LMFDB - Embedded newform 441.4.e.u.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, 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:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.u.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207107 + 0.358719i) q^{2} +(3.91421 + 6.77962i) q^{4} +(-0.0502525 + 0.0870399i) q^{5} -6.55635 q^{8} +O(q^{10})$	\(q+(-0.207107 + 0.358719i) q^{2} +(3.91421 + 6.77962i) q^{4} +(-0.0502525 + 0.0870399i) q^{5} -6.55635 q^{8} +(-0.0208153 - 0.0360531i) q^{10} +(-21.9706 - 38.0541i) q^{11} -16.6447 q^{13} +(-29.9558 + 51.8850i) q^{16} +(-60.8198 - 105.343i) q^{17} +(63.5563 - 110.083i) q^{19} -0.786797 q^{20} +18.2010 q^{22} +(26.7990 - 46.4172i) q^{23} +(62.4949 + 108.244i) q^{25} +(3.44722 - 5.97076i) q^{26} -235.681 q^{29} +(9.35534 + 16.2039i) q^{31} +(-38.6335 - 66.9152i) q^{32} +50.3848 q^{34} +(95.9411 - 166.175i) q^{37} +(26.3259 + 45.5978i) q^{38} +(0.329473 - 0.570664i) q^{40} +319.713 q^{41} -218.579 q^{43} +(171.995 - 297.904i) q^{44} +(11.1005 + 19.2266i) q^{46} +(200.777 - 347.755i) q^{47} -51.7725 q^{50} +(-65.1508 - 112.844i) q^{52} +(321.558 + 556.956i) q^{53} +4.41631 q^{55} +(48.8112 - 84.5434i) q^{58} +(-5.80613 - 10.0565i) q^{59} +(6.12132 - 10.6024i) q^{61} -7.75022 q^{62} -447.288 q^{64} +(0.836436 - 1.44875i) q^{65} +(-334.524 - 579.412i) q^{67} +(476.123 - 824.670i) q^{68} -822.098 q^{71} +(-257.550 - 446.089i) q^{73} +(39.7401 + 68.8319i) q^{74} +995.092 q^{76} +(402.877 - 697.804i) q^{79} +(-3.01071 - 5.21471i) q^{80} +(-66.2147 + 114.687i) q^{82} +394.863 q^{83} +12.2254 q^{85} +(45.2691 - 78.4084i) q^{86} +(144.047 + 249.496i) q^{88} +(336.709 - 583.197i) q^{89} +419.588 q^{92} +(83.1644 + 144.045i) q^{94} +(6.38773 + 11.0639i) q^{95} -1091.11 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 10 q^{4} - 20 q^{5} + 36 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 10 * q^4 - 20 * q^5 + 36 * q^8	$ 4 q + 2 q^{2} + 10 q^{4} - 20 q^{5} + 36 q^{8} + 48 q^{10} - 20 q^{11} - 208 q^{13} - 18 q^{16} - 116 q^{17} + 192 q^{19} - 88 q^{20} + 152 q^{22} + 28 q^{23} - 146 q^{25} - 204 q^{26} - 592 q^{29} - 104 q^{31} + 18 q^{32} + 128 q^{34} + 248 q^{37} - 104 q^{38} - 488 q^{40} + 40 q^{41} - 1440 q^{43} + 292 q^{44} + 84 q^{46} + 96 q^{47} - 1412 q^{50} - 320 q^{52} + 268 q^{53} - 944 q^{55} - 48 q^{58} + 616 q^{59} + 16 q^{61} - 608 q^{62} + 236 q^{64} + 1740 q^{65} + 144 q^{67} + 940 q^{68} - 1976 q^{71} + 104 q^{73} - 56 q^{74} + 2272 q^{76} + 944 q^{79} + 828 q^{80} - 856 q^{82} + 2032 q^{83} - 200 q^{85} - 1120 q^{86} + 876 q^{88} + 388 q^{89} + 728 q^{92} + 904 q^{94} + 1304 q^{95} - 976 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 + 10 * q^4 - 20 * q^5 + 36 * q^8 + 48 * q^10 - 20 * q^11 - 208 * q^13 - 18 * q^16 - 116 * q^17 + 192 * q^19 - 88 * q^20 + 152 * q^22 + 28 * q^23 - 146 * q^25 - 204 * q^26 - 592 * q^29 - 104 * q^31 + 18 * q^32 + 128 * q^34 + 248 * q^37 - 104 * q^38 - 488 * q^40 + 40 * q^41 - 1440 * q^43 + 292 * q^44 + 84 * q^46 + 96 * q^47 - 1412 * q^50 - 320 * q^52 + 268 * q^53 - 944 * q^55 - 48 * q^58 + 616 * q^59 + 16 * q^61 - 608 * q^62 + 236 * q^64 + 1740 * q^65 + 144 * q^67 + 940 * q^68 - 1976 * q^71 + 104 * q^73 - 56 * q^74 + 2272 * q^76 + 944 * q^79 + 828 * q^80 - 856 * q^82 + 2032 * q^83 - 200 * q^85 - 1120 * q^86 + 876 * q^88 + 388 * q^89 + 728 * q^92 + 904 * q^94 + 1304 * q^95 - 976 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.207107	+	0.358719i	−0.0732233	+	0.126826i	−0.900312	−	0.435245i	$-0.856662\pi$
$2$	−0.207107	+	0.358719i	−0.0732233	+	0.126826i	0.827089	+	0.562071i	$0.189995\pi$
$3$		0			0
$3$		0			0
$4$	3.91421	+	6.77962i	0.489277	+	0.847452i
$5$	−0.0502525	+	0.0870399i	−0.00449472	+	0.00778509i	−0.868264	−	0.496102i	$-0.834764\pi$
$5$	−0.0502525	+	0.0870399i	−0.00449472	+	0.00778509i	0.863769	+	0.503887i	$0.168097\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−6.55635			−0.289752
$9$		0			0
$10$	−0.0208153	−	0.0360531i	−0.000658237	−	0.00114010i
$11$	−21.9706	−	38.0541i	−0.602216	−	1.04307i	−0.992485	−	0.122368i	$-0.960951\pi$
$11$	−21.9706	−	38.0541i	−0.602216	−	1.04307i	0.390269	−	0.920701i	$-0.372382\pi$
$12$		0			0
$13$	−16.6447			−0.355108			−0.177554	−	0.984111i	$-0.556818\pi$
$13$	−16.6447			−0.355108			−0.177554	+	0.984111i	$0.556818\pi$
$14$		0			0
$15$		0			0
$16$	−29.9558	+	51.8850i	−0.468060	+	0.810704i
$17$	−60.8198	−	105.343i	−0.867704	−	1.50291i	−0.864337	−	0.502913i	$-0.832262\pi$
$17$	−60.8198	−	105.343i	−0.867704	−	1.50291i	−0.00336718	−	0.999994i	$-0.501072\pi$
$18$		0			0
$19$	63.5563	−	110.083i	0.767412	−	1.32920i	−0.171550	−	0.985175i	$-0.554878\pi$
$19$	63.5563	−	110.083i	0.767412	−	1.32920i	0.938962	−	0.344021i	$-0.111789\pi$
$20$	−0.786797			−0.00879665
$21$		0			0
$22$	18.2010			0.176385
$23$	26.7990	−	46.4172i	0.242955	−	0.420811i	−0.718599	−	0.695424i	$-0.755216\pi$
$23$	26.7990	−	46.4172i	0.242955	−	0.420811i	0.961555	+	0.274613i	$0.0885498\pi$
$24$		0			0
$25$	62.4949	+	108.244i	0.499960	+	0.865955i
$26$	3.44722	−	5.97076i	0.0260021	−	0.0450370i
$27$		0			0
$28$		0			0
$29$	−235.681			−1.50913			−0.754567	−	0.656223i	$-0.772153\pi$
$29$	−235.681			−1.50913			−0.754567	+	0.656223i	$0.772153\pi$
$30$		0			0
$31$	9.35534	+	16.2039i	0.0542022	+	0.0938810i	0.891853	−	0.452324i	$-0.149405\pi$
$31$	9.35534	+	16.2039i	0.0542022	+	0.0938810i	−0.837651	+	0.546205i	$0.816072\pi$
$32$	−38.6335	−	66.9152i	−0.213422	−	0.369658i
$33$		0			0
$34$	50.3848			0.254145
$35$		0			0
$36$		0			0
$37$	95.9411	−	166.175i	0.426287	−	0.738351i	−0.570253	−	0.821469i	$-0.693155\pi$
$37$	95.9411	−	166.175i	0.426287	−	0.738351i	0.996540	+	0.0831185i	$0.0264880\pi$
$38$	26.3259	+	45.5978i	0.112385	+	0.194656i
$39$		0			0
$40$	0.329473	−	0.570664i	0.00130236	−	0.00225575i
$41$	319.713			1.21782			0.608912	−	0.793238i	$-0.291606\pi$
$41$	319.713			1.21782			0.608912	+	0.793238i	$0.291606\pi$
$42$		0			0
$43$	−218.579			−0.775184			−0.387592	−	0.921831i	$-0.626693\pi$
$43$	−218.579			−0.775184			−0.387592	+	0.921831i	$0.626693\pi$
$44$	171.995	−	297.904i	0.589300	−	1.02070i
$45$		0			0
$46$	11.1005	+	19.2266i	0.0355800	+	0.0616264i
$47$	200.777	−	347.755i	0.623113	−	1.07926i	−0.365790	−	0.930697i	$-0.619201\pi$
$47$	200.777	−	347.755i	0.623113	−	1.07926i	0.988903	−	0.148565i	$-0.0474655\pi$
$48$		0			0
$49$		0			0
$50$	−51.7725			−0.146435
$51$		0			0
$52$	−65.1508	−	112.844i	−0.173746	−	0.300937i
$53$	321.558	+	556.956i	0.833386	+	1.44347i	0.895338	+	0.445387i	$0.146934\pi$
$53$	321.558	+	556.956i	0.833386	+	1.44347i	−0.0619521	+	0.998079i	$0.519733\pi$
$54$		0			0
$55$	4.41631			0.0108272
$56$		0			0
$57$		0			0
$58$	48.8112	−	84.5434i	0.110504	−	0.191398i
$59$	−5.80613	−	10.0565i	−0.0128118	−	0.0221906i	0.859548	−	0.511054i	$-0.170745\pi$
$59$	−5.80613	−	10.0565i	−0.0128118	−	0.0221906i	−0.872360	+	0.488864i	$0.837412\pi$
$60$		0			0
$61$	6.12132	−	10.6024i	0.0128484	−	0.0222541i	−0.859530	−	0.511086i	$-0.829243\pi$
$61$	6.12132	−	10.6024i	0.0128484	−	0.0222541i	0.872378	+	0.488832i	$0.162577\pi$
$62$	−7.75022			−0.0158755
$63$		0			0
$64$	−447.288			−0.873610
$65$	0.836436	−	1.44875i	0.00159611	−	0.00276454i
$66$		0			0
$67$	−334.524	−	579.412i	−0.609979	−	1.05651i	−0.991243	−	0.132049i	$-0.957844\pi$
$67$	−334.524	−	579.412i	−0.609979	−	1.05651i	0.381264	−	0.924466i	$-0.375489\pi$
$68$	476.123	−	824.670i	0.849095	−	1.47068i
$69$		0			0
$70$		0			0
$71$	−822.098			−1.37416			−0.687078	−	0.726584i	$-0.741107\pi$
$71$	−822.098			−1.37416			−0.687078	+	0.726584i	$0.741107\pi$
$72$		0			0
$73$	−257.550	−	446.089i	−0.412930	−	0.715217i	0.582278	−	0.812990i	$-0.302161\pi$
$73$	−257.550	−	446.089i	−0.412930	−	0.715217i	−0.995209	+	0.0977730i	$0.968828\pi$
$74$	39.7401	+	68.8319i	0.0624283	+	0.108129i
$75$		0			0
$76$	995.092			1.50191
$77$		0			0
$78$		0			0
$79$	402.877	−	697.804i	0.573762	−	0.993786i	−0.422413	−	0.906404i	$-0.638817\pi$
$79$	402.877	−	697.804i	0.573762	−	0.993786i	0.996175	−	0.0873819i	$-0.0278500\pi$
$80$	−3.01071	−	5.21471i	−0.00420760	−	0.00728778i
$81$		0			0
$82$	−66.2147	+	114.687i	−0.0891730	+	0.154452i
$83$	394.863			0.522191			0.261095	−	0.965313i	$-0.415916\pi$
$83$	394.863			0.522191			0.261095	+	0.965313i	$0.415916\pi$
$84$		0			0
$85$	12.2254			0.0156004
$86$	45.2691	−	78.4084i	0.0567616	−	0.0983139i
$87$		0			0
$88$	144.047	+	249.496i	0.174493	+	0.302232i
$89$	336.709	−	583.197i	0.401024	−	0.694593i	−0.592826	−	0.805331i	$-0.701988\pi$
$89$	336.709	−	583.197i	0.401024	−	0.694593i	0.993850	+	0.110737i	$0.0353212\pi$
$90$		0			0
$91$		0			0
$92$	419.588			0.475490
$93$		0			0
$94$	83.1644	+	144.045i	0.0912527	+	0.158054i
$95$	6.38773	+	11.0639i	0.00689861	+	0.0119487i
$96$		0			0
$97$	−1091.11			−1.14212			−0.571061	−	0.820908i	$-0.693468\pi$
$97$	−1091.11			−1.14212			−0.571061	+	0.820908i	$0.693468\pi$
$98$		0			0
$99$		0			0
$100$	−489.237	+	847.384i	−0.489237	+	0.847384i
$101$	−685.395	−	1187.14i	−0.675242	−	1.16955i	−0.976398	−	0.215978i	$-0.930706\pi$
$101$	−685.395	−	1187.14i	−0.675242	−	1.16955i	0.301157	−	0.953575i	$-0.402627\pi$
$102$		0			0
$103$	706.978	−	1224.52i	0.676316	−	1.17141i	−0.299766	−	0.954013i	$-0.596909\pi$
$103$	706.978	−	1224.52i	0.676316	−	1.17141i	0.976082	−	0.217401i	$-0.0697581\pi$
$104$	109.128			0.102893
$105$		0			0
$106$	−266.388			−0.244093
$107$	−171.770	+	297.514i	−0.155192	+	0.268801i	−0.933129	−	0.359542i	$-0.882933\pi$
$107$	−171.770	+	297.514i	−0.155192	+	0.268801i	0.777937	+	0.628343i	$0.216266\pi$
$108$		0			0
$109$	158.828	+	275.099i	0.139569	+	0.241740i	0.927333	−	0.374236i	$-0.122095\pi$
$109$	158.828	+	275.099i	0.139569	+	0.241740i	−0.787765	+	0.615976i	$0.788762\pi$
$110$	−0.914647	+	1.58421i	−0.000792801	+	0.00137317i
$111$		0			0
$112$		0			0
$113$	−798.373			−0.664643			−0.332321	−	0.943166i	$-0.607832\pi$
$113$	−798.373			−0.664643			−0.332321	+	0.943166i	$0.607832\pi$
$114$		0			0
$115$	2.69343	+	4.66516i	0.00218404	+	0.00378286i
$116$	−922.507	−	1597.83i	−0.738384	−	1.27892i
$117$		0			0
$118$	4.80996			0.00375248
$119$		0			0
$120$		0			0
$121$	−299.911	+	519.462i	−0.225328	+	0.390279i
$122$	2.53553	+	4.39167i	0.00188161	+	0.00325904i
$123$		0			0
$124$	−73.2376	+	126.851i	−0.0530398	+	0.0918676i
$125$	−25.1253			−0.0179782
$126$		0			0
$127$	1071.40			0.748593			0.374297	−	0.927309i	$-0.377884\pi$
$127$	1071.40			0.748593			0.374297	+	0.927309i	$0.377884\pi$
$128$	401.705	−	695.773i	0.277391	−	0.480455i
$129$		0			0
$130$	0.346463	+	0.600092i	0.000233745	+	0.000404858i
$131$	−1257.51	+	2178.07i	−0.838695	+	1.45266i	0.0522910	+	0.998632i	$0.483348\pi$
$131$	−1257.51	+	2178.07i	−0.838695	+	1.45266i	−0.890986	+	0.454031i	$0.849986\pi$
$132$		0			0
$133$		0			0
$134$	277.129			0.178659
$135$		0			0
$136$	398.756	+	690.665i	0.251419	+	0.435471i
$137$	125.532	+	217.428i	0.0782841	+	0.135592i	0.902510	−	0.430670i	$-0.141723\pi$
$137$	125.532	+	217.428i	0.0782841	+	0.135592i	−0.824226	+	0.566262i	$0.808389\pi$
$138$		0			0
$139$	886.067			0.540685			0.270343	−	0.962764i	$-0.412863\pi$
$139$	886.067			0.540685			0.270343	+	0.962764i	$0.412863\pi$
$140$		0			0
$141$		0			0
$142$	170.262	−	294.902i	0.100620	−	0.174279i
$143$	365.693	+	633.398i	0.213851	+	0.370401i
$144$		0			0
$145$	11.8436	−	20.5137i	0.00678314	−	0.0117487i
$146$	213.361			0.120945
$147$		0			0
$148$	1502.14			0.834289
$149$	291.313	−	504.569i	0.160170	−	0.277422i	−0.774760	−	0.632256i	$-0.782129\pi$
$149$	291.313	−	504.569i	0.160170	−	0.277422i	0.934929	+	0.354834i	$0.115463\pi$
$150$		0			0
$151$	1405.88	+	2435.06i	0.757676	+	1.31233i	0.944033	+	0.329851i	$0.106999\pi$
$151$	1405.88	+	2435.06i	0.757676	+	1.31233i	−0.186357	+	0.982482i	$0.559668\pi$
$152$	−416.698	+	721.741i	−0.222359	+	0.385138i
$153$		0			0
$154$		0			0
$155$	−1.88052			−0.000974496
$156$		0			0
$157$	845.672	+	1464.75i	0.429885	+	0.744583i	0.996863	−	0.0791504i	$-0.0252207\pi$
$157$	845.672	+	1464.75i	0.429885	+	0.744583i	−0.566978	+	0.823733i	$0.691887\pi$
$158$	166.877	+	289.040i	0.0840256	+	0.145537i
$159$		0			0
$160$	7.76573			0.00383709
$161$		0			0
$162$		0			0
$163$	20.3616	−	35.2674i	0.00978432	−	0.0169469i	−0.861092	−	0.508450i	$-0.830219\pi$
$163$	20.3616	−	35.2674i	0.00978432	−	0.0169469i	0.870876	+	0.491503i	$0.163552\pi$
$164$	1251.42	+	2167.53i	0.595852	+	1.03205i
$165$		0			0
$166$	−81.7788	+	141.645i	−0.0382365	+	0.0662276i
$167$	−2900.47			−1.34398			−0.671990	−	0.740560i	$-0.734560\pi$
$167$	−2900.47			−1.34398			−0.671990	+	0.740560i	$0.734560\pi$
$168$		0			0
$169$	−1919.96			−0.873899
$170$	−2.53196	+	4.38549i	−0.00114231	+	0.00197854i
$171$		0			0
$172$	−855.563	−	1481.88i	−0.379280	−	0.656932i
$173$	−1073.07	+	1858.62i	−0.471585	+	0.816810i	−0.999472	−	0.0325052i	$-0.989651\pi$
$173$	−1073.07	+	1858.62i	−0.471585	+	0.816810i	0.527886	+	0.849315i	$0.322985\pi$
$174$		0			0
$175$		0			0
$176$	2632.59			1.12749
$177$		0			0
$178$	139.470	+	241.568i	0.0587286	+	0.101721i
$179$	601.770	+	1042.30i	0.251276	+	0.435222i	0.963877	−	0.266347i	$-0.0858166\pi$
$179$	601.770	+	1042.30i	0.251276	+	0.435222i	−0.712602	+	0.701569i	$0.752483\pi$
$180$		0			0
$181$	−2990.47			−1.22807			−0.614033	−	0.789280i	$-0.710454\pi$
$181$	−2990.47			−1.22807			−0.614033	+	0.789280i	$0.710454\pi$
$182$		0			0
$183$		0			0
$184$	−175.704	+	304.327i	−0.0703969	+	0.121931i
$185$	9.64257	+	16.7014i	0.00383209	+	0.00663737i
$186$		0			0
$187$	−2672.49	+	4628.89i	−1.04509	+	1.81015i
$188$	3143.53			1.21950
$189$		0			0
$190$	−5.29177			−0.00202056
$191$	−1403.70	+	2431.29i	−0.531772	+	0.921057i	0.467540	+	0.883972i	$0.345140\pi$
$191$	−1403.70	+	2431.29i	−0.531772	+	0.921057i	−0.999312	+	0.0370847i	$0.988193\pi$
$192$		0			0
$193$	−1668.18	−	2889.38i	−0.622169	−	1.07763i	−0.989081	−	0.147372i	$-0.952919\pi$
$193$	−1668.18	−	2889.38i	−0.622169	−	1.07763i	0.366913	−	0.930255i	$-0.380415\pi$
$194$	225.977	−	391.404i	0.0836299	−	0.144851i
$195$		0			0
$196$		0			0
$197$	4226.65			1.52861			0.764305	−	0.644855i	$-0.223082\pi$
$197$	4226.65			1.52861			0.764305	+	0.644855i	$0.223082\pi$
$198$		0			0
$199$	−2192.85	−	3798.12i	−0.781140	−	1.35297i	−0.931278	−	0.364309i	$-0.881305\pi$
$199$	−2192.85	−	3798.12i	−0.781140	−	1.35297i	0.150139	−	0.988665i	$-0.452028\pi$
$200$	−409.739	−	709.688i	−0.144865	−	0.250913i
$201$		0			0
$202$	567.800			0.197774
$203$		0			0
$204$		0			0
$205$	−16.0664	+	27.8278i	−0.00547378	+	0.00948086i
$206$	292.840	+	507.213i	0.0990442	+	0.171550i
$207$		0			0
$208$	498.605	−	863.609i	0.166212	−	0.287887i
$209$	−5585.48			−1.84859
$210$		0			0
$211$	2291.56			0.747665			0.373833	−	0.927496i	$-0.378043\pi$
$211$	2291.56			0.747665			0.373833	+	0.927496i	$0.378043\pi$
$212$	−2517.30	+	4360.09i	−0.815513	+	1.41251i
$213$		0			0
$214$	−71.1493	−	123.234i	−0.0227274	−	0.0393650i
$215$	10.9841	−	19.0251i	0.00348424	−	0.00603488i
$216$		0			0
$217$		0			0
$218$	−131.578			−0.0408788
$219$		0			0
$220$	17.2864	+	29.9409i	0.00529748	+	0.00917551i
$221$	1012.33	+	1753.40i	0.308128	+	0.533694i
$222$		0			0
$223$	−217.970			−0.0654544			−0.0327272	−	0.999464i	$-0.510419\pi$
$223$	−217.970			−0.0654544			−0.0327272	+	0.999464i	$0.510419\pi$
$224$		0			0
$225$		0			0
$226$	165.349	−	286.392i	0.0486674	−	0.0842943i
$227$	917.680	+	1589.47i	0.268320	+	0.464743i	0.968428	−	0.249293i	$-0.0801983\pi$
$227$	917.680	+	1589.47i	0.268320	+	0.464743i	−0.700108	+	0.714037i	$0.746865\pi$
$228$		0			0
$229$	−1387.00	+	2402.36i	−0.400244	+	0.693243i	−0.993755	−	0.111583i	$-0.964408\pi$
$229$	−1387.00	+	2402.36i	−0.400244	+	0.693243i	0.593511	+	0.804826i	$0.297741\pi$
$230$	−2.23131			−0.000639689
$231$		0			0
$232$	1545.21			0.437275
$233$	−494.356	+	856.250i	−0.138997	+	0.240750i	−0.927117	−	0.374771i	$-0.877721\pi$
$233$	−494.356	+	856.250i	−0.138997	+	0.240750i	0.788120	+	0.615522i	$0.211055\pi$
$234$		0			0
$235$	20.1791	+	34.9512i	0.00560144	+	0.00970197i
$236$	45.4529	−	78.7267i	0.0125370	−	0.0217147i
$237$		0			0
$238$		0			0
$239$	837.928			0.226783			0.113391	−	0.993550i	$-0.463829\pi$
$239$	837.928			0.226783			0.113391	+	0.993550i	$0.463829\pi$
$240$		0			0
$241$	1727.49	+	2992.11i	0.461733	+	0.799745i	0.999047	−	0.0436371i	$-0.0138945\pi$
$241$	1727.49	+	2992.11i	0.461733	+	0.799745i	−0.537315	+	0.843382i	$0.680561\pi$
$242$	−124.227	−	215.168i	−0.0329985	−	0.0571551i
$243$		0			0
$244$	95.8406			0.0251458
$245$		0			0
$246$		0			0
$247$	−1057.87	+	1832.29i	−0.272514	+	0.472008i
$248$	−61.3369	−	106.239i	−0.0157052	−	0.0272022i
$249$		0			0
$250$	5.20361	−	9.01292i	0.00131642	−	0.00228011i
$251$	−5635.01			−1.41705			−0.708523	−	0.705688i	$-0.750638\pi$
$251$	−5635.01			−1.41705			−0.708523	+	0.705688i	$0.750638\pi$
$252$		0			0
$253$	−2355.16			−0.585246
$254$	−221.894	+	384.332i	−0.0548145	+	0.0949414i
$255$		0			0
$256$	−1622.76	−	2810.71i	−0.396182	−	0.686208i
$257$	−1135.58	+	1966.88i	−0.275624	+	0.477395i	−0.970292	−	0.241935i	$-0.922218\pi$
$257$	−1135.58	+	1966.88i	−0.275624	+	0.477395i	0.694668	+	0.719330i	$0.255551\pi$
$258$		0			0
$259$		0			0
$260$	13.0960			0.00312376
$261$		0			0
$262$	−520.877	−	902.186i	−0.122824	−	0.212737i
$263$	81.9336	+	141.913i	0.0192101	+	0.0332728i	0.875471	−	0.483271i	$-0.160552\pi$
$263$	81.9336	+	141.913i	0.0192101	+	0.0332728i	−0.856261	+	0.516544i	$0.827218\pi$
$264$		0			0
$265$	−64.6365			−0.0149834
$266$		0			0
$267$		0			0
$268$	2618.80	−	4535.89i	0.596897	−	1.03386i
$269$	−2583.55	−	4474.84i	−0.585582	−	1.01426i	−0.994803	−	0.101823i	$-0.967533\pi$
$269$	−2583.55	−	4474.84i	−0.585582	−	1.01426i	0.409220	−	0.912436i	$-0.365801\pi$
$270$		0			0
$271$	811.136	−	1404.93i	0.181819	−	0.314920i	−0.760681	−	0.649126i	$-0.775135\pi$
$271$	811.136	−	1404.93i	0.181819	−	0.314920i	0.942500	+	0.334206i	$0.108468\pi$
$272$	7287.63			1.62455
$273$		0			0
$274$	−103.994			−0.0229289
$275$	2746.10	−	4756.38i	0.602167	−	1.04298i
$276$		0			0
$277$	2306.18	+	3994.43i	0.500235	+	0.866433i	1.00000		0.000271708i	$8.64874e-5\pi$
$277$	2306.18	+	3994.43i	0.500235	+	0.866433i	−0.499765	+	0.866161i	$0.666580\pi$
$278$	−183.511	+	317.850i	−0.0395908	+	0.0685732i
$279$		0			0
$280$		0			0
$281$	2125.22			0.451174			0.225587	−	0.974223i	$-0.427570\pi$
$281$	2125.22			0.451174			0.225587	+	0.974223i	$0.427570\pi$
$282$		0			0
$283$	−1285.77	−	2227.02i	−0.270075	−	0.467783i	0.698806	−	0.715311i	$-0.253715\pi$
$283$	−1285.77	−	2227.02i	−0.270075	−	0.467783i	−0.968881	+	0.247528i	$0.920382\pi$
$284$	−3217.87	−	5573.51i	−0.672342	−	1.16453i
$285$		0			0
$286$	−302.950			−0.0626356
$287$		0			0
$288$		0			0
$289$	−4941.60	+	8559.10i	−1.00582	+	1.74213i
$290$	4.90577	+	8.49704i	0.000993368	+	0.00172056i
$291$		0			0
$292$	2016.21	−	3492.18i	0.404075	−	0.699878i
$293$	3324.96			0.662957			0.331478	−	0.943463i	$-0.392453\pi$
$293$	3324.96			0.662957			0.331478	+	0.943463i	$0.392453\pi$
$294$		0			0
$295$	1.16709			0.000230341
$296$	−629.024	+	1089.50i	−0.123518	+	0.213939i
$297$		0			0
$298$	120.666	+	208.999i	0.0234563	+	0.0406275i
$299$	−446.060	+	772.599i	−0.0862753	+	0.149433i
$300$		0			0
$301$		0			0
$302$	−1164.67			−0.221918
$303$		0			0
$304$	3807.77	+	6595.25i	0.718390	+	1.24429i
$305$	0.615224	+	1.06560i	0.000115500	+	0.000200052i
$306$		0			0
$307$	887.096			0.164916			0.0824580	−	0.996595i	$-0.473723\pi$
$307$	887.096			0.164916			0.0824580	+	0.996595i	$0.473723\pi$
$308$		0			0
$309$		0			0
$310$	0.389468	−	0.674578i	7.13558e−5	−	0.000123592i
$311$	2255.41	+	3906.48i	0.411230	+	0.712271i	0.995025	−	0.0996300i	$-0.0317659\pi$
$311$	2255.41	+	3906.48i	0.411230	+	0.712271i	−0.583794	+	0.811902i	$0.698433\pi$
$312$		0			0
$313$	1857.89	−	3217.96i	0.335509	−	0.581118i	−0.648074	−	0.761578i	$-0.724425\pi$
$313$	1857.89	−	3217.96i	0.335509	−	0.581118i	0.983582	+	0.180459i	$0.0577584\pi$
$314$	−700.577			−0.125910
$315$		0			0
$316$	6307.79			1.12291
$317$	3477.26	−	6022.79i	0.616096	−	1.06711i	−0.374095	−	0.927390i	$-0.622047\pi$
$317$	3477.26	−	6022.79i	0.616096	−	1.06711i	0.990191	−	0.139719i	$-0.0446200\pi$
$318$		0			0
$319$	5178.05	+	8968.64i	0.908825	+	1.57413i
$320$	22.4774	−	38.9320i	0.00392664	−	0.00680113i
$321$		0			0
$322$		0			0
$323$	−15461.9			−2.66355
$324$		0			0
$325$	−1040.21	−	1801.69i	−0.177539	−	0.307507i
$326$	8.43406	+	14.6082i	0.00143288	+	0.00248182i
$327$		0			0
$328$	−2096.15			−0.352867
$329$		0			0
$330$		0			0
$331$	4931.59	−	8541.76i	0.818926	−	1.41842i	−0.0875478	−	0.996160i	$-0.527903\pi$
$331$	4931.59	−	8541.76i	0.818926	−	1.41842i	0.906474	−	0.422262i	$-0.138764\pi$
$332$	1545.58	+	2677.02i	0.255496	+	0.442532i
$333$		0			0
$334$	600.706	−	1040.45i	0.0984107	−	0.170452i
$335$	67.2427			0.0109668
$336$		0			0
$337$	−5945.06			−0.960974			−0.480487	−	0.877002i	$-0.659540\pi$
$337$	−5945.06			−0.960974			−0.480487	+	0.877002i	$0.659540\pi$
$338$	397.636	−	688.725i	0.0639897	−	0.110833i
$339$		0			0
$340$	47.8528	+	82.8835i	0.00763289	+	0.0132206i
$341$	411.084	−	712.019i	0.0652829	−	0.113073i
$342$		0			0
$343$		0			0
$344$	1433.08			0.224612
$345$		0			0
$346$	−444.482	−	769.865i	−0.0690621	−	0.119619i
$347$	584.786	+	1012.88i	0.0904697	+	0.156698i	0.907709	−	0.419601i	$-0.137830\pi$
$347$	584.786	+	1012.88i	0.0904697	+	0.156698i	−0.817239	+	0.576299i	$0.804497\pi$
$348$		0			0
$349$	9176.66			1.40749			0.703747	−	0.710451i	$-0.251509\pi$
$349$	9176.66			1.40749			0.703747	+	0.710451i	$0.251509\pi$
$350$		0			0
$351$		0			0
$352$	−1697.60	+	2940.33i	−0.257052	+	0.445228i
$353$	−5293.60	−	9168.78i	−0.798158	−	1.38245i	−0.920814	−	0.390001i	$-0.872474\pi$
$353$	−5293.60	−	9168.78i	−0.798158	−	1.38245i	0.122656	−	0.992449i	$-0.460859\pi$
$354$		0			0
$355$	41.3125	−	71.5553i	0.00617645	−	0.0106979i
$356$	5271.81			0.784846
$357$		0			0
$358$	−498.522			−0.0735970
$359$	4307.61	−	7460.99i	0.633278	−	1.09687i	−0.353599	−	0.935397i	$-0.615042\pi$
$359$	4307.61	−	7460.99i	0.633278	−	1.09687i	0.986877	−	0.161472i	$-0.0516243\pi$
$360$		0			0
$361$	−4649.32	−	8052.86i	−0.677842	−	1.17406i
$362$	619.347	−	1072.74i	0.0899230	−	0.155751i
$363$		0			0
$364$		0			0
$365$	51.7701			0.00742403
$366$		0			0
$367$	4148.89	+	7186.10i	0.590110	+	1.02210i	0.994217	+	0.107389i	$0.0342492\pi$
$367$	4148.89	+	7186.10i	0.590110	+	1.02210i	−0.404107	+	0.914712i	$0.632418\pi$
$368$	1605.57	+	2780.93i	0.227436	+	0.393930i
$369$		0			0
$370$	−7.98817			−0.00112239
$371$		0			0
$372$		0			0
$373$	2561.93	−	4437.39i	0.355634	−	0.615977i	−0.631592	−	0.775301i	$-0.717598\pi$
$373$	2561.93	−	4437.39i	0.355634	−	0.615977i	0.987226	+	0.159324i	$0.0509315\pi$
$374$	−1106.98	−	1917.35i	−0.153050	−	0.265090i
$375$		0			0
$376$	−1316.36	+	2280.01i	−0.180548	+	0.312719i
$377$	3922.83			0.535905
$378$		0			0
$379$	−1502.49			−0.203635			−0.101817	−	0.994803i	$-0.532466\pi$
$379$	−1502.49			−0.203635			−0.101817	+	0.994803i	$0.532466\pi$
$380$	−50.0059	+	86.6128i	−0.00675066	+	0.0116925i
$381$		0			0
$382$	−581.434	−	1007.07i	−0.0778763	−	0.134886i
$383$	5436.47	−	9416.24i	0.725301	−	1.25626i	−0.233548	−	0.972345i	$-0.575034\pi$
$383$	5436.47	−	9416.24i	0.725301	−	1.25626i	0.958850	−	0.283914i	$-0.0916330\pi$
$384$		0			0
$385$		0			0
$386$	1381.97			0.182229
$387$		0			0
$388$	−4270.85	−	7397.33i	−0.558814	−	0.967894i
$389$	2309.50	+	4000.16i	0.301018	+	0.521379i	0.976367	−	0.216120i	$-0.0693402\pi$
$389$	2309.50	+	4000.16i	0.301018	+	0.521379i	−0.675349	+	0.737499i	$0.736007\pi$
$390$		0			0
$391$	−6519.64			−0.843254
$392$		0			0
$393$		0			0
$394$	−875.367	+	1516.18i	−0.111930	+	0.193868i
$395$	40.4912	+	70.1328i	0.00515781	+	0.00893358i
$396$		0			0
$397$	4803.48	−	8319.86i	0.607253	−	1.05179i	−0.384438	−	0.923151i	$-0.625605\pi$
$397$	4803.48	−	8319.86i	0.607253	−	1.05179i	0.991691	−	0.128642i	$-0.0410620\pi$
$398$	1816.61			0.228791
$399$		0			0
$400$	−7488.36			−0.936044
$401$	−5250.52	+	9094.17i	−0.653862	+	1.13252i	0.328316	+	0.944568i	$0.393519\pi$
$401$	−5250.52	+	9094.17i	−0.653862	+	1.13252i	−0.982178	+	0.187954i	$0.939814\pi$
$402$		0			0
$403$	−155.716	−	269.709i	−0.0192476	−	0.0333378i
$404$	5365.57	−	9293.44i	0.660760	−	1.14447i
$405$		0			0
$406$		0			0
$407$	−8431.52			−1.02687
$408$		0			0
$409$	−6033.47	−	10450.3i	−0.729427	−	1.26340i	−0.957126	−	0.289673i	$-0.906453\pi$
$409$	−6033.47	−	10450.3i	−0.729427	−	1.26340i	0.227699	−	0.973732i	$-0.426880\pi$
$410$	−6.65491	−	11.5266i	−0.000801616	−	0.00138844i
$411$		0			0
$412$	11069.0			1.32362
$413$		0			0
$414$		0			0
$415$	−19.8429	+	34.3688i	−0.00234710	+	0.00406530i
$416$	643.042	+	1113.78i	0.0757878	+	0.131268i
$417$		0			0
$418$	1156.79	−	2003.62i	0.135360	−	0.234450i
$419$	−6366.31			−0.742278			−0.371139	−	0.928577i	$-0.621033\pi$
$419$	−6366.31			−0.742278			−0.371139	+	0.928577i	$0.621033\pi$
$420$		0			0
$421$	−4731.84			−0.547781			−0.273890	−	0.961761i	$-0.588311\pi$
$421$	−4731.84			−0.547781			−0.273890	+	0.961761i	$0.588311\pi$
$422$	−474.597	+	822.026i	−0.0547465	+	0.0948237i
$423$		0			0
$424$	−2108.25	−	3651.60i	−0.241476	−	0.418248i
$425$	7601.86	−	13166.8i	0.867634	−	1.50279i
$426$		0			0
$427$		0			0
$428$	−2689.37			−0.303728
$429$		0			0
$430$	4.54978	+	7.88044i	0.000510255	+	0.000883788i
$431$	1876.39	+	3250.01i	0.209704	+	0.363219i	0.951621	−	0.307273i	$-0.0994165\pi$
$431$	1876.39	+	3250.01i	0.209704	+	0.363219i	−0.741917	+	0.670492i	$0.766083\pi$
$432$		0			0
$433$	−11709.2			−1.29956			−0.649780	−	0.760122i	$-0.725139\pi$
$433$	−11709.2			−1.29956			−0.649780	+	0.760122i	$0.725139\pi$
$434$		0			0
$435$		0			0
$436$	−1243.38	+	2153.59i	−0.136576	+	0.236556i
$437$	−3406.49	−	5900.22i	−0.372894	−	0.645871i
$438$		0			0
$439$	−7462.36	+	12925.2i	−0.811296	+	1.40521i	0.100661	+	0.994921i	$0.467904\pi$
$439$	−7462.36	+	12925.2i	−0.811296	+	1.40521i	−0.911957	+	0.410285i	$0.865429\pi$
$440$	−28.9548			−0.00313720
$441$		0			0
$442$	−838.638			−0.0902487
$443$	−4258.83	+	7376.51i	−0.456756	+	0.791125i	−0.998787	−	0.0492333i	$-0.984322\pi$
$443$	−4258.83	+	7376.51i	−0.456756	+	0.791125i	0.542031	+	0.840359i	$0.317656\pi$
$444$		0			0
$445$	33.8410	+	58.6143i	0.00360498	+	0.00624401i
$446$	45.1430	−	78.1900i	0.00479279	−	0.00830135i
$447$		0			0
$448$		0			0
$449$	5965.73			0.627038			0.313519	−	0.949582i	$-0.398492\pi$
$449$	5965.73			0.627038			0.313519	+	0.949582i	$0.398492\pi$
$450$		0			0
$451$	−7024.27	−	12166.4i	−0.733392	−	1.27027i
$452$	−3125.00	−	5412.67i	−0.325194	−	0.563253i
$453$		0			0
$454$	−760.231			−0.0785890
$455$		0			0
$456$		0			0
$457$	6930.28	−	12003.6i	0.709376	−	1.22868i	−0.255712	−	0.966753i	$-0.582310\pi$
$457$	6930.28	−	12003.6i	0.709376	−	1.22868i	0.965089	−	0.261923i	$-0.0843567\pi$
$458$	−574.516	−	995.091i	−0.0586143	−	0.101523i
$459$		0			0
$460$	−21.0854	+	36.5209i	−0.00213719	+	0.00370173i
$461$	−149.312			−0.0150850			−0.00754249	−	0.999972i	$-0.502401\pi$
$461$	−149.312			−0.0150850			−0.00754249	+	0.999972i	$0.502401\pi$
$462$		0			0
$463$	5403.95			0.542425			0.271213	−	0.962519i	$-0.412575\pi$
$463$	5403.95			0.542425			0.271213	+	0.962519i	$0.412575\pi$
$464$	7060.03	−	12228.3i	0.706366	−	1.22346i
$465$		0			0
$466$	−204.769	−	354.670i	−0.0203557	−	0.0352571i
$467$	−1852.33	+	3208.33i	−0.183545	+	0.317909i	−0.943085	−	0.332551i	$-0.892091\pi$
$467$	−1852.33	+	3208.33i	−0.183545	+	0.317909i	0.759540	+	0.650460i	$0.225424\pi$
$468$		0			0
$469$		0			0
$470$	−16.7169			−0.00164062
$471$		0			0
$472$	38.0670	+	65.9340i	0.00371224	+	0.00642979i
$473$	4802.30	+	8317.82i	0.466828	+	0.808570i
$474$		0			0
$475$	15887.8			1.53470
$476$		0			0
$477$		0			0
$478$	−173.540	+	300.581i	−0.0166058	+	0.0287620i
$479$	5335.88	+	9242.02i	0.508982	+	0.881583i	0.999946	+	0.0104033i	$0.00331152\pi$
$479$	5335.88	+	9242.02i	0.508982	+	0.881583i	−0.490963	+	0.871180i	$0.663355\pi$
$480$		0			0
$481$	−1596.91	+	2765.92i	−0.151378	+	0.262194i
$482$	−1431.10			−0.135238
$483$		0			0
$484$	−4695.67			−0.440990
$485$	54.8312	−	94.9705i	0.00513352	−	0.00889152i
$486$		0			0
$487$	−2926.96	−	5069.65i	−0.272348	−	0.471720i	0.697115	−	0.716959i	$-0.254467\pi$
$487$	−2926.96	−	5069.65i	−0.272348	−	0.471720i	−0.969463	+	0.245239i	$0.921133\pi$
$488$	−40.1335	+	69.5133i	−0.00372287	+	0.00644819i
$489$		0			0
$490$		0			0
$491$	−4065.31			−0.373656			−0.186828	−	0.982393i	$-0.559821\pi$
$491$	−4065.31			−0.373656			−0.186828	+	0.982393i	$0.559821\pi$
$492$		0			0
$493$	14334.1	+	24827.4i	1.30948	+	2.26809i
$494$	−438.186	−	758.960i	−0.0399087	−	0.0691239i
$495$		0			0
$496$	−1120.99			−0.101480
$497$		0			0
$498$		0			0
$499$	−2405.59	+	4166.61i	−0.215810	+	0.373794i	−0.953523	−	0.301321i	$-0.902572\pi$
$499$	−2405.59	+	4166.61i	−0.215810	+	0.373794i	0.737713	+	0.675115i	$0.235906\pi$
$500$	−98.3456	−	170.340i	−0.00879630	−	0.0152356i
$501$		0			0
$502$	1167.05	−	2021.39i	0.103761	−	0.179719i
$503$	17001.2			1.50705			0.753526	−	0.657418i	$-0.228351\pi$
$503$	17001.2			1.50705			0.753526	+	0.657418i	$0.228351\pi$
$504$		0			0
$505$	137.771			0.0121401
$506$	487.769	−	844.840i	0.0428537	−	0.0742248i
$507$		0			0
$508$	4193.69	+	7263.68i	0.366269	+	0.634397i
$509$	−6898.61	+	11948.7i	−0.600738	+	1.04051i	0.391972	+	0.919977i	$0.371793\pi$
$509$	−6898.61	+	11948.7i	−0.600738	+	1.04051i	−0.992710	+	0.120531i	$0.961540\pi$
$510$		0			0
$511$		0			0
$512$	7771.61			0.670820
$513$		0			0
$514$	−470.372	−	814.708i	−0.0403642	−	0.0699129i
$515$	71.0548	+	123.071i	0.00607971	+	0.0105304i
$516$		0			0
$517$	−17644.7			−1.50099
$518$		0			0
$519$		0			0
$520$	−5.48397	+	9.49851i	−0.000462477	+	0.000801033i
$521$	−1968.31	−	3409.21i	−0.165515	−	0.286680i	0.771323	−	0.636443i	$-0.219595\pi$
$521$	−1968.31	−	3409.21i	−0.165515	−	0.286680i	−0.936838	+	0.349764i	$0.886262\pi$
$522$		0			0
$523$	8729.63	−	15120.2i	0.729866	−	1.26417i	−0.227073	−	0.973878i	$-0.572916\pi$
$523$	8729.63	−	15120.2i	0.729866	−	1.26417i	0.956939	−	0.290288i	$-0.0937510\pi$
$524$	−19688.6			−1.64142
$525$		0			0
$526$	−67.8760			−0.00562649
$527$	1137.98	−	1971.04i	0.0940630	−	0.162922i
$528$		0			0
$529$	4647.13	+	8049.06i	0.381945	+	0.661549i
$530$	13.3867	−	23.1864i	0.00109713	−	0.00190029i
$531$		0			0
$532$		0			0
$533$	−5321.51			−0.432458
$534$		0			0
$535$	−17.2637	−	29.9016i	−0.00139509	−	0.00241637i
$536$	2193.26	+	3798.83i	0.176743	+	0.306128i
$537$		0			0
$538$	2140.28			0.171513
$539$		0			0
$540$		0			0
$541$	−9550.66	+	16542.2i	−0.758992	+	1.31461i	0.184373	+	0.982856i	$0.440975\pi$
$541$	−9550.66	+	16542.2i	−0.758992	+	1.31461i	−0.943365	+	0.331757i	$0.892359\pi$
$542$	335.983	+	581.940i	0.0266268	+	0.0461190i
$543$		0			0
$544$	−4699.37	+	8139.54i	−0.370374	+	0.641507i
$545$	−31.9261			−0.00250929
$546$		0			0
$547$	15413.5			1.20481			0.602407	−	0.798189i	$-0.294208\pi$
$547$	15413.5			1.20481			0.602407	+	0.798189i	$0.294208\pi$
$548$	−982.718	+	1702.12i	−0.0766052	+	0.132684i
$549$		0			0
$550$	1137.47	+	1970.16i	0.0881853	+	0.152741i
$551$	−14979.0	+	25944.5i	−1.15813	+	2.00594i
$552$		0			0
$553$		0			0
$554$	−1910.51			−0.146516
$555$		0			0
$556$	3468.26	+	6007.20i	0.264545	+	0.458205i
$557$	−10246.4	−	17747.3i	−0.779453	−	1.35005i	−0.932257	−	0.361796i	$-0.882164\pi$
$557$	−10246.4	−	17747.3i	−0.779453	−	1.35005i	0.152804	−	0.988257i	$-0.451170\pi$
$558$		0			0
$559$	3638.17			0.275274
$560$		0			0
$561$		0			0
$562$	−440.147	+	762.357i	−0.0330364	+	0.0572208i
$563$	3571.24	+	6185.57i	0.267336	+	0.463039i	0.968173	−	0.250282i	$-0.0805234\pi$
$563$	3571.24	+	6185.57i	0.267336	+	0.463039i	−0.700837	+	0.713321i	$0.747190\pi$
$564$		0			0
$565$	40.1203	−	69.4904i	0.00298739	−	0.00517430i
$566$	1065.17			0.0791030
$567$		0			0
$568$	5389.96			0.398165
$569$	2048.96	−	3548.90i	0.150961	−	0.261472i	−0.780620	−	0.625006i	$-0.785097\pi$
$569$	2048.96	−	3548.90i	0.150961	−	0.261472i	0.931581	+	0.363534i	$0.118430\pi$
$570$		0			0
$571$	1419.24	+	2458.20i	0.104016	+	0.180162i	0.913336	−	0.407207i	$-0.133497\pi$
$571$	1419.24	+	2458.20i	0.104016	+	0.180162i	−0.809320	+	0.587369i	$0.800164\pi$
$572$	−2862.80	+	4958.51i	−0.209265	+	0.362458i
$573$		0			0
$574$		0			0
$575$	6699.21			0.485872
$576$		0			0
$577$	−7732.23	−	13392.6i	−0.557881	−	0.966277i	−0.997673	−	0.0681781i	$-0.978281\pi$
$577$	−7732.23	−	13392.6i	−0.557881	−	0.966277i	0.439793	−	0.898099i	$-0.355052\pi$
$578$	−2046.88	−	3545.29i	−0.147299	−	0.255129i
$579$		0			0
$580$	185.433			0.0132753
$581$		0			0
$582$		0			0
$583$	14129.6	−	24473.3i	1.00376	−	1.73856i
$584$	1688.59	+	2924.72i	0.119648	+	0.207236i
$585$		0			0
$586$	−688.622	+	1192.73i	−0.0485439	+	0.0840805i
$587$	14003.6			0.984652			0.492326	−	0.870411i	$-0.336147\pi$
$587$	14003.6			0.984652			0.492326	+	0.870411i	$0.336147\pi$
$588$		0			0
$589$	2378.36			0.166382
$590$	−0.241713	+	0.418658i	−1.68664e−5	+	2.92134e-5i
$591$		0			0
$592$	5747.99	+	9955.82i	0.399056	+	0.691185i
$593$	−3252.25	+	5633.06i	−0.225217	+	0.390088i	−0.956385	−	0.292110i	$-0.905643\pi$
$593$	−3252.25	+	5633.06i	−0.225217	+	0.390088i	0.731167	+	0.682198i	$0.238976\pi$
$594$		0			0
$595$		0			0
$596$	4561.04			0.313469
$597$		0			0
$598$	−184.764	−	320.021i	−0.0126347	−	0.0218840i
$599$	−6308.05	−	10925.9i	−0.430284	−	0.745273i	0.566614	−	0.823983i	$-0.308253\pi$
$599$	−6308.05	−	10925.9i	−0.430284	−	0.745273i	−0.996898	+	0.0787104i	$0.974920\pi$
$600$		0			0
$601$	−8270.87			−0.561358			−0.280679	−	0.959802i	$-0.590560\pi$
$601$	−8270.87			−0.561358			−0.280679	+	0.959802i	$0.590560\pi$
$602$		0			0
$603$		0			0
$604$	−11005.8	+	19062.7i	−0.741426	+	1.28419i
$605$	−30.1426	−	52.2085i	−0.00202557	−	0.00350839i
$606$		0			0
$607$	1905.92	−	3301.15i	0.127445	−	0.220740i	−0.795241	−	0.606293i	$-0.792656\pi$
$607$	1905.92	−	3301.15i	0.127445	−	0.220740i	0.922686	+	0.385553i	$0.125989\pi$
$608$	−9821.62			−0.655130
$609$		0			0
$610$	−0.509668			−3.38293e−5
$611$	−3341.86	+	5788.27i	−0.221272	+	0.383254i
$612$		0			0
$613$	−5679.63	−	9837.42i	−0.374222	−	0.648172i	0.615988	−	0.787756i	$-0.288757\pi$
$613$	−5679.63	−	9837.42i	−0.374222	−	0.648172i	−0.990210	+	0.139583i	$0.955424\pi$
$614$	−183.724	+	318.219i	−0.0120757	+	0.0209157i
$615$		0			0
$616$		0			0
$617$	18272.2			1.19224			0.596118	−	0.802896i	$-0.296709\pi$
$617$	18272.2			1.19224			0.596118	+	0.802896i	$0.296709\pi$
$618$		0			0
$619$	14800.1	+	25634.6i	0.961013	+	1.66452i	0.719965	+	0.694010i	$0.244158\pi$
$619$	14800.1	+	25634.6i	0.961013	+	1.66452i	0.241048	+	0.970513i	$0.422509\pi$
$620$	−7.36075	−	12.7492i	−0.000476798	−	0.000825838i
$621$		0			0
$622$	−1868.44			−0.120447
$623$		0			0
$624$		0			0
$625$	−7810.61	+	13528.4i	−0.499879	+	0.865815i
$626$	769.564	+	1332.92i	0.0491341	+	0.0851028i
$627$		0			0
$628$	−6620.28	+	11466.7i	−0.420665	+	0.728614i
$629$	−23340.5			−1.47956
$630$		0			0
$631$	7185.41			0.453322			0.226661	−	0.973974i	$-0.427219\pi$
$631$	7185.41			0.453322			0.226661	+	0.973974i	$0.427219\pi$
$632$	−2641.40	+	4575.05i	−0.166249	+	0.287952i
$633$		0			0
$634$	1440.33	+	2494.72i	0.0902252	+	0.156275i
$635$	−53.8405	+	93.2545i	−0.00336472	+	0.00582786i
$636$		0			0
$637$		0			0
$638$	−4289.64			−0.266189
$639$		0			0
$640$	40.3733	+	69.9287i	0.00249359	+	0.00431902i
$641$	−116.491	−	201.768i	−0.00717803	−	0.0124327i	0.862414	−	0.506203i	$-0.168952\pi$
$641$	−116.491	−	201.768i	−0.00717803	−	0.0124327i	−0.869592	+	0.493771i	$0.835618\pi$
$642$		0			0
$643$	1837.96			0.112725			0.0563624	−	0.998410i	$-0.482050\pi$
$643$	1837.96			0.112725			0.0563624	+	0.998410i	$0.482050\pi$
$644$		0			0
$645$		0			0
$646$	3202.27	−	5546.50i	0.195034	−	0.337808i
$647$	9297.35	+	16103.5i	0.564941	+	0.978506i	0.997055	+	0.0766874i	$0.0244343\pi$
$647$	9297.35	+	16103.5i	0.564941	+	0.978506i	−0.432114	+	0.901819i	$0.642232\pi$
$648$		0			0
$649$	−255.128	+	441.895i	−0.0154309	+	0.0267271i
$650$	861.736			0.0520001
$651$		0			0
$652$	318.799			0.0191490
$653$	−14432.3	+	24997.6i	−0.864902	+	1.49805i	0.00224162	+	0.999997i	$0.499286\pi$
$653$	−14432.3	+	24997.6i	−0.864902	+	1.49805i	−0.867144	+	0.498057i	$0.834047\pi$
$654$		0			0
$655$	−126.386	−	218.907i	−0.00753940	−	0.0130586i
$656$	−9577.27	+	16588.3i	−0.570014	+	0.987294i
$657$		0			0
$658$		0			0
$659$	29066.3			1.71815			0.859076	−	0.511847i	$-0.171039\pi$
$659$	29066.3			1.71815			0.859076	+	0.511847i	$0.171039\pi$
$660$		0			0
$661$	−1989.75	−	3446.36i	−0.117084	−	0.202795i	0.801527	−	0.597959i	$-0.204021\pi$
$661$	−1989.75	−	3446.36i	−0.117084	−	0.202795i	−0.918611	+	0.395163i	$0.870688\pi$
$662$	2042.73	+	3538.11i	0.119929	+	0.207723i
$663$		0			0
$664$	−2588.86			−0.151306
$665$		0			0
$666$		0			0
$667$	−6316.02	+	10939.7i	−0.366653	+	0.635061i
$668$	−11353.0	−	19664.0i	−0.657578	−	1.13896i
$669$		0			0
$670$	−13.9264	+	24.1213i	−0.000803022	+	0.00139087i
$671$	−537.955			−0.0309501
$672$		0			0
$673$	−184.229			−0.0105520			−0.00527601	−	0.999986i	$-0.501679\pi$
$673$	−184.229			−0.0105520			−0.00527601	+	0.999986i	$0.501679\pi$
$674$	1231.26	−	2132.61i	0.0703657	−	0.121877i
$675$		0			0
$676$	−7515.11	−	13016.6i	−0.427578	−	0.740587i
$677$	8341.73	−	14448.3i	0.473558	−	0.820227i	−0.525984	−	0.850495i	$-0.676303\pi$
$677$	8341.73	−	14448.3i	0.473558	−	0.820227i	0.999542	+	0.0302680i	$0.00963607\pi$
$678$		0			0
$679$		0			0
$680$	−80.1540			−0.00452024
$681$		0			0
$682$	170.277	+	294.928i	0.00956045	+	0.0165592i
$683$	8904.11	+	15422.4i	0.498838	+	0.864013i	0.999999	−	0.00134107i	$-0.000426875\pi$
$683$	8904.11	+	15422.4i	0.498838	+	0.864013i	−0.501161	+	0.865354i	$0.667094\pi$
$684$		0			0
$685$	−25.2332			−0.00140746
$686$		0			0
$687$		0			0
$688$	6547.71	−	11341.0i	0.362833	−	0.628445i
$689$	−5352.23	−	9270.34i	−0.295942	−	0.512586i
$690$		0			0
$691$	−10072.8	+	17446.7i	−0.554542	+	0.960495i	0.443397	+	0.896325i	$0.353773\pi$
$691$	−10072.8	+	17446.7i	−0.554542	+	0.960495i	−0.997939	+	0.0641695i	$0.979560\pi$
$692$	−16801.0			−0.922943
$693$		0			0
$694$	−484.453			−0.0264980
$695$	−44.5271	+	77.1232i	−0.00243023	+	0.00420928i
$696$		0			0
$697$	−19444.9	−	33679.5i	−1.05671	−	1.83028i
$698$	−1900.55	+	3291.85i	−0.103061	+	0.178507i
$699$		0			0
$700$		0			0
$701$	2719.67			0.146534			0.0732672	−	0.997312i	$-0.476657\pi$
$701$	2719.67			0.146534			0.0732672	+	0.997312i	$0.476657\pi$
$702$		0			0
$703$	−12195.3	−	21122.9i	−0.654276	−	1.13324i
$704$	9827.18	+	17021.2i	0.526102	+	0.911235i
$705$		0			0
$706$	4385.36			0.233775
$707$		0			0
$708$		0			0
$709$	312.854	−	541.879i	0.0165719	−	0.0287034i	−0.857621	−	0.514283i	$-0.828058\pi$
$709$	312.854	−	541.879i	0.0165719	−	0.0287034i	0.874192	+	0.485580i	$0.161391\pi$
$710$	17.1122	+	29.6392i	0.000904520	+	0.00156667i
$711$		0			0
$712$	−2207.58	+	3823.65i	−0.116198	+	0.201260i
$713$	1002.85			0.0526749
$714$		0			0
$715$	−73.5079			−0.00384481
$716$	−4710.91	+	8159.53i	−0.245887	+	0.425888i
$717$		0			0
$718$	1784.27	+	3090.44i	0.0927414	+	0.160633i
$719$	4788.77	−	8294.39i	0.248388	−	0.430221i	−0.714691	−	0.699441i	$-0.753433\pi$
$719$	4788.77	−	8294.39i	0.248388	−	0.430221i	0.963079	+	0.269220i	$0.0867659\pi$
$720$		0			0
$721$		0			0
$722$	3851.62			0.198535
$723$		0			0
$724$	−11705.3	−	20274.2i	−0.600864	−	1.04073i
$725$	−14728.9	−	25511.2i	−0.754506	−	1.30684i
$726$		0			0
$727$	16741.2			0.854053			0.427027	−	0.904239i	$-0.359561\pi$
$727$	16741.2			0.854053			0.427027	+	0.904239i	$0.359561\pi$
$728$		0			0
$729$		0			0
$730$	−10.7219	+	18.5710i	−0.000543612	+	0.000941564i
$731$	13293.9	+	23025.7i	0.672631	+	1.16503i
$732$		0			0
$733$	−3248.02	+	5625.74i	−0.163668	+	0.283481i	−0.936181	−	0.351517i	$-0.885666\pi$
$733$	−3248.02	+	5625.74i	−0.163668	+	0.283481i	0.772514	+	0.634998i	$0.218999\pi$
$734$	−3437.06			−0.172839
$735$		0			0
$736$	−4141.36			−0.207408
$737$	−14699.4	+	25460.0i	−0.734678	+	1.27250i
$738$		0			0
$739$	−249.640	−	432.389i	−0.0124265	−	0.0215233i	0.859745	−	0.510723i	$-0.170622\pi$
$739$	−249.640	−	432.389i	−0.0124265	−	0.0215233i	−0.872172	+	0.489200i	$0.837289\pi$
$740$	−75.4861	+	130.746i	−0.00374990	+	0.00649502i
$741$		0			0
$742$		0			0
$743$	6367.30			0.314393			0.157196	−	0.987567i	$-0.449754\pi$
$743$	6367.30			0.314393			0.157196	+	0.987567i	$0.449754\pi$
$744$		0			0
$745$	29.2784	+	50.7117i	0.00143984	+	0.00249387i
$746$	1061.19	+	1838.03i	0.0520814	+	0.0902077i
$747$		0			0
$748$	−41842.8			−2.04535
$749$		0			0
$750$		0			0
$751$	−248.049	+	429.634i	−0.0120525	+	0.0208756i	−0.871989	−	0.489526i	$-0.837170\pi$
$751$	−248.049	+	429.634i	−0.0120525	+	0.0208756i	0.859936	+	0.510401i	$0.170503\pi$
$752$	12028.9	+	20834.6i	0.583308	+	1.01032i
$753$		0			0
$754$	−812.446	+	1407.20i	−0.0392407	+	0.0679670i
$755$	−282.597			−0.0136222
$756$		0			0
$757$	13025.9			0.625408			0.312704	−	0.949851i	$-0.398765\pi$
$757$	13025.9			0.625408			0.312704	+	0.949851i	$0.398765\pi$
$758$	311.175	−	538.971i	0.0149108	−	0.0258263i
$759$		0			0
$760$	−41.8802	−	72.5387i	−0.00199889	−	0.00346218i
$761$	12737.3	−	22061.6i	0.606736	−	1.05090i	−0.385039	−	0.922900i	$-0.625812\pi$
$761$	12737.3	−	22061.6i	0.606736	−	1.05090i	0.991775	−	0.127997i	$-0.0408548\pi$
$762$		0			0
$763$		0			0
$764$	−21977.6			−1.04074
$765$		0			0
$766$	2251.86	+	3900.33i	0.106218	+	0.183975i
$767$	96.6411	+	167.387i	0.00454955	+	0.00788006i
$768$		0			0
$769$	29054.0			1.36244			0.681218	−	0.732080i	$-0.261450\pi$
$769$	29054.0			1.36244			0.681218	+	0.732080i	$0.261450\pi$
$770$		0			0
$771$		0			0
$772$	13059.3	−	22619.3i	0.608825	−	1.05452i
$773$	−948.677	−	1643.16i	−0.0441417	−	0.0764557i	0.843110	−	0.537740i	$-0.180722\pi$
$773$	−948.677	−	1643.16i	−0.0441417	−	0.0764557i	−0.887252	+	0.461285i	$0.847389\pi$
$774$		0			0
$775$	−1169.32	+	2025.33i	−0.0541978	+	0.0938734i
$776$	7153.72			0.330933
$777$		0			0
$778$	−1913.25			−0.0881662
$779$	20319.8	−	35194.9i	0.934572	−	1.61873i
$780$		0			0
$781$	18061.9	+	31284.2i	0.827538	+	1.43334i
$782$	1350.26	−	2338.72i	0.0617458	−	0.106947i
$783$		0			0
$784$		0			0
$785$	−169.989			−0.00772886
$786$		0			0
$787$	21325.1	+	36936.2i	0.965895	+	1.67298i	0.707192	+	0.707021i	$0.249961\pi$
$787$	21325.1	+	36936.2i	0.965895	+	1.67298i	0.258702	+	0.965957i	$0.416705\pi$
$788$	16544.0	+	28655.0i	0.747913	+	1.29542i
$789$		0			0
$790$	−33.5440			−0.00151069
$791$		0			0
$792$		0			0
$793$	−101.887	+	176.474i	−0.00456258	+	0.00790262i
$794$	1989.66	+	3446.20i	0.0889302	+	0.154032i
$795$		0			0
$796$	17166.5	−	29733.3i	0.764387	−	1.32396i
$797$	36822.8			1.63655			0.818275	−	0.574828i	$-0.194931\pi$
$797$	36822.8			1.63655			0.818275	+	0.574828i	$0.194931\pi$
$798$		0			0
$799$	−48844.8			−2.16271
$800$	4828.80	−	8363.73i	0.213405	−	0.369628i
$801$		0			0
$802$	−2174.84	−	3766.93i	−0.0957559	−	0.165854i
$803$	−11317.0	+	19601.7i	−0.497347	+	0.861429i
$804$		0			0
$805$		0			0
$806$	129.000			0.00563750
$807$		0			0
$808$	4493.69	+	7783.30i	0.195653	+	0.338881i
$809$	2540.97	+	4401.09i	0.110427	+	0.191266i	0.915943	−	0.401309i	$-0.131445\pi$
$809$	2540.97	+	4401.09i	0.110427	+	0.191266i	−0.805515	+	0.592575i	$0.798111\pi$
$810$		0			0
$811$	−11873.4			−0.514097			−0.257048	−	0.966399i	$-0.582750\pi$
$811$	−11873.4			−0.514097			−0.257048	+	0.966399i	$0.582750\pi$
$812$		0			0
$813$		0			0
$814$	1746.23	−	3024.55i	0.0751906	−	0.130234i
$815$	2.04645	+	3.54455i	8.79557e−5	+	0.000152344i
$816$		0			0
$817$	−13892.1	+	24061.8i	−0.594886	+	1.03037i
$818$	4998.29			0.213644
$819$		0			0
$820$	−251.549			−0.0107128
$821$	8484.72	−	14696.0i	0.360681	−	0.624717i	−0.627392	−	0.778703i	$-0.715878\pi$
$821$	8484.72	−	14696.0i	0.360681	−	0.624717i	0.988073	+	0.153986i	$0.0492111\pi$
$822$		0			0
$823$	−1997.97	−	3460.58i	−0.0846231	−	0.146572i	0.820607	−	0.571492i	$-0.193635\pi$
$823$	−1997.97	−	3460.58i	−0.0846231	−	0.146572i	−0.905231	+	0.424921i	$0.860302\pi$
$824$	−4635.19	+	8028.39i	−0.195964	+	0.339420i
$825$		0			0
$826$		0			0
$827$	13589.7			0.571417			0.285708	−	0.958317i	$-0.407771\pi$
$827$	13589.7			0.571417			0.285708	+	0.958317i	$0.407771\pi$
$828$		0			0
$829$	−15323.0	−	26540.2i	−0.641966	−	1.11192i	−0.984993	−	0.172592i	$-0.944786\pi$
$829$	−15323.0	−	26540.2i	−0.641966	−	1.11192i	0.343028	−	0.939325i	$-0.388547\pi$
$830$	−8.21918	−	14.2360i	−0.000343725	−	0.000595350i
$831$		0			0
$832$	7444.96			0.310226
$833$		0			0
$834$		0			0
$835$	145.756	−	252.456i	0.00604082	−	0.0104630i
$836$	−21862.7	−	37867.4i	−0.904472	−	1.56659i
$837$		0			0
$838$	1318.51	−	2283.72i	0.0543521	−	0.0941405i
$839$	−7497.57			−0.308516			−0.154258	−	0.988031i	$-0.549299\pi$
$839$	−7497.57			−0.308516			−0.154258	+	0.988031i	$0.549299\pi$
$840$		0			0
$841$	31156.6			1.27749
$842$	979.996	−	1697.40i	0.0401103	−	0.0694731i
$843$		0			0
$844$	8969.65	+	15535.9i	0.365815	+	0.633610i
$845$	96.4826	−	167.113i	0.00392793	−	0.00680338i
$846$		0			0
$847$		0			0
$848$	−38530.2			−1.56030
$849$		0			0
$850$	3148.79	+	5453.87i	0.127062	+	0.220078i
$851$	−5142.25	−	8906.64i	−0.207138	−	0.358773i
$852$		0			0
$853$	10347.6			0.415352			0.207676	−	0.978198i	$-0.433410\pi$
$853$	10347.6			0.415352			0.207676	+	0.978198i	$0.433410\pi$
$854$		0			0
$855$		0			0
$856$	1126.18	−	1950.60i	0.0449674	−	0.0778858i
$857$	−774.999	−	1342.34i	−0.0308909	−	0.0535045i	0.850167	−	0.526514i	$-0.176501\pi$
$857$	−774.999	−	1342.34i	−0.0308909	−	0.0535045i	−0.881058	+	0.473009i	$0.843168\pi$
$858$		0			0
$859$	7593.76	−	13152.8i	0.301625	−	0.522430i	−0.674879	−	0.737928i	$-0.735804\pi$
$859$	7593.76	−	13152.8i	0.301625	−	0.522430i	0.976504	+	0.215499i	$0.0691377\pi$
$860$	171.977			0.00681903
$861$		0			0
$862$	−1554.45			−0.0614210
$863$	20775.1	−	35983.5i	0.819459	−	1.41934i	−0.0866230	−	0.996241i	$-0.527608\pi$
$863$	20775.1	−	35983.5i	0.819459	−	1.41934i	0.906082	−	0.423103i	$-0.139059\pi$
$864$		0			0
$865$	−107.849	−	186.801i	−0.00423929	−	0.00734267i
$866$	2425.06	−	4200.33i	0.0951581	−	0.164819i
$867$		0			0
$868$		0			0
$869$	−35405.8			−1.38212
$870$		0			0
$871$	5568.04	+	9644.12i	0.216608	+	0.375176i
$872$	−1041.33	−	1803.64i	−0.0404404	−	0.0700449i
$873$		0			0
$874$	2822.03			0.109218
$875$		0			0
$876$		0			0
$877$	−13918.7	+	24107.9i	−0.535919	+	0.928239i	0.463199	+	0.886254i	$0.346701\pi$
$877$	−13918.7	+	24107.9i	−0.535919	+	0.928239i	−0.999118	+	0.0419846i	$0.986632\pi$
$878$	−3091.01	−	5353.79i	−0.118812	−	0.205788i
$879$		0			0
$880$	−132.294	+	229.140i	−0.00506777	+	0.00877763i
$881$	−2587.85			−0.0989635			−0.0494817	−	0.998775i	$-0.515757\pi$
$881$	−2587.85			−0.0989635			−0.0494817	+	0.998775i	$0.515757\pi$
$882$		0			0
$883$	−16382.0			−0.624346			−0.312173	−	0.950025i	$-0.601057\pi$
$883$	−16382.0			−0.624346			−0.312173	+	0.950025i	$0.601057\pi$
$884$	−7924.91	+	13726.4i	−0.301520	+	0.522248i
$885$		0			0
$886$	−1764.06	−	3055.45i	−0.0668904	−	0.115858i
$887$	11490.1	−	19901.4i	0.434948	−	0.753352i	−0.562343	−	0.826904i	$-0.690100\pi$
$887$	11490.1	−	19901.4i	0.434948	−	0.753352i	0.997291	+	0.0735516i	$0.0234334\pi$
$888$		0			0
$889$		0			0
$890$	−28.0348			−0.00105587
$891$		0			0
$892$	−853.180	−	1477.75i	−0.0320253	−	0.0554695i
$893$	−25521.3	−	44204.1i	−0.956368	−	1.65648i
$894$		0			0
$895$	−120.962			−0.00451766
$896$		0			0
$897$		0			0
$898$	−1235.54	+	2140.02i	−0.0459138	+	0.0795251i
$899$	−2204.88	−	3818.96i	−0.0817984	−	0.141679i
$900$		0			0
$901$	39114.2	−	67747.9i	1.44626	−	2.50500i
$902$	5819.10			0.214806
$903$		0			0
$904$	5234.42			0.192582
$905$	150.279	−	260.290i	0.00551982	−	0.00956060i
$906$		0			0
$907$	11357.7	+	19672.1i	0.415795	+	0.720178i	0.995512	−	0.0946400i	$-0.0301700\pi$
$907$	11357.7	+	19672.1i	0.415795	+	0.720178i	−0.579716	+	0.814818i	$0.696837\pi$
$908$	−7183.99	+	12443.0i	−0.262565	+	0.454776i
$909$		0			0
$910$		0			0
$911$	−34922.3			−1.27006			−0.635031	−	0.772487i	$-0.719013\pi$
$911$	−34922.3			−1.27006			−0.635031	+	0.772487i	$0.719013\pi$
$912$		0			0
$913$	−8675.36	−	15026.2i	−0.314472	−	0.544681i
$914$	2870.62	+	4972.06i	0.103886	+	0.179935i
$915$		0			0
$916$	−21716.1			−0.783320
$917$		0			0
$918$		0			0
$919$	−5851.32	+	10134.8i	−0.210030	+	0.363782i	−0.951724	−	0.306956i	$-0.900689\pi$
$919$	−5851.32	+	10134.8i	−0.210030	+	0.363782i	0.741694	+	0.670739i	$0.234023\pi$
$920$	−17.6591	−	30.5864i	−0.000632829	−	0.00109609i
$921$		0			0
$922$	30.9236	−	53.5613i	0.00110457	−	0.00191317i
$923$	13683.5			0.487973
$924$		0			0
$925$	23983.3			0.852505
$926$	−1119.20	+	1938.50i	−0.0397182	+	0.0687939i
$927$		0			0
$928$	9105.19	+	15770.7i	0.322083	+	0.557863i
$929$	26548.2	−	45982.9i	0.937588	−	1.62395i	0.167637	−	0.985849i	$-0.446386\pi$
$929$	26548.2	−	45982.9i	0.937588	−	1.62395i	0.769952	−	0.638102i	$-0.220280\pi$
$930$		0			0
$931$		0			0
$932$	−7740.06			−0.272032
$933$		0			0
$934$	−767.259	−	1328.93i	−0.0268795	−	0.0465567i
$935$	−268.599	−	465.227i	−0.00939478	−	0.0162722i
$936$		0			0
$937$	39020.6			1.36046			0.680229	−	0.733000i	$-0.261880\pi$
$937$	39020.6			1.36046			0.680229	+	0.733000i	$0.261880\pi$
$938$		0			0
$939$		0			0
$940$	−157.970	+	273.613i	−0.00548131	+	0.00949390i
$941$	−15371.9	−	26624.9i	−0.532528	−	0.922366i	−0.999279	−	0.0379770i	$-0.987909\pi$
$941$	−15371.9	−	26624.9i	−0.532528	−	0.922366i	0.466750	−	0.884389i	$-0.345425\pi$
$942$		0			0
$943$	8567.98	−	14840.2i	0.295877	−	0.512474i
$944$	695.710			0.0239867
$945$		0			0
$946$	−3978.35			−0.136731
$947$	8150.14	−	14116.5i	0.279666	−	0.484396i	−0.691636	−	0.722247i	$-0.743110\pi$
$947$	8150.14	−	14116.5i	0.279666	−	0.484396i	0.971302	+	0.237851i	$0.0764429\pi$
$948$		0			0
$949$	4286.83	+	7425.01i	0.146635	+	0.253979i
$950$	−3290.47	+	5699.26i	−0.112376	+	0.194641i
$951$		0			0
$952$		0			0
$953$	11512.7			0.391325			0.195663	−	0.980671i	$-0.437314\pi$
$953$	11512.7			0.391325			0.195663	+	0.980671i	$0.437314\pi$
$954$		0			0
$955$	−141.079	−	244.357i	−0.00478034	−	0.00827979i
$956$	3279.83	+	5680.83i	0.110959	+	0.192187i
$957$		0			0
$958$	−4420.39			−0.149078
$959$		0			0
$960$		0			0
$961$	14720.5	−	25496.6i	0.494124	−	0.855848i
$962$	−661.461	−	1145.68i	−0.0221688	−	0.0383974i
$963$		0			0
$964$	−13523.6	+	23423.5i	−0.451830	+	0.782593i
$965$	335.322			0.0111859
$966$		0			0
$967$	−18178.4			−0.604528			−0.302264	−	0.953224i	$-0.597742\pi$
$967$	−18178.4			−0.604528			−0.302264	+	0.953224i	$0.597742\pi$
$968$	1966.32	−	3405.77i	0.0652893	−	0.113084i
$969$		0			0
$970$	22.7118	+	39.3381i	0.000751787	+	0.00130213i
$971$	14138.3	−	24488.3i	0.467271	−	0.809338i	−0.532029	−	0.846726i	$-0.678570\pi$
$971$	14138.3	−	24488.3i	0.467271	−	0.809338i	0.999301	+	0.0373880i	$0.0119037\pi$
$972$		0			0
$973$		0			0
$974$	2424.77			0.0797688
$975$		0			0
$976$	366.739	+	635.210i	0.0120277	+	0.0208326i
$977$	−6973.53	−	12078.5i	−0.228355	−	0.395523i	0.728966	−	0.684550i	$-0.240001\pi$
$977$	−6973.53	−	12078.5i	−0.228355	−	0.395523i	−0.957321	+	0.289028i	$0.906668\pi$
$978$		0			0
$979$	−29590.8			−0.966011
$980$		0			0
$981$		0			0
$982$	841.954	−	1458.31i	0.0273603	−	0.0473894i
$983$	−13288.4	−	23016.2i	−0.431164	−	0.746797i	0.565810	−	0.824536i	$-0.308564\pi$
$983$	−13288.4	−	23016.2i	−0.431164	−	0.746797i	−0.996974	+	0.0777381i	$0.975230\pi$
$984$		0			0
$985$	−212.400	+	367.887i	−0.00687068	+	0.0119004i
$986$	−11874.7			−0.383539
$987$		0			0
$988$	−16563.0			−0.533339
$989$	−5857.69	+	10145.8i	−0.188335	+	0.326206i
$990$		0			0
$991$	−8124.96	−	14072.8i	−0.260442	−	0.451099i	0.705917	−	0.708294i	$-0.250535\pi$
$991$	−8124.96	−	14072.8i	−0.260442	−	0.451099i	−0.966359	+	0.257195i	$0.917202\pi$
$992$	722.859	−	1252.03i	0.0231359	−	0.0400725i
$993$		0			0
$994$		0			0
$995$	440.784			0.0140440
$996$		0			0
$997$	−9407.05	−	16293.5i	−0.298821	−	0.517573i	0.677046	−	0.735941i	$-0.263260\pi$
$997$	−9407.05	−	16293.5i	−0.298821	−	0.517573i	−0.975866	+	0.218368i	$0.929927\pi$
$998$	−996.429	−	1725.87i	−0.0316046	−	0.0547408i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.u.226.1		4
3.2	odd	2		147.4.e.j.79.2		4
7.2	even	3		441.4.a.o.1.2		2
7.3	odd	6		441.4.e.v.361.1		4
7.4	even	3	inner	441.4.e.u.361.1		4
7.5	odd	6		441.4.a.n.1.2		2
7.6	odd	2		441.4.e.v.226.1		4
21.2	odd	6		147.4.a.k.1.1	yes	2
21.5	even	6		147.4.a.j.1.1	✓	2
21.11	odd	6		147.4.e.j.67.2		4
21.17	even	6		147.4.e.k.67.2		4
21.20	even	2		147.4.e.k.79.2		4
84.23	even	6		2352.4.a.bl.1.2		2
84.47	odd	6		2352.4.a.cf.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.j.1.1	✓	2	21.5	even	6
147.4.a.k.1.1	yes	2	21.2	odd	6
147.4.e.j.67.2		4	21.11	odd	6
147.4.e.j.79.2		4	3.2	odd	2
147.4.e.k.67.2		4	21.17	even	6
147.4.e.k.79.2		4	21.20	even	2
441.4.a.n.1.2		2	7.5	odd	6
441.4.a.o.1.2		2	7.2	even	3
441.4.e.u.226.1		4	1.1	even	1	trivial
441.4.e.u.361.1		4	7.4	even	3	inner
441.4.e.v.226.1		4	7.6	odd	2
441.4.e.v.361.1		4	7.3	odd	6
2352.4.a.bl.1.2		2	84.23	even	6
2352.4.a.cf.1.1		2	84.47	odd	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{2} +(3.91421 + 6.77962i) q^{4} +(-0.0502525 + 0.0870399i) q^{5} -6.55635 q^{8} +O(q^{10})\)	\(q+(-0.207107 + 0.358719i) q^{2} +(3.91421 + 6.77962i) q^{4} +(-0.0502525 + 0.0870399i) q^{5} -6.55635 q^{8} +(-0.0208153 - 0.0360531i) q^{10} +(-21.9706 - 38.0541i) q^{11} -16.6447 q^{13} +(-29.9558 + 51.8850i) q^{16} +(-60.8198 - 105.343i) q^{17} +(63.5563 - 110.083i) q^{19} -0.786797 q^{20} +18.2010 q^{22} +(26.7990 - 46.4172i) q^{23} +(62.4949 + 108.244i) q^{25} +(3.44722 - 5.97076i) q^{26} -235.681 q^{29} +(9.35534 + 16.2039i) q^{31} +(-38.6335 - 66.9152i) q^{32} +50.3848 q^{34} +(95.9411 - 166.175i) q^{37} +(26.3259 + 45.5978i) q^{38} +(0.329473 - 0.570664i) q^{40} +319.713 q^{41} -218.579 q^{43} +(171.995 - 297.904i) q^{44} +(11.1005 + 19.2266i) q^{46} +(200.777 - 347.755i) q^{47} -51.7725 q^{50} +(-65.1508 - 112.844i) q^{52} +(321.558 + 556.956i) q^{53} +4.41631 q^{55} +(48.8112 - 84.5434i) q^{58} +(-5.80613 - 10.0565i) q^{59} +(6.12132 - 10.6024i) q^{61} -7.75022 q^{62} -447.288 q^{64} +(0.836436 - 1.44875i) q^{65} +(-334.524 - 579.412i) q^{67} +(476.123 - 824.670i) q^{68} -822.098 q^{71} +(-257.550 - 446.089i) q^{73} +(39.7401 + 68.8319i) q^{74} +995.092 q^{76} +(402.877 - 697.804i) q^{79} +(-3.01071 - 5.21471i) q^{80} +(-66.2147 + 114.687i) q^{82} +394.863 q^{83} +12.2254 q^{85} +(45.2691 - 78.4084i) q^{86} +(144.047 + 249.496i) q^{88} +(336.709 - 583.197i) q^{89} +419.588 q^{92} +(83.1644 + 144.045i) q^{94} +(6.38773 + 11.0639i) q^{95} -1091.11 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 10 q^{4} - 20 q^{5} + 36 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 10 * q^4 - 20 * q^5 + 36 * q^8	\( 4 q + 2 q^{2} + 10 q^{4} - 20 q^{5} + 36 q^{8} + 48 q^{10} - 20 q^{11} - 208 q^{13} - 18 q^{16} - 116 q^{17} + 192 q^{19} - 88 q^{20} + 152 q^{22} + 28 q^{23} - 146 q^{25} - 204 q^{26} - 592 q^{29} - 104 q^{31} + 18 q^{32} + 128 q^{34} + 248 q^{37} - 104 q^{38} - 488 q^{40} + 40 q^{41} - 1440 q^{43} + 292 q^{44} + 84 q^{46} + 96 q^{47} - 1412 q^{50} - 320 q^{52} + 268 q^{53} - 944 q^{55} - 48 q^{58} + 616 q^{59} + 16 q^{61} - 608 q^{62} + 236 q^{64} + 1740 q^{65} + 144 q^{67} + 940 q^{68} - 1976 q^{71} + 104 q^{73} - 56 q^{74} + 2272 q^{76} + 944 q^{79} + 828 q^{80} - 856 q^{82} + 2032 q^{83} - 200 q^{85} - 1120 q^{86} + 876 q^{88} + 388 q^{89} + 728 q^{92} + 904 q^{94} + 1304 q^{95} - 976 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 + 10 * q^4 - 20 * q^5 + 36 * q^8 + 48 * q^10 - 20 * q^11 - 208 * q^13 - 18 * q^16 - 116 * q^17 + 192 * q^19 - 88 * q^20 + 152 * q^22 + 28 * q^23 - 146 * q^25 - 204 * q^26 - 592 * q^29 - 104 * q^31 + 18 * q^32 + 128 * q^34 + 248 * q^37 - 104 * q^38 - 488 * q^40 + 40 * q^41 - 1440 * q^43 + 292 * q^44 + 84 * q^46 + 96 * q^47 - 1412 * q^50 - 320 * q^52 + 268 * q^53 - 944 * q^55 - 48 * q^58 + 616 * q^59 + 16 * q^61 - 608 * q^62 + 236 * q^64 + 1740 * q^65 + 144 * q^67 + 940 * q^68 - 1976 * q^71 + 104 * q^73 - 56 * q^74 + 2272 * q^76 + 944 * q^79 + 828 * q^80 - 856 * q^82 + 2032 * q^83 - 200 * q^85 - 1120 * q^86 + 876 * q^88 + 388 * q^89 + 728 * q^92 + 904 * q^94 + 1304 * q^95 - 976 * q^97

Introduction

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