LMFDB - Embedded newform 441.4.e.u.361.2

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			361.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.4.e.u.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 + 2.09077i) q^{2} +(1.08579 - 1.88064i) q^{4} +(-9.94975 - 17.2335i) q^{5} +24.5563 q^{8} +O(q^{10})$	\(q+(1.20711 + 2.09077i) q^{2} +(1.08579 - 1.88064i) q^{4} +(-9.94975 - 17.2335i) q^{5} +24.5563 q^{8} +(24.0208 - 41.6053i) q^{10} +(11.9706 - 20.7336i) q^{11} -87.3553 q^{13} +(20.9558 + 36.2966i) q^{16} +(2.81981 - 4.88405i) q^{17} +(32.4437 + 56.1941i) q^{19} -43.2132 q^{20} +57.7990 q^{22} +(-12.7990 - 22.1685i) q^{23} +(-135.495 + 234.684i) q^{25} +(-105.447 - 182.640i) q^{26} -60.3188 q^{29} +(-61.3553 + 106.271i) q^{31} +(47.6335 - 82.5037i) q^{32} +13.6152 q^{34} +(28.0589 + 48.5994i) q^{37} +(-78.3259 + 135.664i) q^{38} +(-244.329 - 423.191i) q^{40} -299.713 q^{41} -501.421 q^{43} +(-25.9949 - 45.0246i) q^{44} +(30.8995 - 53.5195i) q^{46} +(-152.777 - 264.617i) q^{47} -654.227 q^{50} +(-94.8492 + 164.284i) q^{52} +(-187.558 + 324.861i) q^{53} -476.416 q^{55} +(-72.8112 - 126.113i) q^{58} +(313.806 - 543.528i) q^{59} +(1.87868 + 3.25397i) q^{61} -296.250 q^{62} +565.288 q^{64} +(869.164 + 1505.44i) q^{65} +(406.524 - 704.120i) q^{67} +(-6.12341 - 10.6061i) q^{68} -165.902 q^{71} +(309.550 - 536.156i) q^{73} +(-67.7401 + 117.329i) q^{74} +140.908 q^{76} +(69.1228 + 119.724i) q^{79} +(417.011 - 722.284i) q^{80} +(-361.785 - 626.631i) q^{82} +621.137 q^{83} -112.225 q^{85} +(-605.269 - 1048.36i) q^{86} +(293.953 - 509.142i) q^{88} +(-142.709 - 247.180i) q^{89} -55.5879 q^{92} +(368.836 - 638.842i) q^{94} +(645.612 - 1118.23i) q^{95} +603.114 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.20711	+	2.09077i	0.426777	+	0.739199i	0.996585	−	0.0825791i	$-0.0263157\pi$
$2$	1.20711	+	2.09077i	0.426777	+	0.739199i	−0.569808	+	0.821778i	$0.692982\pi$
$3$		0			0
$3$		0			0
$4$	1.08579	−	1.88064i	0.135723	−	0.235080i
$5$	−9.94975	−	17.2335i	−0.889932	−	1.54141i	−0.839954	−	0.542658i	$-0.817418\pi$
$5$	−9.94975	−	17.2335i	−0.889932	−	1.54141i	−0.0499787	−	0.998750i	$-0.515915\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	24.5563			1.08525
$9$		0			0
$10$	24.0208	−	41.6053i	0.759605	−	1.31567i
$11$	11.9706	−	20.7336i	0.328115	−	0.568311i	−0.654023	−	0.756475i	$-0.726920\pi$
$11$	11.9706	−	20.7336i	0.328115	−	0.568311i	0.982138	+	0.188163i	$0.0602535\pi$
$12$		0			0
$13$	−87.3553			−1.86369			−0.931847	−	0.362852i	$-0.881803\pi$
$13$	−87.3553			−1.86369			−0.931847	+	0.362852i	$0.881803\pi$
$14$		0			0
$15$		0			0
$16$	20.9558	+	36.2966i	0.327435	+	0.567134i
$17$	2.81981	−	4.88405i	0.0402296	−	0.0696797i	−0.845210	−	0.534435i	$-0.820524\pi$
$17$	2.81981	−	4.88405i	0.0402296	−	0.0696797i	0.885439	+	0.464755i	$0.153858\pi$
$18$		0			0
$19$	32.4437	+	56.1941i	0.391741	+	0.678516i	0.992679	−	0.120780i	$-0.0385395\pi$
$19$	32.4437	+	56.1941i	0.391741	+	0.678516i	−0.600938	+	0.799296i	$0.705206\pi$
$20$	−43.2132			−0.483138
$21$		0			0
$22$	57.7990			0.560127
$23$	−12.7990	−	22.1685i	−0.116034	−	0.200976i	0.802159	−	0.597111i	$-0.203685\pi$
$23$	−12.7990	−	22.1685i	−0.116034	−	0.200976i	−0.918192	+	0.396135i	$0.870351\pi$
$24$		0			0
$25$	−135.495	+	234.684i	−1.08396	+	1.87747i
$26$	−105.447	−	182.640i	−0.795381	−	1.37764i
$27$		0			0
$28$		0			0
$29$	−60.3188			−0.386238			−0.193119	−	0.981175i	$-0.561860\pi$
$29$	−60.3188			−0.386238			−0.193119	+	0.981175i	$0.561860\pi$
$30$		0			0
$31$	−61.3553	+	106.271i	−0.355476	+	0.615702i	−0.987199	−	0.159492i	$-0.949014\pi$
$31$	−61.3553	+	106.271i	−0.355476	+	0.615702i	0.631724	+	0.775194i	$0.282348\pi$
$32$	47.6335	−	82.5037i	0.263140	−	0.455773i
$33$		0			0
$34$	13.6152			0.0686762
$35$		0			0
$36$		0			0
$37$	28.0589	+	48.5994i	0.124672	+	0.215938i	0.921605	−	0.388130i	$-0.126879\pi$
$37$	28.0589	+	48.5994i	0.124672	+	0.215938i	−0.796933	+	0.604068i	$0.793546\pi$
$38$	−78.3259	+	135.664i	−0.334372	+	0.579149i
$39$		0			0
$40$	−244.329	−	423.191i	−0.965797	−	1.67281i
$41$	−299.713			−1.14164			−0.570820	−	0.821075i	$-0.693375\pi$
$41$	−299.713			−1.14164			−0.570820	+	0.821075i	$0.693375\pi$
$42$		0			0
$43$	−501.421			−1.77828			−0.889140	−	0.457635i	$-0.848697\pi$
$43$	−501.421			−1.77828			−0.889140	+	0.457635i	$0.848697\pi$
$44$	−25.9949	−	45.0246i	−0.0890656	−	0.154266i
$45$		0			0
$46$	30.8995	−	53.5195i	0.0990409	−	0.171544i
$47$	−152.777	−	264.617i	−0.474144	−	0.821242i	0.525418	−	0.850844i	$-0.323909\pi$
$47$	−152.777	−	264.617i	−0.474144	−	0.821242i	−0.999562	+	0.0296028i	$0.990576\pi$
$48$		0			0
$49$		0			0
$50$	−654.227			−1.85043
$51$		0			0
$52$	−94.8492	+	164.284i	−0.252947	+	0.438116i
$53$	−187.558	+	324.861i	−0.486097	+	0.841944i	−0.999872	−	0.0159802i	$-0.994913\pi$
$53$	−187.558	+	324.861i	−0.486097	+	0.841944i	0.513775	+	0.857925i	$0.328246\pi$
$54$		0			0
$55$	−476.416			−1.16800
$56$		0			0
$57$		0			0
$58$	−72.8112	−	126.113i	−0.164838	−	0.285507i
$59$	313.806	−	543.528i	0.692442	−	1.19934i	−0.278593	−	0.960409i	$-0.589868\pi$
$59$	313.806	−	543.528i	0.692442	−	1.19934i	0.971035	−	0.238936i	$-0.0767985\pi$
$60$		0			0
$61$	1.87868	+	3.25397i	0.00394328	+	0.00682997i	0.867990	−	0.496581i	$-0.165411\pi$
$61$	1.87868	+	3.25397i	0.00394328	+	0.00682997i	−0.864047	+	0.503411i	$0.832078\pi$
$62$	−296.250			−0.606835
$63$		0			0
$64$	565.288			1.10408
$65$	869.164	+	1505.44i	1.65856	+	2.87271i
$66$		0			0
$67$	406.524	−	704.120i	0.741266	−	1.28391i	−0.210653	−	0.977561i	$-0.567559\pi$
$67$	406.524	−	704.120i	0.741266	−	1.28391i	0.951919	−	0.306349i	$-0.0991075\pi$
$68$	−6.12341	−	10.6061i	−0.0109202	−	0.0189143i
$69$		0			0
$70$		0			0
$71$	−165.902			−0.277310			−0.138655	−	0.990341i	$-0.544278\pi$
$71$	−165.902			−0.277310			−0.138655	+	0.990341i	$0.544278\pi$
$72$		0			0
$73$	309.550	−	536.156i	0.496302	−	0.859621i	−0.503689	−	0.863885i	$-0.668024\pi$
$73$	309.550	−	536.156i	0.496302	−	0.859621i	0.999991	+	0.00426452i	$0.00135744\pi$
$74$	−67.7401	+	117.329i	−0.106414	+	0.184314i
$75$		0			0
$76$	140.908			0.212674
$77$		0			0
$78$		0			0
$79$	69.1228	+	119.724i	0.0984421	+	0.170507i	0.911040	−	0.412318i	$-0.135281\pi$
$79$	69.1228	+	119.724i	0.0984421	+	0.170507i	−0.812598	+	0.582825i	$0.801947\pi$
$80$	417.011	−	722.284i	0.582790	−	1.00942i
$81$		0			0
$82$	−361.785	−	626.631i	−0.487226	−	0.843900i
$83$	621.137			0.821430			0.410715	−	0.911764i	$-0.365279\pi$
$83$	621.137			0.821430			0.410715	+	0.911764i	$0.365279\pi$
$84$		0			0
$85$	−112.225			−0.143207
$86$	−605.269	−	1048.36i	−0.758928	−	1.31450i
$87$		0			0
$88$	293.953	−	509.142i	0.356086	−	0.616758i
$89$	−142.709	−	247.180i	−0.169968	−	0.294393i	0.768440	−	0.639921i	$-0.221033\pi$
$89$	−142.709	−	247.180i	−0.169968	−	0.294393i	−0.938408	+	0.345528i	$0.887700\pi$
$90$		0			0
$91$		0			0
$92$	−55.5879			−0.0629939
$93$		0			0
$94$	368.836	−	638.842i	0.404707	−	0.700974i
$95$	645.612	−	1118.23i	0.697247	−	1.20767i
$96$		0			0
$97$	603.114			0.631309			0.315654	−	0.948874i	$-0.397776\pi$
$97$	603.114			0.631309			0.315654	+	0.948874i	$0.397776\pi$
$98$		0			0
$99$		0			0
$100$	294.237	+	509.634i	0.294237	+	0.509634i
$101$	−228.605	+	395.955i	−0.225218	+	0.390089i	−0.956385	−	0.292110i	$-0.905643\pi$
$101$	−228.605	+	395.955i	−0.225218	+	0.390089i	0.731167	+	0.682199i	$0.238976\pi$
$102$		0			0
$103$	393.022	+	680.735i	0.375977	+	0.651211i	0.990473	−	0.137709i	$-0.0439738\pi$
$103$	393.022	+	680.735i	0.375977	+	0.651211i	−0.614496	+	0.788920i	$0.710640\pi$
$104$	−2145.13			−2.02257
$105$		0			0
$106$	−905.612			−0.829819
$107$	−98.2304	−	170.140i	−0.0887504	−	0.153720i	0.818233	−	0.574887i	$-0.194954\pi$
$107$	−98.2304	−	170.140i	−0.0887504	−	0.153720i	−0.906983	+	0.421167i	$0.861621\pi$
$108$		0			0
$109$	153.172	−	265.301i	0.134598	−	0.233130i	−0.790846	−	0.612015i	$-0.790359\pi$
$109$	153.172	−	265.301i	0.134598	−	0.233130i	0.925444	+	0.378885i	$0.123692\pi$
$110$	−575.085	−	996.077i	−0.498475	−	0.863384i
$111$		0			0
$112$		0			0
$113$	−1997.63			−1.66302			−0.831508	−	0.555512i	$-0.812522\pi$
$113$	−1997.63			−1.66302			−0.831508	+	0.555512i	$0.812522\pi$
$114$		0			0
$115$	−254.693	+	441.142i	−0.206524	+	0.357710i
$116$	−65.4933	+	113.438i	−0.0524215	+	0.0907968i
$117$		0			0
$118$	1515.19			1.18207
$119$		0			0
$120$		0			0
$121$	378.911	+	656.294i	0.284682	+	0.493083i
$122$	−4.53553	+	7.85578i	−0.00336580	+	0.00582974i
$123$		0			0
$124$	133.238	+	230.774i	0.0964927	+	0.167130i
$125$	2905.13			2.07874
$126$		0			0
$127$	−2311.40			−1.61499			−0.807494	−	0.589875i	$-0.799177\pi$
$127$	−2311.40			−1.61499			−0.807494	+	0.589875i	$0.799177\pi$
$128$	301.295	+	521.859i	0.208055	+	0.360361i
$129$		0			0
$130$	−2098.35	+	3634.44i	−1.41567	+	2.45201i
$131$	77.5088	+	134.249i	0.0516945	+	0.0895374i	0.890715	−	0.454563i	$-0.150204\pi$
$131$	77.5088	+	134.249i	0.0516945	+	0.0895374i	−0.839020	+	0.544100i	$0.816871\pi$
$132$		0			0
$133$		0			0
$134$	1962.87			1.26542
$135$		0			0
$136$	69.2441	−	119.934i	0.0436591	−	0.0756197i
$137$	258.468	−	447.680i	0.161186	−	0.279181i	−0.774109	−	0.633053i	$-0.781802\pi$
$137$	258.468	−	447.680i	0.161186	−	0.279181i	0.935294	+	0.353871i	$0.115135\pi$
$138$		0			0
$139$	−958.067			−0.584620			−0.292310	−	0.956324i	$-0.594424\pi$
$139$	−958.067			−0.584620			−0.292310	+	0.956324i	$0.594424\pi$
$140$		0			0
$141$		0			0
$142$	−200.262	−	346.864i	−0.118349	−	0.204987i
$143$	−1045.69	+	1811.19i	−0.611505	+	1.05916i
$144$		0			0
$145$	600.156	+	1039.50i	0.343726	+	0.595351i
$146$	1494.64			0.847241
$147$		0			0
$148$	121.864			0.0676834
$149$	−885.313	−	1533.41i	−0.486763	−	0.843098i	0.513121	−	0.858316i	$-0.328489\pi$
$149$	−885.313	−	1533.41i	−0.486763	−	0.843098i	−0.999884	+	0.0152182i	$0.995156\pi$
$150$		0			0
$151$	1270.12	−	2199.91i	0.684508	−	1.18560i	−0.289083	−	0.957304i	$-0.593350\pi$
$151$	1270.12	−	2199.91i	0.684508	−	1.18560i	0.973591	−	0.228299i	$-0.0733163\pi$
$152$	796.698	+	1379.92i	0.425136	+	0.736358i
$153$		0			0
$154$		0			0
$155$	2441.88			1.26540
$156$		0			0
$157$	−541.672	+	938.203i	−0.275351	+	0.476922i	−0.970224	−	0.242211i	$-0.922127\pi$
$157$	−541.672	+	938.203i	−0.275351	+	0.476922i	0.694873	+	0.719133i	$0.255461\pi$
$158$	−166.877	+	289.040i	−0.0840256	+	0.145537i
$159$		0			0
$160$	−1895.77			−0.936709
$161$		0			0
$162$		0			0
$163$	−1484.36	−	2570.99i	−0.713277	−	1.23543i	−0.963620	−	0.267275i	$-0.913877\pi$
$163$	−1484.36	−	2570.99i	−0.713277	−	1.23543i	0.250343	−	0.968157i	$-0.419457\pi$
$164$	−325.424	+	563.651i	−0.154947	+	0.268377i
$165$		0			0
$166$	749.779	+	1298.65i	0.350567	+	0.607200i
$167$	−2091.53			−0.969149			−0.484574	−	0.874750i	$-0.661025\pi$
$167$	−2091.53			−0.969149			−0.484574	+	0.874750i	$0.661025\pi$
$168$		0			0
$169$	5433.96			2.47335
$170$	−135.468	−	234.638i	−0.0611172	−	0.105858i
$171$		0			0
$172$	−544.437	+	942.992i	−0.241354	+	0.418037i
$173$	235.074	+	407.160i	0.103308	+	0.178935i	0.913046	−	0.407857i	$-0.133724\pi$
$173$	235.074	+	407.160i	0.103308	+	0.178935i	−0.809738	+	0.586792i	$0.800391\pi$
$174$		0			0
$175$		0			0
$176$	1003.41			0.429745
$177$		0			0
$178$	344.530	−	596.744i	0.145077	−	0.251280i
$179$	528.230	−	914.922i	0.220569	−	0.382036i	−0.734412	−	0.678704i	$-0.762542\pi$
$179$	528.230	−	914.922i	0.220569	−	0.382036i	0.954981	+	0.296668i	$0.0958753\pi$
$180$		0			0
$181$	406.470			0.166921			0.0834605	−	0.996511i	$-0.473403\pi$
$181$	406.470			0.166921			0.0834605	+	0.996511i	$0.473403\pi$
$182$		0			0
$183$		0			0
$184$	−314.296	−	544.377i	−0.125925	−	0.218109i
$185$	558.357	−	967.103i	0.221899	−	0.384340i
$186$		0			0
$187$	−67.5093	−	116.930i	−0.0263998	−	0.0457259i
$188$	−663.531			−0.257410
$189$		0			0
$190$	3117.29			1.19027
$191$	89.7048	+	155.373i	0.0339833	+	0.0588608i	0.882517	−	0.470281i	$-0.155847\pi$
$191$	89.7048	+	155.373i	0.0339833	+	0.0588608i	−0.848534	+	0.529142i	$0.822514\pi$
$192$		0			0
$193$	1194.18	−	2068.39i	0.445385	−	0.771429i	−0.552694	−	0.833384i	$-0.686400\pi$
$193$	1194.18	−	2068.39i	0.445385	−	0.771429i	0.998079	+	0.0619551i	$0.0197336\pi$
$194$	728.023	+	1260.97i	0.269428	+	0.466663i
$195$		0			0
$196$		0			0
$197$	2665.35			0.963952			0.481976	−	0.876184i	$-0.339919\pi$
$197$	2665.35			0.963952			0.481976	+	0.876184i	$0.339919\pi$
$198$		0			0
$199$	−671.153	+	1162.47i	−0.239079	+	0.414098i	−0.960450	−	0.278451i	$-0.910179\pi$
$199$	−671.153	+	1162.47i	−0.239079	+	0.414098i	0.721371	+	0.692549i	$0.243512\pi$
$200$	−3327.26	+	5762.99i	−1.17636	+	2.03752i
$201$		0			0
$202$	−1103.80			−0.384471
$203$		0			0
$204$		0			0
$205$	2982.07	+	5165.09i	1.01598	+	1.75973i
$206$	−948.840	+	1643.44i	−0.320916	+	0.555844i
$207$		0			0
$208$	−1830.60	−	3170.70i	−0.610239	−	1.05696i
$209$	1553.48			0.514144
$210$		0			0
$211$	628.442			0.205042			0.102521	−	0.994731i	$-0.467309\pi$
$211$	628.442			0.205042			0.102521	+	0.994731i	$0.467309\pi$
$212$	407.297	+	705.459i	0.131949	+	0.228543i
$213$		0			0
$214$	237.149	−	410.755i	0.0757532	−	0.131208i
$215$	4989.02	+	8641.23i	1.58255	+	2.74106i
$216$		0			0
$217$		0			0
$218$	739.578			0.229773
$219$		0			0
$220$	−517.286	+	895.966i	−0.158525	+	0.274573i
$221$	−246.325	+	426.647i	−0.0749756	+	0.129862i
$222$		0			0
$223$	969.970			0.291273			0.145637	−	0.989338i	$-0.453477\pi$
$223$	969.970			0.291273			0.145637	+	0.989338i	$0.453477\pi$
$224$		0			0
$225$		0			0
$226$	−2411.35	−	4176.58i	−0.709737	−	1.22930i
$227$	2374.32	−	4112.44i	0.694225	−	1.20243i	−0.276216	−	0.961096i	$-0.589080\pi$
$227$	2374.32	−	4112.44i	0.694225	−	1.20243i	0.970441	−	0.241338i	$-0.0775862\pi$
$228$		0			0
$229$	−2401.00	−	4158.65i	−0.692848	−	1.20005i	−0.970901	−	0.239482i	$-0.923022\pi$
$229$	−2401.00	−	4158.65i	−0.692848	−	1.20005i	0.278052	−	0.960566i	$-0.410311\pi$
$230$	−1229.77			−0.352559
$231$		0			0
$232$	−1481.21			−0.419164
$233$	−1577.64	−	2732.56i	−0.443583	−	0.768309i	0.554369	−	0.832271i	$-0.312960\pi$
$233$	−1577.64	−	2732.56i	−0.443583	−	0.768309i	−0.997952	+	0.0639623i	$0.979626\pi$
$234$		0			0
$235$	−3040.18	+	5265.74i	−0.843912	+	1.46170i
$236$	−681.453	−	1180.31i	−0.187961	−	0.325558i
$237$		0			0
$238$		0			0
$239$	−4241.93			−1.14806			−0.574032	−	0.818833i	$-0.694622\pi$
$239$	−4241.93			−1.14806			−0.574032	+	0.818833i	$0.694622\pi$
$240$		0			0
$241$	−2171.49	+	3761.14i	−0.580407	+	1.00530i	0.415024	+	0.909811i	$0.363773\pi$
$241$	−2171.49	+	3761.14i	−0.580407	+	1.00530i	−0.995431	+	0.0954844i	$0.969560\pi$
$242$	−914.773	+	1584.43i	−0.242991	+	0.420873i
$243$		0			0
$244$	8.15938			0.00214078
$245$		0			0
$246$		0			0
$247$	−2834.13	−	4908.85i	−0.730086	−	1.26455i
$248$	−1506.66	+	2609.62i	−0.385779	+	0.668189i
$249$		0			0
$250$	3506.80	+	6073.95i	0.887157	+	1.53660i
$251$	3003.01			0.755172			0.377586	−	0.925974i	$-0.376754\pi$
$251$	3003.01			0.755172			0.377586	+	0.925974i	$0.376754\pi$
$252$		0			0
$253$	−612.844			−0.152289
$254$	−2790.11	−	4832.61i	−0.689239	−	1.19380i
$255$		0			0
$256$	1533.76	−	2656.55i	0.374454	−	0.648573i
$257$	−2234.42	−	3870.13i	−0.542332	−	0.939347i	−0.998770	−	0.0495916i	$-0.984208\pi$
$257$	−2234.42	−	3870.13i	−0.542332	−	0.939347i	0.456437	−	0.889756i	$-0.349125\pi$
$258$		0			0
$259$		0			0
$260$	3774.90			0.900422
$261$		0			0
$262$	−187.123	+	324.106i	−0.0441240	+	0.0764250i
$263$	3080.07	−	5334.83i	0.722148	−	1.25080i	−0.237989	−	0.971268i	$-0.576488\pi$
$263$	3080.07	−	5334.83i	0.722148	−	1.25080i	0.960137	−	0.279530i	$-0.0901786\pi$
$264$		0			0
$265$	7464.64			1.73037
$266$		0			0
$267$		0			0
$268$	−882.796	−	1529.05i	−0.201214	−	0.348513i
$269$	−2494.45	+	4320.52i	−0.565388	+	0.979281i	0.431625	+	0.902053i	$0.357940\pi$
$269$	−2494.45	+	4320.52i	−0.565388	+	0.979281i	−0.997013	+	0.0772281i	$0.975393\pi$
$270$		0			0
$271$	2216.86	+	3839.72i	0.496918	+	0.860688i	0.999994	−	0.00355459i	$-0.00113146\pi$
$271$	2216.86	+	3839.72i	0.496918	+	0.860688i	−0.503075	+	0.864243i	$0.667798\pi$
$272$	236.366			0.0526903
$273$		0			0
$274$	1247.99			0.275161
$275$	3243.90	+	5618.60i	0.711326	+	1.23205i
$276$		0			0
$277$	−556.184	+	963.339i	−0.120642	+	0.208958i	−0.920021	−	0.391869i	$-0.871829\pi$
$277$	−556.184	+	963.339i	−0.120642	+	0.208958i	0.799379	+	0.600827i	$0.205162\pi$
$278$	−1156.49	−	2003.10i	−0.249502	−	0.432151i
$279$		0			0
$280$		0			0
$281$	−2813.22			−0.597233			−0.298616	−	0.954373i	$-0.596525\pi$
$281$	−2813.22			−0.597233			−0.298616	+	0.954373i	$0.596525\pi$
$282$		0			0
$283$	1573.77	−	2725.85i	0.330569	−	0.572562i	−0.652055	−	0.758172i	$-0.726093\pi$
$283$	1573.77	−	2725.85i	0.330569	−	0.572562i	0.982623	+	0.185610i	$0.0594262\pi$
$284$	−180.135	+	312.002i	−0.0376374	+	0.0651899i
$285$		0			0
$286$	−5049.05			−1.04390
$287$		0			0
$288$		0			0
$289$	2440.60	+	4227.24i	0.496763	+	0.860419i
$290$	−1448.91	+	2509.58i	−0.293389	+	0.508164i
$291$		0			0
$292$	−672.210	−	1164.30i	−0.134720	−	0.233341i
$293$	9143.04			1.82301			0.911505	−	0.411289i	$-0.134921\pi$
$293$	9143.04			1.82301			0.911505	+	0.411289i	$0.134921\pi$
$294$		0			0
$295$	−12489.2			−2.46491
$296$	689.024	+	1193.42i	0.135300	+	0.234346i
$297$		0			0
$298$	2137.33	−	3701.97i	0.415478	−	0.719629i
$299$	1118.06	+	1936.54i	0.216251	+	0.374558i
$300$		0			0
$301$		0			0
$302$	6132.67			1.16853
$303$		0			0
$304$	−1359.77	+	2355.19i	−0.256540	+	0.444340i
$305$	37.3848	−	64.7523i	0.00701851	−	0.0121564i
$306$		0			0
$307$	4648.90			0.864257			0.432129	−	0.901812i	$-0.357763\pi$
$307$	4648.90			0.864257			0.432129	+	0.901812i	$0.357763\pi$
$308$		0			0
$309$		0			0
$310$	2947.61	+	5105.41i	0.540042	+	0.935380i
$311$	3208.59	−	5557.44i	0.585024	−	1.01329i	−0.409849	−	0.912154i	$-0.634418\pi$
$311$	3208.59	−	5557.44i	0.585024	−	1.01329i	0.994872	−	0.101138i	$-0.0322482\pi$
$312$		0			0
$313$	2934.11	+	5082.02i	0.529858	+	0.917741i	0.999393	+	0.0348275i	$0.0110882\pi$
$313$	2934.11	+	5082.02i	0.529858	+	0.917741i	−0.469535	+	0.882914i	$0.655578\pi$
$314$	−2615.42			−0.470054
$315$		0			0
$316$	300.210			0.0534435
$317$	−1987.26	−	3442.04i	−0.352100	−	0.609855i	0.634517	−	0.772909i	$-0.281199\pi$
$317$	−1987.26	−	3442.04i	−0.352100	−	0.609855i	−0.986617	+	0.163054i	$0.947866\pi$
$318$		0			0
$319$	−722.049	+	1250.63i	−0.126730	+	0.219504i
$320$	−5624.48	−	9741.88i	−0.982556	−	1.70184i
$321$		0			0
$322$		0			0
$323$	365.939			0.0630384
$324$		0			0
$325$	11836.2	−	20500.9i	2.02017	−	3.49903i
$326$	3583.57	−	6206.92i	0.608820	−	1.05451i
$327$		0			0
$328$	−7359.85			−1.23896
$329$		0			0
$330$		0			0
$331$	4456.41	+	7718.73i	0.740020	+	1.28175i	0.952486	+	0.304583i	$0.0985172\pi$
$331$	4456.41	+	7718.73i	0.740020	+	1.28175i	−0.212466	+	0.977168i	$0.568149\pi$
$332$	674.422	−	1168.13i	0.111487	−	0.193101i
$333$		0			0
$334$	−2524.71	−	4372.92i	−0.413610	−	0.716394i
$335$	−16179.2			−2.63871
$336$		0			0
$337$	3977.06			0.642862			0.321431	−	0.946933i	$-0.395836\pi$
$337$	3977.06			0.642862			0.321431	+	0.946933i	$0.395836\pi$
$338$	6559.36	+	11361.2i	1.05557	+	1.82830i
$339$		0			0
$340$	−121.853	+	211.055i	−0.0194365	+	0.0336649i
$341$	1468.92	+	2544.24i	0.233273	+	0.404042i
$342$		0			0
$343$		0			0
$344$	−12313.1			−1.92987
$345$		0			0
$346$	−567.518	+	982.971i	−0.0881791	+	0.152731i
$347$	3413.21	−	5911.86i	0.528043	−	0.914597i	−0.471423	−	0.881907i	$-0.656259\pi$
$347$	3413.21	−	5911.86i	0.528043	−	0.914597i	0.999466	−	0.0326898i	$-0.0104073\pi$
$348$		0			0
$349$	807.342			0.123828			0.0619141	−	0.998081i	$-0.480280\pi$
$349$	807.342			0.123828			0.0619141	+	0.998081i	$0.480280\pi$
$350$		0			0
$351$		0			0
$352$	−1140.40	−	1975.23i	−0.172680	−	0.299091i
$353$	3959.60	−	6858.23i	0.597020	−	1.03407i	−0.396238	−	0.918148i	$-0.629684\pi$
$353$	3959.60	−	6858.23i	0.597020	−	1.03407i	0.993258	−	0.115922i	$-0.0369822\pi$
$354$		0			0
$355$	1650.69	+	2859.07i	0.246787	+	0.427448i
$356$	−619.807			−0.0922744
$357$		0			0
$358$	2550.52			0.376534
$359$	−4409.61	−	7637.66i	−0.648273	−	1.12284i	−0.983535	−	0.180717i	$-0.942158\pi$
$359$	−4409.61	−	7637.66i	−0.648273	−	1.12284i	0.335262	−	0.942125i	$-0.391175\pi$
$360$		0			0
$361$	1324.32	−	2293.79i	0.193078	−	0.334420i
$362$	490.653	+	849.836i	0.0712380	+	0.123388i
$363$		0			0
$364$		0			0
$365$	−12319.8			−1.76670
$366$		0			0
$367$	−5580.89	+	9666.39i	−0.793788	+	1.37488i	0.129817	+	0.991538i	$0.458561\pi$
$367$	−5580.89	+	9666.39i	−0.793788	+	1.37488i	−0.923606	+	0.383344i	$0.874772\pi$
$368$	536.427	−	929.119i	0.0759870	−	0.131613i
$369$		0			0
$370$	2695.99			0.378805
$371$		0			0
$372$		0			0
$373$	−1363.93	−	2362.39i	−0.189334	−	0.327936i	0.755694	−	0.654924i	$-0.227300\pi$
$373$	−1363.93	−	2362.39i	−0.189334	−	0.327936i	−0.945028	+	0.326988i	$0.893966\pi$
$374$	162.982	−	282.293i	0.0225337	−	0.0390295i
$375$		0			0
$376$	−3751.64	−	6498.03i	−0.514564	−	0.891250i
$377$	5269.17			0.719830
$378$		0			0
$379$	4086.49			0.553849			0.276924	−	0.960892i	$-0.410685\pi$
$379$	4086.49			0.553849			0.276924	+	0.960892i	$0.410685\pi$
$380$	−1401.99	−	2428.32i	−0.189265	−	0.327817i
$381$		0			0
$382$	−216.566	+	375.104i	−0.0290066	+	0.0502408i
$383$	−6516.47	−	11286.9i	−0.869389	−	1.50583i	−0.862622	−	0.505848i	$-0.831180\pi$
$383$	−6516.47	−	11286.9i	−0.869389	−	1.50583i	−0.00676631	−	0.999977i	$-0.502154\pi$
$384$		0			0
$385$		0			0
$386$	5766.03			0.760319
$387$		0			0
$388$	654.853	−	1134.24i	0.0856833	−	0.148408i
$389$	−97.4957	+	168.868i	−0.0127075	+	0.0220101i	−0.872309	−	0.488955i	$-0.837378\pi$
$389$	−97.4957	+	168.868i	−0.0127075	+	0.0220101i	0.859602	+	0.510965i	$0.170712\pi$
$390$		0			0
$391$	−144.363			−0.0186719
$392$		0			0
$393$		0			0
$394$	3217.37	+	5572.64i	0.411392	+	0.712553i
$395$	1375.51	−	2382.45i	0.175214	−	0.303479i
$396$		0			0
$397$	−7091.48	−	12282.8i	−0.896501	−	1.55279i	−0.831936	−	0.554872i	$-0.812767\pi$
$397$	−7091.48	−	12282.8i	−0.896501	−	1.55279i	−0.0645653	−	0.997913i	$-0.520566\pi$
$398$	−3240.61			−0.408134
$399$		0			0
$400$	−11357.6			−1.41971
$401$	5002.52	+	8664.63i	0.622978	+	1.07903i	0.988928	+	0.148395i	$0.0474107\pi$
$401$	5002.52	+	8664.63i	0.622978	+	1.07903i	−0.365950	+	0.930634i	$0.619256\pi$
$402$		0			0
$403$	5359.72	−	9283.30i	0.662498	−	1.14748i
$404$	496.431	+	859.844i	0.0611346	+	0.105888i
$405$		0			0
$406$		0			0
$407$	1343.52			0.163626
$408$		0			0
$409$	2317.47	−	4013.97i	0.280174	−	0.485276i	−0.691253	−	0.722613i	$-0.742941\pi$
$409$	2317.47	−	4013.97i	0.280174	−	0.485276i	0.971428	+	0.237336i	$0.0762744\pi$
$410$	−7199.35	+	12469.6i	−0.867196	+	1.50203i
$411$		0			0
$412$	1706.95			0.204115
$413$		0			0
$414$		0			0
$415$	−6180.16	−	10704.3i	−0.731017	−	1.26616i
$416$	−4161.04	+	7207.14i	−0.490413	+	0.849420i
$417$		0			0
$418$	1875.21	+	3247.96i	0.219425	+	0.380055i
$419$	4998.31			0.582777			0.291388	−	0.956605i	$-0.405883\pi$
$419$	4998.31			0.582777			0.291388	+	0.956605i	$0.405883\pi$
$420$		0			0
$421$	−704.160			−0.0815170			−0.0407585	−	0.999169i	$-0.512977\pi$
$421$	−704.160			−0.0815170			−0.0407585	+	0.999169i	$0.512977\pi$
$422$	758.597	+	1313.93i	0.0875069	+	0.151566i
$423$		0			0
$424$	−4605.75	+	7977.39i	−0.527535	+	0.913718i
$425$	764.139	+	1323.53i	0.0872145	+	0.151060i
$426$		0			0
$427$		0			0
$428$	−426.629			−0.0481820
$429$		0			0
$430$	−12044.5	+	20861.8i	−1.35079	+	2.33964i
$431$	−5166.39	+	8948.45i	−0.577393	+	1.00007i	0.418384	+	0.908270i	$0.362597\pi$
$431$	−5166.39	+	8948.45i	−0.577393	+	1.00007i	−0.995777	+	0.0918037i	$0.970737\pi$
$432$		0			0
$433$	−11106.8			−1.23270			−0.616348	−	0.787474i	$-0.711389\pi$
$433$	−11106.8			−1.23270			−0.616348	+	0.787474i	$0.711389\pi$
$434$		0			0
$435$		0			0
$436$	−332.623	−	576.120i	−0.0365362	−	0.0632825i
$437$	830.492	−	1438.45i	0.0909103	−	0.157461i
$438$		0			0
$439$	−3649.64	−	6321.36i	−0.396783	−	0.687249i	0.596544	−	0.802581i	$-0.296540\pi$
$439$	−3649.64	−	6321.36i	−0.396783	−	0.687249i	−0.993327	+	0.115332i	$0.963207\pi$
$440$	−11699.0			−1.26757
$441$		0			0
$442$	−1189.36			−0.127991
$443$	8044.83	+	13934.1i	0.862802	+	1.49442i	0.869213	+	0.494438i	$0.164626\pi$
$443$	8044.83	+	13934.1i	0.862802	+	1.49442i	−0.00641088	+	0.999979i	$0.502041\pi$
$444$		0			0
$445$	−2839.84	+	4918.75i	−0.302520	+	0.523980i
$446$	1170.86	+	2027.98i	0.124309	+	0.215309i
$447$		0			0
$448$		0			0
$449$	−13561.7			−1.42543			−0.712715	−	0.701454i	$-0.752534\pi$
$449$	−13561.7			−1.42543			−0.712715	+	0.701454i	$0.752534\pi$
$450$		0			0
$451$	−3587.73	+	6214.13i	−0.374589	+	0.648807i
$452$	−2169.00	+	3756.81i	−0.225710	+	0.390941i
$453$		0			0
$454$	11464.2			1.18512
$455$		0			0
$456$		0			0
$457$	−5424.28	−	9395.14i	−0.555224	−	0.961676i	−0.997886	−	0.0649876i	$-0.979299\pi$
$457$	−5424.28	−	9395.14i	−0.555224	−	0.961676i	0.442662	−	0.896688i	$-0.354034\pi$
$458$	5796.52	−	10039.9i	0.591383	−	1.02431i
$459$		0			0
$460$	553.085	+	957.972i	0.0560603	+	0.0970993i
$461$	−1758.69			−0.177679			−0.0888397	−	0.996046i	$-0.528316\pi$
$461$	−1758.69			−0.177679			−0.0888397	+	0.996046i	$0.528316\pi$
$462$		0			0
$463$	−5411.95			−0.543228			−0.271614	−	0.962406i	$-0.587557\pi$
$463$	−5411.95			−0.543228			−0.271614	+	0.962406i	$0.587557\pi$
$464$	−1264.03	−	2189.37i	−0.126468	−	0.219049i
$465$		0			0
$466$	3808.77	−	6596.98i	0.378622	−	0.655792i
$467$	−4055.67	−	7024.63i	−0.401872	−	0.696062i	0.592080	−	0.805879i	$-0.298307\pi$
$467$	−4055.67	−	7024.63i	−0.401872	−	0.696062i	−0.993952	+	0.109817i	$0.964974\pi$
$468$		0			0
$469$		0			0
$470$	−14679.3			−1.44065
$471$		0			0
$472$	7705.93	−	13347.1i	0.751471	−	1.30159i
$473$	−6002.30	+	10396.3i	−0.583480	+	1.01062i
$474$		0			0
$475$	−17583.8			−1.69853
$476$		0			0
$477$		0			0
$478$	−5120.46	−	8868.90i	−0.489967	−	0.848648i
$479$	−1047.88	+	1814.98i	−0.0999559	+	0.173129i	−0.911666	−	0.410932i	$-0.865203\pi$
$479$	−1047.88	+	1814.98i	−0.0999559	+	0.173129i	0.811710	+	0.584060i	$0.198537\pi$
$480$		0			0
$481$	−2451.09	−	4245.42i	−0.232350	−	0.402441i
$482$	−10484.9			−0.990817
$483$		0			0
$484$	1645.67			0.154552
$485$	−6000.83	−	10393.7i	−0.561822	−	0.973104i
$486$		0			0
$487$	−4805.04	+	8322.57i	−0.447099	+	0.774398i	−0.998196	−	0.0600435i	$-0.980876\pi$
$487$	−4805.04	+	8322.57i	−0.447099	+	0.774398i	0.551097	+	0.834441i	$0.314209\pi$
$488$	46.1335	+	79.9056i	0.00427944	+	0.00741221i
$489$		0			0
$490$		0			0
$491$	11717.3			1.07698			0.538488	−	0.842633i	$-0.318996\pi$
$491$	11717.3			1.07698			0.538488	+	0.842633i	$0.318996\pi$
$492$		0			0
$493$	−170.087	+	294.600i	−0.0155382	+	0.0269130i
$494$	6842.19	−	11851.0i	0.623167	−	1.07936i
$495$		0			0
$496$	−5143.01			−0.465581
$497$		0			0
$498$		0			0
$499$	4597.59	+	7963.26i	0.412458	+	0.714398i	0.995158	−	0.0982893i	$-0.0313370\pi$
$499$	4597.59	+	7963.26i	0.412458	+	0.714398i	−0.582700	+	0.812687i	$0.698004\pi$
$500$	3154.35	−	5463.49i	0.282133	−	0.488669i
$501$		0			0
$502$	3624.95	+	6278.60i	0.322290	+	0.558222i
$503$	16118.8			1.42883			0.714414	−	0.699724i	$-0.246693\pi$
$503$	16118.8			1.42883			0.714414	+	0.699724i	$0.246693\pi$
$504$		0			0
$505$	9098.23			0.801715
$506$	−739.769	−	1281.32i	−0.0649935	−	0.112572i
$507$		0			0
$508$	−2509.69	+	4346.90i	−0.219192	+	0.379651i
$509$	−2459.39	−	4259.79i	−0.214166	−	0.370947i	0.738848	−	0.673872i	$-0.235370\pi$
$509$	−2459.39	−	4259.79i	−0.214166	−	0.370947i	−0.953014	+	0.302925i	$0.902037\pi$
$510$		0			0
$511$		0			0
$512$	12226.4			1.05534
$513$		0			0
$514$	5394.37	−	9343.33i	0.462910	−	0.801783i
$515$	7820.95	−	13546.3i	0.669188	−	1.15907i
$516$		0			0
$517$	−7315.29			−0.622294
$518$		0			0
$519$		0			0
$520$	21343.5	+	36968.0i	1.79995	+	3.11760i
$521$	−6981.69	+	12092.6i	−0.587089	+	1.01687i	0.407522	+	0.913195i	$0.366393\pi$
$521$	−6981.69	+	12092.6i	−0.587089	+	1.01687i	−0.994611	+	0.103673i	$0.966940\pi$
$522$		0			0
$523$	−6877.63	−	11912.4i	−0.575024	−	0.995972i	−0.996039	−	0.0889177i	$-0.971659\pi$
$523$	−6877.63	−	11912.4i	−0.575024	−	0.995972i	0.421015	−	0.907054i	$-0.361674\pi$
$524$	336.632			0.0280646
$525$		0			0
$526$	14871.9			1.23278
$527$	346.020	+	599.325i	0.0286013	+	0.0495389i
$528$		0			0
$529$	5755.87	−	9969.46i	0.473072	−	0.819385i
$530$	9010.61	+	15606.8i	0.738483	+	1.27909i
$531$		0			0
$532$		0			0
$533$	26181.5			2.12767
$534$		0			0
$535$	−1954.74	+	3385.70i	−0.157964	+	0.273601i
$536$	9982.74	−	17290.6i	0.804457	−	1.39336i
$537$		0			0
$538$	−12044.3			−0.965178
$539$		0			0
$540$		0			0
$541$	−7231.34	−	12525.1i	−0.574676	−	0.995368i	−0.996077	−	0.0884937i	$-0.971795\pi$
$541$	−7231.34	−	12525.1i	−0.574676	−	0.995368i	0.421401	−	0.906875i	$-0.361539\pi$
$542$	−5351.98	+	9269.91i	−0.424146	+	0.734643i
$543$		0			0
$544$	−268.634	−	465.289i	−0.0211721	−	0.0366711i
$545$	−6096.07			−0.479132
$546$		0			0
$547$	13682.5			1.06951			0.534755	−	0.845007i	$-0.320404\pi$
$547$	13682.5			1.06951			0.534755	+	0.845007i	$0.320404\pi$
$548$	−561.282	−	972.169i	−0.0437533	−	0.0757829i
$549$		0			0
$550$	−7831.47	+	13564.5i	−0.607155	+	1.05162i
$551$	−1956.96	−	3389.56i	−0.151306	−	0.262069i
$552$		0			0
$553$		0			0
$554$	−2685.49			−0.205949
$555$		0			0
$556$	−1040.26	+	1801.78i	−0.0793466	+	0.137432i
$557$	−3831.56	+	6636.46i	−0.291470	+	0.504840i	−0.974157	−	0.225870i	$-0.927478\pi$
$557$	−3831.56	+	6636.46i	−0.291470	+	0.504840i	0.682688	+	0.730710i	$0.260811\pi$
$558$		0			0
$559$	43801.8			3.31417
$560$		0			0
$561$		0			0
$562$	−3395.85	−	5881.79i	−0.254885	−	0.441474i
$563$	−8735.24	+	15129.9i	−0.653902	+	1.13259i	0.328266	+	0.944585i	$0.393536\pi$
$563$	−8735.24	+	15129.9i	−0.653902	+	1.13259i	−0.982168	+	0.188006i	$0.939798\pi$
$564$		0			0
$565$	19875.9	+	34426.0i	1.47997	+	2.56339i
$566$	7598.83			0.564316
$567$		0			0
$568$	−4073.96			−0.300950
$569$	−6936.96	−	12015.2i	−0.511094	−	0.885240i	−0.999917	−	0.0128577i	$-0.995907\pi$
$569$	−6936.96	−	12015.2i	−0.511094	−	0.885240i	0.488824	−	0.872383i	$-0.337426\pi$
$570$		0			0
$571$	1888.76	−	3271.43i	0.138428	−	0.239764i	−0.788474	−	0.615068i	$-0.789129\pi$
$571$	1888.76	−	3271.43i	0.138428	−	0.239764i	0.926902	+	0.375305i	$0.122462\pi$
$572$	2270.80	+	3933.14i	0.165991	+	0.287505i
$573$		0			0
$574$		0			0
$575$	6936.79			0.503103
$576$		0			0
$577$	6940.23	−	12020.8i	0.500738	−	0.867303i	−0.499262	−	0.866451i	$-0.666395\pi$
$577$	6940.23	−	12020.8i	0.500738	−	0.867303i	1.00000		0.000852075i	$-0.000271224\pi$
$578$	−5892.12	+	10205.5i	−0.424014	+	0.734414i
$579$		0			0
$580$	2606.57			0.186607
$581$		0			0
$582$		0			0
$583$	4490.36	+	7777.53i	0.318991	+	0.552509i
$584$	7601.41	−	13166.0i	0.538611	−	0.932901i
$585$		0			0
$586$	11036.6	+	19116.0i	0.778018	+	1.34757i
$587$	−2395.61			−0.168445			−0.0842227	−	0.996447i	$-0.526841\pi$
$587$	−2395.61			−0.168445			−0.0842227	+	0.996447i	$0.526841\pi$
$588$		0			0
$589$	−7962.36			−0.557018
$590$	−15075.8	−	26112.0i	−1.05196	−	1.82206i
$591$		0			0
$592$	−1175.99	+	2036.88i	−0.0816437	+	0.141411i
$593$	−3301.75	−	5718.80i	−0.228645	−	0.396025i	0.728762	−	0.684767i	$-0.240096\pi$
$593$	−3301.75	−	5718.80i	−0.228645	−	0.396025i	−0.957407	+	0.288742i	$0.906763\pi$
$594$		0			0
$595$		0			0
$596$	−3845.04			−0.264260
$597$		0			0
$598$	−2699.24	+	4675.21i	−0.184582	+	0.319705i
$599$	8626.05	−	14940.8i	0.588399	−	1.01914i	−0.406044	−	0.913854i	$-0.633092\pi$
$599$	8626.05	−	14940.8i	0.588399	−	1.01914i	0.994442	−	0.105283i	$-0.0335747\pi$
$600$		0			0
$601$	−12833.1			−0.871005			−0.435503	−	0.900187i	$-0.643429\pi$
$601$	−12833.1			−0.871005			−0.435503	+	0.900187i	$0.643429\pi$
$602$		0			0
$603$		0			0
$604$	−2758.15	−	4777.26i	−0.185807	−	0.321828i
$605$	7540.14	−	13059.9i	0.506695	−	0.877621i
$606$		0			0
$607$	4310.08	+	7465.28i	0.288206	+	0.499187i	0.973381	−	0.229191i	$-0.0736080\pi$
$607$	4310.08	+	7465.28i	0.288206	+	0.499187i	−0.685176	+	0.728378i	$0.740275\pi$
$608$	6181.62			0.412332
$609$		0			0
$610$	180.510			0.0119813
$611$	13345.9	+	23115.7i	0.883659	+	1.53054i
$612$		0			0
$613$	−2568.37	+	4448.54i	−0.169226	+	0.293107i	−0.938148	−	0.346235i	$-0.887460\pi$
$613$	−2568.37	+	4448.54i	−0.169226	+	0.293107i	0.768922	+	0.639342i	$0.220793\pi$
$614$	5611.72	+	9719.79i	0.368845	+	0.638858i
$615$		0			0
$616$		0			0
$617$	1759.82			0.114826			0.0574131	−	0.998351i	$-0.481715\pi$
$617$	1759.82			0.114826			0.0574131	+	0.998351i	$0.481715\pi$
$618$		0			0
$619$	−1780.12	+	3083.26i	−0.115588	+	0.200205i	−0.918015	−	0.396546i	$-0.870209\pi$
$619$	−1780.12	+	3083.26i	−0.115588	+	0.200205i	0.802427	+	0.596751i	$0.203542\pi$
$620$	2651.36	−	4592.29i	0.171744	−	0.297469i
$621$		0			0
$622$	15492.4			0.998698
$623$		0			0
$624$		0			0
$625$	−11968.4	−	20729.9i	−0.765977	−	1.32671i
$626$	−7083.56	+	12269.1i	−0.452262	+	0.783341i
$627$		0			0
$628$	1176.28	+	2037.38i	0.0747431	+	0.129459i
$629$	316.482			0.0200620
$630$		0			0
$631$	−27321.4			−1.72369			−0.861845	−	0.507172i	$-0.830691\pi$
$631$	−27321.4			−1.72369			−0.861845	+	0.507172i	$0.830691\pi$
$632$	1697.40	+	2939.99i	0.106834	+	0.185042i
$633$		0			0
$634$	4797.67	−	8309.81i	0.300536	−	0.520544i
$635$	22997.8	+	39833.4i	1.43723	+	2.48936i
$636$		0			0
$637$		0			0
$638$	−3486.36			−0.216342
$639$		0			0
$640$	5995.63	−	10384.7i	0.370309	−	0.641395i
$641$	−10963.5	+	18989.4i	−0.675558	+	1.17010i	0.300748	+	0.953704i	$0.402764\pi$
$641$	−10963.5	+	18989.4i	−0.675558	+	1.17010i	−0.976306	+	0.216397i	$0.930570\pi$
$642$		0			0
$643$	5826.04			0.357320			0.178660	−	0.983911i	$-0.442824\pi$
$643$	5826.04			0.357320			0.178660	+	0.983911i	$0.442824\pi$
$644$		0			0
$645$		0			0
$646$	441.728	+	765.095i	0.0269033	+	0.0465979i
$647$	−12105.4	+	20967.1i	−0.735565	+	1.27404i	0.218910	+	0.975745i	$0.429750\pi$
$647$	−12105.4	+	20967.1i	−0.735565	+	1.27404i	−0.954475	+	0.298291i	$0.903583\pi$
$648$		0			0
$649$	−7512.87	−	13012.7i	−0.454401	−	0.787045i
$650$	57150.3			3.44864
$651$		0			0
$652$	−6446.80			−0.387233
$653$	−12811.7	−	22190.4i	−0.767778	−	1.32983i	−0.938765	−	0.344557i	$-0.888029\pi$
$653$	−12811.7	−	22190.4i	−0.767778	−	1.32983i	0.170988	−	0.985273i	$-0.445304\pi$
$654$		0			0
$655$	1542.39	−	2671.49i	0.0920092	−	0.159365i
$656$	−6280.73	−	10878.6i	−0.373813	−	0.647463i
$657$		0			0
$658$		0			0
$659$	23273.7			1.37574			0.687871	−	0.725833i	$-0.258545\pi$
$659$	23273.7			1.37574			0.687871	+	0.725833i	$0.258545\pi$
$660$		0			0
$661$	−10018.2	+	17352.1i	−0.589508	+	1.02106i	0.404789	+	0.914410i	$0.367345\pi$
$661$	−10018.2	+	17352.1i	−0.589508	+	1.02106i	−0.994297	+	0.106647i	$0.965988\pi$
$662$	−10758.7	+	18634.7i	−0.631646	+	1.09404i
$663$		0			0
$664$	15252.9			0.891454
$665$		0			0
$666$		0			0
$667$	772.019	+	1337.18i	0.0448166	+	0.0776247i
$668$	−2270.96	+	3933.42i	−0.131536	+	0.227827i
$669$		0			0
$670$	−19530.1	−	33827.1i	−1.12614	−	1.95053i
$671$	89.9554			0.00517540
$672$		0			0
$673$	−18127.8			−1.03830			−0.519149	−	0.854684i	$-0.673751\pi$
$673$	−18127.8			−1.03830			−0.519149	+	0.854684i	$0.673751\pi$
$674$	4800.74	+	8315.12i	0.274358	+	0.475203i
$675$		0			0
$676$	5900.11	−	10219.3i	0.335692	−	0.581435i
$677$	−6907.73	−	11964.5i	−0.392150	−	0.679224i	0.600583	−	0.799563i	$-0.294935\pi$
$677$	−6907.73	−	11964.5i	−0.392150	−	0.679224i	−0.992733	+	0.120339i	$0.961602\pi$
$678$		0			0
$679$		0			0
$680$	−2755.85			−0.155415
$681$		0			0
$682$	−3546.28	+	6142.33i	−0.199111	+	0.344871i
$683$	−2302.11	+	3987.38i	−0.128972	+	0.223386i	−0.923279	−	0.384131i	$-0.874501\pi$
$683$	−2302.11	+	3987.38i	−0.128972	+	0.223386i	0.794306	+	0.607517i	$0.207834\pi$
$684$		0			0
$685$	−10286.8			−0.573777
$686$		0			0
$687$		0			0
$688$	−10507.7	−	18199.9i	−0.582271	−	1.00852i
$689$	16384.2	−	28378.3i	0.905935	−	1.56913i
$690$		0			0
$691$	8956.83	+	15513.7i	0.493103	+	0.854079i	0.999968	−	0.00794632i	$-0.00252942\pi$
$691$	8956.83	+	15513.7i	0.493103	+	0.854079i	−0.506866	+	0.862025i	$0.669196\pi$
$692$	1020.96			0.0560854
$693$		0			0
$694$	16480.5			0.901426
$695$	9532.53	+	16510.8i	0.520272	+	0.901138i
$696$		0			0
$697$	−845.132	+	1463.81i	−0.0459278	+	0.0795492i
$698$	974.548	+	1687.97i	0.0528470	+	0.0915336i
$699$		0			0
$700$		0			0
$701$	−11303.7			−0.609035			−0.304518	−	0.952507i	$-0.598495\pi$
$701$	−11303.7			−0.609035			−0.304518	+	0.952507i	$0.598495\pi$
$702$		0			0
$703$	−1820.66	+	3153.48i	−0.0976780	+	0.169183i
$704$	6766.82	−	11720.5i	0.362264	−	0.627460i
$705$		0			0
$706$	19118.6			1.01918
$707$		0			0
$708$		0			0
$709$	8023.15	+	13896.5i	0.424987	+	0.736099i	0.996419	−	0.0845505i	$-0.0269454\pi$
$709$	8023.15	+	13896.5i	0.424987	+	0.736099i	−0.571432	+	0.820649i	$0.693612\pi$
$710$	−3985.11	+	6902.42i	−0.210646	+	0.364849i
$711$		0			0
$712$	−3504.42	−	6069.83i	−0.184457	−	0.319489i
$713$	3141.15			0.164989
$714$		0			0
$715$	41617.5			2.17679
$716$	−1147.09	−	1986.82i	−0.0598726	−	0.103702i
$717$		0			0
$718$	10645.7	−	18438.9i	0.553336	−	0.958406i
$719$	12595.2	+	21815.6i	0.653300	+	1.13155i	0.982317	+	0.187225i	$0.0599493\pi$
$719$	12595.2	+	21815.6i	0.653300	+	1.13155i	−0.329017	+	0.944324i	$0.606717\pi$
$720$		0			0
$721$		0			0
$722$	6394.38			0.329604
$723$		0			0
$724$	441.340	−	764.424i	0.0226551	−	0.0392397i
$725$	8172.89	−	14155.9i	0.418667	−	0.725152i
$726$		0			0
$727$	−11277.2			−0.575307			−0.287653	−	0.957735i	$-0.592875\pi$
$727$	−11277.2			−0.575307			−0.287653	+	0.957735i	$0.592875\pi$
$728$		0			0
$729$		0			0
$730$	−14871.3	−	25757.8i	−0.753987	−	1.30594i
$731$	−1413.91	+	2448.96i	−0.0715395	+	0.123910i
$732$		0			0
$733$	11860.0	+	20542.2i	0.597626	+	1.03512i	0.993171	+	0.116672i	$0.0372226\pi$
$733$	11860.0	+	20542.2i	0.597626	+	1.03512i	−0.395544	+	0.918447i	$0.629444\pi$
$734$	−26946.9			−1.35508
$735$		0			0
$736$	−2438.64			−0.122133
$737$	−9732.64	−	16857.4i	−0.486440	−	0.842539i
$738$		0			0
$739$	−4062.36	+	7036.21i	−0.202214	+	0.350245i	−0.949242	−	0.314548i	$-0.898147\pi$
$739$	−4062.36	+	7036.21i	−0.202214	+	0.350245i	0.747027	+	0.664793i	$0.231480\pi$
$740$	−1212.51	−	2100.14i	−0.0602336	−	0.104328i
$741$		0			0
$742$		0			0
$743$	−20955.3			−1.03469			−0.517346	−	0.855777i	$-0.673080\pi$
$743$	−20955.3			−1.03469			−0.517346	+	0.855777i	$0.673080\pi$
$744$		0			0
$745$	−17617.3	+	30514.0i	−0.866372	+	1.50060i
$746$	3292.81	−	5703.32i	0.161607	−	0.279911i
$747$		0			0
$748$	−293.203			−0.0143323
$749$		0			0
$750$		0			0
$751$	19104.0	+	33089.2i	0.928251	+	1.60778i	0.786247	+	0.617912i	$0.212021\pi$
$751$	19104.0	+	33089.2i	0.928251	+	1.60778i	0.142004	+	0.989866i	$0.454645\pi$
$752$	6403.13	−	11090.5i	0.310503	−	0.537807i
$753$		0			0
$754$	6360.45	+	11016.6i	0.307207	+	0.532097i
$755$	−50549.4			−2.43666
$756$		0			0
$757$	30958.1			1.48638			0.743191	−	0.669079i	$-0.233311\pi$
$757$	30958.1			1.48638			0.743191	+	0.669079i	$0.233311\pi$
$758$	4932.82	+	8543.90i	0.236370	+	0.409404i
$759$		0			0
$760$	15853.9	−	27459.7i	0.756685	−	1.31062i
$761$	20024.7	+	34683.8i	0.953871	+	1.65215i	0.736932	+	0.675967i	$0.236274\pi$
$761$	20024.7	+	34683.8i	0.953871	+	1.65215i	0.216939	+	0.976185i	$0.430393\pi$
$762$		0			0
$763$		0			0
$764$	389.601			0.0184493
$765$		0			0
$766$	15732.1	−	27248.9i	0.742070	−	1.28530i
$767$	−27412.6	+	47480.1i	−1.29050	+	2.23521i
$768$		0			0
$769$	8002.01			0.375240			0.187620	−	0.982242i	$-0.439923\pi$
$769$	8002.01			0.375240			0.187620	+	0.982242i	$0.439923\pi$
$770$		0			0
$771$		0			0
$772$	−2593.26	−	4491.65i	−0.120898	−	0.209402i
$773$	6966.68	−	12066.6i	0.324158	−	0.561458i	−0.657184	−	0.753730i	$-0.728252\pi$
$773$	6966.68	−	12066.6i	0.324158	−	0.561458i	0.981342	+	0.192273i	$0.0615858\pi$
$774$		0			0
$775$	−16626.7	−	28798.2i	−0.770642	−	1.33479i
$776$	14810.3			0.685126
$777$		0			0
$778$	−470.751			−0.0216931
$779$	−9723.78	−	16842.1i	−0.447228	−	0.774621i
$780$		0			0
$781$	−1985.95	+	3439.76i	−0.0909894	+	0.157598i
$782$	−174.261	−	301.829i	−0.00796875	−	0.0138023i
$783$		0			0
$784$		0			0
$785$	21558.0			0.980175
$786$		0			0
$787$	18790.9	−	32546.7i	0.851108	−	1.47416i	−0.0291013	−	0.999576i	$-0.509265\pi$
$787$	18790.9	−	32546.7i	0.851108	−	1.47416i	0.880209	−	0.474586i	$-0.157402\pi$
$788$	2894.01	−	5012.56i	0.130831	−	0.226606i
$789$		0			0
$790$	6641.54			0.299108
$791$		0			0
$792$		0			0
$793$	−164.113	−	284.252i	−0.00734907	−	0.0127290i
$794$	17120.3	−	29653.3i	0.765212	−	1.32539i
$795$		0			0
$796$	1457.46	+	2524.39i	0.0648973	+	0.112405i
$797$	−9458.78			−0.420385			−0.210193	−	0.977660i	$-0.567409\pi$
$797$	−9458.78			−0.420385			−0.210193	+	0.977660i	$0.567409\pi$
$798$		0			0
$799$	−1723.20			−0.0762985
$800$	12908.2	+	22357.7i	0.570467	+	0.988078i
$801$		0			0
$802$	−12077.2	+	20918.3i	−0.531745	+	0.921009i
$803$	−7410.97	−	12836.2i	−0.325688	−	0.564108i
$804$		0			0
$805$		0			0
$806$	25879.0			1.13095
$807$		0			0
$808$	−5613.69	+	9723.20i	−0.244417	+	0.423343i
$809$	−954.968	+	1654.05i	−0.0415017	+	0.0718831i	−0.886030	−	0.463628i	$-0.846548\pi$
$809$	−954.968	+	1654.05i	−0.0415017	+	0.0718831i	0.844528	+	0.535511i	$0.179881\pi$
$810$		0			0
$811$	−43110.6			−1.86661			−0.933303	−	0.359091i	$-0.883087\pi$
$811$	−43110.6			−1.86661			−0.933303	+	0.359091i	$0.883087\pi$
$812$		0			0
$813$		0			0
$814$	1621.77	+	2809.00i	0.0698319	+	0.120952i
$815$	−29538.0	+	51161.4i	−1.26954	+	2.19890i
$816$		0			0
$817$	−16267.9	−	28176.9i	−0.696626	−	1.20659i
$818$	11189.7			0.478287
$819$		0			0
$820$	12951.5			0.551570
$821$	2013.28	+	3487.10i	0.0855834	+	0.148235i	0.905640	−	0.424048i	$-0.139391\pi$
$821$	2013.28	+	3487.10i	0.0855834	+	0.148235i	−0.820056	+	0.572283i	$0.806058\pi$
$822$		0			0
$823$	−19834.0	+	34353.5i	−0.840062	+	1.45503i	0.0497799	+	0.998760i	$0.484148\pi$
$823$	−19834.0	+	34353.5i	−0.840062	+	1.45503i	−0.889842	+	0.456269i	$0.849185\pi$
$824$	9651.19	+	16716.4i	0.408028	+	0.706726i
$825$		0			0
$826$		0			0
$827$	−30137.7			−1.26722			−0.633611	−	0.773652i	$-0.718428\pi$
$827$	−30137.7			−1.26722			−0.633611	+	0.773652i	$0.718428\pi$
$828$		0			0
$829$	11639.0	−	20159.3i	0.487622	−	0.844587i	−0.512276	−	0.858821i	$-0.671198\pi$
$829$	11639.0	−	20159.3i	0.487622	−	0.844587i	0.999899	+	0.0142341i	$0.00453100\pi$
$830$	14920.2	−	25842.6i	0.623962	−	1.08073i
$831$		0			0
$832$	−49381.0			−2.05766
$833$		0			0
$834$		0			0
$835$	20810.2	+	36044.4i	0.862477	+	1.49385i
$836$	1686.74	−	2921.52i	0.0697813	−	0.120865i
$837$		0			0
$838$	6033.49	+	10450.3i	0.248716	+	0.430788i
$839$	−9494.43			−0.390684			−0.195342	−	0.980735i	$-0.562582\pi$
$839$	−9494.43			−0.390684			−0.195342	+	0.980735i	$0.562582\pi$
$840$		0			0
$841$	−20750.6			−0.850820
$842$	−849.996	−	1472.24i	−0.0347896	−	0.0602573i
$843$		0			0
$844$	682.354	−	1181.87i	0.0278289	−	0.0482011i
$845$	−54066.5	−	93645.9i	−2.20112	−	3.81245i
$846$		0			0
$847$		0			0
$848$	−15721.8			−0.636661
$849$		0			0
$850$	−1844.79	+	3195.28i	−0.0744423	+	0.128938i
$851$	718.251	−	1244.05i	0.0289322	−	0.0501121i
$852$		0			0
$853$	12692.4			0.509471			0.254736	−	0.967011i	$-0.418012\pi$
$853$	12692.4			0.509471			0.254736	+	0.967011i	$0.418012\pi$
$854$		0			0
$855$		0			0
$856$	−2412.18	−	4178.02i	−0.0963162	−	0.166825i
$857$	−11103.0	+	19231.0i	−0.442557	+	0.766531i	−0.997878	−	0.0651047i	$-0.979262\pi$
$857$	−11103.0	+	19231.0i	−0.442557	+	0.766531i	0.555322	+	0.831636i	$0.312595\pi$
$858$		0			0
$859$	9910.24	+	17165.0i	0.393636	+	0.681797i	0.992926	−	0.118735i	$-0.0378838\pi$
$859$	9910.24	+	17165.0i	0.393636	+	0.681797i	−0.599290	+	0.800532i	$0.704550\pi$
$860$	21668.0			0.859155
$861$		0			0
$862$	−24945.5			−0.985671
$863$	18206.9	+	31535.3i	0.718157	+	1.24389i	0.961729	+	0.274002i	$0.0883476\pi$
$863$	18206.9	+	31535.3i	0.718157	+	1.24389i	−0.243572	+	0.969883i	$0.578319\pi$
$864$		0			0
$865$	4677.85	−	8102.27i	0.183875	−	0.318480i
$866$	−13407.1	−	23221.7i	−0.526086	−	0.911208i
$867$		0			0
$868$		0			0
$869$	3309.76			0.129201
$870$		0			0
$871$	−35512.0	+	61508.7i	−1.38149	+	2.39281i
$872$	3761.33	−	6514.82i	0.146072	−	0.253004i
$873$		0			0
$874$	4009.97			0.155194
$875$		0			0
$876$		0			0
$877$	−9721.31	−	16837.8i	−0.374305	−	0.648315i	0.615918	−	0.787810i	$-0.288785\pi$
$877$	−9721.31	−	16837.8i	−0.374305	−	0.648315i	−0.990223	+	0.139496i	$0.955452\pi$
$878$	8811.01	−	15261.1i	0.338676	−	0.586603i
$879$		0			0
$880$	−9983.71	−	17292.3i	−0.382444	−	0.662412i
$881$	−25184.2			−0.963082			−0.481541	−	0.876423i	$-0.659923\pi$
$881$	−25184.2			−0.963082			−0.481541	+	0.876423i	$0.659923\pi$
$882$		0			0
$883$	−4050.03			−0.154354			−0.0771769	−	0.997017i	$-0.524591\pi$
$883$	−4050.03			−0.154354			−0.0771769	+	0.997017i	$0.524591\pi$
$884$	534.913	+	926.496i	0.0203519	+	0.0352505i
$885$		0			0
$886$	−19421.9	+	33639.8i	−0.736448	+	1.27556i
$887$	−20802.1	−	36030.3i	−0.787447	−	1.36390i	−0.927526	−	0.373758i	$-0.878069\pi$
$887$	−20802.1	−	36030.3i	−0.787447	−	1.36390i	0.140080	−	0.990140i	$-0.455264\pi$
$888$		0			0
$889$		0			0
$890$	−13712.0			−0.516434
$891$		0			0
$892$	1053.18	−	1824.16i	0.0395326	−	0.0684725i
$893$	9913.27	−	17170.3i	0.371484	−	0.643428i
$894$		0			0
$895$	−21023.0			−0.785165
$896$		0			0
$897$		0			0
$898$	−16370.5	−	28354.5i	−0.608340	−	1.05368i
$899$	3700.88	−	6410.11i	0.137298	−	0.237808i
$900$		0			0
$901$	1057.76	+	1832.09i	0.0391110	+	0.0677422i
$902$	−17323.1			−0.639463
$903$		0			0
$904$	−49054.4			−1.80478
$905$	−4044.28	−	7004.90i	−0.148548	−	0.257294i
$906$		0			0
$907$	1786.30	−	3093.96i	0.0653949	−	0.113267i	−0.831474	−	0.555563i	$-0.812503\pi$
$907$	1786.30	−	3093.96i	0.0653949	−	0.113267i	0.896869	+	0.442296i	$0.145836\pi$
$908$	−5156.01	−	8930.47i	−0.188445	−	0.326397i
$909$		0			0
$910$		0			0
$911$	−29457.7			−1.07133			−0.535663	−	0.844432i	$-0.679938\pi$
$911$	−29457.7			−1.07133			−0.535663	+	0.844432i	$0.679938\pi$
$912$		0			0
$913$	7435.36	−	12878.4i	0.269523	−	0.466828i
$914$	13095.4	−	22681.9i	0.473913	−	0.820842i
$915$		0			0
$916$	−10427.9			−0.376143
$917$		0			0
$918$		0			0
$919$	1655.32	+	2867.10i	0.0594168	+	0.102913i	0.894204	−	0.447660i	$-0.147743\pi$
$919$	1655.32	+	2867.10i	0.0594168	+	0.102913i	−0.834787	+	0.550573i	$0.814409\pi$
$920$	−6254.34	+	10832.8i	−0.224130	+	0.388204i
$921$		0			0
$922$	−2122.92	−	3677.01i	−0.0758295	−	0.131340i
$923$	14492.5			0.516820
$924$		0			0
$925$	−15207.3			−0.540556
$926$	−6532.80	−	11315.1i	−0.231837	−	0.401554i
$927$		0			0
$928$	−2873.19	+	4976.52i	−0.101635	+	0.176037i
$929$	15733.8	+	27251.7i	0.555660	+	0.962431i	0.997852	+	0.0655103i	$0.0208675\pi$
$929$	15733.8	+	27251.7i	0.555660	+	0.962431i	−0.442192	+	0.896920i	$0.645799\pi$
$930$		0			0
$931$		0			0
$932$	−6851.94			−0.240818
$933$		0			0
$934$	9791.26	−	16959.0i	0.343019	−	0.594126i
$935$	−1343.40	+	2326.84i	−0.0469881	+	0.0813859i
$936$		0			0
$937$	17363.4			0.605375			0.302688	−	0.953090i	$-0.402116\pi$
$937$	17363.4			0.605375			0.302688	+	0.953090i	$0.402116\pi$
$938$		0			0
$939$		0			0
$940$	6601.97	+	11434.9i	0.229077	+	0.396773i
$941$	2773.89	−	4804.51i	0.0960958	−	0.166443i	−0.813970	−	0.580907i	$-0.802698\pi$
$941$	2773.89	−	4804.51i	0.0960958	−	0.166443i	0.910065	+	0.414465i	$0.136031\pi$
$942$		0			0
$943$	3836.02	+	6644.18i	0.132469	+	0.229443i
$944$	26304.3			0.906919
$945$		0			0
$946$	−28981.6			−0.996062
$947$	−18980.1	−	32874.6i	−0.651290	−	1.12807i	−0.982810	−	0.184619i	$-0.940895\pi$
$947$	−18980.1	−	32874.6i	−0.651290	−	1.12807i	0.331520	−	0.943448i	$-0.392438\pi$
$948$		0			0
$949$	−27040.8	+	46836.1i	−0.924955	+	1.60207i
$950$	−21225.5	−	36763.7i	−0.724892	−	1.25555i
$951$		0			0
$952$		0			0
$953$	10019.3			0.340563			0.170282	−	0.985395i	$-0.445532\pi$
$953$	10019.3			0.340563			0.170282	+	0.985395i	$0.445532\pi$
$954$		0			0
$955$	1785.08	−	3091.85i	0.0604857	−	0.104764i
$956$	−4605.83	+	7977.53i	−0.155819	+	0.269887i
$957$		0			0
$958$	−5059.61			−0.170635
$959$		0			0
$960$		0			0
$961$	7366.54	+	12759.2i	0.247274	+	0.428291i
$962$	5917.46	−	10249.3i	0.198323	−	0.343505i
$963$		0			0
$964$	4715.56	+	8167.58i	0.157550	+	0.272884i
$965$	−47527.3			−1.58545
$966$		0			0
$967$	27834.4			0.925641			0.462820	−	0.886452i	$-0.346837\pi$
$967$	27834.4			0.925641			0.462820	+	0.886452i	$0.346837\pi$
$968$	9304.68	+	16116.2i	0.308950	+	0.535117i
$969$		0			0
$970$	14487.3	−	25092.7i	0.479545	−	0.830597i
$971$	9137.67	+	15826.9i	0.302000	+	0.523079i	0.976589	−	0.215115i	$-0.0690125\pi$
$971$	9137.67	+	15826.9i	0.302000	+	0.523079i	−0.674589	+	0.738193i	$0.735679\pi$
$972$		0			0
$973$		0			0
$974$	−23200.8			−0.763245
$975$		0			0
$976$	−78.7386	+	136.379i	−0.00258234	+	0.00447274i
$977$	−21514.5	+	37264.2i	−0.704513	+	1.22025i	0.262354	+	0.964972i	$0.415501\pi$
$977$	−21514.5	+	37264.2i	−0.704513	+	1.22025i	−0.966867	+	0.255280i	$0.917832\pi$
$978$		0			0
$979$	−6833.24			−0.223076
$980$		0			0
$981$		0			0
$982$	14144.0	+	24498.2i	0.459628	+	0.796099i
$983$	−15279.6	+	26465.1i	−0.495772	+	0.858702i	−0.999988	−	0.00487535i	$-0.998448\pi$
$983$	−15279.6	+	26465.1i	−0.495772	+	0.858702i	0.504216	+	0.863577i	$0.331781\pi$
$984$		0			0
$985$	−26519.6	−	45933.3i	−0.857853	−	1.48584i
$986$	−821.253			−0.0265254
$987$		0			0
$988$	−12309.0			−0.396358
$989$	6417.69	+	11115.8i	0.206340	+	0.357392i
$990$		0			0
$991$	22473.0	−	38924.3i	0.720360	−	1.24770i	−0.240495	−	0.970650i	$-0.577310\pi$
$991$	22473.0	−	38924.3i	0.720360	−	1.24770i	0.960855	−	0.277050i	$-0.0893569\pi$
$992$	5845.14	+	10124.1i	0.187080	+	0.324032i
$993$		0			0
$994$		0			0
$995$	26711.2			0.851058
$996$		0			0
$997$	14503.1	−	25120.0i	0.460698	−	0.797953i	−0.538297	−	0.842755i	$-0.680932\pi$
$997$	14503.1	−	25120.0i	0.460698	−	0.797953i	0.998996	+	0.0448018i	$0.0142656\pi$
$998$	−11099.6	+	19225.0i	−0.352055	+	0.609777i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.u.361.2		4
3.2	odd	2		147.4.e.j.67.1		4
7.2	even	3	inner	441.4.e.u.226.2		4
7.3	odd	6		441.4.a.n.1.1		2
7.4	even	3		441.4.a.o.1.1		2
7.5	odd	6		441.4.e.v.226.2		4
7.6	odd	2		441.4.e.v.361.2		4
21.2	odd	6		147.4.e.j.79.1		4
21.5	even	6		147.4.e.k.79.1		4
21.11	odd	6		147.4.a.k.1.2	yes	2
21.17	even	6		147.4.a.j.1.2	✓	2
21.20	even	2		147.4.e.k.67.1		4
84.11	even	6		2352.4.a.bl.1.1		2
84.59	odd	6		2352.4.a.cf.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.j.1.2	✓	2	21.17	even	6
147.4.a.k.1.2	yes	2	21.11	odd	6
147.4.e.j.67.1		4	3.2	odd	2
147.4.e.j.79.1		4	21.2	odd	6
147.4.e.k.67.1		4	21.20	even	2
147.4.e.k.79.1		4	21.5	even	6
441.4.a.n.1.1		2	7.3	odd	6
441.4.a.o.1.1		2	7.4	even	3
441.4.e.u.226.2		4	7.2	even	3	inner
441.4.e.u.361.2		4	1.1	even	1	trivial
441.4.e.v.226.2		4	7.5	odd	6
441.4.e.v.361.2		4	7.6	odd	2
2352.4.a.bl.1.1		2	84.11	even	6
2352.4.a.cf.1.2		2	84.59	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)

\(f(q)\)	\(=\)	\(q+(1.20711 + 2.09077i) q^{2} +(1.08579 - 1.88064i) q^{4} +(-9.94975 - 17.2335i) q^{5} +24.5563 q^{8} +O(q^{10})\)	\(q+(1.20711 + 2.09077i) q^{2} +(1.08579 - 1.88064i) q^{4} +(-9.94975 - 17.2335i) q^{5} +24.5563 q^{8} +(24.0208 - 41.6053i) q^{10} +(11.9706 - 20.7336i) q^{11} -87.3553 q^{13} +(20.9558 + 36.2966i) q^{16} +(2.81981 - 4.88405i) q^{17} +(32.4437 + 56.1941i) q^{19} -43.2132 q^{20} +57.7990 q^{22} +(-12.7990 - 22.1685i) q^{23} +(-135.495 + 234.684i) q^{25} +(-105.447 - 182.640i) q^{26} -60.3188 q^{29} +(-61.3553 + 106.271i) q^{31} +(47.6335 - 82.5037i) q^{32} +13.6152 q^{34} +(28.0589 + 48.5994i) q^{37} +(-78.3259 + 135.664i) q^{38} +(-244.329 - 423.191i) q^{40} -299.713 q^{41} -501.421 q^{43} +(-25.9949 - 45.0246i) q^{44} +(30.8995 - 53.5195i) q^{46} +(-152.777 - 264.617i) q^{47} -654.227 q^{50} +(-94.8492 + 164.284i) q^{52} +(-187.558 + 324.861i) q^{53} -476.416 q^{55} +(-72.8112 - 126.113i) q^{58} +(313.806 - 543.528i) q^{59} +(1.87868 + 3.25397i) q^{61} -296.250 q^{62} +565.288 q^{64} +(869.164 + 1505.44i) q^{65} +(406.524 - 704.120i) q^{67} +(-6.12341 - 10.6061i) q^{68} -165.902 q^{71} +(309.550 - 536.156i) q^{73} +(-67.7401 + 117.329i) q^{74} +140.908 q^{76} +(69.1228 + 119.724i) q^{79} +(417.011 - 722.284i) q^{80} +(-361.785 - 626.631i) q^{82} +621.137 q^{83} -112.225 q^{85} +(-605.269 - 1048.36i) q^{86} +(293.953 - 509.142i) q^{88} +(-142.709 - 247.180i) q^{89} -55.5879 q^{92} +(368.836 - 638.842i) q^{94} +(645.612 - 1118.23i) q^{95} +603.114 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 10 q^{4} - 20 q^{5} + 36 q^{8}+O(q^{10}) \) 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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