LMFDB - Embedded newform 171.4.y.a.53.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(53,171)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 11]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("171.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.y (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.16
Character	$\chi$	$=$	171.53
Dual form			171.4.y.a.71.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.36331 + 1.22414i) q^{2} +(3.68495 + 3.09204i) q^{4} +(-13.3019 - 15.8526i) q^{5} +(-7.77429 + 13.4655i) q^{7} +(-5.70811 - 9.88673i) q^{8} +O(q^{10})$	\(q+(3.36331 + 1.22414i) q^{2} +(3.68495 + 3.09204i) q^{4} +(-13.3019 - 15.8526i) q^{5} +(-7.77429 + 13.4655i) q^{7} +(-5.70811 - 9.88673i) q^{8} +(-25.3325 - 69.6004i) q^{10} +(0.507963 - 0.293273i) q^{11} +(-46.3397 - 8.17093i) q^{13} +(-42.6310 + 35.7717i) q^{14} +(-13.7778 - 78.1379i) q^{16} +(10.6943 - 29.3824i) q^{17} +(-31.0413 - 76.7818i) q^{19} -99.5459i q^{20} +(2.06744 - 0.364546i) q^{22} +(-15.0014 + 17.8779i) q^{23} +(-52.6577 + 298.637i) q^{25} +(-145.852 - 84.2078i) q^{26} +(-70.2837 + 25.5812i) q^{28} +(267.617 - 97.4045i) q^{29} +(86.4832 + 49.9311i) q^{31} +(33.4537 - 189.726i) q^{32} +(71.9366 - 85.7307i) q^{34} +(316.875 - 55.8736i) q^{35} -53.8378i q^{37} +(-10.4094 - 296.240i) q^{38} +(-80.8014 + 222.000i) q^{40} +(58.8231 + 333.603i) q^{41} +(-199.580 + 167.468i) q^{43} +(2.77863 + 0.489948i) q^{44} +(-72.3393 + 41.7651i) q^{46} +(-210.832 - 579.255i) q^{47} +(50.6207 + 87.6777i) q^{49} +(-542.678 + 939.946i) q^{50} +(-145.495 - 173.394i) q^{52} +(116.390 + 97.6631i) q^{53} +(-11.4060 - 4.15144i) q^{55} +177.506 q^{56} +1019.31 q^{58} +(-425.794 - 154.976i) q^{59} +(-479.767 - 402.572i) q^{61} +(229.747 + 273.801i) q^{62} +(27.3934 - 47.4467i) q^{64} +(486.874 + 843.291i) q^{65} +(-309.378 - 850.010i) q^{67} +(130.260 - 75.2055i) q^{68} +(1134.14 + 199.980i) q^{70} +(186.080 - 156.140i) q^{71} +(59.3899 + 336.817i) q^{73} +(65.9052 - 181.073i) q^{74} +(123.027 - 378.918i) q^{76} +9.11995i q^{77} +(551.538 - 97.2510i) q^{79} +(-1055.41 + 1257.79i) q^{80} +(-210.537 + 1194.02i) q^{82} +(-518.748 - 299.499i) q^{83} +(-608.041 + 221.309i) q^{85} +(-876.255 + 318.931i) q^{86} +(-5.79902 - 3.34806i) q^{88} +(207.685 - 1177.84i) q^{89} +(470.284 - 560.462i) q^{91} +(-110.559 + 19.4944i) q^{92} -2206.30i q^{94} +(-804.281 + 1513.42i) q^{95} +(71.1316 - 195.432i) q^{97} +(62.9230 + 356.854i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 36 q^{4}+O(q^{10}) $ 120 * q - 36 * q^4	$ 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55} + 5616 q^{58} - 5736 q^{61} - 4524 q^{64} + 372 q^{67} + 7848 q^{70} - 276 q^{73} + 4320 q^{76} + 10536 q^{79} + 3960 q^{82} - 11592 q^{85} - 11664 q^{88} - 120 q^{91} + 5904 q^{97}+O(q^{100}) $ 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	3.36331	+	1.22414i	1.18911	+	0.432800i	0.859410	−	0.511286i	$-0.170831\pi$
$2$	3.36331	+	1.22414i	1.18911	+	0.432800i	0.329698	+	0.944086i	$0.393053\pi$
$3$		0			0
$3$		0			0
$4$	3.68495	+	3.09204i	0.460619	+	0.386505i
$5$	−13.3019	−	15.8526i	−1.18976	−	1.41790i	−0.885079	−	0.465440i	$-0.845896\pi$
$5$	−13.3019	−	15.8526i	−1.18976	−	1.41790i	−0.304677	−	0.952456i	$-0.598548\pi$
$6$		0			0
$7$	−7.77429	+	13.4655i	−0.419772	+	0.727067i	−0.995916	−	0.0902812i	$-0.971223\pi$
$7$	−7.77429	+	13.4655i	−0.419772	+	0.727067i	0.576144	+	0.817348i	$0.304557\pi$
$8$	−5.70811	−	9.88673i	−0.252265	−	0.436936i
$9$		0			0
$10$	−25.3325	−	69.6004i	−0.801084	−	2.20096i
$11$	0.507963	−	0.293273i	0.0139233	−	0.00803864i	−0.493022	−	0.870017i	$-0.664108\pi$
$11$	0.507963	−	0.293273i	0.0139233	−	0.00803864i	0.506946	+	0.861978i	$0.330775\pi$
$12$		0			0
$13$	−46.3397	−	8.17093i	−0.988639	−	0.174324i	−0.344131	−	0.938922i	$-0.611827\pi$
$13$	−46.3397	−	8.17093i	−0.988639	−	0.174324i	−0.644508	+	0.764598i	$0.722938\pi$
$14$	−42.6310	+	35.7717i	−0.813830	+	0.682884i
$15$		0			0
$16$	−13.7778	−	78.1379i	−0.215278	−	1.22090i
$17$	10.6943	−	29.3824i	0.152574	−	0.419193i	−0.839732	−	0.543000i	$-0.817288\pi$
$17$	10.6943	−	29.3824i	0.152574	−	0.419193i	0.992306	+	0.123807i	$0.0395104\pi$
$18$		0			0
$19$	−31.0413	−	76.7818i	−0.374808	−	0.927102i
$19$	−31.0413	−	76.7818i	−0.374808	−	0.927102i
$20$		−	99.5459i		−	1.11296i
$21$		0			0
$22$	2.06744	−	0.364546i	0.0200355	−	0.00353280i
$23$	−15.0014	+	17.8779i	−0.136000	+	0.162078i	−0.829746	−	0.558141i	$-0.811515\pi$
$23$	−15.0014	+	17.8779i	−0.136000	+	0.162078i	0.693746	+	0.720220i	$0.255959\pi$
$24$		0			0
$25$	−52.6577	+	298.637i	−0.421261	+	2.38909i
$26$	−145.852	−	84.2078i	−1.10015	−	0.635173i
$27$		0			0
$28$	−70.2837	+	25.5812i	−0.474370	+	0.172657i
$29$	267.617	−	97.4045i	1.71363	−	0.623709i	0.716369	−	0.697721i	$-0.245803\pi$
$29$	267.617	−	97.4045i	1.71363	−	0.623709i	0.997257	+	0.0740120i	$0.0235803\pi$
$30$		0			0
$31$	86.4832	+	49.9311i	0.501059	+	0.289287i	0.729151	−	0.684353i	$-0.239915\pi$
$31$	86.4832	+	49.9311i	0.501059	+	0.289287i	−0.228092	+	0.973640i	$0.573249\pi$
$32$	33.4537	−	189.726i	0.184808	−	1.04810i
$33$		0			0
$34$	71.9366	−	85.7307i	0.362854	−	0.432432i
$35$	316.875	−	55.8736i	1.53033	−	0.269839i
$36$		0			0
$37$		−	53.8378i		−	0.239213i	−0.992821	−	0.119606i	$-0.961837\pi$
$37$		−	53.8378i		−	0.239213i	0.992821	−	0.119606i	$-0.0381633\pi$
$38$	−10.4094	−	296.240i	−0.0444374	−	1.26464i
$39$		0			0
$40$	−80.8014	+	222.000i	−0.319396	+	0.877533i
$41$	58.8231	+	333.603i	0.224064	+	1.27073i	0.864466	+	0.502691i	$0.167657\pi$
$41$	58.8231	+	333.603i	0.224064	+	1.27073i	−0.640402	+	0.768040i	$0.721232\pi$
$42$		0			0
$43$	−199.580	+	167.468i	−0.707808	+	0.593921i	−0.923983	−	0.382433i	$-0.875086\pi$
$43$	−199.580	+	167.468i	−0.707808	+	0.593921i	0.216175	+	0.976355i	$0.430642\pi$
$44$	2.77863	+	0.489948i	0.00952033	+	0.00167869i
$45$		0			0
$46$	−72.3393	+	41.7651i	−0.231866	+	0.133868i
$47$	−210.832	−	579.255i	−0.654318	−	1.79772i	−0.601147	−	0.799138i	$-0.705290\pi$
$47$	−210.832	−	579.255i	−0.654318	−	1.79772i	−0.0531704	−	0.998585i	$-0.516933\pi$
$48$		0			0
$49$	50.6207	+	87.6777i	0.147582	+	0.255620i
$50$	−542.678	+	939.946i	−1.53493	+	2.65857i
$51$		0			0
$52$	−145.495	−	173.394i	−0.388009	−	0.462411i
$53$	116.390	+	97.6631i	0.301650	+	0.253114i	0.781031	−	0.624493i	$-0.214694\pi$
$53$	116.390	+	97.6631i	0.301650	+	0.253114i	−0.479381	+	0.877607i	$0.659139\pi$
$54$		0			0
$55$	−11.4060	−	4.15144i	−0.0279633	−	0.0101778i
$56$	177.506			0.423576
$57$		0			0
$58$	1019.31			2.30763
$59$	−425.794	−	154.976i	−0.939554	−	0.341970i	−0.173564	−	0.984823i	$-0.555528\pi$
$59$	−425.794	−	154.976i	−0.939554	−	0.341970i	−0.765990	+	0.642853i	$0.777751\pi$
$60$		0			0
$61$	−479.767	−	402.572i	−1.00701	−	0.844985i	−0.0190729	−	0.999818i	$-0.506071\pi$
$61$	−479.767	−	402.572i	−1.00701	−	0.844985i	−0.987941	+	0.154833i	$0.950516\pi$
$62$	229.747	+	273.801i	0.470611	+	0.560852i
$63$		0			0
$64$	27.3934	−	47.4467i	0.0535027	−	0.0926694i
$65$	486.874	+	843.291i	0.929066	+	1.60919i
$66$		0			0
$67$	−309.378	−	850.010i	−0.564128	−	1.54993i	−0.813527	−	0.581528i	$-0.802455\pi$
$67$	−309.378	−	850.010i	−0.564128	−	1.54993i	0.249399	−	0.968401i	$-0.419767\pi$
$68$	130.260	−	75.2055i	0.232299	−	0.134118i
$69$		0			0
$70$	1134.14	+	199.980i	1.93652	+	0.341460i
$71$	186.080	−	156.140i	0.311037	−	0.260991i	−0.473883	−	0.880588i	$-0.657148\pi$
$71$	186.080	−	156.140i	0.311037	−	0.260991i	0.784921	+	0.619596i	$0.212704\pi$
$72$		0			0
$73$	59.3899	+	336.817i	0.0952200	+	0.540020i	0.994680	+	0.103016i	$0.0328492\pi$
$73$	59.3899	+	336.817i	0.0952200	+	0.540020i	−0.899460	+	0.437004i	$0.856040\pi$
$74$	65.9052	−	181.073i	0.103531	−	0.284450i
$75$		0			0
$76$	123.027	−	378.918i	0.185686	−	0.571906i
$77$			9.11995i			0.0134976i
$78$		0			0
$79$	551.538	−	97.2510i	0.785479	−	0.138501i	0.233497	−	0.972357i	$-0.424983\pi$
$79$	551.538	−	97.2510i	0.785479	−	0.138501i	0.551982	+	0.833856i	$0.313872\pi$
$80$	−1055.41	+	1257.79i	−1.47499	+	1.75782i
$81$		0			0
$82$	−210.537	+	1194.02i	−0.283536	+	1.60801i
$83$	−518.748	−	299.499i	−0.686024	−	0.396076i	0.116097	−	0.993238i	$-0.462962\pi$
$83$	−518.748	−	299.499i	−0.686024	−	0.396076i	−0.802121	+	0.597162i	$0.796295\pi$
$84$		0			0
$85$	−608.041	+	221.309i	−0.775898	+	0.282404i
$86$	−876.255	+	318.931i	−1.09871	+	0.399898i
$87$		0			0
$88$	−5.79902	−	3.34806i	−0.00702474	−	0.00405574i
$89$	207.685	−	1177.84i	0.247355	−	1.40282i	−0.567605	−	0.823301i	$-0.692130\pi$
$89$	207.685	−	1177.84i	0.247355	−	1.40282i	0.814960	−	0.579518i	$-0.196759\pi$
$90$		0			0
$91$	470.284	−	560.462i	0.541748	−	0.645631i
$92$	−110.559	+	19.4944i	−0.125288	+	0.0220917i
$93$		0			0
$94$		−	2206.30i		−	2.42088i
$95$	−804.281	+	1513.42i	−0.868605	+	1.63446i
$96$		0			0
$97$	71.1316	−	195.432i	0.0744569	−	0.204569i	−0.896881	−	0.442272i	$-0.854172\pi$
$97$	71.1316	−	195.432i	0.0744569	−	0.204569i	0.971338	+	0.237704i	$0.0763947\pi$
$98$	62.9230	+	356.854i	0.0648590	+	0.367834i
$99$		0			0
$100$	−1117.44	+	937.642i	−1.11744	+	0.937642i
$101$	1472.31	+	259.609i	1.45050	+	0.255762i	0.842724	−	0.538345i	$-0.180950\pi$
$101$	1472.31	+	259.609i	1.45050	+	0.255762i	0.607777	+	0.794108i	$0.292062\pi$
$102$		0			0
$103$	−592.237	+	341.928i	−0.566552	+	0.327099i	−0.755771	−	0.654836i	$-0.772738\pi$
$103$	−592.237	+	341.928i	−0.566552	+	0.327099i	0.189219	+	0.981935i	$0.439404\pi$
$104$	183.728	+	504.788i	0.173231	+	0.475948i
$105$		0			0
$106$	271.903	+	470.949i	0.249146	+	0.431534i
$107$	403.890	−	699.557i	0.364911	−	0.632044i	−0.623851	−	0.781543i	$-0.714433\pi$
$107$	403.890	−	699.557i	0.364911	−	0.632044i	0.988762	+	0.149499i	$0.0477661\pi$
$108$		0			0
$109$	202.419	+	241.233i	0.177873	+	0.211981i	0.847613	−	0.530615i	$-0.178039\pi$
$109$	202.419	+	241.233i	0.177873	+	0.211981i	−0.669740	+	0.742596i	$0.733594\pi$
$110$	−33.2799	−	27.9251i	−0.0288465	−	0.0242051i
$111$		0			0
$112$	1159.28	+	421.942i	0.978048	+	0.355980i
$113$	−397.509			−0.330925			−0.165462	−	0.986216i	$-0.552912\pi$
$113$	−397.509			−0.330925			−0.165462	+	0.986216i	$0.552912\pi$
$114$		0			0
$115$	482.957			0.391617
$116$	1287.33	+	468.551i	1.03040	+	0.375033i
$117$		0			0
$118$	−1242.36	−	1042.47i	−0.969227	−	0.813278i
$119$	312.507	+	372.432i	0.240735	+	0.286897i
$120$		0			0
$121$	−665.328	+	1152.38i	−0.499871	+	0.865802i
$122$	−1120.80	−	1941.28i	−0.831739	−	1.44061i
$123$		0			0
$124$	164.297	+	451.403i	0.118987	+	0.326913i
$125$	3194.40	−	1844.29i	2.28573	−	1.31967i
$126$		0			0
$127$	1404.21	+	247.599i	0.981127	+	0.172999i	0.641134	−	0.767429i	$-0.278464\pi$
$127$	1404.21	+	247.599i	0.981127	+	0.172999i	0.339993	+	0.940428i	$0.389575\pi$
$128$	−1030.43	+	864.632i	−0.711546	+	0.597058i
$129$		0			0
$130$	605.198	+	3432.25i	0.408303	+	2.31560i
$131$	621.100	−	1706.46i	0.414242	−	1.13812i	−0.540670	−	0.841235i	$-0.681829\pi$
$131$	621.100	−	1706.46i	0.414242	−	1.13812i	0.954913	−	0.296887i	$-0.0959485\pi$
$132$		0			0
$133$	1275.23	+	178.939i	0.831400	+	0.116661i
$134$		−	3237.57i		−	2.08719i
$135$		0			0
$136$	−351.540	+	61.9861i	−0.221650	+	0.0390828i
$137$	−71.1041	+	84.7386i	−0.0443419	+	0.0528446i	−0.787760	−	0.615983i	$-0.788759\pi$
$137$	−71.1041	+	84.7386i	−0.0443419	+	0.0528446i	0.743418	+	0.668827i	$0.233203\pi$
$138$		0			0
$139$	−307.402	+	1743.37i	−0.187579	+	1.06382i	0.735017	+	0.678049i	$0.237174\pi$
$139$	−307.402	+	1743.37i	−0.187579	+	1.06382i	−0.922596	+	0.385767i	$0.873937\pi$
$140$	1340.43	+	773.899i	0.809194	+	0.467188i
$141$		0			0
$142$	816.982	−	297.357i	0.482814	−	0.175730i
$143$	−25.9352	+	9.43963i	−0.0151665	+	0.00552015i
$144$		0			0
$145$	−5103.92	−	2946.75i	−2.92315	−	1.68768i
$146$	−212.566	+	1205.52i	−0.120494	+	0.683353i
$147$		0			0
$148$	166.469	−	198.390i	0.0924570	−	0.110186i
$149$	−1037.46	+	182.932i	−0.570417	+	0.100580i	−0.451415	−	0.892314i	$-0.649081\pi$
$149$	−1037.46	+	182.932i	−0.570417	+	0.100580i	−0.119002	+	0.992894i	$0.537969\pi$
$150$		0			0
$151$		−	1020.14i		−	0.549789i	−0.961474	−	0.274895i	$-0.911357\pi$
$151$		−	1020.14i		−	0.549789i	0.961474	−	0.274895i	$-0.0886430\pi$
$152$	−581.934	+	745.175i	−0.310533	+	0.397643i
$153$		0			0
$154$	−11.1641	+	30.6732i	−0.00584176	+	0.0160501i
$155$	−358.853	−	2035.16i	−0.185960	−	1.05463i
$156$		0			0
$157$	2296.68	−	1927.14i	1.16748	−	0.979634i	0.167502	−	0.985872i	$-0.446430\pi$
$157$	2296.68	−	1927.14i	1.16748	−	0.979634i	0.999981	+	0.00623754i	$0.00198549\pi$
$158$	1974.04	+	348.077i	0.993963	+	0.175263i
$159$		0			0
$160$	−3452.63	+	1993.38i	−1.70597	+	0.984940i
$161$	−124.110	−	340.988i	−0.0607529	−	0.166917i
$162$		0			0
$163$	−773.278	−	1339.36i	−0.371582	−	0.643599i	0.618227	−	0.785999i	$-0.287851\pi$
$163$	−773.278	−	1339.36i	−0.371582	−	0.643599i	−0.989809	+	0.142401i	$0.954518\pi$
$164$	−814.753	+	1411.19i	−0.387936	+	0.671925i
$165$		0			0
$166$	−1378.08	−	1642.33i	−0.644336	−	0.767889i
$167$	−3156.36	−	2648.50i	−1.46255	−	1.22723i	−0.922730	−	0.385448i	$-0.874047\pi$
$167$	−3156.36	−	2648.50i	−1.46255	−	1.22723i	−0.539822	−	0.841779i	$-0.681509\pi$
$168$		0			0
$169$	16.0952	+	5.85818i	0.00732600	+	0.00266645i
$170$	−2315.94			−1.04485
$171$		0			0
$172$	−1253.26			−0.555583
$173$	−3385.01	−	1232.04i	−1.48761	−	0.541448i	−0.534794	−	0.844982i	$-0.679611\pi$
$173$	−3385.01	−	1232.04i	−1.48761	−	0.541448i	−0.952820	+	0.303535i	$0.901833\pi$
$174$		0			0
$175$	−3611.91	−	3030.75i	−1.56020	−	1.30916i
$176$	−29.9144	−	35.6505i	−0.0128118	−	0.0152685i
$177$		0			0
$178$	2140.36	−	3707.20i	0.901272	−	1.56105i
$179$	389.679	+	674.943i	0.162715	+	0.281830i	0.935841	−	0.352421i	$-0.114642\pi$
$179$	389.679	+	674.943i	0.162715	+	0.281830i	−0.773127	+	0.634252i	$0.781308\pi$
$180$		0			0
$181$	296.501	+	814.631i	0.121761	+	0.334536i	0.985566	−	0.169290i	$-0.0541474\pi$
$181$	296.501	+	814.631i	0.121761	+	0.334536i	−0.863805	+	0.503826i	$0.831925\pi$
$182$	2267.79	−	1309.31i	0.923627	−	0.533256i
$183$		0			0
$184$	262.383	+	46.2653i	0.105126	+	0.0185365i
$185$	−853.467	+	716.144i	−0.339179	+	0.284605i
$186$		0			0
$187$	−3.18474	−	18.0615i	−0.00124541	−	0.00706305i
$188$	1014.18	−	2786.43i	0.393438	−	1.08096i
$189$		0			0
$190$	−4557.69	+	4105.56i	−1.74026	+	1.56762i
$191$			3746.70i			1.41938i	0.704514	+	0.709690i	$0.251165\pi$
$191$			3746.70i			1.41938i	−0.704514	+	0.709690i	$0.748835\pi$
$192$		0			0
$193$	1602.36	−	282.539i	0.597617	−	0.105376i	0.133347	−	0.991069i	$-0.457428\pi$
$193$	1602.36	−	282.539i	0.597617	−	0.105376i	0.464271	+	0.885693i	$0.346316\pi$
$194$	478.475	−	570.224i	0.177075	−	0.211029i
$195$		0			0
$196$	−84.5681	+	479.610i	−0.0308193	+	0.174785i
$197$	319.858	+	184.670i	0.115680	+	0.0667878i	0.556724	−	0.830698i	$-0.312058\pi$
$197$	319.858	+	184.670i	0.115680	+	0.0667878i	−0.441044	+	0.897486i	$0.645392\pi$
$198$		0			0
$199$	2623.17	−	954.754i	0.934429	−	0.340104i	0.170465	−	0.985364i	$-0.445473\pi$
$199$	2623.17	−	954.754i	0.934429	−	0.340104i	0.763963	+	0.645259i	$0.223251\pi$
$200$	3253.11	−	1184.04i	1.15015	−	0.418620i
$201$		0			0
$202$	4634.04	+	2675.47i	1.61411	+	0.931907i
$203$	−768.933	+	4360.84i	−0.265855	+	1.50774i
$204$		0			0
$205$	4506.00	−	5370.04i	1.53518	−	1.82956i
$206$	−2410.45	+	425.027i	−0.815261	+	0.143752i
$207$		0			0
$208$			3733.46i			1.24456i
$209$	−38.2858	−	29.8988i	−0.0126712	−	0.00989541i
$210$		0			0
$211$	674.084	−	1852.03i	0.219933	−	0.604261i	−0.779831	−	0.625990i	$-0.784695\pi$
$211$	674.084	−	1852.03i	0.219933	−	0.604261i	0.999764	+	0.0217291i	$0.00691714\pi$
$212$	126.914	+	719.767i	0.0411156	+	0.233178i
$213$		0			0
$214$	2214.76	−	1858.41i	0.707468	−	0.593636i
$215$	5309.59	+	936.224i	1.68424	+	0.296976i
$216$		0			0
$217$	−1344.69	+	776.358i	−0.420662	+	0.242869i
$218$	385.492	+	1059.13i	0.119765	+	0.329052i
$219$		0			0
$220$	−29.1941	−	50.5656i	−0.00894666	−	0.0154961i
$221$	−735.653	+	1274.19i	−0.223916	+	0.387834i
$222$		0			0
$223$	3862.31	+	4602.93i	1.15982	+	1.38222i	0.910352	+	0.413835i	$0.135811\pi$
$223$	3862.31	+	4602.93i	1.15982	+	1.38222i	0.249467	+	0.968383i	$0.419745\pi$
$224$	2294.67	+	1925.45i	0.684459	+	0.574329i
$225$		0			0
$226$	−1336.95	−	486.608i	−0.393506	−	0.143224i
$227$	−2018.84			−0.590287			−0.295143	−	0.955453i	$-0.595367\pi$
$227$	−2018.84			−0.590287			−0.295143	+	0.955453i	$0.595367\pi$
$228$		0			0
$229$	4532.55			1.30794			0.653972	−	0.756519i	$-0.273101\pi$
$229$	4532.55			1.30794			0.653972	+	0.756519i	$0.273101\pi$
$230$	1624.33	+	591.209i	0.465675	+	0.169492i
$231$		0			0
$232$	−2490.60	−	2089.86i	−0.704809	−	0.591405i
$233$	−2069.78	−	2466.67i	−0.581957	−	0.693550i	0.392082	−	0.919930i	$-0.371755\pi$
$233$	−2069.78	−	2466.67i	−0.581957	−	0.693550i	−0.974039	+	0.226381i	$0.927311\pi$
$234$		0			0
$235$	−6378.22	+	11047.4i	−1.77051	+	3.06661i
$236$	−1089.84	−	1887.65i	−0.300603	−	0.520660i
$237$		0			0
$238$	595.148	+	1635.16i	0.162091	+	0.445342i
$239$	−4014.76	+	2317.92i	−1.08658	+	0.627339i	−0.932664	−	0.360745i	$-0.882522\pi$
$239$	−4014.76	+	2317.92i	−1.08658	+	0.627339i	−0.153918	+	0.988084i	$0.549189\pi$
$240$		0			0
$241$	−6641.51	−	1171.08i	−1.77517	−	0.313011i	−0.812356	−	0.583162i	$-0.801815\pi$
$241$	−6641.51	−	1171.08i	−1.77517	−	0.313011i	−0.962818	+	0.270151i	$0.912927\pi$
$242$	−3648.38	+	3061.36i	−0.969120	+	0.813188i
$243$		0			0
$244$	−523.147	−	2966.92i	−0.137259	−	0.778432i
$245$	716.565	−	1968.75i	0.186856	−	0.513382i
$246$		0			0
$247$	811.062	+	3811.68i	0.208934	+	0.981908i
$248$		−	1140.05i		−	0.291908i
$249$		0			0
$250$	13001.4	−	2292.50i	3.28913	−	0.579963i
$251$	−2630.37	+	3134.75i	−0.661463	+	0.788301i	−0.987595	−	0.157023i	$-0.949810\pi$
$251$	−2630.37	+	3134.75i	−0.661463	+	0.788301i	0.326132	+	0.945324i	$0.394255\pi$
$252$		0			0
$253$	−2.37703	+	13.4808i	−0.000590683	+	0.00334993i
$254$	4419.68	+	2551.70i	1.09179	+	0.630347i
$255$		0			0
$256$	−4935.94	+	1796.54i	−1.20506	+	0.438608i
$257$	5250.22	−	1910.92i	1.27432	−	0.463814i	0.385769	−	0.922595i	$-0.373936\pi$
$257$	5250.22	−	1910.92i	1.27432	−	0.463814i	0.888549	+	0.458781i	$0.151714\pi$
$258$		0			0
$259$	724.951	+	418.551i	0.173924	+	0.100415i
$260$	−813.382	+	4612.92i	−0.194015	+	1.10031i
$261$		0			0
$262$	4177.90	−	4979.03i	0.985158	−	1.17407i
$263$	7263.49	−	1280.75i	1.70299	−	0.300283i	0.764251	−	0.644918i	$-0.223109\pi$
$263$	7263.49	−	1280.75i	1.70299	−	0.300283i	0.938737	+	0.344636i	$0.111998\pi$
$264$		0			0
$265$		−	3144.19i		−	0.728852i
$266$	4069.93	+	2162.89i	0.938133	+	0.498553i
$267$		0			0
$268$	1488.22	−	4088.86i	0.339207	−	0.931965i
$269$	−177.720	−	1007.90i	−0.0402816	−	0.228448i	0.958020	−	0.286700i	$-0.0925584\pi$
$269$	−177.720	−	1007.90i	−0.0402816	−	0.228448i	−0.998302	+	0.0582520i	$0.981447\pi$
$270$		0			0
$271$	−4082.96	+	3426.01i	−0.915212	+	0.767954i	−0.973103	−	0.230369i	$-0.926007\pi$
$271$	−4082.96	+	3426.01i	−0.915212	+	0.767954i	0.0578917	+	0.998323i	$0.481562\pi$
$272$	−2443.23	−	430.807i	−0.544641	−	0.0960349i
$273$		0			0
$274$	−342.877	+	197.960i	−0.0755984	+	0.0436468i
$275$	60.8338	+	167.140i	0.0133397	+	0.0366505i
$276$		0			0
$277$	2776.61	+	4809.22i	0.602274	+	1.04317i	0.992476	+	0.122440i	$0.0390721\pi$
$277$	2776.61	+	4809.22i	0.602274	+	1.04317i	−0.390201	+	0.920730i	$0.627595\pi$
$278$	−3168.02	+	5487.17i	−0.683472	+	1.18381i
$279$		0			0
$280$	−2361.16	−	2813.92i	−0.503952	−	0.600586i
$281$	5678.68	+	4764.98i	1.20556	+	1.01158i	0.999454	+	0.0330525i	$0.0105228\pi$
$281$	5678.68	+	4764.98i	1.20556	+	1.01158i	0.206104	+	0.978530i	$0.433922\pi$
$282$		0			0
$283$	3476.62	+	1265.39i	0.730260	+	0.265793i	0.680275	−	0.732957i	$-0.261860\pi$
$283$	3476.62	+	1265.39i	0.730260	+	0.265793i	0.0499849	+	0.998750i	$0.484083\pi$
$284$	1168.49			0.244144
$285$		0			0
$286$	−98.7834			−0.0204237
$287$	−4949.42	−	1801.44i	−1.01796	−	0.370508i
$288$		0			0
$289$	3014.62	+	2529.57i	0.613600	+	0.514872i
$290$	−13558.8	−	16158.7i	−2.74552	−	3.27198i
$291$		0			0
$292$	−822.603	+	1424.79i	−0.164860	+	0.285546i
$293$	158.920	+	275.257i	0.0316867	+	0.0548830i	0.881434	−	0.472307i	$-0.156579\pi$
$293$	158.920	+	275.257i	0.0316867	+	0.0548830i	−0.849747	+	0.527190i	$0.823245\pi$
$294$		0			0
$295$	3207.09	+	8811.41i	0.632963	+	1.73905i
$296$	−532.280	+	307.312i	−0.104521	+	0.0603451i
$297$		0			0
$298$	−3713.24	−	654.744i	−0.721819	−	0.127276i
$299$	841.237	−	705.882i	0.162709	−	0.136529i
$300$		0			0
$301$	−703.437	−	3989.39i	−0.134702	−	0.763935i
$302$	1248.80	−	3431.06i	0.237949	−	0.653759i
$303$		0			0
$304$	−5571.89	+	3483.38i	−1.05122	+	0.657190i
$305$			12960.5i			2.43317i
$306$		0			0
$307$	2868.16	−	505.735i	0.533208	−	0.0940189i	0.0994398	−	0.995044i	$-0.468295\pi$
$307$	2868.16	−	505.735i	0.533208	−	0.0940189i	0.433768	+	0.901025i	$0.357184\pi$
$308$	−28.1993	+	33.6066i	−0.00521689	+	0.00621725i
$309$		0			0
$310$	1284.39	−	7284.15i	0.235318	−	1.33455i
$311$	−4209.45	−	2430.33i	−0.767512	−	0.443123i	0.0644743	−	0.997919i	$-0.479463\pi$
$311$	−4209.45	−	2430.33i	−0.767512	−	0.443123i	−0.831986	+	0.554796i	$0.812796\pi$
$312$		0			0
$313$	−4039.58	+	1470.29i	−0.729491	+	0.265513i	−0.679950	−	0.733259i	$-0.737998\pi$
$313$	−4039.58	+	1470.29i	−0.729491	+	0.265513i	−0.0495418	+	0.998772i	$0.515776\pi$
$314$	10083.5	−	3670.10i	1.81225	−	0.659605i
$315$		0			0
$316$	2333.09	+	1347.01i	0.415338	+	0.239795i
$317$	710.113	−	4027.25i	0.125817	−	0.713542i	−0.855003	−	0.518623i	$-0.826445\pi$
$317$	710.113	−	4027.25i	0.125817	−	0.713542i	0.980819	−	0.194919i	$-0.0624442\pi$
$318$		0			0
$319$	107.373	−	127.963i	0.0188456	−	0.0224593i
$320$	−1116.54	+	196.875i	−0.195051	+	0.0343927i
$321$		0			0
$322$		−	1298.78i		−	0.224776i
$323$	−2588.00	+	90.9378i	−0.445821	+	0.0156654i
$324$		0			0
$325$	4880.28	−	13408.5i	0.832951	−	2.28851i
$326$	−961.207	−	5451.27i	−0.163302	−	0.926129i
$327$		0			0
$328$	2962.47	−	2485.81i	0.498704	−	0.418463i
$329$	9439.01	+	1664.35i	1.58173	+	0.278902i
$330$		0			0
$331$	−4107.97	+	2371.74i	−0.682158	+	0.393844i	−0.800668	−	0.599109i	$-0.795522\pi$
$331$	−4107.97	+	2371.74i	−0.682158	+	0.393844i	0.118509	+	0.992953i	$0.462188\pi$
$332$	−985.498	−	2707.63i	−0.162910	−	0.447592i
$333$		0			0
$334$	−7373.65	−	12771.5i	−1.20799	−	2.09230i
$335$	−9359.52	+	16211.2i	−1.52646	+	2.64391i
$336$		0			0
$337$	3482.36	+	4150.11i	0.562897	+	0.670834i	0.970157	−	0.242478i	$-0.0779603\pi$
$337$	3482.36	+	4150.11i	0.562897	+	0.670834i	−0.407260	+	0.913312i	$0.633516\pi$
$338$	46.9619	+	39.4057i	0.00755738	+	0.00634139i
$339$		0			0
$340$	−2924.90	−	1064.58i	−0.466544	−	0.169808i
$341$	58.5737			0.00930189
$342$		0			0
$343$	−6907.33			−1.08735
$344$	2794.94	+	1017.27i	0.438061	+	0.159441i
$345$		0			0
$346$	−9876.62	−	8287.47i	−1.53460	−	1.28768i
$347$	−4198.08	−	5003.07i	−0.649466	−	0.774003i	0.336368	−	0.941731i	$-0.390802\pi$
$347$	−4198.08	−	5003.07i	−0.649466	−	0.774003i	−0.985833	+	0.167728i	$0.946357\pi$
$348$		0			0
$349$	2007.68	−	3477.41i	0.307934	−	0.533357i	−0.669977	−	0.742382i	$-0.733696\pi$
$349$	2007.68	−	3477.41i	0.307934	−	0.533357i	0.977910	+	0.209026i	$0.0670292\pi$
$350$	−8437.88	−	14614.8i	−1.28864	−	2.23199i
$351$		0			0
$352$	−38.6481	−	106.185i	−0.00585213	−	0.0160786i
$353$	2038.50	−	1176.93i	0.307361	−	0.177455i	−0.338384	−	0.941008i	$-0.609880\pi$
$353$	2038.50	−	1176.93i	0.307361	−	0.177455i	0.645745	+	0.763553i	$0.276547\pi$
$354$		0			0
$355$	−4950.43	−	872.894i	−0.740117	−	0.130503i
$356$	4407.24	−	3698.12i	0.656133	−	0.550561i
$357$		0			0
$358$	484.381	+	2747.06i	0.0715094	+	0.405550i
$359$	730.862	−	2008.03i	0.107447	−	0.295208i	−0.874304	−	0.485378i	$-0.838682\pi$
$359$	730.862	−	2008.03i	0.107447	−	0.295208i	0.981751	+	0.190170i	$0.0609041\pi$
$360$		0			0
$361$	−4931.88	+	4766.81i	−0.719038	+	0.694971i
$362$			3102.81i			0.450498i
$363$		0			0
$364$	3465.94	−	611.139i	0.499079	−	0.0880011i
$365$	4549.41	−	5421.78i	0.652403	−	0.777504i
$366$		0			0
$367$	548.074	−	3108.28i	0.0779543	−	0.442101i	−0.920701	−	0.390268i	$-0.872383\pi$
$367$	548.074	−	3108.28i	0.0779543	−	0.442101i	0.998656	−	0.0518331i	$-0.0165064\pi$
$368$	1603.63	+	925.856i	0.227160	+	0.131151i
$369$		0			0
$370$	−3747.13	+	1363.85i	−0.526498	+	0.191630i
$371$	−2219.93	+	807.989i	−0.310655	+	0.113069i
$372$		0			0
$373$	−6283.68	−	3627.89i	−0.872270	−	0.503605i	−0.00416822	−	0.999991i	$-0.501327\pi$
$373$	−6283.68	−	3627.89i	−0.872270	−	0.503605i	−0.868102	+	0.496386i	$0.834660\pi$
$374$	11.3987	−	64.6451i	0.00157597	−	0.00893775i
$375$		0			0
$376$	−4523.49	+	5390.88i	−0.620428	+	0.739398i
$377$	−13197.2	+	2327.01i	−1.80289	+	0.317897i
$378$		0			0
$379$			5263.86i			0.713420i	0.934215	+	0.356710i	$0.116102\pi$
$379$			5263.86i			0.713420i	−0.934215	+	0.356710i	$0.883898\pi$
$380$	−7643.31	+	3090.03i	−1.03182	+	0.417145i
$381$		0			0
$382$	−4586.50	+	12601.3i	−0.614308	+	1.68780i
$383$	−976.746	−	5539.40i	−0.130312	−	0.739035i	−0.978010	−	0.208556i	$-0.933124\pi$
$383$	−976.746	−	5539.40i	−0.130312	−	0.739035i	0.847699	−	0.530478i	$-0.177988\pi$
$384$		0			0
$385$	144.575	−	121.312i	0.0191382	−	0.0160588i
$386$	5735.09	+	1011.25i	0.756239	+	0.133345i
$387$		0			0
$388$	866.401	−	500.217i	0.113363	−	0.0654502i
$389$	−2418.52	−	6644.84i	−0.315229	−	0.866084i	−0.991579	−	0.129504i	$-0.958662\pi$
$389$	−2418.52	−	6644.84i	−0.315229	−	0.866084i	0.676350	−	0.736580i	$-0.263561\pi$
$390$		0			0
$391$	364.867	+	631.968i	0.0471921	+	0.0817392i
$392$	577.897	−	1000.95i	0.0744597	−	0.128968i
$393$		0			0
$394$	849.717	+	1012.65i	0.108650	+	0.129484i
$395$	−8878.16	−	7449.66i	−1.13091	−	0.948945i
$396$		0			0
$397$	9183.64	+	3342.57i	1.16099	+	0.422566i	0.849452	−	0.527667i	$-0.176933\pi$
$397$	9183.64	+	3342.57i	1.16099	+	0.422566i	0.311540	+	0.950233i	$0.399155\pi$
$398$	9991.27			1.25833
$399$		0			0
$400$	24060.3			3.00754
$401$	4793.19	+	1744.58i	0.596909	+	0.217257i	0.622765	−	0.782409i	$-0.286009\pi$
$401$	4793.19	+	1744.58i	0.596909	+	0.217257i	−0.0258567	+	0.999666i	$0.508231\pi$
$402$		0			0
$403$	−3599.62	−	3020.44i	−0.444937	−	0.373347i
$404$	4622.68	+	5509.10i	0.569275	+	0.678435i
$405$		0			0
$406$	−7924.45	+	13725.5i	−0.968679	+	1.67780i
$407$	−15.7892	−	27.3476i	−0.00192295	−	0.00333064i
$408$		0			0
$409$	−16.0667	−	44.1429i	−0.00194242	−	0.00533674i	0.938718	−	0.344687i	$-0.112015\pi$
$409$	−16.0667	−	44.1429i	−0.00194242	−	0.00533674i	−0.940660	+	0.339350i	$0.889793\pi$
$410$	21728.7	−	12545.1i	2.61733	−	1.51112i
$411$		0			0
$412$	−3239.62	−	571.233i	−0.387390	−	0.0683073i
$413$	5397.08	−	4528.69i	0.643034	−	0.539569i
$414$		0			0
$415$	2152.49	+	12207.4i	0.254607	+	1.44395i
$416$	−3100.47	+	8518.47i	−0.365416	+	1.00397i
$417$		0			0
$418$	−92.1666	−	147.426i	−0.0107847	−	0.0172508i
$419$		−	4773.84i		−	0.556605i	−0.960494	−	0.278302i	$-0.910228\pi$
$419$		−	4773.84i		−	0.556605i	0.960494	−	0.278302i	$-0.0897717\pi$
$420$		0			0
$421$	864.150	−	152.373i	0.100038	−	0.0176394i	−0.123405	−	0.992356i	$-0.539381\pi$
$421$	864.150	−	152.373i	0.100038	−	0.0176394i	0.223443	+	0.974717i	$0.428270\pi$
$422$	4534.31	−	5403.78i	0.523049	−	0.623345i
$423$		0			0
$424$	301.200	−	1708.19i	0.0344990	−	0.195653i
$425$	8211.53	+	4740.93i	0.937218	+	0.541103i
$426$		0			0
$427$	9150.67	−	3330.57i	1.03708	−	0.377465i
$428$	3651.37	−	1328.99i	0.412373	−	0.150092i
$429$		0			0
$430$	16711.7	+	9648.51i	1.87421	+	1.08208i
$431$	−592.556	+	3360.55i	−0.0662237	+	0.375573i	0.933626	+	0.358249i	$0.116626\pi$
$431$	−592.556	+	3360.55i	−0.0662237	+	0.375573i	−0.999850	+	0.0173246i	$0.994485\pi$
$432$		0			0
$433$	5080.87	−	6055.15i	0.563905	−	0.672036i	−0.406463	−	0.913667i	$-0.633238\pi$
$433$	5080.87	−	6055.15i	0.563905	−	0.672036i	0.970368	+	0.241631i	$0.0776824\pi$
$434$	−5472.98	+	965.035i	−0.605326	+	0.106735i
$435$		0			0
$436$			1514.82i			0.166392i
$437$	1838.36	+	596.878i	0.201237	+	0.0653376i
$438$		0			0
$439$	5891.95	−	16188.0i	0.640564	−	1.75994i	−0.00938327	−	0.999956i	$-0.502987\pi$
$439$	5891.95	−	16188.0i	0.640564	−	1.75994i	0.649947	−	0.759979i	$-0.274791\pi$
$440$	24.0624	+	136.465i	0.00260712	+	0.0147857i
$441$		0			0
$442$	−4034.02	+	3384.94i	−0.434115	+	0.364265i
$443$	6847.95	+	1207.48i	0.734438	+	0.129501i	0.528343	−	0.849031i	$-0.322813\pi$
$443$	6847.95	+	1207.48i	0.734438	+	0.129501i	0.206095	+	0.978532i	$0.433925\pi$
$444$		0			0
$445$	−21434.4	+	12375.2i	−2.28334	+	1.31829i
$446$	7355.50	+	20209.1i	0.780926	+	2.14558i
$447$		0			0
$448$	425.928	+	737.730i	0.0449179	+	0.0778001i
$449$	−1530.82	+	2651.46i	−0.160899	+	0.278686i	−0.935192	−	0.354142i	$-0.884773\pi$
$449$	−1530.82	+	2651.46i	−0.160899	+	0.278686i	0.774292	+	0.632828i	$0.218106\pi$
$450$		0			0
$451$	127.717	+	152.207i	0.0133347	+	0.0158916i
$452$	−1464.80	−	1229.11i	−0.152430	−	0.127904i
$453$		0			0
$454$	−6789.98	−	2471.35i	−0.701915	−	0.255476i
$455$	−15140.4			−1.55999
$456$		0			0
$457$	−13086.6			−1.33953			−0.669766	−	0.742572i	$-0.733606\pi$
$457$	−13086.6			−1.33953			−0.669766	+	0.742572i	$0.733606\pi$
$458$	15244.3	+	5548.49i	1.55529	+	0.566078i
$459$		0			0
$460$	1779.67	+	1493.32i	0.180386	+	0.151362i
$461$	6745.89	+	8039.44i	0.681535	+	0.812221i	0.990304	−	0.138916i	$-0.0443617\pi$
$461$	6745.89	+	8039.44i	0.681535	+	0.812221i	−0.308770	+	0.951137i	$0.599917\pi$
$462$		0			0
$463$	7339.34	−	12712.1i	0.736691	−	1.27599i	−0.217286	−	0.976108i	$-0.569721\pi$
$463$	7339.34	−	12712.1i	0.736691	−	1.27599i	0.953977	−	0.299878i	$-0.0969461\pi$
$464$	−11298.2	−	19569.0i	−1.13040	−	1.95790i
$465$		0			0
$466$	−3941.76	−	10829.9i	−0.391842	−	1.07658i
$467$	−4543.90	+	2623.42i	−0.450250	+	0.259952i	−0.707936	−	0.706277i	$-0.750373\pi$
$467$	−4543.90	+	2623.42i	−0.450250	+	0.259952i	0.257686	+	0.966229i	$0.417040\pi$
$468$		0			0
$469$	13851.0	+	2442.30i	1.36371	+	0.240458i
$470$	−34975.5	+	29347.9i	−3.43255	+	2.88025i
$471$		0			0
$472$	898.269	+	5094.33i	0.0875978	+	0.496792i
$473$	−52.2658	+	143.599i	−0.00508073	+	0.0139592i
$474$		0			0
$475$	24564.4	−	5226.90i	2.37283	−	0.504898i
$476$			2338.68i			0.225196i
$477$		0			0
$478$	−16340.3	+	2881.24i	−1.56358	+	0.275701i
$479$	3625.56	−	4320.77i	0.345837	−	0.412153i	−0.564887	−	0.825169i	$-0.691080\pi$
$479$	3625.56	−	4320.77i	0.345837	−	0.412153i	0.910724	+	0.413016i	$0.135525\pi$
$480$		0			0
$481$	−439.905	+	2494.83i	−0.0417005	+	0.236495i
$482$	−20903.9	−	12068.8i	−1.97540	−	1.14050i
$483$		0			0
$484$	−6014.91	+	2189.25i	−0.564887	+	0.205602i
$485$	−4044.29	+	1472.00i	−0.378642	+	0.137815i
$486$		0			0
$487$	7501.19	+	4330.81i	0.697970	+	0.402973i	0.806591	−	0.591110i	$-0.201310\pi$
$487$	7501.19	+	4330.81i	0.697970	+	0.402973i	−0.108621	+	0.994083i	$0.534643\pi$
$488$	−1241.56	+	7041.25i	−0.115170	+	0.653160i
$489$		0			0
$490$	4820.06	−	5744.32i	0.444384	−	0.529596i
$491$	−13111.7	+	2311.95i	−1.20514	+	0.212499i	−0.739920	−	0.672695i	$-0.765137\pi$
$491$	−13111.7	+	2311.95i	−1.20514	+	0.212499i	−0.465222	+	0.885194i	$0.654026\pi$
$492$		0			0
$493$		−	8904.90i		−	0.813502i
$494$	−1938.19	+	13812.7i	−0.176525	+	1.25802i
$495$		0			0
$496$	2709.96	−	7445.56i	0.245324	−	0.674023i
$497$	655.854	+	3719.53i	0.0591933	+	0.335702i
$498$		0			0
$499$	−6868.77	+	5763.59i	−0.616209	+	0.517061i	−0.896609	−	0.442822i	$-0.853977\pi$
$499$	−6868.77	+	5763.59i	−0.616209	+	0.517061i	0.280400	+	0.959883i	$0.409533\pi$
$500$	17473.8	+	3081.11i	1.56291	+	0.275583i
$501$		0			0
$502$	−12684.1	+	7323.17i	−1.12773	+	0.651094i
$503$	−732.241	−	2011.81i	−0.0649085	−	0.178335i	0.902998	−	0.429644i	$-0.141361\pi$
$503$	−732.241	−	2011.81i	−0.0649085	−	0.178335i	−0.967907	+	0.251309i	$0.919139\pi$
$504$		0			0
$505$	−15469.1	−	26793.2i	−1.36310	−	2.36095i
$506$	−24.4971	+	42.4303i	−0.00215223	+	0.00372778i
$507$		0			0
$508$	4408.84	+	5254.25i	0.385060	+	0.458897i
$509$	16941.6	+	14215.7i	1.47529	+	1.23792i	0.911042	+	0.412315i	$0.135280\pi$
$509$	16941.6	+	14215.7i	1.47529	+	1.23792i	0.564251	+	0.825603i	$0.309165\pi$
$510$		0			0
$511$	−4997.11	−	1818.80i	−0.432601	−	0.157454i
$512$	−8039.28			−0.693925
$513$		0			0
$514$	19997.4			1.71604
$515$	13298.3	+	4840.19i	1.13785	+	0.414144i
$516$		0			0
$517$	−276.974	−	232.409i	−0.0235615	−	0.0197705i
$518$	1925.87	+	2295.16i	0.163355	+	0.194679i
$519$		0			0
$520$	5558.26	−	9627.19i	0.468742	−	0.811885i
$521$	−1634.47	−	2830.98i	−0.137442	−	0.238057i	0.789086	−	0.614283i	$-0.210555\pi$
$521$	−1634.47	−	2830.98i	−0.137442	−	0.238057i	−0.926528	+	0.376227i	$0.877221\pi$
$522$		0			0
$523$	−2224.28	−	6111.15i	−0.185967	−	0.510941i	0.811316	−	0.584608i	$-0.198752\pi$
$523$	−2224.28	−	6111.15i	−0.185967	−	0.510941i	−0.997283	+	0.0736677i	$0.976530\pi$
$524$	7565.16	−	4367.75i	0.630698	−	0.364134i
$525$		0			0
$526$	25997.2	+	4584.00i	2.15500	+	0.379985i
$527$	2391.98	−	2007.11i	0.197716	−	0.165903i
$528$		0			0
$529$	2018.20	+	11445.8i	0.165875	+	0.940722i
$530$	3848.94	−	10574.9i	0.315447	−	0.866684i
$531$		0			0
$532$	4145.86	+	4602.43i	0.337868	+	0.375077i
$533$		−	15939.7i		−	1.29535i
$534$		0			0
$535$	−16462.3	+	2902.74i	−1.33033	+	0.234573i
$536$	−6637.85	+	7910.69i	−0.534910	+	0.637481i
$537$		0			0
$538$	636.086	−	3607.42i	0.0509733	−	0.289084i
$539$	51.4270	+	29.6914i	0.00410968	+	0.00237272i
$540$		0			0
$541$	20922.5	−	7615.15i	1.66271	−	0.605178i	0.671926	−	0.740618i	$-0.265467\pi$
$541$	20922.5	−	7615.15i	1.66271	−	0.605178i	0.990785	+	0.135441i	$0.0432450\pi$
$542$	−17926.2	+	6524.60i	−1.42066	+	0.517077i
$543$		0			0
$544$	−5216.83	−	3011.94i	−0.411158	−	0.237382i
$545$	1131.62	−	6417.71i	0.0889415	−	0.504412i
$546$		0			0
$547$	−2657.93	+	3167.60i	−0.207761	+	0.247599i	−0.859855	−	0.510538i	$-0.829446\pi$
$547$	−2657.93	+	3167.60i	−0.207761	+	0.247599i	0.652094	+	0.758138i	$0.273891\pi$
$548$	−524.030	+	92.4007i	−0.0408494	+	0.00720285i
$549$		0			0
$550$			636.611i			0.0493549i
$551$	−15786.1	−	17524.5i	−1.22052	−	1.35494i
$552$		0			0
$553$	−2978.29	+	8182.77i	−0.229023	+	0.629235i
$554$	3451.40	+	19573.9i	0.264686	+	1.50111i
$555$		0			0
$556$	−6523.32	+	5473.72i	−0.497573	+	0.417513i
$557$	−3266.41	−	575.957i	−0.248478	−	0.0438134i	0.0480217	−	0.998846i	$-0.484708\pi$
$557$	−3266.41	−	575.957i	−0.248478	−	0.0438134i	−0.296500	+	0.955033i	$0.595819\pi$
$558$		0			0
$559$	10616.9	−	6129.65i	0.803301	−	0.463786i
$560$	−8731.69	−	23990.1i	−0.658895	−	1.81030i
$561$		0			0
$562$	13266.1	+	22977.6i	0.995725	+	1.72465i
$563$	−8843.07	+	15316.6i	−0.661973	+	1.14657i	0.318123	+	0.948049i	$0.396947\pi$
$563$	−8843.07	+	15316.6i	−0.661973	+	1.14657i	−0.980096	+	0.198522i	$0.936386\pi$
$564$		0			0
$565$	5287.62	+	6301.54i	0.393720	+	0.469217i
$566$	10143.9	+	8511.76i	0.753323	+	0.632113i
$567$		0			0
$568$	−2605.88	−	948.462i	−0.192500	−	0.0700644i
$569$	10925.5			0.804959			0.402480	−	0.915429i	$-0.368148\pi$
$569$	10925.5			0.804959			0.402480	+	0.915429i	$0.368148\pi$
$570$		0			0
$571$	−13116.4			−0.961305			−0.480652	−	0.876911i	$-0.659600\pi$
$571$	−13116.4			−0.961305			−0.480652	+	0.876911i	$0.659600\pi$
$572$	−124.758	−	45.4080i	−0.00911954	−	0.00331924i
$573$		0			0
$574$	−14441.2	−	12117.6i	−1.05011	−	0.881149i
$575$	−4549.06	−	5421.36i	−0.329929	−	0.393194i
$576$		0			0
$577$	−4494.99	+	7785.54i	−0.324313	+	0.561727i	−0.981373	−	0.192111i	$-0.938467\pi$
$577$	−4494.99	+	7785.54i	−0.324313	+	0.561727i	0.657060	+	0.753838i	$0.271800\pi$
$578$	7042.54	+	12198.0i	0.506801	+	0.877805i
$579$		0			0
$580$	−9696.22	−	26640.1i	−0.694161	−	1.90719i
$581$	8065.80	−	4656.79i	0.575948	−	0.332524i
$582$		0			0
$583$	87.7639	+	15.4751i	0.00623467	+	0.00109934i
$584$	2991.01	−	2509.76i	0.211933	−	0.177833i
$585$		0			0
$586$	197.542	+	1120.32i	0.0139256	+	0.0789758i
$587$	6445.89	−	17709.9i	0.453237	−	1.24526i	−0.477196	−	0.878797i	$-0.658347\pi$
$587$	6445.89	−	17709.9i	0.453237	−	1.24526i	0.930433	−	0.366462i	$-0.119431\pi$
$588$		0			0
$589$	1149.25	−	8190.26i	0.0803974	−	0.572960i
$590$			33561.4i			2.34187i
$591$		0			0
$592$	−4206.77	+	741.768i	−0.292056	+	0.0514974i
$593$	5754.77	−	6858.27i	0.398516	−	0.474933i	−0.529051	−	0.848590i	$-0.677452\pi$
$593$	5754.77	−	6858.27i	0.398516	−	0.474933i	0.927567	+	0.373657i	$0.121896\pi$
$594$		0			0
$595$	1747.06	−	9908.08i	0.120374	−	0.682675i
$596$	−4388.63	−	2533.78i	−0.301620	−	0.174140i
$597$		0			0
$598$	3693.44	−	1344.30i	0.252568	−	0.0919274i
$599$	−9574.28	+	3484.75i	−0.653079	+	0.237701i	−0.647246	−	0.762281i	$-0.724079\pi$
$599$	−9574.28	+	3484.75i	−0.653079	+	0.237701i	−0.00583382	+	0.999983i	$0.501857\pi$
$600$		0			0
$601$	−1647.80	−	951.360i	−0.111839	−	0.0645704i	0.443037	−	0.896503i	$-0.353901\pi$
$601$	−1647.80	−	951.360i	−0.111839	−	0.0645704i	−0.554876	+	0.831933i	$0.687234\pi$
$602$	2517.71	−	14278.6i	0.170456	−	0.966701i
$603$		0			0
$604$	3154.33	−	3759.18i	0.212496	−	0.253243i
$605$	27118.3	−	4781.69i	1.82234	−	0.321328i
$606$		0			0
$607$			3728.13i			0.249292i	0.992201	+	0.124646i	$0.0397795\pi$
$607$			3728.13i			0.249292i	−0.992201	+	0.124646i	$0.960221\pi$
$608$	−15605.9	+	3320.68i	−1.04096	+	0.221499i
$609$		0			0
$610$	−15865.5	+	43590.1i	−1.05307	+	2.89330i
$611$	5036.81	+	28565.2i	0.333498	+	1.89136i
$612$		0			0
$613$	−3839.31	+	3221.57i	−0.252966	+	0.212264i	−0.760448	−	0.649398i	$-0.775021\pi$
$613$	−3839.31	+	3221.57i	−0.252966	+	0.212264i	0.507482	+	0.861662i	$0.330576\pi$
$614$	10265.6	+	1810.10i	0.674733	+	0.118974i
$615$		0			0
$616$	90.1665	−	52.0577i	0.00589759	−	0.00340497i
$617$	−7116.73	−	19553.0i	−0.464358	−	1.27581i	−0.922178	−	0.386767i	$-0.873592\pi$
$617$	−7116.73	−	19553.0i	−0.464358	−	1.27581i	0.457820	−	0.889045i	$-0.348630\pi$
$618$		0			0
$619$	6410.57	+	11103.4i	0.416256	+	0.720977i	0.995559	−	0.0941351i	$-0.0300086\pi$
$619$	6410.57	+	11103.4i	0.416256	+	0.720977i	−0.579303	+	0.815112i	$0.696675\pi$
$620$	4970.43	−	8609.04i	0.321964	−	0.557657i
$621$		0			0
$622$	−11182.6	−	13326.9i	−0.720871	−	0.859101i
$623$	14245.6	+	11953.5i	0.916111	+	0.768708i
$624$		0			0
$625$	−36108.8	−	13142.5i	−2.31096	−	0.841122i
$626$	−15386.2			−0.982359
$627$		0			0
$628$	14421.9			0.916398
$629$	−1581.88	−	575.759i	−0.100276	−	0.0364976i
$630$		0			0
$631$	18059.7	+	15153.9i	1.13937	+	0.956047i	0.999418	−	0.0341111i	$-0.0108600\pi$
$631$	18059.7	+	15153.9i	1.13937	+	0.956047i	0.139954	+	0.990158i	$0.455304\pi$
$632$	−4109.73	−	4897.79i	−0.258665	−	0.308265i
$633$		0			0
$634$	7318.26	−	12675.6i	0.458431	−	0.794025i
$635$	−14753.5	−	25553.8i	−0.922007	−	1.59696i
$636$		0			0
$637$	−1629.34	−	4476.57i	−0.101345	−	0.278443i
$638$	517.774	−	298.937i	0.0321299	−	0.0185502i
$639$		0			0
$640$	27413.3	+	4833.70i	1.69313	+	0.298545i
$641$	6448.66	−	5411.07i	0.397358	−	0.333423i	−0.422113	−	0.906543i	$-0.638712\pi$
$641$	6448.66	−	5411.07i	0.397358	−	0.333423i	0.819472	+	0.573120i	$0.194267\pi$
$642$		0			0
$643$	−525.679	−	2981.27i	−0.0322407	−	0.182846i	0.964435	−	0.264321i	$-0.0851479\pi$
$643$	−525.679	−	2981.27i	−0.0322407	−	0.182846i	−0.996675	+	0.0814754i	$0.974037\pi$
$644$	597.012	−	1640.28i	0.0365304	−	0.100366i
$645$		0			0
$646$	−8815.56	−	2862.23i	−0.536909	−	0.174324i
$647$			8844.45i			0.537421i	0.963221	+	0.268710i	$0.0865975\pi$
$647$			8844.45i			0.537421i	−0.963221	+	0.268710i	$0.913403\pi$
$648$		0			0
$649$	−261.738	+	46.1515i	−0.0158307	+	0.00279138i
$650$	32827.8	−	39122.6i	1.98094	−	2.36079i
$651$		0			0
$652$	1291.86	−	7326.48i	0.0775966	−	0.440072i
$653$	−5428.18	−	3133.96i	−0.325300	−	0.187812i	0.328452	−	0.944521i	$-0.393473\pi$
$653$	−5428.18	−	3133.96i	−0.325300	−	0.187812i	−0.653753	+	0.756708i	$0.726806\pi$
$654$		0			0
$655$	−35313.5	+	12853.1i	−2.10659	+	0.766734i
$656$	25256.6	−	9192.63i	1.50321	−	0.547122i
$657$		0			0
$658$	29708.9	+	17152.4i	1.76014	+	1.01622i
$659$	1752.32	−	9937.90i	0.103582	−	0.587444i	−0.888195	−	0.459467i	$-0.848041\pi$
$659$	1752.32	−	9937.90i	0.103582	−	0.587444i	0.991777	−	0.127977i	$-0.0408484\pi$
$660$		0			0
$661$	−6084.26	+	7250.94i	−0.358019	+	0.426670i	−0.914749	−	0.404024i	$-0.867611\pi$
$661$	−6084.26	+	7250.94i	−0.358019	+	0.426670i	0.556730	+	0.830694i	$0.312056\pi$
$662$	−16719.7	+	2948.14i	−0.981616	+	0.173085i
$663$		0			0
$664$			6838.30i			0.399665i
$665$	−14126.3	−	22595.8i	−0.823749	−	1.31764i
$666$		0			0
$667$	−2273.22	+	6245.63i	−0.131963	+	0.362566i
$668$	−3441.76	−	19519.2i	−0.199350	−	1.13057i
$669$		0			0
$670$	−51323.7	+	43065.7i	−2.95942	+	2.48324i
$671$	−361.767	−	63.7893i	−0.0208135	−	0.00366998i
$672$		0			0
$673$	−2930.86	+	1692.13i	−0.167870	+	0.0969196i	−0.581581	−	0.813489i	$-0.697566\pi$
$673$	−2930.86	+	1692.13i	−0.167870	+	0.0969196i	0.413711	+	0.910408i	$0.364232\pi$
$674$	6631.91	+	18221.0i	0.379008	+	1.04132i
$675$		0			0
$676$	41.1964	+	71.3542i	0.00234390	+	0.00405975i
$677$	−6198.39	+	10735.9i	−0.351881	+	0.609476i	−0.986579	−	0.163284i	$-0.947791\pi$
$677$	−6198.39	+	10735.9i	−0.351881	+	0.609476i	0.634698	+	0.772760i	$0.281124\pi$
$678$		0			0
$679$	2078.59	+	2477.17i	0.117480	+	0.140007i
$680$	5658.78	+	4748.28i	0.319124	+	0.267777i
$681$		0			0
$682$	197.001	+	71.7027i	0.0110610	+	0.00402586i
$683$	18080.6			1.01293			0.506466	−	0.862260i	$-0.330951\pi$
$683$	18080.6			1.01293			0.506466	+	0.862260i	$0.330951\pi$
$684$		0			0
$685$	2289.14			0.127684
$686$	−23231.5	−	8455.56i	−1.29298	−	0.470605i
$687$		0			0
$688$	15835.4	+	13287.5i	0.877497	+	0.736307i
$689$	−4595.49	−	5476.69i	−0.254099	−	0.302823i
$690$		0			0
$691$	9026.08	−	15633.6i	0.496915	−	0.860682i	−0.503079	−	0.864241i	$-0.667799\pi$
$691$	9026.08	−	15633.6i	0.496915	−	0.860682i	0.999994	+	0.00355848i	$0.00113270\pi$
$692$	−8664.06	−	15006.6i	−0.475951	−	0.824372i
$693$		0			0
$694$	−7994.94	−	21965.9i	−0.437297	−	1.20146i
$695$	31725.8	−	18316.9i	1.73155	−	0.999713i
$696$		0			0
$697$	10431.1	+	1839.29i	0.566868	+	0.0999541i
$698$	11009.3	−	9237.90i	0.597003	−	0.500945i
$699$		0			0
$700$	−3938.50	−	22336.3i	−0.212659	−	1.20605i
$701$	5123.61	−	14077.0i	0.276057	−	0.758460i	−0.721743	−	0.692161i	$-0.756659\pi$
$701$	5123.61	−	14077.0i	0.276057	−	0.758460i	0.997800	−	0.0662989i	$-0.0211191\pi$
$702$		0			0
$703$	−4133.76	+	1671.19i	−0.221775	+	0.0896589i
$704$		−	32.1349i		−	0.00172036i
$705$		0			0
$706$	8296.84	−	1462.96i	0.442289	−	0.0779874i
$707$	−14941.9	+	17807.1i	−0.794837	+	0.947250i
$708$		0			0
$709$	4549.43	−	25801.1i	0.240984	−	1.36669i	−0.588654	−	0.808385i	$-0.700342\pi$
$709$	4549.43	−	25801.1i	0.240984	−	1.36669i	0.829638	−	0.558302i	$-0.188547\pi$
$710$	−15581.3	−	8995.85i	−0.823598	−	0.475505i
$711$		0			0
$712$	−12830.5	+	4669.91i	−0.675341	+	0.245804i
$713$	−2190.03	+	797.105i	−0.115031	+	0.0418679i
$714$		0			0
$715$	494.629	+	285.574i	0.0258714	+	0.0149369i
$716$	−651.005	+	3692.04i	−0.0339794	+	0.192706i
$717$		0			0
$718$	4916.23	−	5858.93i	0.255532	−	0.304531i
$719$	25947.0	−	4575.16i	1.34584	−	0.237308i	0.546135	−	0.837697i	$-0.316099\pi$
$719$	25947.0	−	4575.16i	1.34584	−	0.237308i	0.799708	+	0.600389i	$0.204988\pi$
$720$		0			0
$721$		−	10633.0i		−	0.549229i
$722$	−22422.7	+	9994.90i	−1.15580	+	0.515196i
$723$		0			0
$724$	−1426.28	+	3918.67i	−0.0732144	+	0.201155i
$725$	14996.5	+	85049.2i	0.768214	+	4.35676i
$726$		0			0
$727$	−2045.11	+	1716.05i	−0.104331	+	0.0875443i	−0.693461	−	0.720494i	$-0.743915\pi$
$727$	−2045.11	+	1716.05i	−0.104331	+	0.0875443i	0.589130	+	0.808038i	$0.299471\pi$
$728$	−8225.57	−	1450.39i	−0.418763	−	0.0738393i
$729$		0			0
$730$	21938.1	−	12666.0i	1.11228	−	0.642176i
$731$	2786.23	+	7655.11i	0.140975	+	0.387325i
$732$		0			0
$733$	−13594.0	−	23545.5i	−0.685002	−	1.18646i	−0.973436	−	0.228959i	$-0.926468\pi$
$733$	−13594.0	−	23545.5i	−0.685002	−	1.18646i	0.288434	−	0.957500i	$-0.406865\pi$
$734$	5648.32	−	9783.18i	0.284037	−	0.491967i
$735$		0			0
$736$	2890.05	+	3444.22i	0.144740	+	0.172494i
$737$	−406.438	−	341.042i	−0.0203139	−	0.0170454i
$738$		0			0
$739$	−1733.94	−	631.102i	−0.0863111	−	0.0314147i	0.298504	−	0.954408i	$-0.403512\pi$
$739$	−1733.94	−	631.102i	−0.0863111	−	0.0314147i	−0.384815	+	0.922994i	$0.625735\pi$
$740$	−5359.33			−0.266234
$741$		0			0
$742$	−8455.41			−0.418339
$743$	−25271.5	−	9198.07i	−1.24781	−	0.454165i	−0.368148	−	0.929767i	$-0.620008\pi$
$743$	−25271.5	−	9198.07i	−1.24781	−	0.454165i	−0.879660	+	0.475602i	$0.842230\pi$
$744$		0			0
$745$	16700.1	+	14013.1i	0.821269	+	0.689126i
$746$	−16692.9	−	19893.8i	−0.819264	−	0.976360i
$747$		0			0
$748$	44.1114	−	76.4033i	0.00215625	−	0.00373473i
$749$	6279.91	+	10877.1i	0.306359	+	0.530630i
$750$		0			0
$751$	−5931.55	−	16296.8i	−0.288209	−	0.791849i	−0.996317	−	0.0857445i	$-0.972673\pi$
$751$	−5931.55	−	16296.8i	−0.288209	−	0.791849i	0.708108	−	0.706104i	$-0.249549\pi$
$752$	−42357.0	+	24454.8i	−2.05399	+	1.18587i
$753$		0			0
$754$	−47234.7	−	8328.75i	−2.28141	−	0.402275i
$755$	−16171.9	+	13569.8i	−0.779544	+	0.654115i
$756$		0			0
$757$	−1788.97	−	10145.7i	−0.0858931	−	0.487124i	−0.997160	−	0.0753083i	$-0.976006\pi$
$757$	−1788.97	−	10145.7i	−0.0858931	−	0.487124i	0.911267	−	0.411816i	$-0.135105\pi$
$758$	−6443.72	+	17704.0i	−0.308768	+	0.848334i
$759$		0			0
$760$	19553.7	−	687.085i	0.933275	−	0.0327937i
$761$		−	22833.9i		−	1.08769i	−0.839187	−	0.543843i	$-0.816969\pi$
$761$		−	22833.9i		−	1.08769i	0.839187	−	0.543843i	$-0.183031\pi$
$762$		0			0
$763$	−4821.98	+	850.246i	−0.228791	+	0.0403420i
$764$	−11584.9	+	13806.4i	−0.548598	+	0.653793i
$765$		0			0
$766$	3495.93	−	19826.4i	0.164899	−	0.935191i
$767$	18464.9	+	10660.7i	0.869266	+	0.501871i
$768$		0			0
$769$	23430.0	−	8527.84i	1.09871	−	0.399898i	0.271870	−	0.962334i	$-0.412358\pi$
$769$	23430.0	−	8527.84i	1.09871	−	0.399898i	0.826841	+	0.562436i	$0.190136\pi$
$770$	634.753	−	231.031i	0.0297077	−	0.0108127i
$771$		0			0
$772$	6778.23	+	3913.41i	0.316002	+	0.182444i
$773$	−340.976	+	1933.77i	−0.0158655	+	0.0899779i	−0.991712	−	0.128478i	$-0.958991\pi$
$773$	−340.976	+	1933.77i	−0.0158655	+	0.0899779i	0.975847	+	0.218456i	$0.0701020\pi$
$774$		0			0
$775$	−19465.3	+	23197.8i	−0.902210	+	1.07521i
$776$	−2338.21	+	412.290i	−0.108166	+	0.0190726i
$777$		0			0
$778$		−	25309.2i		−	1.16630i
$779$	23788.7	−	14872.0i	1.09412	−	0.684011i
$780$		0			0
$781$	48.7304	−	133.886i	0.00223266	−	0.00613419i
$782$	453.540	+	2572.15i	0.0207398	+	0.117622i
$783$		0			0
$784$	6153.51	−	5163.41i	0.280317	−	0.235214i
$785$	−61100.2	−	10773.6i	−2.77804	−	0.489843i
$786$		0			0
$787$	−23562.3	+	13603.7i	−1.06723	+	0.616163i	−0.927422	−	0.374016i	$-0.877980\pi$
$787$	−23562.3	+	13603.7i	−1.06723	+	0.616163i	−0.139803	+	0.990179i	$0.544647\pi$
$788$	607.653	+	1669.51i	0.0274705	+	0.0754746i
$789$		0			0
$790$	−20740.5	−	35923.7i	−0.934070	−	1.61786i
$791$	3090.35	−	5352.65i	0.138913	−	0.240605i
$792$		0			0
$793$	18942.8	+	22575.2i	0.848272	+	1.01093i
$794$	26795.6	+	22484.2i	1.19766	+	1.00495i
$795$		0			0
$796$	12618.4	+	4592.71i	0.561868	+	0.204503i
$797$	13880.4			0.616899			0.308449	−	0.951241i	$-0.400190\pi$
$797$	13880.4			0.616899			0.308449	+	0.951241i	$0.400190\pi$
$798$		0			0
$799$	−19274.6			−0.853425
$800$	54897.4	+	19981.0i	2.42615	+	0.883045i
$801$		0			0
$802$	13985.3	+	11735.1i	0.615760	+	0.516684i
$803$	128.947	+	153.673i	0.00566681	+	0.00675344i
$804$		0			0
$805$	−3754.65	+	6503.24i	−0.164390	+	0.284732i
$806$	−8409.17	−	14565.1i	−0.367494	−	0.636519i
$807$		0			0
$808$	−5837.44	−	16038.2i	−0.254159	−	0.698296i
$809$	−9580.31	+	5531.20i	−0.416348	+	0.240379i	−0.693514	−	0.720443i	$-0.743938\pi$
$809$	−9580.31	+	5531.20i	−0.416348	+	0.240379i	0.277165	+	0.960822i	$0.410605\pi$
$810$		0			0
$811$	6132.92	+	1081.40i	0.265544	+	0.0468225i	0.304835	−	0.952405i	$-0.401399\pi$
$811$	6132.92	+	1081.40i	0.265544	+	0.0468225i	−0.0392909	+	0.999228i	$0.512510\pi$
$812$	−16317.4	+	13691.9i	−0.705206	+	0.591738i
$813$		0			0
$814$	−19.6264	−	111.307i	−0.000845091	−	0.00479275i
$815$	−10946.2	+	30074.4i	−0.470464	+	1.29259i
$816$		0			0
$817$	19053.7	+	10125.7i	0.815918	+	0.433604i
$818$		−	168.134i		−	0.00718665i
$819$		0			0
$820$	33208.8	−	5855.60i	1.41427	−	0.249374i
$821$	9106.86	−	10853.1i	0.387128	−	0.461361i	−0.536923	−	0.843631i	$-0.680413\pi$
$821$	9106.86	−	10853.1i	0.387128	−	0.461361i	0.924050	+	0.382271i	$0.124858\pi$
$822$		0			0
$823$	973.517	−	5521.09i	0.0412329	−	0.233843i	−0.957226	−	0.289342i	$-0.906564\pi$
$823$	973.517	−	5521.09i	0.0412329	−	0.233843i	0.998459	+	0.0554984i	$0.0176748\pi$
$824$	6761.11	+	3903.53i	0.285843	+	0.165031i
$825$		0			0
$826$	23695.8	−	8624.57i	0.998163	−	0.363301i
$827$	13477.3	−	4905.34i	0.566690	−	0.206258i	−0.0427566	−	0.999086i	$-0.513614\pi$
$827$	13477.3	−	4905.34i	0.566690	−	0.206258i	0.609446	+	0.792827i	$0.291392\pi$
$828$		0			0
$829$	17268.0	+	9969.69i	0.723453	+	0.417686i	0.816022	−	0.578020i	$-0.196175\pi$
$829$	17268.0	+	9969.69i	0.723453	+	0.417686i	−0.0925691	+	0.995706i	$0.529508\pi$
$830$	−7704.11	+	43692.2i	−0.322185	+	1.82720i
$831$		0			0
$832$	−1657.08	+	1974.84i	−0.0690494	+	0.0822898i
$833$	3117.54	−	549.706i	0.129671	−	0.0228646i
$834$		0			0
$835$			85266.3i			3.53385i
$836$	−48.6332	−	228.557i	−0.00201198	−	0.00945551i
$837$		0			0
$838$	5843.87	−	16055.9i	0.240899	−	0.661864i
$839$	−6999.02	−	39693.4i	−0.288001	−	1.63334i	−0.694364	−	0.719624i	$-0.744314\pi$
$839$	−6999.02	−	39693.4i	−0.288001	−	1.63334i	0.406362	−	0.913712i	$-0.366797\pi$
$840$		0			0
$841$	43448.0	−	36457.2i	1.78146	−	1.49482i
$842$	3092.93	+	545.367i	0.126591	+	0.0223214i
$843$		0			0
$844$	8210.53	−	4740.35i	0.334855	−	0.193329i
$845$	−121.230	−	333.075i	−0.00493541	−	0.0135599i
$846$		0			0
$847$	−10344.9	−	17917.9i	−0.419664	−	0.726879i
$848$	6027.58	−	10440.1i	0.244090	−	0.422776i
$849$		0			0
$850$	21814.3	+	25997.3i	0.880264	+	1.04906i
$851$	962.508	+	807.640i	0.0387713	+	0.0325329i
$852$		0			0
$853$	−21299.9	−	7752.55i	−0.854978	−	0.311187i	−0.122910	−	0.992418i	$-0.539223\pi$
$853$	−21299.9	−	7752.55i	−0.854978	−	0.311187i	−0.732068	+	0.681231i	$0.761445\pi$
$854$	34853.6			1.39656
$855$		0			0
$856$	−9221.78			−0.368217
$857$	9943.89	+	3619.28i	0.396355	+	0.144262i	0.532505	−	0.846427i	$-0.321251\pi$
$857$	9943.89	+	3619.28i	0.396355	+	0.144262i	−0.136150	+	0.990688i	$0.543473\pi$
$858$		0			0
$859$	9275.48	+	7783.06i	0.368423	+	0.309144i	0.808137	−	0.588994i	$-0.200476\pi$
$859$	9275.48	+	7783.06i	0.368423	+	0.309144i	−0.439714	+	0.898138i	$0.644920\pi$
$860$	16670.7	+	19867.4i	0.661009	+	0.787759i
$861$		0			0
$862$	−6106.74	+	10577.2i	−0.241295	+	0.417936i
$863$	873.926	+	1513.68i	0.0344714	+	0.0597062i	0.882746	−	0.469850i	$-0.155692\pi$
$863$	873.926	+	1513.68i	0.0344714	+	0.0597062i	−0.848275	+	0.529556i	$0.822359\pi$
$864$		0			0
$865$	25495.9	+	70049.5i	1.00218	+	2.75347i
$866$	24500.9	−	14145.6i	0.961402	−	0.555066i
$867$		0			0
$868$	−7355.65	−	1297.00i	−0.287635	−	0.0507178i
$869$	251.640	−	211.151i	0.00982313	−	0.00824258i
$870$		0			0
$871$	7391.11	+	41917.1i	0.287530	+	1.63066i
$872$	1229.58	−	3378.25i	0.0477510	−	0.131195i
$873$		0			0
$874$	5452.30	+	4257.90i	0.211015	+	0.164789i
$875$			57352.2i			2.21584i
$876$		0			0
$877$	−38701.9	+	6824.19i	−1.49016	+	0.262755i	−0.858630	−	0.512596i	$-0.828684\pi$
$877$	−38701.9	+	6824.19i	−1.49016	+	0.262755i	−0.631530	+	0.775351i	$0.717573\pi$
$878$	39632.9	−	47232.7i	1.52340	−	1.81552i
$879$		0			0
$880$	−167.235	+	948.438i	−0.00640625	+	0.0363316i
$881$	−34092.5	−	19683.3i	−1.30375	−	0.752722i	−0.322707	−	0.946499i	$-0.604593\pi$
$881$	−34092.5	−	19683.3i	−1.30375	−	0.752722i	−0.981046	+	0.193777i	$0.937926\pi$
$882$		0			0
$883$	11453.2	−	4168.64i	0.436503	−	0.158874i	−0.114416	−	0.993433i	$-0.536500\pi$
$883$	11453.2	−	4168.64i	0.436503	−	0.158874i	0.550919	+	0.834559i	$0.314277\pi$
$884$	−6650.69	+	2420.65i	−0.253040	+	0.0920988i
$885$		0			0
$886$	21553.6	+	12444.0i	0.817278	+	0.471856i
$887$	1295.85	−	7349.15i	0.0490535	−	0.278196i	−0.950408	−	0.311006i	$-0.899334\pi$
$887$	1295.85	−	7349.15i	0.0490535	−	0.278196i	0.999462	+	0.0328091i	$0.0104453\pi$
$888$		0			0
$889$	−14250.7	+	16983.4i	−0.537632	+	0.640725i
$890$	−87239.4	+	15382.7i	−3.28570	+	0.579357i
$891$		0			0
$892$			28904.0i			1.08495i
$893$	−37931.7	+	34168.8i	−1.42143	+	1.28042i
$894$		0			0
$895$	5516.12	−	15155.4i	0.206015	−	0.566022i
$896$	−3631.83	−	20597.1i	−0.135414	−	0.767970i
$897$		0			0
$898$	−8394.38	+	7043.72i	−0.311942	+	0.261751i
$899$	28007.9	+	4938.54i	1.03906	+	0.183214i
$900$		0			0
$901$	4114.29	−	2375.39i	0.152128	−	0.0878309i
$902$	243.227	+	668.261i	0.00897847	+	0.0246681i
$903$		0			0
$904$	2269.02	+	3930.07i	0.0834808	+	0.144593i
$905$	8969.96	−	15536.4i	0.329471	−	0.570661i
$906$		0			0
$907$	−14099.2	−	16802.7i	−0.516158	−	0.615133i	0.443510	−	0.896270i	$-0.353733\pi$
$907$	−14099.2	−	16802.7i	−0.516158	−	0.615133i	−0.959668	+	0.281136i	$0.909289\pi$
$908$	−7439.32	−	6242.33i	−0.271897	−	0.228149i
$909$		0			0
$910$	−50921.9	−	18534.0i	−1.85499	−	0.675162i
$911$	24183.3			0.879505			0.439752	−	0.898119i	$-0.355066\pi$
$911$	24183.3			0.879505			0.439752	+	0.898119i	$0.355066\pi$
$912$		0			0
$913$	−351.340			−0.0127357
$914$	−44014.3	−	16019.9i	−1.59285	−	0.579750i
$915$		0			0
$916$	16702.2	+	14014.8i	0.602464	+	0.505527i
$917$	18149.6	+	21629.9i	0.653603	+	0.778934i
$918$		0			0
$919$	24138.2	−	41808.5i	0.866425	−	1.50069i	0.000800280	−	1.00000i	$-0.499745\pi$
$919$	24138.2	−	41808.5i	0.866425	−	1.50069i	0.865625	−	0.500693i	$-0.166921\pi$
$920$	−2756.77	−	4774.86i	−0.0987913	−	0.171112i
$921$		0			0
$922$	12847.1	+	35297.0i	0.458889	+	1.26079i
$923$	−9898.70	+	5715.02i	−0.353001	+	0.203805i
$924$		0			0
$925$	16077.9	+	2834.97i	0.571502	+	0.100771i
$926$	40245.9	−	33770.3i	1.42825	−	1.19845i
$927$		0			0
$928$	−9527.35	−	54032.3i	−0.337016	−	1.91131i
$929$	−12132.2	+	33333.0i	−0.428466	+	1.17720i	0.518278	+	0.855212i	$0.326573\pi$
$929$	−12132.2	+	33333.0i	−0.428466	+	1.17720i	−0.946744	+	0.321988i	$0.895649\pi$
$930$		0			0
$931$	5160.72	−	6608.38i	0.181671	−	0.232632i
$932$		−	15489.4i		−	0.544392i
$933$		0			0
$934$	−18494.0	+	3260.99i	−0.647903	+	0.114243i
$935$	−243.959	+	290.739i	−0.00853295	+	0.0101692i
$936$		0			0
$937$	5916.58	−	33554.6i	0.206282	−	1.16988i	−0.689128	−	0.724640i	$-0.742006\pi$
$937$	5916.58	−	33554.6i	0.206282	−	1.16988i	0.895410	−	0.445243i	$-0.146883\pi$
$938$	43595.4	+	25169.8i	1.51753	+	0.876144i
$939$		0			0
$940$	−57662.4	+	20987.4i	−2.00079	+	0.728227i
$941$	18113.4	−	6592.72i	0.627501	−	0.228392i	−0.00864207	−	0.999963i	$-0.502751\pi$
$941$	18113.4	−	6592.72i	0.627501	−	0.228392i	0.636143	+	0.771571i	$0.280529\pi$
$942$		0			0
$943$	−6846.55	−	3952.86i	−0.236431	−	0.136503i
$944$	−6243.02	+	35405.9i	−0.215247	+	1.22072i
$945$		0			0
$946$	−351.572	+	418.987i	−0.0120831	+	0.0144000i
$947$	−33803.9	+	5960.54i	−1.15996	+	0.204532i	−0.720319	−	0.693643i	$-0.756005\pi$
$947$	−33803.9	+	5960.54i	−1.15996	+	0.204532i	−0.439638	+	0.898175i	$0.644893\pi$
$948$		0			0
$949$		−	16093.2i		−	0.550484i
$950$	89016.1	+	12490.7i	3.04007	+	0.426580i
$951$		0			0
$952$	1898.31	−	5215.55i	0.0646265	−	0.177560i
$953$	160.465	+	910.044i	0.00545434	+	0.0309331i	0.987413	−	0.158160i	$-0.0505562\pi$
$953$	160.465	+	910.044i	0.00545434	+	0.0309331i	−0.981959	+	0.189093i	$0.939445\pi$
$954$		0			0
$955$	59394.7	−	49838.1i	2.01253	−	1.68872i
$956$	−21961.3	−	3872.37i	−0.742970	−	0.131006i
$957$		0			0
$958$	17483.1	−	10093.9i	0.589618	−	0.340416i
$959$	−588.261	−	1616.23i	−0.0198081	−	0.0544222i
$960$		0			0
$961$	−9909.27	−	17163.4i	−0.332626	−	0.576126i
$962$	−4533.56	+	7852.36i	−0.151942	+	0.263171i
$963$		0			0
$964$	−20852.6	−	24851.2i	−0.696698	−	0.830293i
$965$	−25793.3	−	21643.2i	−0.860431	−	0.721988i
$966$		0			0
$967$	24660.1	+	8975.53i	0.820077	+	0.298483i	0.717780	−	0.696270i	$-0.245159\pi$
$967$	24660.1	+	8975.53i	0.820077	+	0.298483i	0.102297	+	0.994754i	$0.467381\pi$
$968$	15191.1			0.504400
$969$		0			0
$970$	−15404.1			−0.509893
$971$	18612.1	+	6774.26i	0.615131	+	0.223889i	0.630747	−	0.775989i	$-0.282749\pi$
$971$	18612.1	+	6774.26i	0.615131	+	0.223889i	−0.0156160	+	0.999878i	$0.504971\pi$
$972$		0			0
$973$	−21085.4	−	17692.8i	−0.694725	−	0.582943i
$974$	19927.3	+	23748.4i	0.655555	+	0.781260i
$975$		0			0
$976$	−24846.0	+	43034.5i	−0.814857	+	1.41137i
$977$	−9613.30	−	16650.7i	−0.314797	−	0.545245i	0.664597	−	0.747202i	$-0.268603\pi$
$977$	−9613.30	−	16650.7i	−0.314797	−	0.545245i	−0.979394	+	0.201957i	$0.935270\pi$
$978$		0			0
$979$	−239.932	−	659.208i	−0.00783276	−	0.0215203i
$980$	8727.95	−	5039.09i	0.284494	−	0.164253i
$981$		0			0
$982$	−46929.0	−	8274.85i	−1.52501	−	0.268901i
$983$	−31572.8	+	26492.7i	−1.02443	+	0.859601i	−0.990178	−	0.139813i	$-0.955350\pi$
$983$	−31572.8	+	26492.7i	−1.02443	+	0.859601i	−0.0342541	+	0.999413i	$0.510906\pi$
$984$		0			0
$985$	−1327.22	−	7527.02i	−0.0429326	−	0.243483i
$986$	10900.9	−	29949.9i	0.352084	−	0.967343i
$987$		0			0
$988$	−8797.14	+	16553.7i	−0.283274	+	0.533039i
$989$		−	6080.33i		−	0.195494i
$990$		0			0
$991$	−3507.79	+	618.518i	−0.112441	+	0.0198263i	−0.229585	−	0.973289i	$-0.573737\pi$
$991$	−3507.79	+	618.518i	−0.112441	+	0.0198263i	0.117145	+	0.993115i	$0.462626\pi$
$992$	12366.4	−	14737.7i	0.395800	−	0.471696i
$993$		0			0
$994$	−2347.40	+	13312.8i	−0.0749046	+	0.424805i
$995$	−50028.3	−	28883.9i	−1.59397	−	0.920282i
$996$		0			0
$997$	448.486	−	163.236i	0.0142464	−	0.00518528i	−0.334887	−	0.942258i	$-0.608698\pi$
$997$	448.486	−	163.236i	0.0142464	−	0.00518528i	0.349134	+	0.937073i	$0.386476\pi$
$998$	−30157.3	+	10976.3i	−0.956524	+	0.348146i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.y.a.53.16	yes	120
3.2	odd	2	inner	171.4.y.a.53.5	✓	120
19.14	odd	18	inner	171.4.y.a.71.5	yes	120
57.14	even	18	inner	171.4.y.a.71.16	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.4.y.a.53.5	✓	120	3.2	odd	2	inner
171.4.y.a.53.16	yes	120	1.1	even	1	trivial
171.4.y.a.71.5	yes	120	19.14	odd	18	inner
171.4.y.a.71.16	yes	120	57.14	even	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.y (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(3.36331 + 1.22414i) q^{2} +(3.68495 + 3.09204i) q^{4} +(-13.3019 - 15.8526i) q^{5} +(-7.77429 + 13.4655i) q^{7} +(-5.70811 - 9.88673i) q^{8} +O(q^{10})\)	\(q+(3.36331 + 1.22414i) q^{2} +(3.68495 + 3.09204i) q^{4} +(-13.3019 - 15.8526i) q^{5} +(-7.77429 + 13.4655i) q^{7} +(-5.70811 - 9.88673i) q^{8} +(-25.3325 - 69.6004i) q^{10} +(0.507963 - 0.293273i) q^{11} +(-46.3397 - 8.17093i) q^{13} +(-42.6310 + 35.7717i) q^{14} +(-13.7778 - 78.1379i) q^{16} +(10.6943 - 29.3824i) q^{17} +(-31.0413 - 76.7818i) q^{19} -99.5459i q^{20} +(2.06744 - 0.364546i) q^{22} +(-15.0014 + 17.8779i) q^{23} +(-52.6577 + 298.637i) q^{25} +(-145.852 - 84.2078i) q^{26} +(-70.2837 + 25.5812i) q^{28} +(267.617 - 97.4045i) q^{29} +(86.4832 + 49.9311i) q^{31} +(33.4537 - 189.726i) q^{32} +(71.9366 - 85.7307i) q^{34} +(316.875 - 55.8736i) q^{35} -53.8378i q^{37} +(-10.4094 - 296.240i) q^{38} +(-80.8014 + 222.000i) q^{40} +(58.8231 + 333.603i) q^{41} +(-199.580 + 167.468i) q^{43} +(2.77863 + 0.489948i) q^{44} +(-72.3393 + 41.7651i) q^{46} +(-210.832 - 579.255i) q^{47} +(50.6207 + 87.6777i) q^{49} +(-542.678 + 939.946i) q^{50} +(-145.495 - 173.394i) q^{52} +(116.390 + 97.6631i) q^{53} +(-11.4060 - 4.15144i) q^{55} +177.506 q^{56} +1019.31 q^{58} +(-425.794 - 154.976i) q^{59} +(-479.767 - 402.572i) q^{61} +(229.747 + 273.801i) q^{62} +(27.3934 - 47.4467i) q^{64} +(486.874 + 843.291i) q^{65} +(-309.378 - 850.010i) q^{67} +(130.260 - 75.2055i) q^{68} +(1134.14 + 199.980i) q^{70} +(186.080 - 156.140i) q^{71} +(59.3899 + 336.817i) q^{73} +(65.9052 - 181.073i) q^{74} +(123.027 - 378.918i) q^{76} +9.11995i q^{77} +(551.538 - 97.2510i) q^{79} +(-1055.41 + 1257.79i) q^{80} +(-210.537 + 1194.02i) q^{82} +(-518.748 - 299.499i) q^{83} +(-608.041 + 221.309i) q^{85} +(-876.255 + 318.931i) q^{86} +(-5.79902 - 3.34806i) q^{88} +(207.685 - 1177.84i) q^{89} +(470.284 - 560.462i) q^{91} +(-110.559 + 19.4944i) q^{92} -2206.30i q^{94} +(-804.281 + 1513.42i) q^{95} +(71.1316 - 195.432i) q^{97} +(62.9230 + 356.854i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 36 q^{4}+O(q^{10}) \) 120 * q - 36 * q^4	\( 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55} + 5616 q^{58} - 5736 q^{61} - 4524 q^{64} + 372 q^{67} + 7848 q^{70} - 276 q^{73} + 4320 q^{76} + 10536 q^{79} + 3960 q^{82} - 11592 q^{85} - 11664 q^{88} - 120 q^{91} + 5904 q^{97}+O(q^{100}) \) 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

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