LMFDB - Embedded newform 441.4.e.v.361.1

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			361.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.4.e.v.226.1

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.827089	−	0.562071i	$-0.189995\pi$
$2$	−0.207107	−	0.358719i	−0.0732233	−	0.126826i	−0.900312	+	0.435245i	$0.856662\pi$
$3$		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	$-0.165236\pi$
$5$	0.0502525	+	0.0870399i	0.00449472	+	0.00778509i	−0.863769	+	0.503887i	$0.831903\pi$
$6$		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	0.390269	+	0.920701i	$0.372382\pi$
$11$	−21.9706	+	38.0541i	−0.602216	+	1.04307i	−0.992485	+	0.122368i	$0.960951\pi$
$12$		0			0
$13$	16.6447			0.355108			0.177554	−	0.984111i	$-0.443182\pi$
$13$	16.6447			0.355108			0.177554	+	0.984111i	$0.443182\pi$
$14$		0			0
$15$		0			0
$16$	−29.9558	−	51.8850i	−0.468060	−	0.810704i
$17$	60.8198	−	105.343i	0.867704	−	1.50291i	0.00336718	−	0.999994i	$-0.498928\pi$
$17$	60.8198	−	105.343i	0.867704	−	1.50291i	0.864337	−	0.502913i	$-0.167738\pi$
$18$		0			0
$19$	−63.5563	−	110.083i	−0.767412	−	1.32920i	−0.938962	−	0.344021i	$-0.888211\pi$
$19$	−63.5563	−	110.083i	−0.767412	−	1.32920i	0.171550	−	0.985175i	$-0.445122\pi$
$20$	0.786797			0.00879665
$21$		0			0
$22$	18.2010			0.176385
$23$	26.7990	+	46.4172i	0.242955	+	0.420811i	0.961555	−	0.274613i	$-0.0885498\pi$
$23$	26.7990	+	46.4172i	0.242955	+	0.420811i	−0.718599	+	0.695424i	$0.755216\pi$
$24$		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	$-0.850595\pi$
$31$	−9.35534	+	16.2039i	−0.0542022	+	0.0938810i	0.837651	+	0.546205i	$0.183928\pi$
$32$	−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	0.996540	−	0.0831185i	$-0.0264880\pi$
$37$	95.9411	+	166.175i	0.426287	+	0.738351i	−0.570253	+	0.821469i	$0.693155\pi$
$38$	−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	$-0.708394\pi$
$41$	−319.713			−1.21782			−0.608912	+	0.793238i	$0.708394\pi$
$42$		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	−0.988903	−	0.148565i	$-0.952535\pi$
$47$	−200.777	−	347.755i	−0.623113	−	1.07926i	0.365790	−	0.930697i	$-0.380799\pi$
$48$		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	−0.0619521	−	0.998079i	$-0.519733\pi$
$53$	321.558	−	556.956i	0.833386	−	1.44347i	0.895338	−	0.445387i	$-0.146934\pi$
$54$		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	$-0.829255\pi$
$59$	5.80613	−	10.0565i	0.0128118	−	0.0221906i	0.872360	+	0.488864i	$0.162588\pi$
$60$		0			0
$61$	−6.12132	−	10.6024i	−0.0128484	−	0.0222541i	0.859530	−	0.511086i	$-0.170757\pi$
$61$	−6.12132	−	10.6024i	−0.0128484	−	0.0222541i	−0.872378	+	0.488832i	$0.837423\pi$
$62$	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	0.381264	+	0.924466i	$0.375489\pi$
$67$	−334.524	+	579.412i	−0.609979	+	1.05651i	−0.991243	+	0.132049i	$0.957844\pi$
$68$	−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	$-0.697839\pi$
$73$	257.550	−	446.089i	0.412930	−	0.715217i	0.995209	+	0.0977730i	$0.0311719\pi$
$74$	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	0.996175	+	0.0873819i	$0.0278500\pi$
$79$	402.877	+	697.804i	0.573762	+	0.993786i	−0.422413	+	0.906404i	$0.638817\pi$
$80$	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	$-0.584084\pi$
$83$	−394.863			−0.522191			−0.261095	+	0.965313i	$0.584084\pi$
$84$		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	$-0.298012\pi$
$89$	−336.709	−	583.197i	−0.401024	−	0.694593i	−0.993850	+	0.110737i	$0.964679\pi$
$90$		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	$-0.306532\pi$
$97$	1091.11			1.14212			0.571061	+	0.820908i	$0.306532\pi$
$98$		0			0
$99$		0			0
$100$	−489.237	−	847.384i	−0.489237	−	0.847384i
$101$	685.395	−	1187.14i	0.675242	−	1.16955i	−0.301157	−	0.953575i	$-0.597373\pi$
$101$	685.395	−	1187.14i	0.675242	−	1.16955i	0.976398	−	0.215978i	$-0.0692940\pi$
$102$		0			0
$103$	−706.978	−	1224.52i	−0.676316	−	1.17141i	−0.976082	−	0.217401i	$-0.930242\pi$
$103$	−706.978	−	1224.52i	−0.676316	−	1.17141i	0.299766	−	0.954013i	$-0.403091\pi$
$104$	−109.128			−0.102893
$105$		0			0
$106$	−266.388			−0.244093
$107$	−171.770	−	297.514i	−0.155192	−	0.268801i	0.777937	−	0.628343i	$-0.216266\pi$
$107$	−171.770	−	297.514i	−0.155192	−	0.268801i	−0.933129	+	0.359542i	$0.882933\pi$
$108$		0			0
$109$	158.828	−	275.099i	0.139569	−	0.241740i	−0.787765	−	0.615976i	$-0.788762\pi$
$109$	158.828	−	275.099i	0.139569	−	0.241740i	0.927333	+	0.374236i	$0.122095\pi$
$110$	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	0.890986	+	0.454031i	$0.150014\pi$
$131$	1257.51	+	2178.07i	0.838695	+	1.45266i	−0.0522910	+	0.998632i	$0.516652\pi$
$132$		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	−0.824226	−	0.566262i	$-0.808389\pi$
$137$	125.532	−	217.428i	0.0782841	−	0.135592i	0.902510	+	0.430670i	$0.141723\pi$
$138$		0			0
$139$	−886.067			−0.540685			−0.270343	−	0.962764i	$-0.587137\pi$
$139$	−886.067			−0.540685			−0.270343	+	0.962764i	$0.587137\pi$
$140$		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	0.934929	−	0.354834i	$-0.115463\pi$
$149$	291.313	+	504.569i	0.160170	+	0.277422i	−0.774760	+	0.632256i	$0.782129\pi$
$150$		0			0
$151$	1405.88	−	2435.06i	0.757676	−	1.31233i	−0.186357	−	0.982482i	$-0.559668\pi$
$151$	1405.88	−	2435.06i	0.757676	−	1.31233i	0.944033	−	0.329851i	$-0.106999\pi$
$152$	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	$-0.974779\pi$
$157$	−845.672	+	1464.75i	−0.429885	+	0.744583i	0.566978	+	0.823733i	$0.308113\pi$
$158$	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	0.870876	−	0.491503i	$-0.163552\pi$
$163$	20.3616	+	35.2674i	0.00978432	+	0.0169469i	−0.861092	+	0.508450i	$0.830219\pi$
$164$	−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	$-0.265440\pi$
$167$	2900.47			1.34398			0.671990	+	0.740560i	$0.265440\pi$
$168$		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	$-0.0103485\pi$
$173$	1073.07	+	1858.62i	0.471585	+	0.816810i	−0.527886	+	0.849315i	$0.677015\pi$
$174$		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	−0.712602	−	0.701569i	$-0.752483\pi$
$179$	601.770	−	1042.30i	0.251276	−	0.435222i	0.963877	+	0.266347i	$0.0858166\pi$
$180$		0			0
$181$	2990.47			1.22807			0.614033	−	0.789280i	$-0.289546\pi$
$181$	2990.47			1.22807			0.614033	+	0.789280i	$0.289546\pi$
$182$		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	−0.999312	−	0.0370847i	$-0.988193\pi$
$191$	−1403.70	−	2431.29i	−0.531772	−	0.921057i	0.467540	−	0.883972i	$-0.345140\pi$
$192$		0			0
$193$	−1668.18	+	2889.38i	−0.622169	+	1.07763i	0.366913	+	0.930255i	$0.380415\pi$
$193$	−1668.18	+	2889.38i	−0.622169	+	1.07763i	−0.989081	+	0.147372i	$0.952919\pi$
$194$	−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	−0.150139	−	0.988665i	$-0.547972\pi$
$199$	2192.85	−	3798.12i	0.781140	−	1.35297i	0.931278	−	0.364309i	$-0.118695\pi$
$200$	−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	$-0.489581\pi$
$223$	217.970			0.0654544			0.0327272	+	0.999464i	$0.489581\pi$
$224$		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	$-0.919802\pi$
$227$	−917.680	+	1589.47i	−0.268320	+	0.464743i	0.700108	+	0.714037i	$0.253135\pi$
$228$		0			0
$229$	1387.00	+	2402.36i	0.400244	+	0.693243i	0.993755	−	0.111583i	$-0.0355921\pi$
$229$	1387.00	+	2402.36i	0.400244	+	0.693243i	−0.593511	+	0.804826i	$0.702259\pi$
$230$	2.23131			0.000639689
$231$		0			0
$232$	1545.21			0.437275
$233$	−494.356	−	856.250i	−0.138997	−	0.240750i	0.788120	−	0.615522i	$-0.211055\pi$
$233$	−494.356	−	856.250i	−0.138997	−	0.240750i	−0.927117	+	0.374771i	$0.877721\pi$
$234$		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	$-0.986105\pi$
$241$	−1727.49	+	2992.11i	−0.461733	+	0.799745i	0.537315	+	0.843382i	$0.319439\pi$
$242$	−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	$-0.249362\pi$
$251$	5635.01			1.41705			0.708523	+	0.705688i	$0.249362\pi$
$252$		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	$-0.0777821\pi$
$257$	1135.58	+	1966.88i	0.275624	+	0.477395i	−0.694668	+	0.719330i	$0.744449\pi$
$258$		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	−0.856261	−	0.516544i	$-0.827218\pi$
$263$	81.9336	−	141.913i	0.0192101	−	0.0332728i	0.875471	+	0.483271i	$0.160552\pi$
$264$		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	−0.409220	−	0.912436i	$-0.634199\pi$
$269$	2583.55	−	4474.84i	0.585582	−	1.01426i	0.994803	−	0.101823i	$-0.0324675\pi$
$270$		0			0
$271$	−811.136	−	1404.93i	−0.181819	−	0.314920i	0.760681	−	0.649126i	$-0.224865\pi$
$271$	−811.136	−	1404.93i	−0.181819	−	0.314920i	−0.942500	+	0.334206i	$0.891532\pi$
$272$	−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	−0.499765	−	0.866161i	$-0.666580\pi$
$277$	2306.18	−	3994.43i	0.500235	−	0.866433i	1.00000		0.000271708i	$-8.64874e-5\pi$
$278$	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	$-0.746285\pi$
$283$	1285.77	−	2227.02i	0.270075	−	0.467783i	0.968881	+	0.247528i	$0.0796183\pi$
$284$	−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	$-0.607547\pi$
$293$	−3324.96			−0.662957			−0.331478	+	0.943463i	$0.607547\pi$
$294$		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	$-0.526277\pi$
$307$	−887.096			−0.164916			−0.0824580	+	0.996595i	$0.526277\pi$
$308$		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	$-0.968234\pi$
$311$	−2255.41	+	3906.48i	−0.411230	+	0.712271i	0.583794	+	0.811902i	$0.301567\pi$
$312$		0			0
$313$	−1857.89	−	3217.96i	−0.335509	−	0.581118i	0.648074	−	0.761578i	$-0.275575\pi$
$313$	−1857.89	−	3217.96i	−0.335509	−	0.581118i	−0.983582	+	0.180459i	$0.942242\pi$
$314$	700.577			0.125910
$315$		0			0
$316$	6307.79			1.12291
$317$	3477.26	+	6022.79i	0.616096	+	1.06711i	0.990191	+	0.139719i	$0.0446200\pi$
$317$	3477.26	+	6022.79i	0.616096	+	1.06711i	−0.374095	+	0.927390i	$0.622047\pi$
$318$		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	0.906474	+	0.422262i	$0.138764\pi$
$331$	4931.59	+	8541.76i	0.818926	+	1.41842i	−0.0875478	+	0.996160i	$0.527903\pi$
$332$	−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	−0.817239	−	0.576299i	$-0.804497\pi$
$347$	584.786	−	1012.88i	0.0904697	−	0.156698i	0.907709	+	0.419601i	$0.137830\pi$
$348$		0			0
$349$	−9176.66			−1.40749			−0.703747	−	0.710451i	$-0.748491\pi$
$349$	−9176.66			−1.40749			−0.703747	+	0.710451i	$0.748491\pi$
$350$		0			0
$351$		0			0
$352$	−1697.60	−	2940.33i	−0.257052	−	0.445228i
$353$	5293.60	−	9168.78i	0.798158	−	1.38245i	−0.122656	−	0.992449i	$-0.539141\pi$
$353$	5293.60	−	9168.78i	0.798158	−	1.38245i	0.920814	−	0.390001i	$-0.127526\pi$
$354$		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	0.986877	+	0.161472i	$0.0516243\pi$
$359$	4307.61	+	7460.99i	0.633278	+	1.09687i	−0.353599	+	0.935397i	$0.615042\pi$
$360$		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	0.404107	+	0.914712i	$0.367582\pi$
$367$	−4148.89	+	7186.10i	−0.590110	+	1.02210i	−0.994217	+	0.107389i	$0.965751\pi$
$368$	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	0.987226	−	0.159324i	$-0.0509315\pi$
$373$	2561.93	+	4437.39i	0.355634	+	0.615977i	−0.631592	+	0.775301i	$0.717598\pi$
$374$	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	−0.958850	−	0.283914i	$-0.908367\pi$
$383$	−5436.47	−	9416.24i	−0.725301	−	1.25626i	0.233548	−	0.972345i	$-0.424966\pi$
$384$		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	−0.675349	−	0.737499i	$-0.736007\pi$
$389$	2309.50	−	4000.16i	0.301018	−	0.521379i	0.976367	+	0.216120i	$0.0693402\pi$
$390$		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	−0.991691	−	0.128642i	$-0.958938\pi$
$397$	−4803.48	−	8319.86i	−0.607253	−	1.05179i	0.384438	−	0.923151i	$-0.374395\pi$
$398$	−1816.61			−0.228791
$399$		0			0
$400$	−7488.36			−0.936044
$401$	−5250.52	−	9094.17i	−0.653862	−	1.13252i	−0.982178	−	0.187954i	$-0.939814\pi$
$401$	−5250.52	−	9094.17i	−0.653862	−	1.13252i	0.328316	−	0.944568i	$-0.393519\pi$
$402$		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	−0.227699	−	0.973732i	$-0.573120\pi$
$409$	6033.47	−	10450.3i	0.729427	−	1.26340i	0.957126	−	0.289673i	$-0.0935466\pi$
$410$	−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	$-0.378967\pi$
$419$	6366.31			0.742278			0.371139	+	0.928577i	$0.378967\pi$
$420$		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	−0.741917	−	0.670492i	$-0.766083\pi$
$431$	1876.39	−	3250.01i	0.209704	−	0.363219i	0.951621	+	0.307273i	$0.0994165\pi$
$432$		0			0
$433$	11709.2			1.29956			0.649780	−	0.760122i	$-0.274861\pi$
$433$	11709.2			1.29956			0.649780	+	0.760122i	$0.274861\pi$
$434$		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	0.911957	+	0.410285i	$0.134571\pi$
$439$	7462.36	+	12925.2i	0.811296	+	1.40521i	−0.100661	+	0.994921i	$0.532096\pi$
$440$	28.9548			0.00313720
$441$		0			0
$442$	−838.638			−0.0902487
$443$	−4258.83	−	7376.51i	−0.456756	−	0.791125i	0.542031	−	0.840359i	$-0.317656\pi$
$443$	−4258.83	−	7376.51i	−0.456756	−	0.791125i	−0.998787	+	0.0492333i	$0.984322\pi$
$444$		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	0.965089	+	0.261923i	$0.0843567\pi$
$457$	6930.28	+	12003.6i	0.709376	+	1.22868i	−0.255712	+	0.966753i	$0.582310\pi$
$458$	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	$-0.497599\pi$
$461$	149.312			0.0150850			0.00754249	+	0.999972i	$0.497599\pi$
$462$		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	$-0.107909\pi$
$467$	1852.33	+	3208.33i	0.183545	+	0.317909i	−0.759540	+	0.650460i	$0.774576\pi$
$468$		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	0.490963	+	0.871180i	$0.336645\pi$
$479$	−5335.88	+	9242.02i	−0.508982	+	0.881583i	−0.999946	+	0.0104033i	$0.996688\pi$
$480$		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	−0.969463	−	0.245239i	$-0.921133\pi$
$487$	−2926.96	+	5069.65i	−0.272348	+	0.471720i	0.697115	+	0.716959i	$0.254467\pi$
$488$	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	0.737713	−	0.675115i	$-0.235906\pi$
$499$	−2405.59	−	4166.61i	−0.215810	−	0.373794i	−0.953523	+	0.301321i	$0.902572\pi$
$500$	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	$-0.771649\pi$
$503$	−17001.2			−1.50705			−0.753526	+	0.657418i	$0.771649\pi$
$504$		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	0.992710	+	0.120531i	$0.0384597\pi$
$509$	6898.61	+	11948.7i	0.600738	+	1.04051i	−0.391972	+	0.919977i	$0.628207\pi$
$510$		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	$-0.780405\pi$
$521$	1968.31	−	3409.21i	0.165515	−	0.286680i	0.936838	+	0.349764i	$0.113738\pi$
$522$		0			0
$523$	−8729.63	−	15120.2i	−0.729866	−	1.26417i	−0.956939	−	0.290288i	$-0.906249\pi$
$523$	−8729.63	−	15120.2i	−0.729866	−	1.26417i	0.227073	−	0.973878i	$-0.427084\pi$
$524$	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	−0.943365	−	0.331757i	$-0.892359\pi$
$541$	−9550.66	−	16542.2i	−0.758992	−	1.31461i	0.184373	−	0.982856i	$-0.440975\pi$
$542$	−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	0.152804	+	0.988257i	$0.451170\pi$
$557$	−10246.4	+	17747.3i	−0.779453	+	1.35005i	−0.932257	+	0.361796i	$0.882164\pi$
$558$		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	$-0.919477\pi$
$563$	−3571.24	+	6185.57i	−0.267336	+	0.463039i	0.700837	+	0.713321i	$0.252810\pi$
$564$		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	0.931581	−	0.363534i	$-0.118430\pi$
$569$	2048.96	+	3548.90i	0.150961	+	0.261472i	−0.780620	+	0.625006i	$0.785097\pi$
$570$		0			0
$571$	1419.24	−	2458.20i	0.104016	−	0.180162i	−0.809320	−	0.587369i	$-0.800164\pi$
$571$	1419.24	−	2458.20i	0.104016	−	0.180162i	0.913336	+	0.407207i	$0.133497\pi$
$572$	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	−0.439793	−	0.898099i	$-0.644948\pi$
$577$	7732.23	−	13392.6i	0.557881	−	0.966277i	0.997673	−	0.0681781i	$-0.0217186\pi$
$578$	−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	$-0.663853\pi$
$587$	−14003.6			−0.984652			−0.492326	+	0.870411i	$0.663853\pi$
$588$		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	$-0.0943574\pi$
$593$	3252.25	+	5633.06i	0.225217	+	0.390088i	−0.731167	+	0.682198i	$0.761024\pi$
$594$		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	−0.996898	−	0.0787104i	$-0.974920\pi$
$599$	−6308.05	+	10925.9i	−0.430284	+	0.745273i	0.566614	+	0.823983i	$0.308253\pi$
$600$		0			0
$601$	8270.87			0.561358			0.280679	−	0.959802i	$-0.409440\pi$
$601$	8270.87			0.561358			0.280679	+	0.959802i	$0.409440\pi$
$602$		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	$-0.207344\pi$
$607$	−1905.92	−	3301.15i	−0.127445	−	0.220740i	−0.922686	+	0.385553i	$0.874011\pi$
$608$	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	−0.990210	−	0.139583i	$-0.955424\pi$
$613$	−5679.63	+	9837.42i	−0.374222	+	0.648172i	0.615988	+	0.787756i	$0.288757\pi$
$614$	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	−0.241048	+	0.970513i	$0.577491\pi$
$619$	−14800.1	+	25634.6i	−0.961013	+	1.66452i	−0.719965	+	0.694010i	$0.755842\pi$
$620$	−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	−0.869592	−	0.493771i	$-0.835618\pi$
$641$	−116.491	+	201.768i	−0.00717803	+	0.0124327i	0.862414	+	0.506203i	$0.168952\pi$
$642$		0			0
$643$	−1837.96			−0.112725			−0.0563624	−	0.998410i	$-0.517950\pi$
$643$	−1837.96			−0.112725			−0.0563624	+	0.998410i	$0.517950\pi$
$644$		0			0
$645$		0			0
$646$	3202.27	+	5546.50i	0.195034	+	0.337808i
$647$	−9297.35	+	16103.5i	−0.564941	+	0.978506i	0.432114	+	0.901819i	$0.357768\pi$
$647$	−9297.35	+	16103.5i	−0.564941	+	0.978506i	−0.997055	+	0.0766874i	$0.975566\pi$
$648$		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	−0.867144	−	0.498057i	$-0.834047\pi$
$653$	−14432.3	−	24997.6i	−0.864902	−	1.49805i	0.00224162	−	0.999997i	$-0.499286\pi$
$654$		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	$-0.795979\pi$
$661$	1989.75	−	3446.36i	0.117084	−	0.202795i	0.918611	+	0.395163i	$0.129312\pi$
$662$	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	$-0.323697\pi$
$677$	−8341.73	−	14448.3i	−0.473558	−	0.820227i	−0.999542	+	0.0302680i	$0.990364\pi$
$678$		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	−0.501161	−	0.865354i	$-0.667094\pi$
$683$	8904.11	−	15422.4i	0.498838	−	0.864013i	0.999999	+	0.00134107i	$0.000426875\pi$
$684$		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	0.997939	+	0.0641695i	$0.0204398\pi$
$691$	10072.8	+	17446.7i	0.554542	+	0.960495i	−0.443397	+	0.896325i	$0.646227\pi$
$692$	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	0.874192	−	0.485580i	$-0.161391\pi$
$709$	312.854	+	541.879i	0.0165719	+	0.0287034i	−0.857621	+	0.514283i	$0.828058\pi$
$710$	−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	$-0.246567\pi$
$719$	−4788.77	−	8294.39i	−0.248388	−	0.430221i	−0.963079	+	0.269220i	$0.913234\pi$
$720$		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	$-0.640439\pi$
$727$	−16741.2			−0.854053			−0.427027	+	0.904239i	$0.640439\pi$
$728$		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	$-0.114334\pi$
$733$	3248.02	+	5625.74i	0.163668	+	0.283481i	−0.772514	+	0.634998i	$0.781001\pi$
$734$	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	−0.872172	−	0.489200i	$-0.837289\pi$
$739$	−249.640	+	432.389i	−0.0124265	+	0.0215233i	0.859745	+	0.510723i	$0.170622\pi$
$740$	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	0.859936	−	0.510401i	$-0.170503\pi$
$751$	−248.049	−	429.634i	−0.0120525	−	0.0208756i	−0.871989	+	0.489526i	$0.837170\pi$
$752$	−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	−0.991775	−	0.127997i	$-0.959145\pi$
$761$	−12737.3	−	22061.6i	−0.606736	−	1.05090i	0.385039	−	0.922900i	$-0.374188\pi$
$762$		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	$-0.738550\pi$
$769$	−29054.0			−1.36244			−0.681218	+	0.732080i	$0.738550\pi$
$770$		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	$-0.819278\pi$
$773$	948.677	−	1643.16i	0.0441417	−	0.0764557i	0.887252	+	0.461285i	$0.152611\pi$
$774$		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	−0.258702	+	0.965957i	$0.583295\pi$
$787$	−21325.1	+	36936.2i	−0.965895	+	1.67298i	−0.707192	+	0.707021i	$0.750039\pi$
$788$	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	$-0.805069\pi$
$797$	−36822.8			−1.63655			−0.818275	+	0.574828i	$0.805069\pi$
$798$		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	−0.805515	−	0.592575i	$-0.798111\pi$
$809$	2540.97	−	4401.09i	0.110427	−	0.191266i	0.915943	+	0.401309i	$0.131445\pi$
$810$		0			0
$811$	11873.4			0.514097			0.257048	−	0.966399i	$-0.417250\pi$
$811$	11873.4			0.514097			0.257048	+	0.966399i	$0.417250\pi$
$812$		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	0.988073	−	0.153986i	$-0.0492111\pi$
$821$	8484.72	+	14696.0i	0.360681	+	0.624717i	−0.627392	+	0.778703i	$0.715878\pi$
$822$		0			0
$823$	−1997.97	+	3460.58i	−0.0846231	+	0.146572i	−0.905231	−	0.424921i	$-0.860302\pi$
$823$	−1997.97	+	3460.58i	−0.0846231	+	0.146572i	0.820607	+	0.571492i	$0.193635\pi$
$824$	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	−0.343028	−	0.939325i	$-0.611453\pi$
$829$	15323.0	−	26540.2i	0.641966	−	1.11192i	0.984993	−	0.172592i	$-0.0552141\pi$
$830$	−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	$-0.450701\pi$
$839$	7497.57			0.308516			0.154258	+	0.988031i	$0.450701\pi$
$840$		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	$-0.566590\pi$
$853$	−10347.6			−0.415352			−0.207676	+	0.978198i	$0.566590\pi$
$854$		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	$-0.823499\pi$
$857$	774.999	−	1342.34i	0.0308909	−	0.0535045i	0.881058	+	0.473009i	$0.156832\pi$
$858$		0			0
$859$	−7593.76	−	13152.8i	−0.301625	−	0.522430i	0.674879	−	0.737928i	$-0.264196\pi$
$859$	−7593.76	−	13152.8i	−0.301625	−	0.522430i	−0.976504	+	0.215499i	$0.930862\pi$
$860$	−171.977			−0.00681903
$861$		0			0
$862$	−1554.45			−0.0614210
$863$	20775.1	+	35983.5i	0.819459	+	1.41934i	0.906082	+	0.423103i	$0.139059\pi$
$863$	20775.1	+	35983.5i	0.819459	+	1.41934i	−0.0866230	+	0.996241i	$0.527608\pi$
$864$		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	−0.999118	−	0.0419846i	$-0.986632\pi$
$877$	−13918.7	−	24107.9i	−0.535919	−	0.928239i	0.463199	−	0.886254i	$-0.346701\pi$
$878$	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	$-0.484243\pi$
$881$	2587.85			0.0989635			0.0494817	+	0.998775i	$0.484243\pi$
$882$		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	$-0.309900\pi$
$887$	−11490.1	−	19901.4i	−0.434948	−	0.753352i	−0.997291	+	0.0735516i	$0.976567\pi$
$888$		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	−0.579716	−	0.814818i	$-0.696837\pi$
$907$	11357.7	−	19672.1i	0.415795	−	0.720178i	0.995512	+	0.0946400i	$0.0301700\pi$
$908$	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	0.741694	−	0.670739i	$-0.234023\pi$
$919$	−5851.32	−	10134.8i	−0.210030	−	0.363782i	−0.951724	+	0.306956i	$0.900689\pi$
$920$	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	−0.769952	−	0.638102i	$-0.779720\pi$
$929$	−26548.2	−	45982.9i	−0.937588	−	1.62395i	−0.167637	−	0.985849i	$-0.553614\pi$
$930$		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	$-0.738120\pi$
$937$	−39020.6			−1.36046			−0.680229	+	0.733000i	$0.738120\pi$
$938$		0			0
$939$		0			0
$940$	−157.970	−	273.613i	−0.00548131	−	0.00949390i
$941$	15371.9	−	26624.9i	0.532528	−	0.922366i	−0.466750	−	0.884389i	$-0.654575\pi$
$941$	15371.9	−	26624.9i	0.532528	−	0.922366i	0.999279	−	0.0379770i	$-0.0120914\pi$
$942$		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	0.971302	−	0.237851i	$-0.0764429\pi$
$947$	8150.14	+	14116.5i	0.279666	+	0.484396i	−0.691636	+	0.722247i	$0.743110\pi$
$948$		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	$-0.321430\pi$
$971$	−14138.3	−	24488.3i	−0.467271	−	0.809338i	−0.999301	+	0.0373880i	$0.988096\pi$
$972$		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	−0.957321	−	0.289028i	$-0.906668\pi$
$977$	−6973.53	+	12078.5i	−0.228355	+	0.395523i	0.728966	+	0.684550i	$0.240001\pi$
$978$		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	$-0.691436\pi$
$983$	13288.4	−	23016.2i	0.431164	−	0.746797i	0.996974	+	0.0777381i	$0.0247698\pi$
$984$		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	−0.966359	−	0.257195i	$-0.917202\pi$
$991$	−8124.96	+	14072.8i	−0.260442	+	0.451099i	0.705917	+	0.708294i	$0.250535\pi$
$992$	−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	$-0.736740\pi$
$997$	9407.05	−	16293.5i	0.298821	−	0.517573i	0.975866	+	0.218368i	$0.0700734\pi$
$998$	−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.v.361.1		4
3.2	odd	2		147.4.e.k.67.2		4
7.2	even	3	inner	441.4.e.v.226.1		4
7.3	odd	6		441.4.a.o.1.2		2
7.4	even	3		441.4.a.n.1.2		2
7.5	odd	6		441.4.e.u.226.1		4
7.6	odd	2		441.4.e.u.361.1		4
21.2	odd	6		147.4.e.k.79.2		4
21.5	even	6		147.4.e.j.79.2		4
21.11	odd	6		147.4.a.j.1.1	✓	2
21.17	even	6		147.4.a.k.1.1	yes	2
21.20	even	2		147.4.e.j.67.2		4
84.11	even	6		2352.4.a.cf.1.1		2
84.59	odd	6		2352.4.a.bl.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.j.1.1	✓	2	21.11	odd	6
147.4.a.k.1.1	yes	2	21.17	even	6
147.4.e.j.67.2		4	21.20	even	2
147.4.e.j.79.2		4	21.5	even	6
147.4.e.k.67.2		4	3.2	odd	2
147.4.e.k.79.2		4	21.2	odd	6
441.4.a.n.1.2		2	7.4	even	3
441.4.a.o.1.2		2	7.3	odd	6
441.4.e.u.226.1		4	7.5	odd	6
441.4.e.u.361.1		4	7.6	odd	2
441.4.e.v.226.1		4	7.2	even	3	inner
441.4.e.v.361.1		4	1.1	even	1	trivial
2352.4.a.bl.1.2		2	84.59	odd	6
2352.4.a.cf.1.1		2	84.11	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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

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