LMFDB - Embedded newform 448.3.s.g.129.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,3,Mod(129,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("448.129");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.s (of order $6$, degree $2$, not 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:	$12.2071158433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 $ x^16 + 36x^14 + 522x^12 + 3644x^10 + 12219x^8 + 15156x^6 + 15478x^4 - 10992*x^2 + 11025
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.5
Root			$0.707107 - 0.358323i$ of defining polynomial
Character	$\chi$	$=$	448.129
Dual form			448.3.s.g.257.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438854 + 0.253372i) q^{3} +(4.59219 - 2.65130i) q^{5} +(5.27770 - 4.59846i) q^{7} +(-4.37160 - 7.57184i) q^{9} +O(q^{10})$	\(q+(0.438854 + 0.253372i) q^{3} +(4.59219 - 2.65130i) q^{5} +(5.27770 - 4.59846i) q^{7} +(-4.37160 - 7.57184i) q^{9} +(8.54498 - 14.8003i) q^{11} +21.4744i q^{13} +2.68707 q^{15} +(-20.7992 - 12.0084i) q^{17} +(-10.5831 + 6.11016i) q^{19} +(3.48126 - 0.680829i) q^{21} +(-20.1464 - 34.8946i) q^{23} +(1.55882 - 2.69996i) q^{25} -8.99128i q^{27} +26.0770 q^{29} +(21.8789 + 12.6318i) q^{31} +(7.50000 - 4.33013i) q^{33} +(12.0443 - 35.1098i) q^{35} +(6.48126 + 11.2259i) q^{37} +(-5.44101 + 9.42411i) q^{39} +33.8721i q^{41} +29.9958 q^{43} +(-40.1505 - 23.1809i) q^{45} +(48.2788 - 27.8738i) q^{47} +(6.70828 - 48.5386i) q^{49} +(-6.08521 - 10.5399i) q^{51} +(-4.36362 + 7.55801i) q^{53} -90.6214i q^{55} -6.19259 q^{57} +(-43.2893 - 24.9931i) q^{59} +(-3.40886 + 1.96811i) q^{61} +(-57.8909 - 19.8593i) q^{63} +(56.9351 + 98.6144i) q^{65} +(52.9426 - 91.6994i) q^{67} -20.4182i q^{69} +35.0232 q^{71} +(40.3712 + 23.3083i) q^{73} +(1.36819 - 0.789926i) q^{75} +(-22.9610 - 117.406i) q^{77} +(43.4998 + 75.3438i) q^{79} +(-37.0663 + 64.2007i) q^{81} +64.0079i q^{83} -127.352 q^{85} +(11.4440 + 6.60721i) q^{87} +(37.2272 - 21.4932i) q^{89} +(98.7491 + 113.335i) q^{91} +(6.40109 + 11.0870i) q^{93} +(-32.3998 + 56.1181i) q^{95} -28.7493i q^{97} -149.421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^9	$ 16 q + 8 q^{9} + 48 q^{17} - 56 q^{21} + 16 q^{25} - 112 q^{29} + 120 q^{33} - 8 q^{37} + 72 q^{45} - 128 q^{49} + 24 q^{53} - 528 q^{57} + 360 q^{61} - 8 q^{65} + 72 q^{73} + 32 q^{81} - 720 q^{85} + 408 q^{89} + 232 q^{93}+O(q^{100}) $ 16 * q + 8 * q^9 + 48 * q^17 - 56 * q^21 + 16 * q^25 - 112 * q^29 + 120 * q^33 - 8 * q^37 + 72 * q^45 - 128 * q^49 + 24 * q^53 - 528 * q^57 + 360 * q^61 - 8 * q^65 + 72 * q^73 + 32 * q^81 - 720 * q^85 + 408 * q^89 + 232 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	0.438854	+	0.253372i	0.146285	+	0.0844575i	0.571356	−	0.820702i	$-0.306418\pi$
$3$	0.438854	+	0.253372i	0.146285	+	0.0844575i	−0.425071	+	0.905160i	$0.639751\pi$
$4$		0			0
$5$	4.59219	−	2.65130i	0.918439	−	0.530261i	0.0353020	−	0.999377i	$-0.488761\pi$
$5$	4.59219	−	2.65130i	0.918439	−	0.530261i	0.883137	+	0.469116i	$0.155427\pi$
$6$		0			0
$7$	5.27770	−	4.59846i	0.753957	−	0.656923i
$7$	5.27770	−	4.59846i	0.753957	−	0.656923i
$8$		0			0
$9$	−4.37160	−	7.57184i	−0.485734	−	0.841316i
$10$		0			0
$11$	8.54498	−	14.8003i	0.776817	−	1.34549i	−0.156951	−	0.987606i	$-0.550167\pi$
$11$	8.54498	−	14.8003i	0.776817	−	1.34549i	0.933768	−	0.357880i	$-0.116500\pi$
$12$		0			0
$13$			21.4744i			1.65187i	0.563762	+	0.825937i	$0.309353\pi$
$13$			21.4744i			1.65187i	−0.563762	+	0.825937i	$0.690647\pi$
$14$		0			0
$15$	2.68707			0.179138
$16$		0			0
$17$	−20.7992	−	12.0084i	−1.22348	−	0.706378i	−0.257824	−	0.966192i	$-0.583005\pi$
$17$	−20.7992	−	12.0084i	−1.22348	−	0.706378i	−0.965659	+	0.259814i	$0.916339\pi$
$18$		0			0
$19$	−10.5831	+	6.11016i	−0.557006	+	0.321588i	−0.751943	−	0.659228i	$-0.770883\pi$
$19$	−10.5831	+	6.11016i	−0.557006	+	0.321588i	0.194937	+	0.980816i	$0.437550\pi$
$20$		0			0
$21$	3.48126	−	0.680829i	0.165775	−	0.0324205i
$22$		0			0
$23$	−20.1464	−	34.8946i	−0.875932	−	1.51716i	−0.855767	−	0.517361i	$-0.826914\pi$
$23$	−20.1464	−	34.8946i	−0.875932	−	1.51716i	−0.0201644	−	0.999797i	$-0.506419\pi$
$24$		0			0
$25$	1.55882	−	2.69996i	0.0623530	−	0.107998i
$26$		0			0
$27$		−	8.99128i		−	0.333010i
$28$		0			0
$29$	26.0770			0.899209			0.449604	−	0.893228i	$-0.351565\pi$
$29$	26.0770			0.899209			0.449604	+	0.893228i	$0.351565\pi$
$30$		0			0
$31$	21.8789	+	12.6318i	0.705770	+	0.407477i	0.809493	−	0.587130i	$-0.199742\pi$
$31$	21.8789	+	12.6318i	0.705770	+	0.407477i	−0.103723	+	0.994606i	$0.533075\pi$
$32$		0			0
$33$	7.50000	−	4.33013i	0.227273	−	0.131216i
$34$		0			0
$35$	12.0443	−	35.1098i	0.344123	−	1.00314i
$36$		0			0
$37$	6.48126	+	11.2259i	0.175169	+	0.303402i	0.940220	−	0.340568i	$-0.110619\pi$
$37$	6.48126	+	11.2259i	0.175169	+	0.303402i	−0.765051	+	0.643970i	$0.777286\pi$
$38$		0			0
$39$	−5.44101	+	9.42411i	−0.139513	+	0.241644i
$40$		0			0
$41$			33.8721i			0.826150i	0.910697	+	0.413075i	$0.135545\pi$
$41$			33.8721i			0.826150i	−0.910697	+	0.413075i	$0.864455\pi$
$42$		0			0
$43$	29.9958			0.697576			0.348788	−	0.937202i	$-0.386593\pi$
$43$	29.9958			0.697576			0.348788	+	0.937202i	$0.386593\pi$
$44$		0			0
$45$	−40.1505	−	23.1809i	−0.892233	−	0.515131i
$46$		0			0
$47$	48.2788	−	27.8738i	1.02721	−	0.593060i	0.111025	−	0.993818i	$-0.464587\pi$
$47$	48.2788	−	27.8738i	1.02721	−	0.593060i	0.916184	+	0.400758i	$0.131253\pi$
$48$		0			0
$49$	6.70828	−	48.5386i	0.136904	−	0.990584i
$50$		0			0
$51$	−6.08521	−	10.5399i	−0.119318	−	0.206665i
$52$		0			0
$53$	−4.36362	+	7.55801i	−0.0823324	+	0.142604i	−0.904251	−	0.427001i	$-0.859570\pi$
$53$	−4.36362	+	7.55801i	−0.0823324	+	0.142604i	0.821919	+	0.569604i	$0.192904\pi$
$54$		0			0
$55$		−	90.6214i		−	1.64766i
$56$		0			0
$57$	−6.19259			−0.108642
$58$		0			0
$59$	−43.2893	−	24.9931i	−0.733718	−	0.423612i	0.0860631	−	0.996290i	$-0.472571\pi$
$59$	−43.2893	−	24.9931i	−0.733718	−	0.423612i	−0.819781	+	0.572678i	$0.805905\pi$
$60$		0			0
$61$	−3.40886	+	1.96811i	−0.0558829	+	0.0322640i	−0.527681	−	0.849443i	$-0.676938\pi$
$61$	−3.40886	+	1.96811i	−0.0558829	+	0.0322640i	0.471798	+	0.881707i	$0.343605\pi$
$62$		0			0
$63$	−57.8909	−	19.8593i	−0.918903	−	0.315226i
$64$		0			0
$65$	56.9351	+	98.6144i	0.875924	+	1.51715i
$66$		0			0
$67$	52.9426	−	91.6994i	0.790189	−	1.36865i	−0.135661	−	0.990755i	$-0.543316\pi$
$67$	52.9426	−	91.6994i	0.790189	−	1.36865i	0.925850	−	0.377892i	$-0.123351\pi$
$68$		0			0
$69$		−	20.4182i		−	0.295916i
$70$		0			0
$71$	35.0232			0.493285			0.246642	−	0.969107i	$-0.420673\pi$
$71$	35.0232			0.493285			0.246642	+	0.969107i	$0.420673\pi$
$72$		0			0
$73$	40.3712	+	23.3083i	0.553030	+	0.319292i	0.750343	−	0.661049i	$-0.229888\pi$
$73$	40.3712	+	23.3083i	0.553030	+	0.319292i	−0.197313	+	0.980340i	$0.563222\pi$
$74$		0			0
$75$	1.36819	−	0.789926i	0.0182426	−	0.0105323i
$76$		0			0
$77$	−22.9610	−	117.406i	−0.298194	−	1.52475i
$78$		0			0
$79$	43.4998	+	75.3438i	0.550630	+	0.953719i	0.998229	+	0.0594846i	$0.0189457\pi$
$79$	43.4998	+	75.3438i	0.550630	+	0.953719i	−0.447599	+	0.894234i	$0.647721\pi$
$80$		0			0
$81$	−37.0663	+	64.2007i	−0.457609	+	0.792601i
$82$		0			0
$83$			64.0079i			0.771180i	0.922670	+	0.385590i	$0.126002\pi$
$83$			64.0079i			0.771180i	−0.922670	+	0.385590i	$0.873998\pi$
$84$		0			0
$85$	−127.352			−1.49826
$86$		0			0
$87$	11.4440	+	6.60721i	0.131540	+	0.0759449i
$88$		0			0
$89$	37.2272	−	21.4932i	0.418284	−	0.241496i	−0.276059	−	0.961141i	$-0.589029\pi$
$89$	37.2272	−	21.4932i	0.418284	−	0.241496i	0.694343	+	0.719645i	$0.255695\pi$
$90$		0			0
$91$	98.7491	+	113.335i	1.08515	+	1.24544i
$92$		0			0
$93$	6.40109	+	11.0870i	0.0688289	+	0.119215i
$94$		0			0
$95$	−32.3998	+	56.1181i	−0.341051	+	0.590717i
$96$		0			0
$97$		−	28.7493i		−	0.296384i	−0.988959	−	0.148192i	$-0.952655\pi$
$97$		−	28.7493i		−	0.296384i	0.988959	−	0.148192i	$-0.0473454\pi$
$98$		0			0
$99$	−149.421			−1.50930
$100$		0			0
$101$	53.2337	+	30.7345i	0.527067	+	0.304302i	0.739821	−	0.672804i	$-0.234910\pi$
$101$	53.2337	+	30.7345i	0.527067	+	0.304302i	−0.212754	+	0.977106i	$0.568243\pi$
$102$		0			0
$103$	−51.7263	+	29.8642i	−0.502197	+	0.289944i	−0.729620	−	0.683852i	$-0.760303\pi$
$103$	−51.7263	+	29.8642i	−0.502197	+	0.289944i	0.227423	+	0.973796i	$0.426970\pi$
$104$		0			0
$105$	14.1816	−	12.3564i	0.135062	−	0.117680i
$106$		0			0
$107$	65.8380	+	114.035i	0.615308	+	1.06574i	0.990330	+	0.138729i	$0.0443017\pi$
$107$	65.8380	+	114.035i	0.615308	+	1.06574i	−0.375022	+	0.927016i	$0.622365\pi$
$108$		0			0
$109$	−18.9045	+	32.7436i	−0.173436	+	0.300400i	−0.939619	−	0.342222i	$-0.888820\pi$
$109$	−18.9045	+	32.7436i	−0.173436	+	0.300400i	0.766183	+	0.642623i	$0.222154\pi$
$110$		0			0
$111$			6.56870i			0.0591774i
$112$		0			0
$113$	−46.4443			−0.411012			−0.205506	−	0.978656i	$-0.565884\pi$
$113$	−46.4443			−0.411012			−0.205506	+	0.978656i	$0.565884\pi$
$114$		0			0
$115$	−185.033	−	106.829i	−1.60898	−	0.928944i
$116$		0			0
$117$	162.601	−	93.8774i	1.38975	−	0.802371i
$118$		0			0
$119$	−164.992	+	32.2675i	−1.38649	+	0.271155i
$120$		0			0
$121$	−85.5335	−	148.148i	−0.706888	−	1.22437i
$122$		0			0
$123$	−8.58227	+	14.8649i	−0.0697745	+	0.120853i
$124$		0			0
$125$			116.034i			0.928268i
$126$		0			0
$127$	−12.7816			−0.100642			−0.0503211	−	0.998733i	$-0.516024\pi$
$127$	−12.7816			−0.100642			−0.0503211	+	0.998733i	$0.516024\pi$
$128$		0			0
$129$	13.1638	+	7.60010i	0.102045	+	0.0589155i
$130$		0			0
$131$	0.929338	−	0.536554i	0.00709418	−	0.00409583i	−0.496449	−	0.868066i	$-0.665363\pi$
$131$	0.929338	−	0.536554i	0.00709418	−	0.00409583i	0.503543	+	0.863970i	$0.332030\pi$
$132$		0			0
$133$	−27.7572	+	80.9137i	−0.208700	+	0.608374i
$134$		0			0
$135$	−23.8386	−	41.2897i	−0.176582	−	0.305850i
$136$		0			0
$137$	33.4330	−	57.9076i	0.244036	−	0.422683i	−0.717824	−	0.696225i	$-0.754862\pi$
$137$	33.4330	−	57.9076i	0.244036	−	0.422683i	0.961860	+	0.273541i	$0.0881951\pi$
$138$		0			0
$139$			221.071i			1.59044i	0.606322	+	0.795219i	$0.292644\pi$
$139$			221.071i			1.59044i	−0.606322	+	0.795219i	$0.707356\pi$
$140$		0			0
$141$	28.2498			0.200353
$142$		0			0
$143$	317.828	+	183.498i	2.22257	+	1.28320i
$144$		0			0
$145$	119.751	−	69.1382i	0.825868	−	0.476815i
$146$		0			0
$147$	15.2423	−	19.6017i	0.103689	−	0.133345i
$148$		0			0
$149$	−19.7606	−	34.2264i	−0.132621	−	0.229707i	0.792065	−	0.610437i	$-0.209006\pi$
$149$	−19.7606	−	34.2264i	−0.132621	−	0.229707i	−0.924686	+	0.380730i	$0.875673\pi$
$150$		0			0
$151$	−111.362	+	192.885i	−0.737499	+	1.27739i	0.216119	+	0.976367i	$0.430660\pi$
$151$	−111.362	+	192.885i	−0.737499	+	1.27739i	−0.953618	+	0.301019i	$0.902673\pi$
$152$		0			0
$153$			209.984i			1.37245i
$154$		0			0
$155$	133.963			0.864275
$156$		0			0
$157$	175.081	+	101.083i	1.11516	+	0.643840i	0.940162	−	0.340728i	$-0.110673\pi$
$157$	175.081	+	101.083i	1.11516	+	0.643840i	0.175002	+	0.984568i	$0.444007\pi$
$158$		0			0
$159$	−3.82998	+	2.21124i	−0.0240879	+	0.0139072i
$160$		0			0
$161$	−266.789	−	91.5209i	−1.65707	−	0.568453i
$162$		0			0
$163$	−1.31509	−	2.27780i	−0.00806802	−	0.0139742i	0.861963	−	0.506971i	$-0.169235\pi$
$163$	−1.31509	−	2.27780i	−0.00806802	−	0.0139742i	−0.870031	+	0.492997i	$0.835901\pi$
$164$		0			0
$165$	22.9610	−	39.7696i	0.139157	−	0.241028i
$166$		0			0
$167$		−	133.004i		−	0.796434i	−0.917291	−	0.398217i	$-0.869629\pi$
$167$		−	133.004i		−	0.796434i	0.917291	−	0.398217i	$-0.130371\pi$
$168$		0			0
$169$	−292.148			−1.72869
$170$		0			0
$171$	92.5304	+	53.4224i	0.541113	+	0.312412i
$172$		0			0
$173$	−84.0786	+	48.5428i	−0.486004	+	0.280594i	−0.722915	−	0.690937i	$-0.757198\pi$
$173$	−84.0786	+	48.5428i	−0.486004	+	0.280594i	0.236911	+	0.971531i	$0.423865\pi$
$174$		0			0
$175$	−4.18867	−	21.4178i	−0.0239352	−	0.122387i
$176$		0			0
$177$	−12.6651	−	21.9367i	−0.0715544	−	0.123936i
$178$		0			0
$179$	42.0185	−	72.7782i	0.234740	−	0.406582i	−0.724457	−	0.689320i	$-0.757909\pi$
$179$	42.0185	−	72.7782i	0.234740	−	0.406582i	0.959197	+	0.282738i	$0.0912427\pi$
$180$		0			0
$181$			214.347i			1.18424i	0.805851	+	0.592119i	$0.201708\pi$
$181$			214.347i			1.18424i	−0.805851	+	0.592119i	$0.798292\pi$
$182$		0			0
$183$	−1.99466			−0.0108998
$184$		0			0
$185$	59.5264	+	34.3676i	0.321765	+	0.185771i
$186$		0			0
$187$	−355.458	+	205.224i	−1.90084	+	1.09745i
$188$		0			0
$189$	−41.3461	−	47.4533i	−0.218762	−	0.251076i
$190$		0			0
$191$	−27.3687	−	47.4040i	−0.143292	−	0.248188i	0.785443	−	0.618934i	$-0.212435\pi$
$191$	−27.3687	−	47.4040i	−0.143292	−	0.248188i	−0.928734	+	0.370746i	$0.879102\pi$
$192$		0			0
$193$	174.150	−	301.637i	0.902332	−	1.56289i	0.0778732	−	0.996963i	$-0.475187\pi$
$193$	174.150	−	301.637i	0.902332	−	1.56289i	0.824459	−	0.565922i	$-0.191480\pi$
$194$		0			0
$195$			57.7031i			0.295913i
$196$		0			0
$197$	−161.606			−0.820337			−0.410169	−	0.912010i	$-0.634530\pi$
$197$	−161.606			−0.820337			−0.410169	+	0.912010i	$0.634530\pi$
$198$		0			0
$199$	−119.186	−	68.8121i	−0.598925	−	0.345789i	0.169694	−	0.985497i	$-0.445722\pi$
$199$	−119.186	−	68.8121i	−0.598925	−	0.345789i	−0.768618	+	0.639707i	$0.779056\pi$
$200$		0			0
$201$	46.4682	−	26.8284i	0.231185	−	0.133475i
$202$		0			0
$203$	137.627	−	119.914i	0.677965	−	0.590711i
$204$		0			0
$205$	89.8053	+	155.547i	0.438075	+	0.758768i
$206$		0			0
$207$	−176.144	+	305.091i	−0.850939	+	1.47387i
$208$		0			0
$209$			208.845i			0.999258i
$210$		0			0
$211$	−101.563			−0.481341			−0.240670	−	0.970607i	$-0.577367\pi$
$211$	−101.563			−0.481341			−0.240670	+	0.970607i	$0.577367\pi$
$212$		0			0
$213$	15.3701	+	8.87392i	0.0721600	+	0.0416616i
$214$		0			0
$215$	137.746	−	79.5279i	0.640681	−	0.369897i
$216$		0			0
$217$	173.557	−	33.9425i	0.799802	−	0.156417i
$218$		0			0
$219$	11.8114	+	20.4579i	0.0539332	+	0.0934150i
$220$		0			0
$221$	257.873	−	446.650i	1.16685	−	2.02104i
$222$		0			0
$223$			180.573i			0.809744i	0.914373	+	0.404872i	$0.132684\pi$
$223$			180.573i			0.809744i	−0.914373	+	0.404872i	$0.867316\pi$
$224$		0			0
$225$	−27.2582			−0.121148
$226$		0			0
$227$	−43.9146	−	25.3541i	−0.193456	−	0.111692i	0.400143	−	0.916453i	$-0.368960\pi$
$227$	−43.9146	−	25.3541i	−0.193456	−	0.111692i	−0.593600	+	0.804761i	$0.702294\pi$
$228$		0			0
$229$	172.801	−	99.7665i	0.754588	−	0.435661i	−0.0727614	−	0.997349i	$-0.523181\pi$
$229$	172.801	−	99.7665i	0.754588	−	0.435661i	0.827349	+	0.561688i	$0.189848\pi$
$230$		0			0
$231$	19.6708	−	57.3416i	0.0851551	−	0.248232i
$232$		0			0
$233$	88.5790	+	153.423i	0.380167	+	0.658469i	0.991086	−	0.133224i	$-0.0425330\pi$
$233$	88.5790	+	153.423i	0.380167	+	0.658469i	−0.610919	+	0.791693i	$0.709200\pi$
$234$		0			0
$235$	147.804	−	256.004i	0.628952	−	1.08938i
$236$		0			0
$237$			44.0866i			0.186019i
$238$		0			0
$239$	135.694			0.567756			0.283878	−	0.958860i	$-0.408379\pi$
$239$	135.694			0.567756			0.283878	+	0.958860i	$0.408379\pi$
$240$		0			0
$241$	273.872	+	158.120i	1.13640	+	0.656101i	0.945537	−	0.325516i	$-0.105538\pi$
$241$	273.872	+	158.120i	1.13640	+	0.656101i	0.190863	+	0.981617i	$0.438871\pi$
$242$		0			0
$243$	−102.613	+	59.2439i	−0.422278	+	0.243802i
$244$		0			0
$245$	−97.8850	−	240.684i	−0.399530	−	0.982386i
$246$		0			0
$247$	−131.212	−	227.266i	−0.531222	−	0.920104i
$248$		0			0
$249$	−16.2179	+	28.0901i	−0.0651319	+	0.112812i
$250$		0			0
$251$			40.1231i			0.159853i	0.996801	+	0.0799265i	$0.0254686\pi$
$251$			40.1231i			0.159853i	−0.996801	+	0.0799265i	$0.974531\pi$
$252$		0			0
$253$	−688.603			−2.72175
$254$		0			0
$255$	−55.8889	−	32.2675i	−0.219172	−	0.126539i
$256$		0			0
$257$	−150.405	+	86.8366i	−0.585235	+	0.337886i	−0.763211	−	0.646149i	$-0.776378\pi$
$257$	−150.405	+	86.8366i	−0.585235	+	0.337886i	0.177976	+	0.984035i	$0.443045\pi$
$258$		0			0
$259$	85.8280	+	29.4430i	0.331382	+	0.113680i
$260$		0			0
$261$	−113.999	−	197.451i	−0.436776	−	0.756518i
$262$		0			0
$263$	182.291	−	315.737i	0.693120	−	1.20052i	−0.277690	−	0.960671i	$-0.589569\pi$
$263$	182.291	−	315.737i	0.693120	−	1.20052i	0.970810	−	0.239848i	$-0.0770977\pi$
$264$		0			0
$265$			46.2771i			0.174631i
$266$		0			0
$267$	21.7831			0.0815846
$268$		0			0
$269$	−15.0874	−	8.71074i	−0.0560871	−	0.0323819i	0.471694	−	0.881762i	$-0.343643\pi$
$269$	−15.0874	−	8.71074i	−0.0560871	−	0.0323819i	−0.527781	+	0.849380i	$0.676976\pi$
$270$		0			0
$271$	112.812	−	65.1322i	0.416281	−	0.240340i	−0.277204	−	0.960811i	$-0.589408\pi$
$271$	112.812	−	65.1322i	0.416281	−	0.240340i	0.693485	+	0.720471i	$0.256074\pi$
$272$		0			0
$273$	14.6204	+	74.7580i	0.0535545	+	0.273839i
$274$		0			0
$275$	−26.6402	−	46.1423i	−0.0968736	−	0.167790i
$276$		0			0
$277$	−124.595	+	215.804i	−0.449801	+	0.779077i	−0.998373	−	0.0570258i	$-0.981838\pi$
$277$	−124.595	+	215.804i	−0.449801	+	0.779077i	0.548572	+	0.836103i	$0.315172\pi$
$278$		0			0
$279$		−	220.885i		−	0.791701i
$280$		0			0
$281$	−197.454			−0.702684			−0.351342	−	0.936247i	$-0.614275\pi$
$281$	−197.454			−0.702684			−0.351342	+	0.936247i	$0.614275\pi$
$282$		0			0
$283$	−185.615	−	107.165i	−0.655884	−	0.378675i	0.134823	−	0.990870i	$-0.456953\pi$
$283$	−185.615	−	107.165i	−0.655884	−	0.378675i	−0.790707	+	0.612195i	$0.790287\pi$
$284$		0			0
$285$	−28.4376	+	16.4184i	−0.0997809	+	0.0576085i
$286$		0			0
$287$	155.760	+	178.767i	0.542717	+	0.622882i
$288$		0			0
$289$	143.904	+	249.250i	0.497939	+	0.862456i
$290$		0			0
$291$	7.28427	−	12.6167i	0.0250319	−	0.0433565i
$292$		0			0
$293$			71.8385i			0.245182i	0.992457	+	0.122591i	$0.0391204\pi$
$293$			71.8385i			0.245182i	−0.992457	+	0.122591i	$0.960880\pi$
$294$		0			0
$295$	−265.057			−0.898499
$296$		0			0
$297$	−133.074	−	76.8304i	−0.448061	−	0.258688i
$298$		0			0
$299$	749.340	−	432.632i	2.50615	−	1.44693i
$300$		0			0
$301$	158.309	−	137.934i	0.525943	−	0.458254i
$302$		0			0
$303$	15.5746	+	26.9759i	0.0514012	+	0.0890295i
$304$		0			0
$305$	−10.4361	+	18.0758i	−0.0342167	+	0.0592651i
$306$		0			0
$307$		−	507.046i		−	1.65162i	−0.563951	−	0.825808i	$-0.690719\pi$
$307$		−	507.046i		−	1.65162i	0.563951	−	0.825808i	$-0.309281\pi$
$308$		0			0
$309$	−30.2671			−0.0979516
$310$		0			0
$311$	269.089	+	155.359i	0.865239	+	0.499546i	0.865763	−	0.500454i	$-0.166833\pi$
$311$	269.089	+	155.359i	0.865239	+	0.499546i	−0.000524087		1.00000i	$0.500167\pi$
$312$		0			0
$313$	475.367	−	274.453i	1.51875	−	0.876848i	0.518989	−	0.854781i	$-0.326309\pi$
$313$	475.367	−	274.453i	1.51875	−	0.876848i	0.999756	−	0.0220674i	$-0.00702483\pi$
$314$		0			0
$315$	−318.499	+	62.2887i	−1.01111	+	0.197742i
$316$		0			0
$317$	70.9651	+	122.915i	0.223865	+	0.387745i	0.955978	−	0.293437i	$-0.0947993\pi$
$317$	70.9651	+	122.915i	0.223865	+	0.387745i	−0.732113	+	0.681183i	$0.761466\pi$
$318$		0			0
$319$	222.828	−	385.949i	0.698520	−	1.20987i
$320$		0			0
$321$			66.7261i			0.207869i
$322$		0			0
$323$	293.494			0.908649
$324$		0			0
$325$	57.9800	+	33.4748i	0.178400	+	0.102999i
$326$		0			0
$327$	−16.5927	+	9.57978i	−0.0507421	+	0.0292960i
$328$		0			0
$329$	126.625	−	369.118i	0.384877	−	1.12194i
$330$		0			0
$331$	−18.4325	−	31.9260i	−0.0556873	−	0.0964533i	0.836838	−	0.547451i	$-0.184402\pi$
$331$	−18.4325	−	31.9260i	−0.0556873	−	0.0964533i	−0.892525	+	0.450997i	$0.851068\pi$
$332$		0			0
$333$	56.6671	−	98.1502i	0.170171	−	0.294745i
$334$		0			0
$335$		−	561.468i		−	1.67602i
$336$		0			0
$337$	−541.604			−1.60713			−0.803567	−	0.595214i	$-0.797067\pi$
$337$	−541.604			−1.60713			−0.803567	+	0.595214i	$0.797067\pi$
$338$		0			0
$339$	−20.3823	−	11.7677i	−0.0601247	−	0.0347130i
$340$		0			0
$341$	373.909	−	215.877i	1.09651	−	0.633069i
$342$		0			0
$343$	−187.799	−	287.020i	−0.547518	−	0.836794i
$344$		0			0
$345$	−54.1348	−	93.7643i	−0.156913	−	0.271781i
$346$		0			0
$347$	−122.201	+	211.658i	−0.352164	+	0.609966i	−0.986628	−	0.162986i	$-0.947887\pi$
$347$	−122.201	+	211.658i	−0.352164	+	0.609966i	0.634464	+	0.772952i	$0.281221\pi$
$348$		0			0
$349$			190.205i			0.545001i	0.962156	+	0.272501i	$0.0878507\pi$
$349$			190.205i			0.545001i	−0.962156	+	0.272501i	$0.912149\pi$
$350$		0			0
$351$	193.082			0.550091
$352$		0			0
$353$	341.878	+	197.383i	0.968493	+	0.559160i	0.898777	−	0.438407i	$-0.144457\pi$
$353$	341.878	+	197.383i	0.968493	+	0.559160i	0.0697166	+	0.997567i	$0.477791\pi$
$354$		0			0
$355$	160.833	−	92.8572i	0.453052	−	0.261570i
$356$		0			0
$357$	−80.5832	−	27.6438i	−0.225723	−	0.0774336i
$358$		0			0
$359$	148.162	+	256.625i	0.412709	+	0.714833i	0.995185	−	0.0980151i	$-0.0312494\pi$
$359$	148.162	+	256.625i	0.412709	+	0.714833i	−0.582476	+	0.812848i	$0.697916\pi$
$360$		0			0
$361$	−105.832	+	183.306i	−0.293163	+	0.507773i
$362$		0			0
$363$		−	86.6873i		−	0.238808i
$364$		0			0
$365$	247.190			0.677232
$366$		0			0
$367$	−521.865	−	301.299i	−1.42198	−	0.820978i	−0.425507	−	0.904955i	$-0.639904\pi$
$367$	−521.865	−	301.299i	−1.42198	−	0.820978i	−0.996468	+	0.0839772i	$0.973238\pi$
$368$		0			0
$369$	256.474	−	148.076i	0.695053	−	0.401289i
$370$		0			0
$371$	11.7253	+	59.9548i	0.0316047	+	0.161603i
$372$		0			0
$373$	53.4998	+	92.6644i	0.143431	+	0.248430i	0.928787	−	0.370615i	$-0.120853\pi$
$373$	53.4998	+	92.6644i	0.143431	+	0.248430i	−0.785355	+	0.619045i	$0.787520\pi$
$374$		0			0
$375$	−29.3997	+	50.9218i	−0.0783992	+	0.135791i
$376$		0			0
$377$			559.988i			1.48538i
$378$		0			0
$379$	−539.901			−1.42454			−0.712270	−	0.701906i	$-0.752333\pi$
$379$	−539.901			−1.42454			−0.712270	+	0.701906i	$0.752333\pi$
$380$		0			0
$381$	−5.60924	−	3.23849i	−0.0147224	−	0.00849998i
$382$		0			0
$383$	−115.719	+	66.8102i	−0.302137	+	0.174439i	−0.643403	−	0.765528i	$-0.722478\pi$
$383$	−115.719	+	66.8102i	−0.302137	+	0.174439i	0.341265	+	0.939967i	$0.389145\pi$
$384$		0			0
$385$	−416.719	−	478.273i	−1.08239	−	1.24227i
$386$		0			0
$387$	−131.130	−	227.123i	−0.338836	−	0.586882i
$388$		0			0
$389$	−285.627	+	494.721i	−0.734260	+	1.27178i	0.220787	+	0.975322i	$0.429138\pi$
$389$	−285.627	+	494.721i	−0.734260	+	1.27178i	−0.955047	+	0.296454i	$0.904196\pi$
$390$		0			0
$391$			967.707i			2.47495i
$392$		0			0
$393$	0.543792			0.00138369
$394$		0			0
$395$	399.518	+	230.662i	1.01144	+	0.583955i
$396$		0			0
$397$	172.662	−	99.6863i	0.434916	−	0.251099i	−0.266523	−	0.963829i	$-0.585875\pi$
$397$	172.662	−	99.6863i	0.434916	−	0.251099i	0.701439	+	0.712730i	$0.252541\pi$
$398$		0			0
$399$	−32.6826	+	28.4764i	−0.0819114	+	0.0713694i
$400$		0			0
$401$	−317.211	−	549.426i	−0.791050	−	1.37014i	−0.925317	−	0.379194i	$-0.876201\pi$
$401$	−317.211	−	549.426i	−0.791050	−	1.37014i	0.134267	−	0.990945i	$-0.457132\pi$
$402$		0			0
$403$	−271.259	+	469.835i	−0.673100	+	1.16584i
$404$		0			0
$405$			393.096i			0.970608i
$406$		0			0
$407$	221.529			0.544298
$408$		0			0
$409$	−597.403	−	344.911i	−1.46064	−	0.843303i	−0.461602	−	0.887087i	$-0.652725\pi$
$409$	−597.403	−	344.911i	−1.46064	−	0.843303i	−0.999041	+	0.0437846i	$0.986058\pi$
$410$		0			0
$411$	29.3444	−	16.9420i	0.0713975	−	0.0412214i
$412$		0			0
$413$	−343.398	+	67.1582i	−0.831472	+	0.162611i
$414$		0			0
$415$	169.704	+	293.937i	0.408926	+	0.708281i
$416$		0			0
$417$	−56.0133	+	97.0179i	−0.134324	+	0.232657i
$418$		0			0
$419$		−	43.8224i		−	0.104588i	−0.998632	−	0.0522940i	$-0.983347\pi$
$419$		−	43.8224i		−	0.104588i	0.998632	−	0.0522940i	$-0.0166533\pi$
$420$		0			0
$421$	357.611			0.849433			0.424717	−	0.905326i	$-0.360374\pi$
$421$	357.611			0.849433			0.424717	+	0.905326i	$0.360374\pi$
$422$		0			0
$423$	−422.112	−	243.706i	−0.997901	−	0.576138i
$424$		0			0
$425$	−64.8446	+	37.4380i	−0.152575	+	0.0880895i
$426$		0			0
$427$	−8.94068	+	26.0626i	−0.0209384	+	0.0610365i
$428$		0			0
$429$	92.9867	+	161.058i	0.216752	+	0.375426i
$430$		0			0
$431$	143.259	−	248.131i	0.332387	−	0.575711i	−0.650592	−	0.759427i	$-0.725479\pi$
$431$	143.259	−	248.131i	0.332387	−	0.575711i	0.982979	+	0.183716i	$0.0588127\pi$
$432$		0			0
$433$		−	407.880i		−	0.941986i	−0.882137	−	0.470993i	$-0.843896\pi$
$433$		−	407.880i		−	0.941986i	0.882137	−	0.470993i	$-0.156104\pi$
$434$		0			0
$435$	70.0708			0.161082
$436$		0			0
$437$	426.424	+	246.196i	0.975798	+	0.563377i
$438$		0			0
$439$	46.8249	−	27.0344i	0.106663	−	0.0615817i	−0.445720	−	0.895173i	$-0.647052\pi$
$439$	46.8249	−	27.0344i	0.106663	−	0.0615817i	0.552382	+	0.833591i	$0.313719\pi$
$440$		0			0
$441$	−396.853	+	161.398i	−0.899893	+	0.365981i
$442$		0			0
$443$	−158.497	−	274.526i	−0.357782	−	0.619697i	0.629808	−	0.776751i	$-0.283134\pi$
$443$	−158.497	−	274.526i	−0.357782	−	0.619697i	−0.987590	+	0.157054i	$0.949800\pi$
$444$		0			0
$445$	113.970	−	197.401i	0.256112	−	0.443599i
$446$		0			0
$447$		−	20.0272i		−	0.0448035i
$448$		0			0
$449$	544.261			1.21216			0.606081	−	0.795403i	$-0.292741\pi$
$449$	544.261			1.21216			0.606081	+	0.795403i	$0.292741\pi$
$450$		0			0
$451$	501.319	+	289.437i	1.11157	+	0.641767i
$452$		0			0
$453$	−97.7437	+	56.4323i	−0.215770	+	0.124575i
$454$		0			0
$455$	753.961	+	258.644i	1.65706	+	0.568448i
$456$		0			0
$457$	343.708	+	595.320i	0.752096	+	1.30267i	0.946805	+	0.321808i	$0.104291\pi$
$457$	343.708	+	595.320i	0.752096	+	1.30267i	−0.194709	+	0.980861i	$0.562376\pi$
$458$		0			0
$459$	−107.971	+	187.011i	−0.235231	+	0.407432i
$460$		0			0
$461$			676.260i			1.46694i	0.679721	+	0.733470i	$0.262101\pi$
$461$			676.260i			1.46694i	−0.679721	+	0.733470i	$0.737899\pi$
$462$		0			0
$463$	−559.738			−1.20894			−0.604469	−	0.796629i	$-0.706615\pi$
$463$	−559.738			−1.20894			−0.604469	+	0.796629i	$0.706615\pi$
$464$		0			0
$465$	58.7901	+	33.9425i	0.126430	+	0.0729945i
$466$		0			0
$467$	−319.886	+	184.686i	−0.684981	+	0.395474i	−0.801729	−	0.597687i	$-0.796086\pi$
$467$	−319.886	+	184.686i	−0.684981	+	0.395474i	0.116748	+	0.993162i	$0.462753\pi$
$468$		0			0
$469$	−142.261	−	727.417i	−0.303327	−	1.55100i
$470$		0			0
$471$	51.2233	+	88.7213i	0.108754	+	0.188368i
$472$		0			0
$473$	256.313	−	443.948i	0.541889	−	0.938579i
$474$		0			0
$475$			38.0987i			0.0802077i
$476$		0			0
$477$	76.3040			0.159967
$478$		0			0
$479$	−270.362	−	156.094i	−0.564430	−	0.325874i	0.190492	−	0.981689i	$-0.438992\pi$
$479$	−270.362	−	156.094i	−0.564430	−	0.325874i	−0.754922	+	0.655815i	$0.772325\pi$
$480$		0			0
$481$	−241.069	+	139.181i	−0.501182	+	0.289358i
$482$		0			0
$483$	−93.8923	−	107.761i	−0.194394	−	0.223108i
$484$		0			0
$485$	−76.2231	−	132.022i	−0.157161	−	0.272211i
$486$		0			0
$487$	140.195	−	242.824i	0.287874	−	0.498613i	−0.685428	−	0.728140i	$-0.740385\pi$
$487$	140.195	−	242.824i	0.287874	−	0.498613i	0.973302	+	0.229528i	$0.0737182\pi$
$488$		0			0
$489$		−	1.33283i		−	0.00272562i
$490$		0			0
$491$	423.804			0.863145			0.431573	−	0.902078i	$-0.357959\pi$
$491$	423.804			0.863145			0.431573	+	0.902078i	$0.357959\pi$
$492$		0			0
$493$	−542.382	−	313.144i	−1.10017	−	0.635181i
$494$		0			0
$495$	−686.171	+	396.161i	−1.38620	+	0.800325i
$496$		0			0
$497$	184.842	−	161.053i	0.371916	−	0.324050i
$498$		0			0
$499$	83.0243	+	143.802i	0.166381	+	0.288181i	0.937145	−	0.348940i	$-0.113458\pi$
$499$	83.0243	+	143.802i	0.166381	+	0.288181i	−0.770764	+	0.637121i	$0.780125\pi$
$500$		0			0
$501$	33.6997	−	58.3695i	0.0672648	−	0.116506i
$502$		0			0
$503$			632.164i			1.25679i	0.777896	+	0.628393i	$0.216287\pi$
$503$			632.164i			1.25679i	−0.777896	+	0.628393i	$0.783713\pi$
$504$		0			0
$505$	325.946			0.645438
$506$		0			0
$507$	−128.211	−	74.0224i	−0.252881	−	0.146001i
$508$		0			0
$509$	269.053	−	155.338i	0.528592	−	0.305183i	−0.211851	−	0.977302i	$-0.567949\pi$
$509$	269.053	−	155.338i	0.528592	−	0.305183i	0.740443	+	0.672119i	$0.234616\pi$
$510$		0			0
$511$	320.249	−	62.6310i	0.626711	−	0.122566i
$512$		0			0
$513$	54.9382	+	95.1558i	0.107092	+	0.185489i
$514$		0			0
$515$	−158.358	+	274.284i	−0.307491	+	0.532591i
$516$		0			0
$517$		−	952.725i		−	1.84279i
$518$		0			0
$519$	−49.1977			−0.0947932
$520$		0			0
$521$	58.0568	+	33.5191i	0.111433	+	0.0643361i	0.554681	−	0.832063i	$-0.312840\pi$
$521$	58.0568	+	33.5191i	0.111433	+	0.0643361i	−0.443247	+	0.896399i	$0.646174\pi$
$522$		0			0
$523$	−462.718	+	267.150i	−0.884738	+	0.510804i	−0.872218	−	0.489118i	$-0.837319\pi$
$523$	−462.718	+	267.150i	−0.884738	+	0.510804i	−0.0125204	+	0.999922i	$0.503985\pi$
$524$		0			0
$525$	3.58846	−	10.4606i	0.00683517	−	0.0199249i
$526$		0			0
$527$	−303.375	−	525.462i	−0.575665	−	0.997081i
$528$		0			0
$529$	−547.257	+	947.877i	−1.03451	+	1.79183i
$530$		0			0
$531$			437.040i			0.823051i
$532$		0			0
$533$	−727.383			−1.36470
$534$		0			0
$535$	604.681	+	349.113i	1.13025	+	0.652547i
$536$		0			0
$537$	36.8800	−	21.2927i	0.0686778	−	0.0396512i
$538$		0			0
$539$	−661.066	−	514.047i	−1.22647	−	0.953704i
$540$		0			0
$541$	75.6707	+	131.065i	0.139872	+	0.242265i	0.927448	−	0.373952i	$-0.121998\pi$
$541$	75.6707	+	131.065i	0.139872	+	0.242265i	−0.787576	+	0.616217i	$0.788664\pi$
$542$		0			0
$543$	−54.3096	+	94.0670i	−0.100018	+	0.173236i
$544$		0			0
$545$			200.487i			0.367865i
$546$		0			0
$547$	775.543			1.41781			0.708906	−	0.705303i	$-0.249189\pi$
$547$	775.543			1.41781			0.708906	+	0.705303i	$0.249189\pi$
$548$		0			0
$549$	29.8044	+	17.2076i	0.0542885	+	0.0313435i
$550$		0			0
$551$	−275.976	+	159.335i	−0.500865	+	0.289174i
$552$		0			0
$553$	576.044	+	197.610i	1.04167	+	0.357342i
$554$		0			0
$555$	17.4156	+	30.1647i	0.0313795	+	0.0543508i
$556$		0			0
$557$	32.2200	−	55.8066i	0.0578455	−	0.100191i	−0.835653	−	0.549258i	$-0.814910\pi$
$557$	32.2200	−	55.8066i	0.0578455	−	0.100191i	0.893498	+	0.449067i	$0.148244\pi$
$558$		0			0
$559$			644.140i			1.15231i
$560$		0			0
$561$	−207.992			−0.370752
$562$		0			0
$563$	789.688	+	455.927i	1.40264	+	0.809816i	0.994663	−	0.103175i	$-0.0329000\pi$
$563$	789.688	+	455.927i	1.40264	+	0.809816i	0.407980	+	0.912991i	$0.366233\pi$
$564$		0			0
$565$	−213.281	+	123.138i	−0.377489	+	0.217943i
$566$		0			0
$567$	99.5997	+	509.280i	0.175661	+	0.898201i
$568$		0			0
$569$	−118.002	−	204.386i	−0.207385	−	0.359201i	0.743505	−	0.668730i	$-0.233162\pi$
$569$	−118.002	−	204.386i	−0.207385	−	0.359201i	−0.950890	+	0.309529i	$0.899829\pi$
$570$		0			0
$571$	−414.770	+	718.403i	−0.726392	+	1.25815i	0.232006	+	0.972714i	$0.425471\pi$
$571$	−414.770	+	718.403i	−0.726392	+	1.25815i	−0.958398	+	0.285434i	$0.907862\pi$
$572$		0			0
$573$		−	27.7379i		−	0.0484082i
$574$		0			0
$575$	−125.619			−0.218468
$576$		0			0
$577$	380.226	+	219.524i	0.658971	+	0.380457i	0.791885	−	0.610671i	$-0.209100\pi$
$577$	380.226	+	219.524i	0.658971	+	0.380457i	−0.132914	+	0.991128i	$0.542433\pi$
$578$		0			0
$579$	152.853	−	88.2497i	0.263995	−	0.152417i
$580$		0			0
$581$	294.338	+	337.815i	0.506606	+	0.581437i
$582$		0			0
$583$	74.5741	+	129.166i	0.127914	+	0.221554i
$584$		0			0
$585$	497.795	−	862.207i	0.850932	−	1.47386i
$586$		0			0
$587$		−	871.738i		−	1.48507i	−0.669805	−	0.742537i	$-0.733622\pi$
$587$		−	871.738i		−	1.48507i	0.669805	−	0.742537i	$-0.266378\pi$
$588$		0			0
$589$	−308.729			−0.524158
$590$		0			0
$591$	−70.9216	−	40.9466i	−0.120003	−	0.0692836i
$592$		0			0
$593$	662.637	−	382.574i	1.11743	−	0.645149i	0.176688	−	0.984267i	$-0.443462\pi$
$593$	662.637	−	382.574i	1.11743	−	0.645149i	0.940744	+	0.339117i	$0.110128\pi$
$594$		0			0
$595$	−672.125	+	585.623i	−1.12962	+	0.984240i
$596$		0			0
$597$	−34.8702	−	60.3969i	−0.0584090	−	0.101167i
$598$		0			0
$599$	−146.400	+	253.571i	−0.244407	+	0.423325i	−0.961965	−	0.273174i	$-0.911926\pi$
$599$	−146.400	+	253.571i	−0.244407	+	0.423325i	0.717558	+	0.696499i	$0.245260\pi$
$600$		0			0
$601$			748.440i			1.24532i	0.782491	+	0.622662i	$0.213949\pi$
$601$			748.440i			1.24532i	−0.782491	+	0.622662i	$0.786051\pi$
$602$		0			0
$603$	−925.777			−1.53529
$604$		0			0
$605$	−785.572	−	453.550i	−1.29847	−	0.749670i
$606$		0			0
$607$	53.7404	−	31.0270i	0.0885344	−	0.0511154i	−0.455079	−	0.890451i	$-0.650389\pi$
$607$	53.7404	−	31.0270i	0.0885344	−	0.0511154i	0.543614	+	0.839336i	$0.317056\pi$
$608$		0			0
$609$	90.7811	−	17.7540i	0.149066	−	0.0291527i
$610$		0			0
$611$	598.572	+	1036.76i	0.979660	+	1.69682i
$612$		0			0
$613$	22.3280	−	38.6732i	0.0364241	−	0.0630884i	−0.847239	−	0.531212i	$-0.821737\pi$
$613$	22.3280	−	38.6732i	0.0364241	−	0.0630884i	0.883663	+	0.468124i	$0.155070\pi$
$614$		0			0
$615$			91.0168i			0.147995i
$616$		0			0
$617$	−832.160			−1.34872			−0.674360	−	0.738403i	$-0.735580\pi$
$617$	−832.160			−1.34872			−0.674360	+	0.738403i	$0.735580\pi$
$618$		0			0
$619$	216.394	+	124.935i	0.349586	+	0.201834i	0.664503	−	0.747285i	$-0.268643\pi$
$619$	216.394	+	124.935i	0.349586	+	0.201834i	−0.314917	+	0.949119i	$0.601977\pi$
$620$		0			0
$621$	−313.747	+	181.142i	−0.505229	+	0.291694i
$622$		0			0
$623$	97.6388	−	284.623i	0.156724	−	0.456858i
$624$		0			0
$625$	346.611	+	600.347i	0.554577	+	0.960556i
$626$		0			0
$627$	−52.9156	+	91.6525i	−0.0843948	+	0.146176i
$628$		0			0
$629$		−	311.319i		−	0.494943i
$630$		0			0
$631$	−26.0372			−0.0412634			−0.0206317	−	0.999787i	$-0.506568\pi$
$631$	−26.0372			−0.0412634			−0.0206317	+	0.999787i	$0.506568\pi$
$632$		0			0
$633$	−44.5713	−	25.7332i	−0.0704128	−	0.0406528i
$634$		0			0
$635$	−58.6954	+	33.8878i	−0.0924336	+	0.0533666i
$636$		0			0
$637$	1042.34	+	144.056i	1.63632	+	0.226148i
$638$		0			0
$639$	−153.108	−	265.190i	−0.239605	−	0.415008i
$640$		0			0
$641$	−235.195	+	407.370i	−0.366920	+	0.635523i	−0.989082	−	0.147365i	$-0.952921\pi$
$641$	−235.195	+	407.370i	−0.366920	+	0.635523i	0.622163	+	0.782888i	$0.286254\pi$
$642$		0			0
$643$		−	668.123i		−	1.03907i	−0.854449	−	0.519536i	$-0.826105\pi$
$643$		−	668.123i		−	1.03907i	0.854449	−	0.519536i	$-0.173895\pi$
$644$		0			0
$645$	80.6007			0.124962
$646$		0			0
$647$	−925.107	−	534.111i	−1.42984	−	0.825519i	−0.432733	−	0.901522i	$-0.642451\pi$
$647$	−925.107	−	534.111i	−1.42984	−	0.825519i	−0.997108	+	0.0760031i	$0.975784\pi$
$648$		0			0
$649$	−739.813	+	427.131i	−1.13993	+	0.658138i
$650$		0			0
$651$	84.7662	+	29.0788i	0.130209	+	0.0446678i
$652$		0			0
$653$	−389.917	−	675.357i	−0.597117	−	1.03424i	−0.993244	−	0.116041i	$-0.962980\pi$
$653$	−389.917	−	675.357i	−0.597117	−	1.03424i	0.396128	−	0.918195i	$-0.370354\pi$
$654$		0			0
$655$	2.84513	−	4.92792i	0.00434371	−	0.00752353i
$656$		0			0
$657$		−	407.579i		−	0.620363i
$658$		0			0
$659$	−1017.20			−1.54355			−0.771774	−	0.635897i	$-0.780630\pi$
$659$	−1017.20			−1.54355			−0.771774	+	0.635897i	$0.780630\pi$
$660$		0			0
$661$	819.200	+	472.966i	1.23934	+	0.715530i	0.968958	−	0.247224i	$-0.0795184\pi$
$661$	819.200	+	472.966i	1.23934	+	0.715530i	0.270377	+	0.962755i	$0.412852\pi$
$662$		0			0
$663$	226.337	−	130.676i	0.341384	−	0.197098i
$664$		0			0
$665$	87.0605	+	445.164i	0.130918	+	0.669419i
$666$		0			0
$667$	−525.359	−	909.949i	−0.787645	−	1.36424i
$668$		0			0
$669$	−45.7522	+	79.2452i	−0.0683890	+	0.118453i
$670$		0			0
$671$			67.2697i			0.100253i
$672$		0			0
$673$	−76.8911			−0.114251			−0.0571256	−	0.998367i	$-0.518194\pi$
$673$	−76.8911			−0.114251			−0.0571256	+	0.998367i	$0.518194\pi$
$674$		0			0
$675$	−24.2761	−	14.0158i	−0.0359646	−	0.0207642i
$676$		0			0
$677$	−555.161	+	320.523i	−0.820031	+	0.473445i	−0.850427	−	0.526093i	$-0.823657\pi$
$677$	−555.161	+	320.523i	−0.820031	+	0.473445i	0.0303959	+	0.999538i	$0.490323\pi$
$678$		0			0
$679$	−132.202	−	151.730i	−0.194702	−	0.223461i
$680$		0			0
$681$	−12.8481	−	22.2535i	−0.0188665	−	0.0326777i
$682$		0			0
$683$	511.461	−	885.877i	0.748845	−	1.29704i	−0.199531	−	0.979891i	$-0.563942\pi$
$683$	511.461	−	885.877i	0.748845	−	1.29704i	0.948377	−	0.317147i	$-0.102725\pi$
$684$		0			0
$685$		−	354.564i		−	0.517611i
$686$		0			0
$687$	101.112			0.147180
$688$		0			0
$689$	−162.303	−	93.7059i	−0.235564	−	0.136003i
$690$		0			0
$691$	597.595	−	345.021i	0.864826	−	0.499307i	−0.000799666	−	1.00000i	$-0.500255\pi$
$691$	597.595	−	345.021i	0.864826	−	0.499307i	0.865625	+	0.500692i	$0.166921\pi$
$692$		0			0
$693$	−788.600	+	687.108i	−1.13795	+	0.991497i
$694$		0			0
$695$	586.126	+	1015.20i	0.843347	+	1.46072i
$696$		0			0
$697$	406.751	−	704.513i	0.583574	−	1.01078i
$698$		0			0
$699$			89.7739i			0.128432i
$700$		0			0
$701$	361.922			0.516294			0.258147	−	0.966106i	$-0.416888\pi$
$701$	361.922			0.516294			0.258147	+	0.966106i	$0.416888\pi$
$702$		0			0
$703$	−137.184	−	79.2032i	−0.195141	−	0.112665i
$704$		0			0
$705$	129.729	−	74.8988i	0.184012	−	0.106239i
$706$		0			0
$707$	422.283	−	82.5858i	0.597289	−	0.116812i
$708$		0			0
$709$	260.952	+	451.982i	0.368056	+	0.637492i	0.989262	−	0.146156i	$-0.0466900\pi$
$709$	260.952	+	451.982i	0.368056	+	0.637492i	−0.621205	+	0.783648i	$0.713357\pi$
$710$		0			0
$711$	380.327	−	658.746i	0.534919	−	0.926507i
$712$		0			0
$713$		−	1017.94i		−	1.42769i
$714$		0			0
$715$	1946.04			2.72173
$716$		0			0
$717$	59.5497	+	34.3810i	0.0830540	+	0.0479513i
$718$		0			0
$719$	573.144	−	330.905i	0.797141	−	0.460230i	−0.0453294	−	0.998972i	$-0.514434\pi$
$719$	573.144	−	330.905i	0.797141	−	0.460230i	0.842470	+	0.538743i	$0.181100\pi$
$720$		0			0
$721$	−135.667	+	395.476i	−0.188164	+	0.548510i
$722$		0			0
$723$	80.1267	+	138.783i	0.110825	+	0.191955i
$724$		0			0
$725$	40.6495	−	70.4070i	0.0560683	−	0.0971132i
$726$		0			0
$727$		−	1169.62i		−	1.60882i	−0.594071	−	0.804412i	$-0.702480\pi$
$727$		−	1169.62i		−	1.60882i	0.594071	−	0.804412i	$-0.297520\pi$
$728$		0			0
$729$	607.150			0.832854
$730$		0			0
$731$	−623.888	−	360.202i	−0.853472	−	0.492752i
$732$		0			0
$733$	391.800	−	226.206i	0.534516	−	0.308603i	−0.208338	−	0.978057i	$-0.566805\pi$
$733$	391.800	−	226.206i	0.534516	−	0.308603i	0.742853	+	0.669454i	$0.233472\pi$
$734$		0			0
$735$	18.0256	−	130.427i	0.0245246	−	0.177451i
$736$		0			0
$737$	−904.788	−	1567.14i	−1.22766	−	2.12638i
$738$		0			0
$739$	2.75378	−	4.76968i	0.00372636	−	0.00645424i	−0.864156	−	0.503224i	$-0.832147\pi$
$739$	2.75378	−	4.76968i	0.00372636	−	0.00645424i	0.867883	+	0.496769i	$0.165481\pi$
$740$		0			0
$741$		−	132.982i		−	0.179463i
$742$		0			0
$743$	866.020			1.16557			0.582786	−	0.812626i	$-0.301963\pi$
$743$	866.020			1.16557			0.582786	+	0.812626i	$0.301963\pi$
$744$		0			0
$745$	−181.489	−	104.783i	−0.243609	−	0.140648i
$746$		0			0
$747$	484.658	−	279.817i	0.648806	−	0.374588i
$748$		0			0
$749$	871.857	+	299.088i	1.16403	+	0.399316i
$750$		0			0
$751$	230.421	+	399.101i	0.306819	+	0.531426i	0.977665	−	0.210171i	$-0.0674020\pi$
$751$	230.421	+	399.101i	0.306819	+	0.531426i	−0.670846	+	0.741597i	$0.734069\pi$
$752$		0			0
$753$	−10.1661	+	17.6082i	−0.0135008	+	0.0233840i
$754$		0			0
$755$			1181.02i			1.56427i
$756$		0			0
$757$	547.987			0.723893			0.361946	−	0.932199i	$-0.382112\pi$
$757$	547.987			0.723893			0.361946	+	0.932199i	$0.382112\pi$
$758$		0			0
$759$	−302.196	−	174.473i	−0.398151	−	0.229872i
$760$		0			0
$761$	−1129.20	+	651.942i	−1.48383	+	0.856691i	−0.999831	−	0.0183760i	$-0.994150\pi$
$761$	−1129.20	+	651.942i	−1.48383	+	0.856691i	−0.484002	+	0.875067i	$0.660817\pi$
$762$		0			0
$763$	50.7978	+	259.743i	0.0665764	+	0.340423i
$764$		0			0
$765$	556.732	+	964.289i	0.727755	+	1.26051i
$766$		0			0
$767$	536.711	−	929.611i	0.699754	−	1.21201i
$768$		0			0
$769$		−	771.004i		−	1.00261i	−0.865272	−	0.501303i	$-0.832854\pi$
$769$		−	771.004i		−	1.00261i	0.865272	−	0.501303i	$-0.167146\pi$
$770$		0			0
$771$	−88.0080			−0.114148
$772$		0			0
$773$	922.592	+	532.659i	1.19352	+	0.689080i	0.959104	−	0.283056i	$-0.0913481\pi$
$773$	922.592	+	532.659i	1.19352	+	0.689080i	0.234418	+	0.972136i	$0.424681\pi$
$774$		0			0
$775$	68.2106	−	39.3814i	0.0880137	−	0.0508147i
$776$		0			0
$777$	30.2059	+	34.6676i	0.0388750	+	0.0446173i
$778$		0			0
$779$	−206.964	−	358.473i	−0.265679	−	0.460170i
$780$		0			0
$781$	299.273	−	518.356i	0.383192	−	0.663708i
$782$		0			0
$783$		−	234.466i		−	0.299446i
$784$		0			0
$785$	1072.01			1.36561
$786$		0			0
$787$	−818.075	−	472.316i	−1.03948	−	0.600147i	−0.119798	−	0.992798i	$-0.538225\pi$
$787$	−818.075	−	472.316i	−1.03948	−	0.600147i	−0.919687	+	0.392651i	$0.871558\pi$
$788$		0			0
$789$	159.998	−	92.3748i	0.202786	−	0.117078i
$790$		0			0
$791$	−245.119	+	213.572i	−0.309885	+	0.270003i
$792$		0			0
$793$	−42.2638	−	73.2031i	−0.0532961	−	0.0923116i
$794$		0			0
$795$	−11.7253	+	20.3089i	−0.0147489	+	0.0255458i
$796$		0			0
$797$			1245.89i			1.56322i	0.623765	+	0.781612i	$0.285602\pi$
$797$			1245.89i			1.56322i	−0.623765	+	0.781612i	$0.714398\pi$
$798$		0			0
$799$	−1338.88			−1.67570
$800$		0			0
$801$	−325.486	−	187.919i	−0.406349	−	0.234606i
$802$		0			0
$803$	689.942	−	398.338i	0.859205	−	0.496062i
$804$		0			0
$805$	−1467.79	+	287.056i	−1.82335	+	0.356591i
$806$		0			0
$807$	−4.41412	−	7.64548i	−0.00546979	−	0.00947396i
$808$		0			0
$809$	88.6536	−	153.553i	0.109584	−	0.189805i	−0.806018	−	0.591891i	$-0.798381\pi$
$809$	88.6536	−	153.553i	0.109584	−	0.189805i	0.915602	+	0.402086i	$0.131715\pi$
$810$		0			0
$811$		−	1212.71i		−	1.49532i	−0.664079	−	0.747662i	$-0.731176\pi$
$811$		−	1212.71i		−	1.49532i	0.664079	−	0.747662i	$-0.268824\pi$
$812$		0			0
$813$	66.0108			0.0811941
$814$		0			0
$815$	−12.0783	−	6.97339i	−0.0148200	−	0.00855631i
$816$		0			0
$817$	−317.449	+	183.279i	−0.388554	+	0.224332i
$818$		0			0
$819$	426.465	−	1243.17i	0.520714	−	1.51791i
$820$		0			0
$821$	−532.253	−	921.889i	−0.648298	−	1.12289i	−0.983529	−	0.180749i	$-0.942148\pi$
$821$	−532.253	−	921.889i	−0.648298	−	1.12289i	0.335231	−	0.942136i	$-0.391186\pi$
$822$		0			0
$823$	142.824	−	247.378i	0.173540	−	0.300581i	−0.766115	−	0.642704i	$-0.777813\pi$
$823$	142.824	−	247.378i	0.173540	−	0.300581i	0.939655	+	0.342123i	$0.111146\pi$
$824$		0			0
$825$		−	26.9996i		−	0.0327268i
$826$		0			0
$827$	−1182.30			−1.42962			−0.714811	−	0.699317i	$-0.753487\pi$
$827$	−1182.30			−1.42962			−0.714811	+	0.699317i	$0.753487\pi$
$828$		0			0
$829$	−624.399	−	360.497i	−0.753195	−	0.434857i	0.0736521	−	0.997284i	$-0.476535\pi$
$829$	−624.399	−	360.497i	−0.753195	−	0.434857i	−0.826847	+	0.562427i	$0.809868\pi$
$830$		0			0
$831$	−109.358	+	63.1378i	−0.131598	+	0.0759781i
$832$		0			0
$833$	−722.399	+	929.009i	−0.867226	+	1.11526i
$834$		0			0
$835$	−352.635	−	610.782i	−0.422317	−	0.731475i
$836$		0			0
$837$	113.576	−	196.719i	0.135694	−	0.235029i
$838$		0			0
$839$		−	548.052i		−	0.653221i	−0.945159	−	0.326610i	$-0.894094\pi$
$839$		−	548.052i		−	0.653221i	0.945159	−	0.326610i	$-0.105906\pi$
$840$		0			0
$841$	−160.988			−0.191424
$842$		0			0
$843$	−86.6536	−	50.0295i	−0.102792	−	0.0593469i
$844$		0			0
$845$	−1341.60	+	774.574i	−1.58769	+	0.916656i
$846$		0			0
$847$	−1132.67	−	388.560i	−1.33728	−	0.458749i
$848$		0			0
$849$	−54.3053	−	94.0596i	−0.0639639	−	0.110789i
$850$		0			0
$851$	261.149	−	452.323i	0.306873	−	0.531519i
$852$		0			0
$853$		−	1110.62i		−	1.30201i	−0.759072	−	0.651007i	$-0.774347\pi$
$853$		−	1110.62i		−	1.30201i	0.759072	−	0.651007i	$-0.225653\pi$
$854$		0			0
$855$	566.556			0.662639
$856$		0			0
$857$	−125.717	−	72.5826i	−0.146694	−	0.0846939i	0.424856	−	0.905261i	$-0.360325\pi$
$857$	−125.717	−	72.5826i	−0.146694	−	0.0846939i	−0.571551	+	0.820567i	$0.693658\pi$
$858$		0			0
$859$	−1156.42	+	667.660i	−1.34624	+	0.777252i	−0.987715	−	0.156268i	$-0.950054\pi$
$859$	−1156.42	+	667.660i	−1.34624	+	0.777252i	−0.358526	+	0.933520i	$0.616720\pi$
$860$		0			0
$861$	23.0612	+	117.918i	0.0267841	+	0.136955i
$862$		0			0
$863$	−281.425	−	487.443i	−0.326101	−	0.564824i	0.655633	−	0.755079i	$-0.272402\pi$
$863$	−281.425	−	487.443i	−0.326101	−	0.564824i	−0.981735	+	0.190255i	$0.939068\pi$
$864$		0			0
$865$	−257.404	+	445.836i	−0.297576	+	0.515417i
$866$		0			0
$867$			145.846i			0.168219i
$868$		0			0
$869$	1486.82			1.71095
$870$		0			0
$871$	1969.19	+	1136.91i	2.26083	+	1.30529i
$872$		0			0
$873$	−217.685	+	125.680i	−0.249353	+	0.143964i
$874$		0			0
$875$	533.576	+	612.390i	0.609801	+	0.699875i
$876$		0			0
$877$	−453.268	−	785.084i	−0.516840	−	0.895193i	−0.999809	−	0.0195553i	$-0.993775\pi$
$877$	−453.268	−	785.084i	−0.516840	−	0.895193i	0.482969	−	0.875637i	$-0.339558\pi$
$878$		0			0
$879$	−18.2019	+	31.5266i	−0.0207075	+	0.0358664i
$880$		0			0
$881$		−	422.614i		−	0.479698i	−0.970810	−	0.239849i	$-0.922902\pi$
$881$		−	422.614i		−	0.479698i	0.970810	−	0.239849i	$-0.0770979\pi$
$882$		0			0
$883$	310.036			0.351116			0.175558	−	0.984469i	$-0.443827\pi$
$883$	310.036			0.351116			0.175558	+	0.984469i	$0.443827\pi$
$884$		0			0
$885$	−116.321	−	67.1582i	−0.131437	−	0.0758850i
$886$		0			0
$887$	−983.657	+	567.915i	−1.10897	+	0.640265i	−0.938563	−	0.345109i	$-0.887842\pi$
$887$	−983.657	+	567.915i	−1.10897	+	0.640265i	−0.170408	+	0.985374i	$0.554509\pi$
$888$		0			0
$889$	−67.4572	+	58.7755i	−0.0758799	+	0.0661142i
$890$		0			0
$891$	633.462	+	1097.19i	0.710956	+	1.23141i
$892$		0			0
$893$	−340.627	+	589.983i	−0.381441	+	0.660676i
$894$		0			0
$895$		−	445.616i		−	0.497895i
$896$		0			0
$897$	438.468			0.488816
$898$		0			0
$899$	570.536	+	329.399i	0.634635	+	0.366406i
$900$		0			0
$901$	181.519	−	104.800i	0.201464	−	0.116316i
$902$		0			0
$903$	104.423	−	20.4220i	0.115640	−	0.0226157i
$904$		0			0
$905$	568.299	+	984.323i	0.627955	+	1.08765i
$906$		0			0
$907$	−40.4633	+	70.0846i	−0.0446123	+	0.0772707i	−0.887469	−	0.460867i	$-0.847539\pi$
$907$	−40.4633	+	70.0846i	−0.0446123	+	0.0772707i	0.842857	+	0.538138i	$0.180872\pi$
$908$		0			0
$909$		−	537.436i		−	0.591239i
$910$		0			0
$911$	1285.92			1.41155			0.705774	−	0.708437i	$-0.250599\pi$
$911$	1285.92			1.41155			0.705774	+	0.708437i	$0.250599\pi$
$912$		0			0
$913$	947.340	+	546.947i	1.03761	+	0.599065i
$914$		0			0
$915$	−9.15984	+	5.28844i	−0.0100108	+	0.00577971i
$916$		0			0
$917$	2.43745	−	7.10530i	0.00265807	−	0.00774842i
$918$		0			0
$919$	−856.410	−	1483.35i	−0.931894	−	1.61409i	−0.780082	−	0.625678i	$-0.784823\pi$
$919$	−856.410	−	1483.35i	−0.931894	−	1.61409i	−0.151812	−	0.988409i	$-0.548511\pi$
$920$		0			0
$921$	128.472	−	222.519i	0.139491	−	0.241606i
$922$		0			0
$923$			752.101i			0.814845i
$924$		0			0
$925$	40.4126			0.0436893
$926$		0			0
$927$	452.254	+	261.109i	0.487868	+	0.281671i
$928$		0			0
$929$	1178.70	−	680.522i	1.26878	−	0.732531i	0.294024	−	0.955798i	$-0.405005\pi$
$929$	1178.70	−	680.522i	1.26878	−	0.732531i	0.974757	+	0.223267i	$0.0716720\pi$
$930$		0			0
$931$	225.585	+	554.679i	0.242303	+	0.595788i
$932$		0			0
$933$	78.7273	+	136.360i	0.0843808	+	0.146152i
$934$		0			0
$935$	−1088.22	+	1884.85i	−1.16387	+	2.01588i
$936$		0			0
$937$		−	314.858i		−	0.336028i	−0.985785	−	0.168014i	$-0.946265\pi$
$937$		−	314.858i		−	0.336028i	0.985785	−	0.168014i	$-0.0537354\pi$
$938$		0			0
$939$	278.156			0.296226
$940$		0			0
$941$	261.326	+	150.877i	0.277711	+	0.160336i	0.632387	−	0.774653i	$-0.282075\pi$
$941$	261.326	+	150.877i	0.277711	+	0.160336i	−0.354676	+	0.934989i	$0.615409\pi$
$942$		0			0
$943$	1181.96	−	682.403i	1.25340	−	0.723651i
$944$		0			0
$945$	−315.682	−	108.294i	−0.334055	−	0.114597i
$946$		0			0
$947$	−726.588	−	1258.49i	−0.767252	−	1.32892i	−0.939048	−	0.343787i	$-0.888290\pi$
$947$	−726.588	−	1258.49i	−0.767252	−	1.32892i	0.171796	−	0.985133i	$-0.445043\pi$
$948$		0			0
$949$	−500.531	+	866.945i	−0.527430	+	0.913536i
$950$		0			0
$951$			71.9225i			0.0756282i
$952$		0			0
$953$	977.784			1.02601			0.513003	−	0.858387i	$-0.328533\pi$
$953$	977.784			1.02601			0.513003	+	0.858387i	$0.328533\pi$
$954$		0			0
$955$	−251.365	−	145.126i	−0.263209	−	0.151964i
$956$		0			0
$957$	195.578	−	112.917i	0.204366	−	0.117991i
$958$		0			0
$959$	−89.8367	−	459.359i	−0.0936775	−	0.478998i
$960$		0			0
$961$	−161.377	−	279.512i	−0.167926	−	0.290856i
$962$		0			0
$963$	575.635	−	997.029i	0.597752	−	1.03534i
$964$		0			0
$965$		−	1846.90i		−	1.91389i
$966$		0			0
$967$	−181.044			−0.187222			−0.0936109	−	0.995609i	$-0.529841\pi$
$967$	−181.044			−0.187222			−0.0936109	+	0.995609i	$0.529841\pi$
$968$		0			0
$969$	128.801	+	74.3632i	0.132921	+	0.0767422i
$970$		0			0
$971$	210.470	−	121.515i	0.216756	−	0.125144i	−0.387691	−	0.921789i	$-0.626727\pi$
$971$	210.470	−	121.515i	0.216756	−	0.125144i	0.604447	+	0.796645i	$0.293394\pi$
$972$		0			0
$973$	1016.59	+	1166.75i	1.04480	+	1.19912i
$974$		0			0
$975$	16.9632	+	29.3811i	0.0173981	+	0.0301344i
$976$		0			0
$977$	−715.865	+	1239.91i	−0.732717	+	1.26910i	0.223000	+	0.974818i	$0.428415\pi$
$977$	−715.865	+	1239.91i	−0.732717	+	1.26910i	−0.955718	+	0.294285i	$0.904918\pi$
$978$		0			0
$979$		−	734.635i		−	0.750393i
$980$		0			0
$981$	330.573			0.336975
$982$		0			0
$983$	−384.934	−	222.241i	−0.391591	−	0.226085i	0.291259	−	0.956644i	$-0.405926\pi$
$983$	−384.934	−	222.241i	−0.391591	−	0.226085i	−0.682849	+	0.730559i	$0.739259\pi$
$984$		0			0
$985$	−742.128	+	428.468i	−0.753429	+	0.434993i
$986$		0			0
$987$	149.094	−	129.906i	0.151058	−	0.131617i
$988$		0			0
$989$	−604.308	−	1046.69i	−0.611029	−	1.05833i
$990$		0			0
$991$	−902.358	+	1562.93i	−0.910553	+	1.57712i	−0.0972693	+	0.995258i	$0.531011\pi$
$991$	−902.358	+	1562.93i	−0.910553	+	1.57712i	−0.813284	+	0.581867i	$0.802323\pi$
$992$		0			0
$993$		−	18.6812i		−	0.0188128i
$994$		0			0
$995$	−729.767			−0.733434
$996$		0			0
$997$	−1649.18	−	952.153i	−1.65414	−	0.955018i	−0.975344	−	0.220691i	$-0.929169\pi$
$997$	−1649.18	−	952.153i	−1.65414	−	0.955018i	−0.678796	−	0.734327i	$-0.737498\pi$
$998$		0			0
$999$	100.935	−	58.2749i	0.101036	−	0.0583332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.3.s.g.129.5		16
4.3	odd	2	inner	448.3.s.g.129.4		16
7.5	odd	6	inner	448.3.s.g.257.5		16
8.3	odd	2		224.3.s.a.129.5	yes	16
8.5	even	2		224.3.s.a.129.4	yes	16
28.19	even	6	inner	448.3.s.g.257.4		16
56.3	even	6		1568.3.c.h.97.10		16
56.5	odd	6		224.3.s.a.33.4	✓	16
56.11	odd	6		1568.3.c.h.97.7		16
56.19	even	6		224.3.s.a.33.5	yes	16
56.45	odd	6		1568.3.c.h.97.8		16
56.53	even	6		1568.3.c.h.97.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.a.33.4	✓	16	56.5	odd	6
224.3.s.a.33.5	yes	16	56.19	even	6
224.3.s.a.129.4	yes	16	8.5	even	2
224.3.s.a.129.5	yes	16	8.3	odd	2
448.3.s.g.129.4		16	4.3	odd	2	inner
448.3.s.g.129.5		16	1.1	even	1	trivial
448.3.s.g.257.4		16	28.19	even	6	inner
448.3.s.g.257.5		16	7.5	odd	6	inner
1568.3.c.h.97.7		16	56.11	odd	6
1568.3.c.h.97.8		16	56.45	odd	6
1568.3.c.h.97.9		16	56.53	even	6
1568.3.c.h.97.10		16	56.3	even	6

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.438854 + 0.253372i) q^{3} +(4.59219 - 2.65130i) q^{5} +(5.27770 - 4.59846i) q^{7} +(-4.37160 - 7.57184i) q^{9} +O(q^{10})\)	\(q+(0.438854 + 0.253372i) q^{3} +(4.59219 - 2.65130i) q^{5} +(5.27770 - 4.59846i) q^{7} +(-4.37160 - 7.57184i) q^{9} +(8.54498 - 14.8003i) q^{11} +21.4744i q^{13} +2.68707 q^{15} +(-20.7992 - 12.0084i) q^{17} +(-10.5831 + 6.11016i) q^{19} +(3.48126 - 0.680829i) q^{21} +(-20.1464 - 34.8946i) q^{23} +(1.55882 - 2.69996i) q^{25} -8.99128i q^{27} +26.0770 q^{29} +(21.8789 + 12.6318i) q^{31} +(7.50000 - 4.33013i) q^{33} +(12.0443 - 35.1098i) q^{35} +(6.48126 + 11.2259i) q^{37} +(-5.44101 + 9.42411i) q^{39} +33.8721i q^{41} +29.9958 q^{43} +(-40.1505 - 23.1809i) q^{45} +(48.2788 - 27.8738i) q^{47} +(6.70828 - 48.5386i) q^{49} +(-6.08521 - 10.5399i) q^{51} +(-4.36362 + 7.55801i) q^{53} -90.6214i q^{55} -6.19259 q^{57} +(-43.2893 - 24.9931i) q^{59} +(-3.40886 + 1.96811i) q^{61} +(-57.8909 - 19.8593i) q^{63} +(56.9351 + 98.6144i) q^{65} +(52.9426 - 91.6994i) q^{67} -20.4182i q^{69} +35.0232 q^{71} +(40.3712 + 23.3083i) q^{73} +(1.36819 - 0.789926i) q^{75} +(-22.9610 - 117.406i) q^{77} +(43.4998 + 75.3438i) q^{79} +(-37.0663 + 64.2007i) q^{81} +64.0079i q^{83} -127.352 q^{85} +(11.4440 + 6.60721i) q^{87} +(37.2272 - 21.4932i) q^{89} +(98.7491 + 113.335i) q^{91} +(6.40109 + 11.0870i) q^{93} +(-32.3998 + 56.1181i) q^{95} -28.7493i q^{97} -149.421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^9	\( 16 q + 8 q^{9} + 48 q^{17} - 56 q^{21} + 16 q^{25} - 112 q^{29} + 120 q^{33} - 8 q^{37} + 72 q^{45} - 128 q^{49} + 24 q^{53} - 528 q^{57} + 360 q^{61} - 8 q^{65} + 72 q^{73} + 32 q^{81} - 720 q^{85} + 408 q^{89} + 232 q^{93}+O(q^{100}) \) 16 * q + 8 * q^9 + 48 * q^17 - 56 * q^21 + 16 * q^25 - 112 * q^29 + 120 * q^33 - 8 * q^37 + 72 * q^45 - 128 * q^49 + 24 * q^53 - 528 * q^57 + 360 * q^61 - 8 * q^65 + 72 * q^73 + 32 * q^81 - 720 * q^85 + 408 * q^89 + 232 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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