.146270	+	0.208789i
$576$		0			0
$577$	590.803	+	590.803i	1.02392	+	1.02392i	0.999707	+	0.0242155i	$0.00770879\pi$
$577$	590.803	+	590.803i	1.02392	+	1.02392i	0.0242155	+	0.999707i	$0.492291\pi$
$578$		0			0
$579$			492.157i			0.850013i
$580$		0			0
$581$	−31.5526	+	521.563i	−0.0543073	+	0.897699i
$582$		0			0
$583$	400.781	−	400.781i	0.687445	−	0.687445i
$584$		0			0
$585$	−376.307	−	315.835i	−0.643259	−	0.539889i
$586$		0			0
$587$	−528.165	+	528.165i	−0.899769	+	0.899769i	−0.995415	−	0.0956459i	$-0.969508\pi$
$587$	−528.165	+	528.165i	−0.899769	+	0.899769i	0.0956459	+	0.995415i	$0.469508\pi$
$588$		0			0
$589$			25.6026i			0.0434679i
$590$		0			0
$591$	1103.88			1.86781
$592$		0			0
$593$	110.999	−	110.999i	0.187183	−	0.187183i	−0.607294	−	0.794477i	$-0.707745\pi$
$593$	110.999	−	110.999i	0.187183	−	0.187183i	0.794477	+	0.607294i	$0.207745\pi$
$594$		0			0
$595$	−6.19718	−	231.832i	−0.0104154	−	0.389634i
$596$		0			0
$597$	198.816	−	198.816i	0.333025	−	0.333025i
$598$		0			0
$599$	183.200			0.305843			0.152921	−	0.988238i	$-0.451132\pi$
$599$	183.200			0.305843			0.152921	+	0.988238i	$0.451132\pi$
$600$		0			0
$601$		−	206.129i		−	0.342977i	−0.985186	−	0.171488i	$-0.945142\pi$
$601$		−	206.129i		−	0.342977i	0.985186	−	0.171488i	$-0.0548576\pi$
$602$		0			0
$603$	327.978	−	327.978i	0.543910	−	0.543910i
$604$		0			0
$605$	−279.582	+	24.4267i	−0.462118	+	0.0403747i
$606$		0			0
$607$	−222.323	+	222.323i	−0.366265	+	0.366265i	−0.866113	−	0.499848i	$-0.833389\pi$
$607$	−222.323	+	222.323i	−0.366265	+	0.366265i	0.499848	+	0.866113i	$0.333389\pi$
$608$		0			0
$609$	−1145.34	−	69.2887i	−1.88069	−	0.113775i
$610$		0			0
$611$			1199.85i			1.96375i
$612$		0			0
$613$	685.546	+	685.546i	1.11835	+	1.11835i	0.991984	+	0.126362i	$0.0403302\pi$
$613$	685.546	+	685.546i	1.11835	+	1.11835i	0.126362	+	0.991984i	$0.459670\pi$
$614$		0			0
$615$	634.871	−	756.427i	1.03231	−	1.22996i
$616$		0			0
$617$	−233.208	+	233.208i	−0.377971	+	0.377971i	−0.870370	−	0.492399i	$-0.836120\pi$
$617$	−233.208	+	233.208i	−0.377971	+	0.377971i	0.492399	+	0.870370i	$0.336120\pi$
$618$		0			0
$619$		−	315.750i		−	0.510097i	−0.966928	−	0.255049i	$-0.917909\pi$
$619$		−	315.750i		−	0.510097i	0.966928	−	0.255049i	$-0.0820915\pi$
$620$		0			0
$621$		−	73.6085i		−	0.118532i
$622$		0			0
$623$	148.217	+	167.305i	0.237909	+	0.268547i
$624$		0			0
$625$	587.410	−	213.483i	0.939855	−	0.341573i
$626$		0			0
$627$	−76.3965	−	76.3965i	−0.121845	−	0.121845i
$628$		0			0
$629$	−97.6289			−0.155213
$630$		0			0
$631$			458.035i			0.725888i	0.931811	+	0.362944i	$0.118228\pi$
$631$			458.035i			0.725888i	−0.931811	+	0.362944i	$0.881772\pi$
$632$		0			0
$633$	−375.736	+	375.736i	−0.593580	+	0.593580i
$634$		0			0
$635$	−242.643	−	203.651i	−0.382115	−	0.320710i
$636$		0			0
$637$	518.286	+	661.562i	0.813635	+	1.03856i
$638$		0			0
$639$	261.566			0.409336
$640$		0			0
$641$	325.712			0.508131			0.254066	−	0.967187i	$-0.418232\pi$
$641$	325.712			0.508131			0.254066	+	0.967187i	$0.418232\pi$
$642$		0			0
$643$	716.243	+	716.243i	1.11391	+	1.11391i	0.992617	+	0.121291i	$0.0387034\pi$
$643$	716.243	+	716.243i	1.11391	+	1.11391i	0.121291	+	0.992617i	$0.461297\pi$
$644$		0			0
$645$	1023.79	−	89.4469i	1.58727	−	0.138677i
$646$		0			0
$647$	260.893	−	260.893i	0.403234	−	0.403234i	−0.476137	−	0.879371i	$-0.657963\pi$
$647$	260.893	−	260.893i	0.403234	−	0.403234i	0.879371	+	0.476137i	$0.157963\pi$
$648$		0			0
$649$	602.183			0.927864
$650$		0			0
$651$	−11.8828	+	196.423i	−0.0182532	+	0.301726i
$652$		0			0
$653$	−81.2648	−	81.2648i	−0.124448	−	0.124448i	0.642139	−	0.766588i	$-0.278047\pi$
$653$	−81.2648	−	81.2648i	−0.124448	−	0.124448i	−0.766588	+	0.642139i	$0.778047\pi$
$654$		0			0
$655$	299.444	−	26.1620i	0.457166	−	0.0399420i
$656$		0			0
$657$	303.774	+	303.774i	0.462366	+	0.462366i
$658$		0			0
$659$	384.242			0.583069			0.291534	−	0.956560i	$-0.405834\pi$
$659$	384.242			0.583069			0.291534	+	0.956560i	$0.405834\pi$
$660$		0			0
$661$			285.270i			0.431573i	0.976441	+	0.215786i	$0.0692315\pi$
$661$			285.270i			0.431573i	−0.976441	+	0.215786i	$0.930768\pi$
$662$		0			0
$663$	−308.407	−	308.407i	−0.465169	−	0.465169i
$664$		0			0
$665$	−84.1610	+	88.7840i	−0.126558	+	0.133510i
$666$		0			0
$667$	177.082	+	177.082i	0.265490	+	0.265490i
$668$		0			0
$669$		−	754.160i		−	1.12729i
$670$		0			0
$671$	347.758			0.518268
$672$		0			0
$673$	198.014	+	198.014i	0.294226	+	0.294226i	0.838747	−	0.544521i	$-0.183289\pi$
$673$	198.014	+	198.014i	0.294226	+	0.294226i	−0.544521	+	0.838747i	$0.683289\pi$
$674$		0			0
$675$	−180.079	+	257.050i	−0.266784	+	0.380814i
$676$		0			0
$677$	−31.7972	−	31.7972i	−0.0469679	−	0.0469679i	0.683233	−	0.730201i	$-0.260573\pi$
$677$	−31.7972	−	31.7972i	−0.0469679	−	0.0469679i	−0.730201	+	0.683233i	$0.760573\pi$
$678$		0			0
$679$	11.6933	−	193.291i	0.0172214	−	0.284670i
$680$		0			0
$681$	−577.260			−0.847665
$682$		0			0
$683$	−38.6769	+	38.6769i	−0.0566280	+	0.0566280i	−0.734854	−	0.678226i	$-0.762749\pi$
$683$	−38.6769	+	38.6769i	−0.0566280	+	0.0566280i	0.678226	+	0.734854i	$0.262749\pi$
$684$		0			0
$685$	−790.696	+	942.087i	−1.15430	+	1.37531i
$686$		0			0
$687$	−713.387	−	713.387i	−1.03841	−	1.03841i
$688$		0			0
$689$	−1206.96			−1.75175
$690$		0			0
$691$	534.276			0.773193			0.386597	−	0.922249i	$-0.373651\pi$
$691$	534.276			0.773193			0.386597	+	0.922249i	$0.373651\pi$
$692$		0			0
$693$	−214.181	−	241.763i	−0.309063	−	0.348865i
$694$		0			0
$695$	101.012	+	1156.15i	0.145341	+	1.66353i
$696$		0			0
$697$	241.128	−	241.128i	0.345952	−	0.345952i
$698$		0			0
$699$			537.382i			0.768787i
$700$		0			0
$701$	−824.261			−1.17584			−0.587918	−	0.808920i	$-0.700052\pi$
$701$	−824.261			−1.17584			−0.587918	+	0.808920i	$0.700052\pi$
$702$		0			0
$703$	36.4152	+	36.4152i	0.0517997	+	0.0517997i
$704$		0			0
$705$	−1337.33	+	116.841i	−1.89692	+	0.165731i
$706$		0			0
$707$	−73.8714	+	65.4434i	−0.104486	+	0.0925649i
$708$		0			0
$709$			1221.60i			1.72300i	0.507761	+	0.861498i	$0.330473\pi$
$709$			1221.60i			1.72300i	−0.507761	+	0.861498i	$0.669527\pi$
$710$		0			0
$711$			552.433i			0.776980i
$712$		0			0
$713$	30.3691	−	30.3691i	0.0425934	−	0.0425934i
$714$		0			0
$715$	−529.052	−	444.035i	−0.739933	−	0.621028i
$716$		0			0
$717$	647.354	+	647.354i	0.902864	+	0.902864i
$718$		0			0
$719$		−	582.080i		−	0.809569i	−0.914412	−	0.404785i	$-0.867347\pi$
$719$		−	582.080i		−	0.809569i	0.914412	−	0.404785i	$-0.132653\pi$
$720$		0			0
$721$	1.79131	−	29.6103i	0.00248448	−	0.0410684i
$722$		0			0
$723$	1107.01	−	1107.01i	1.53113	−	1.53113i
$724$		0			0
$725$	−185.170	−	1051.61i	−0.255406	−	1.45050i
$726$		0			0
$727$	−12.6800	+	12.6800i	−0.0174416	+	0.0174416i	−0.715774	−	0.698332i	$-0.753926\pi$
$727$	−12.6800	+	12.6800i	−0.0174416	+	0.0174416i	0.698332	+	0.715774i	$0.253926\pi$
$728$		0			0
$729$			137.772i			0.188988i
$730$		0			0
$731$	354.868			0.485456
$732$		0			0
$733$	87.2303	−	87.2303i	0.119005	−	0.119005i	−0.645097	−	0.764101i	$-0.723183\pi$
$733$	87.2303	−	87.2303i	0.119005	−	0.119005i	0.764101	+	0.645097i	$0.223183\pi$
$734$		0			0
$735$	−686.891	+	642.090i	−0.934545	+	0.873592i
$736$		0			0
$737$	461.107	−	461.107i	0.625654	−	0.625654i
$738$		0			0
$739$	−242.125			−0.327639			−0.163819	−	0.986490i	$-0.552381\pi$
$739$	−242.125			−0.327639			−0.163819	+	0.986490i	$0.552381\pi$
$740$		0			0
$741$			230.069i			0.310485i
$742$		0			0
$743$	−655.242	+	655.242i	−0.881887	+	0.881887i	−0.993726	−	0.111840i	$-0.964326\pi$
$743$	−655.242	+	655.242i	−0.881887	+	0.881887i	0.111840	+	0.993726i	$0.464326\pi$
$744$		0			0
$745$	1.34984	+	15.4499i	0.00181186	+	0.0207381i
$746$		0			0
$747$	−302.381	+	302.381i	−0.404794	+	0.404794i
$748$		0			0
$749$	−82.0514	+	1356.31i	−0.109548	+	1.81083i
$750$		0			0
$751$		−	817.498i		−	1.08855i	−0.838908	−	0.544273i	$-0.816805\pi$
$751$		−	817.498i		−	1.08855i	0.838908	−	0.544273i	$-0.183195\pi$
$752$		0			0
$753$	−231.763	−	231.763i	−0.307787	−	0.307787i
$754$		0			0
$755$	63.7981	+	730.217i	0.0845008	+	0.967175i
$756$		0			0
$757$	571.452	−	571.452i	0.754891	−	0.754891i	−0.220497	−	0.975388i	$-0.570768\pi$
$757$	571.452	−	571.452i	0.754891	−	0.754891i	0.975388	+	0.220497i	$0.0707679\pi$
$758$		0			0
$759$			181.239i			0.238786i
$760$		0			0
$761$			156.705i			0.205920i	0.994685	+	0.102960i	$0.0328314\pi$
$761$			156.705i			0.205920i	−0.994685	+	0.102960i	$0.967169\pi$
$762$		0			0
$763$	941.673	−	834.238i	1.23417	−	1.09337i
$764$		0			0
$765$	122.019	−	145.381i	0.159502	−	0.190041i
$766$		0			0
$767$	−906.741	−	906.741i	−1.18219	−	1.18219i
$768$		0			0
$769$	1491.18			1.93912			0.969558	−	0.244861i	$-0.0787424\pi$
$769$	1491.18			1.93912			0.969558	+	0.244861i	$0.0787424\pi$
$770$		0			0
$771$			361.367i			0.468699i
$772$		0			0
$773$	674.400	−	674.400i	0.872445	−	0.872445i	−0.120294	−	0.992738i	$-0.538384\pi$
$773$	674.400	−	674.400i	0.872445	−	0.872445i	0.992738	+	0.120294i	$0.0383836\pi$
$774$		0			0
$775$	−180.349	+	31.7561i	−0.232708	+	0.0409756i
$776$		0			0
$777$	262.476	+	296.279i	0.337808	+	0.381311i
$778$		0			0
$779$	−179.880			−0.230911
$780$		0			0
$781$	367.737			0.470854
$782$		0			0
$783$	379.154	+	379.154i	0.484233	+	0.484233i
$784$		0			0
$785$	−1097.51	−	921.141i	−1.39810	−	1.17343i
$786$		0			0
$787$	50.5124	−	50.5124i	0.0641834	−	0.0641834i	−0.674286	−	0.738470i	$-0.735549\pi$
$787$	50.5124	−	50.5124i	0.0641834	−	0.0641834i	0.738470	+	0.674286i	$0.235549\pi$
$788$		0			0
$789$	91.4437			0.115898
$790$		0			0
$791$	49.0994	−	811.613i	0.0620726	−	1.02606i
$792$		0			0
$793$	−523.639	−	523.639i	−0.660326	−	0.660326i
$794$		0			0
$795$	−117.532	−	1345.24i	−0.147839	−	1.69213i
$796$		0			0
$797$	−321.559	−	321.559i	−0.403462	−	0.403462i	0.475989	−	0.879451i	$-0.342090\pi$
$797$	−321.559	−	321.559i	−0.403462	−	0.403462i	−0.879451	+	0.475989i	$0.842090\pi$
$798$		0			0
$799$	−463.548			−0.580161
$800$		0			0
$801$			182.927i			0.228373i
$802$		0			0
$803$	427.079	+	427.079i	0.531854	+	0.531854i
$804$		0			0
$805$	205.143	−	5.48373i	0.254835	−	0.00681209i
$806$		0			0
$807$	−12.8273	−	12.8273i	−0.0158951	−	0.0158951i
$808$		0			0
$809$		−	540.944i		−	0.668657i	−0.942457	−	0.334329i	$-0.891490\pi$
$809$		−	540.944i		−	0.668657i	0.942457	−	0.334329i	$-0.108510\pi$
$810$		0			0
$811$	−1197.03			−1.47600			−0.737998	−	0.674803i	$-0.764229\pi$
$811$	−1197.03			−1.47600			−0.737998	+	0.674803i	$0.764229\pi$
$812$		0			0
$813$	1321.95	+	1321.95i	1.62602	+	1.62602i
$814$		0			0
$815$	421.924	−	502.708i	0.517698	−	0.616820i
$816$		0			0
$817$	−132.364	−	132.364i	−0.162013	−	0.162013i
$818$		0			0
$819$	−41.5330	+	686.540i	−0.0507119	+	0.838267i
$820$		0			0
$821$	−410.181			−0.499612			−0.249806	−	0.968296i	$-0.580367\pi$
$821$	−410.181			−0.499612			−0.249806	+	0.968296i	$0.580367\pi$
$822$		0			0
$823$	−462.410	+	462.410i	−0.561859	+	0.561859i	−0.929835	−	0.367976i	$-0.880051\pi$
$823$	−462.410	+	462.410i	−0.561859	+	0.561859i	0.367976	+	0.929835i	$0.380051\pi$
$824$		0			0
$825$	443.392	−	632.908i	0.537444	−	0.767161i
$826$		0			0
$827$	−642.183	−	642.183i	−0.776521	−	0.776521i	0.202717	−	0.979237i	$-0.435023\pi$
$827$	−642.183	−	642.183i	−0.776521	−	0.776521i	−0.979237	+	0.202717i	$0.935023\pi$
$828$		0			0
$829$	−709.957			−0.856402			−0.428201	−	0.903684i	$-0.640852\pi$
$829$	−709.957			−0.856402			−0.428201	+	0.903684i	$0.640852\pi$
$830$		0			0
$831$	1730.07			2.08191
$832$		0			0
$833$	−255.586	+	200.233i	−0.306826	+	0.240376i
$834$		0			0
$835$	−115.957	+	138.159i	−0.138871	+	0.165460i
$836$		0			0
$837$	65.0240	−	65.0240i	0.0776870	−	0.0776870i
$838$		0			0
$839$		−	920.669i		−	1.09734i	−0.836039	−	0.548671i	$-0.815134\pi$
$839$		−	920.669i		−	1.09734i	0.836039	−	0.548671i	$-0.184866\pi$
$840$		0			0
$841$	−983.282			−1.16918
$842$		0			0
$843$	−864.542	−	864.542i	−1.02555	−	1.02555i
$844$		0			0
$845$	54.4691	+	623.439i	0.0644604	+	0.737798i
$846$		0			0
$847$	260.542	+	294.096i	0.307606	+	0.347220i
$848$		0			0
$849$			1482.78i			1.74650i
$850$		0			0
$851$		−	86.3894i		−	0.101515i
$852$		0			0
$853$	−331.808	+	331.808i	−0.388989	+	0.388989i	−0.874327	−	0.485338i	$-0.838697\pi$
$853$	−331.808	+	331.808i	−0.388989	+	0.388989i	0.485338	+	0.874327i	$0.338697\pi$
$854$		0			0
$855$	−99.7393	+	8.71409i	−0.116654	+	0.0101919i
$856$		0			0
$857$	−421.769	−	421.769i	−0.492146	−	0.492146i	0.416836	−	0.908982i	$-0.363139\pi$
$857$	−421.769	−	421.769i	−0.492146	−	0.492146i	−0.908982	+	0.416836i	$0.863139\pi$
$858$		0			0
$859$			147.485i			0.171694i	0.996308	+	0.0858471i	$0.0273596\pi$
$859$			147.485i			0.171694i	−0.996308	+	0.0858471i	$0.972640\pi$
$860$		0			0
$861$	−1380.04	−	83.4870i	−1.60283	−	0.0969652i
$862$		0			0
$863$	388.305	−	388.305i	0.449948	−	0.449948i	−0.445389	−	0.895337i	$-0.646935\pi$
$863$	388.305	−	388.305i	0.449948	−	0.449948i	0.895337	+	0.445389i	$0.146935\pi$
$864$		0			0
$865$	931.152	−	1109.44i	1.07648	−	1.28258i
$866$		0			0
$867$	−665.124	+	665.124i	−0.767155	+	0.767155i
$868$		0			0
$869$			776.670i			0.893751i
$870$		0			0
$871$	−1388.63			−1.59429
$872$		0			0
$873$	112.062	−	112.062i	0.128364	−	0.128364i
$874$		0			0
$875$	−729.798	−	482.721i	−0.834055	−	0.551681i
$876$		0			0
$877$	−797.774	+	797.774i	−0.909662	+	0.909662i	−0.996245	−	0.0865827i	$-0.972405\pi$
$877$	−797.774	+	797.774i	−0.909662	+	0.909662i	0.0865827	+	0.996245i	$0.472405\pi$
$878$		0			0
$879$	1263.91			1.43790
$880$		0			0
$881$		−	1227.74i		−	1.39357i	−0.717279	−	0.696786i	$-0.754613\pi$
$881$		−	1227.74i		−	1.39357i	0.717279	−	0.696786i	$-0.245387\pi$
$882$		0			0
$883$	−41.4471	+	41.4471i	−0.0469389	+	0.0469389i	−0.730187	−	0.683248i	$-0.760567\pi$
$883$	−41.4471	+	41.4471i	−0.0469389	+	0.0469389i	0.683248	+	0.730187i	$0.260567\pi$
$884$		0			0
$885$	922.334	−	1098.93i	1.04219	−	1.24173i
$886$		0			0
$887$	909.377	−	909.377i	1.02523	−	1.02523i	0.0255540	−	0.999673i	$-0.491865\pi$
$887$	909.377	−	909.377i	1.02523	−	1.02523i	0.999673	−	0.0255540i	$-0.00813499\pi$
$888$		0			0
$889$	−26.7805	+	442.682i	−0.0301243	+	0.497955i
$890$		0			0
$891$			803.329i			0.901603i
$892$		0			0
$893$	172.902	+	172.902i	0.193619	+	0.193619i
$894$		0			0
$895$	41.8504	−	3.65642i	0.0467602	−	0.00408538i
$896$		0			0
$897$	272.902	−	272.902i	0.304238	−	0.304238i
$898$		0			0
$899$			312.860i			0.348009i
$900$		0			0
$901$		−	466.292i		−	0.517528i
$902$		0			0
$903$	−954.067	−	1076.94i	−1.05655	−	1.19262i
$904$		0			0
$905$	6.57156	+	75.2164i	0.00726139	+	0.0831120i
$906$		0			0
$907$	−265.458	−	265.458i	−0.292677	−	0.292677i	0.545460	−	0.838137i	$-0.316355\pi$
$907$	−265.458	−	265.458i	−0.292677	−	0.292677i	−0.838137	+	0.545460i	$0.816355\pi$
$908$		0			0
$909$	−80.7690			−0.0888548
$910$		0			0
$911$			276.253i			0.303242i	0.988439	+	0.151621i	$0.0484493\pi$
$911$			276.253i			0.303242i	−0.988439	+	0.151621i	$0.951551\pi$
$912$		0			0
$913$	−425.120	+	425.120i	−0.465630	+	0.465630i
$914$		0			0
$915$	532.643	−	634.626i	0.582124	−	0.693580i
$916$		0			0
$917$	−279.052	−	314.989i	−0.304310	−	0.343500i
$918$		0			0
$919$	330.187			0.359289			0.179645	−	0.983732i	$-0.442505\pi$
$919$	330.187			0.359289			0.179645	+	0.983732i	$0.442505\pi$
$920$		0			0
$921$	−1953.11			−2.12064
$922$		0			0
$923$	−553.722	−	553.722i	−0.599916	−	0.599916i
$924$		0			0
$925$	−211.347	+	301.682i	−0.228483	+	0.326143i
$926$		0			0
$927$	17.1668	−	17.1668i	0.0185187	−	0.0185187i
$928$		0			0
$929$	572.280			0.616017			0.308009	−	0.951384i	$-0.400337\pi$
$929$	572.280			0.616017			0.308009	+	0.951384i	$0.400337\pi$
$930$		0			0
$931$	170.019	+	20.6465i	0.182620	+	0.0221767i
$932$		0			0
$933$	1299.03	+	1299.03i	1.39231	+	1.39231i
$934$		0			0
$935$	171.547	−	204.393i	0.183473	−	0.218602i
$936$		0			0
$937$	−309.136	−	309.136i	−0.329921	−	0.329921i	0.522636	−	0.852556i	$-0.324949\pi$
$937$	−309.136	−	309.136i	−0.329921	−	0.329921i	−0.852556	+	0.522636i	$0.824949\pi$
$938$		0			0
$939$	−1080.86			−1.15108
$940$		0			0
$941$		−	58.1636i		−	0.0618104i	−0.999522	−	0.0309052i	$-0.990161\pi$
$941$		−	58.1636i		−	0.0618104i	0.999522	−	0.0309052i	$-0.00983900\pi$
$942$		0			0
$943$	213.368	+	213.368i	0.226266	+	0.226266i
$944$		0			0
$945$	439.236	−	11.7414i	0.464800	−	0.0124247i
$946$		0			0
$947$	762.634	+	762.634i	0.805316	+	0.805316i	0.983921	−	0.178605i	$-0.0571584\pi$
$947$	762.634	+	762.634i	0.805316	+	0.805316i	−0.178605	+	0.983921i	$0.557158\pi$
$948$		0			0
$949$		−	1286.15i		−	1.35527i
$950$		0			0
$951$	−1936.55			−2.03633
$952$		0			0
$953$	435.670	+	435.670i	0.457157	+	0.457157i	0.897721	−	0.440564i	$-0.145222\pi$
$953$	435.670	+	435.670i	0.457157	+	0.457157i	−0.440564	+	0.897721i	$0.645222\pi$
$954$		0			0
$955$	106.650	+	1220.69i	0.111676	+	1.27821i
$956$		0			0
$957$	−933.554	−	933.554i	−0.975501	−	0.975501i
$958$		0			0
$959$	1718.76	+	103.978i	1.79224	+	0.108424i
$960$		0			0
$961$	−907.345			−0.944168
$962$		0			0
$963$	−786.332	+	786.332i	−0.816544	+	0.816544i
$964$		0			0
$965$	491.134	+	412.210i	0.508947	+	0.427161i
$966$		0			0
$967$	339.744	+	339.744i	0.351338	+	0.351338i	0.860607	−	0.509269i	$-0.170084\pi$
$967$	339.744	+	339.744i	0.351338	+	0.351338i	−0.509269	+	0.860607i	$0.670084\pi$
$968$		0			0
$969$	−88.8843			−0.0917279
$970$		0			0
$971$	−888.261			−0.914790			−0.457395	−	0.889264i	$-0.651217\pi$
$971$	−888.261			−0.914790			−0.457395	+	0.889264i	$0.651217\pi$
$972$		0			0
$973$	1216.17	−	1077.42i	1.24992	−	1.10732i
$974$		0			0
$975$	−1620.65	+	285.366i	−1.66220	+	0.292683i
$976$		0			0
$977$	676.782	−	676.782i	0.692714	−	0.692714i	−0.270114	−	0.962828i	$-0.587061\pi$
$977$	676.782	−	676.782i	0.692714	−	0.692714i	0.962828	+	0.270114i	$0.0870615\pi$
$978$		0			0
$979$			257.178i			0.262695i
$980$		0			0
$981$	1029.60			1.04954
$982$		0			0
$983$	767.070	+	767.070i	0.780335	+	0.780335i	0.979887	−	0.199552i	$-0.0639487\pi$
$983$	767.070	+	767.070i	0.780335	+	0.780335i	−0.199552	+	0.979887i	$0.563949\pi$
$984$		0			0
$985$	924.560	−	1101.58i	0.938639	−	1.11836i
$986$		0			0
$987$	1246.26	+	1406.75i	1.26267	+	1.42528i
$988$		0			0
$989$			314.014i			0.317507i
$990$		0			0
$991$			688.241i			0.694491i	0.937774	+	0.347246i	$0.112883\pi$
$991$			688.241i			0.694491i	−0.937774	+	0.347246i	$0.887117\pi$
$992$		0			0
$993$	375.209	−	375.209i	0.377854	−	0.377854i
$994$		0			0
$995$	−31.8828	−	364.922i	−0.0320430	−	0.366756i
$996$		0			0
$997$	−705.546	−	705.546i	−0.707669	−	0.707669i	0.258375	−	0.966045i	$-0.416813\pi$
$997$	−705.546	−	705.546i	−0.707669	−	0.707669i	−0.966045	+	0.258375i	$0.916813\pi$
$998$		0			0
$999$		−	184.971i		−	0.185156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.v.b.223.5	✓	64
4.3	odd	2	inner	560.3.v.b.223.28	yes	64
5.2	odd	4	inner	560.3.v.b.447.6	yes	64
7.6	odd	2	inner	560.3.v.b.223.27	yes	64
20.7	even	4	inner	560.3.v.b.447.27	yes	64
28.27	even	2	inner	560.3.v.b.223.6	yes	64
35.27	even	4	inner	560.3.v.b.447.28	yes	64
140.27	odd	4	inner	560.3.v.b.447.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.3.v.b.223.5	✓	64	1.1	even	1	trivial
560.3.v.b.223.6	yes	64	28.27	even	2	inner
560.3.v.b.223.27	yes	64	7.6	odd	2	inner
560.3.v.b.223.28	yes	64	4.3	odd	2	inner
560.3.v.b.447.5	yes	64	140.27	odd	4	inner
560.3.v.b.447.6	yes	64	5.2	odd	4	inner
560.3.v.b.447.27	yes	64	20.7	even	4	inner
560.3.v.b.447.28	yes	64	35.27	even	4	inner

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.71375 - 2.71375i) q^{3} +(-4.98103 + 0.435186i) q^{5} +(4.64182 + 5.23961i) q^{7} +5.72885i q^{9} +8.05423i q^{11} +(12.1277 - 12.1277i) q^{13} +(14.6982 + 12.3363i) q^{15} +(4.68539 + 4.68539i) q^{17} -3.49526i q^{19} +(1.62225 - 26.8157i) q^{21} +(-4.14599 + 4.14599i) q^{23} +(24.6212 - 4.33534i) q^{25} +(-8.87708 + 8.87708i) q^{27} -42.7116i q^{29} -7.32494 q^{31} +(21.8572 - 21.8572i) q^{33} +(-25.4012 - 24.0786i) q^{35} +(-10.4184 + 10.4184i) q^{37} -65.8231 q^{39} -51.4638i q^{41} +(37.8696 - 37.8696i) q^{43} +(-2.49311 - 28.5355i) q^{45} +(-49.4674 + 49.4674i) q^{47} +(-5.90700 + 48.6426i) q^{49} -25.4299i q^{51} +(-49.7603 - 49.7603i) q^{53} +(-3.50509 - 40.1183i) q^{55} +(-9.48526 + 9.48526i) q^{57} -74.7661i q^{59} -43.1770i q^{61} +(-30.0169 + 26.5923i) q^{63} +(-55.1306 + 65.6862i) q^{65} +(-57.2502 - 57.2502i) q^{67} +22.5023 q^{69} -45.6576i q^{71} +(53.0254 - 53.0254i) q^{73} +(-78.5808 - 55.0508i) q^{75} +(-42.2010 + 37.3863i) q^{77} +96.4300 q^{79} +99.7399 q^{81} +(52.7822 + 52.7822i) q^{83} +(-25.3771 - 21.2990i) q^{85} +(-115.909 + 115.909i) q^{87} +31.9308 q^{89} +(119.839 + 7.24980i) q^{91} +(19.8780 + 19.8780i) q^{93} +(1.52109 + 17.4100i) q^{95} +(-19.5610 - 19.5610i) q^{97} -46.1415 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{21} - 72 q^{25} + 72 q^{37} + 272 q^{53} - 376 q^{57} - 88 q^{65} + 24 q^{77} - 432 q^{81} + 384 q^{85} + 840 q^{93}+O(q^{100}) \) 64 * q + 16 * q^21 - 72 * q^25 + 72 * q^37 + 272 * q^53 - 376 * q^57 - 88 * q^65 + 24 * q^77 - 432 * q^81 + 384 * q^85 + 840 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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