LMFDB - Embedded newform 441.4.p.d.80.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(80,441)]

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([3, 1]))

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

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

chi := DirichletCharacter("441.80");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.13
Character	$\chi$	$=$	441.80
Dual form			441.4.p.d.215.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.555155 - 0.320519i) q^{2} +(-3.79454 + 6.57233i) q^{4} +(-6.03646 - 10.4555i) q^{5} +9.99318i q^{8} +O(q^{10})$	\(q+(0.555155 - 0.320519i) q^{2} +(-3.79454 + 6.57233i) q^{4} +(-6.03646 - 10.4555i) q^{5} +9.99318i q^{8} +(-6.70234 - 3.86960i) q^{10} +(38.0525 + 21.9696i) q^{11} -66.9783i q^{13} +(-27.1533 - 47.0309i) q^{16} +(-19.7155 + 34.1482i) q^{17} +(-50.1554 + 28.9572i) q^{19} +91.6223 q^{20} +28.1667 q^{22} +(-39.9687 + 23.0759i) q^{23} +(-10.3778 + 17.9748i) q^{25} +(-21.4678 - 37.1833i) q^{26} +201.623i q^{29} +(160.666 + 92.7605i) q^{31} +(-99.3833 - 57.3790i) q^{32} +25.2767i q^{34} +(205.402 + 355.767i) q^{37} +(-18.5626 + 32.1515i) q^{38} +(104.483 - 60.3234i) q^{40} +408.886 q^{41} +129.530 q^{43} +(-288.783 + 166.729i) q^{44} +(-14.7925 + 25.6214i) q^{46} +(257.340 + 445.726i) q^{47} +13.3051i q^{50} +(440.204 + 254.152i) q^{52} +(-378.958 - 218.792i) q^{53} -530.475i q^{55} +(64.6241 + 111.932i) q^{58} +(-303.953 + 526.462i) q^{59} +(21.2342 - 12.2596i) q^{61} +118.926 q^{62} +360.888 q^{64} +(-700.289 + 404.312i) q^{65} +(-220.750 + 382.350i) q^{67} +(-149.622 - 259.153i) q^{68} +1150.89i q^{71} +(-454.730 - 262.539i) q^{73} +(228.060 + 131.671i) q^{74} -439.517i q^{76} +(75.9251 + 131.506i) q^{79} +(-327.820 + 567.800i) q^{80} +(226.995 - 131.055i) q^{82} +1302.05 q^{83} +476.047 q^{85} +(71.9094 - 41.5169i) q^{86} +(-219.546 + 380.266i) q^{88} +(-291.595 - 505.057i) q^{89} -350.250i q^{92} +(285.727 + 164.965i) q^{94} +(605.522 + 349.598i) q^{95} -1091.84i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4}+O(q^{10}) $ 48 * q + 96 * q^4	$ 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) $ 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.555155	−	0.320519i	0.196277	−	0.113320i	−0.398641	−	0.917107i	$-0.630518\pi$
$2$	0.555155	−	0.320519i	0.196277	−	0.113320i	0.594918	+	0.803787i	$0.297185\pi$
$3$		0			0
$3$		0			0
$4$	−3.79454	+	6.57233i	−0.474317	+	0.821541i
$5$	−6.03646	−	10.4555i	−0.539918	−	0.935165i	−0.998908	−	0.0467235i	$-0.985122\pi$
$5$	−6.03646	−	10.4555i	−0.539918	−	0.935165i	0.458990	−	0.888441i	$-0.348211\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			9.99318i			0.441640i
$9$		0			0
$10$	−6.70234	−	3.86960i	−0.211947	−	0.122367i
$11$	38.0525	+	21.9696i	1.04302	+	0.602190i	0.920688	−	0.390298i	$-0.127628\pi$
$11$	38.0525	+	21.9696i	1.04302	+	0.602190i	0.122336	+	0.992489i	$0.460962\pi$
$12$		0			0
$13$		−	66.9783i		−	1.42896i	−0.699657	−	0.714479i	$-0.746664\pi$
$13$		−	66.9783i		−	1.42896i	0.699657	−	0.714479i	$-0.253336\pi$
$14$		0			0
$15$		0			0
$16$	−27.1533	−	47.0309i	−0.424270	−	0.734857i
$17$	−19.7155	+	34.1482i	−0.281277	+	0.487186i	−0.971700	−	0.236220i	$-0.924091\pi$
$17$	−19.7155	+	34.1482i	−0.281277	+	0.487186i	0.690423	+	0.723406i	$0.257425\pi$
$18$		0			0
$19$	−50.1554	+	28.9572i	−0.605601	+	0.349644i	−0.771242	−	0.636542i	$-0.780364\pi$
$19$	−50.1554	+	28.9572i	−0.605601	+	0.349644i	0.165641	+	0.986186i	$0.447031\pi$
$20$	91.6223			1.02437
$21$		0			0
$22$	28.1667			0.272962
$23$	−39.9687	+	23.0759i	−0.362350	+	0.209203i	−0.670111	−	0.742261i	$-0.733754\pi$
$23$	−39.9687	+	23.0759i	−0.362350	+	0.209203i	0.307761	+	0.951464i	$0.400420\pi$
$24$		0			0
$25$	−10.3778	+	17.9748i	−0.0830221	+	0.143799i
$26$	−21.4678	−	37.1833i	−0.161930	−	0.280471i
$27$		0			0
$28$		0			0
$29$			201.623i			1.29105i	0.763738	+	0.645526i	$0.223362\pi$
$29$			201.623i			1.29105i	−0.763738	+	0.645526i	$0.776638\pi$
$30$		0			0
$31$	160.666	+	92.7605i	0.930853	+	0.537428i	0.887081	−	0.461613i	$-0.152729\pi$
$31$	160.666	+	92.7605i	0.930853	+	0.537428i	0.0437720	+	0.999042i	$0.486062\pi$
$32$	−99.3833	−	57.3790i	−0.549020	−	0.316977i
$33$		0			0
$34$			25.2767i			0.127498i
$35$		0			0
$36$		0			0
$37$	205.402	+	355.767i	0.912647	+	1.58075i	0.810310	+	0.586002i	$0.199299\pi$
$37$	205.402	+	355.767i	0.912647	+	1.58075i	0.102338	+	0.994750i	$0.467368\pi$
$38$	−18.5626	+	32.1515i	−0.0792437	+	0.137254i
$39$		0			0
$40$	104.483	−	60.3234i	0.413006	−	0.238449i
$41$	408.886			1.55749			0.778746	−	0.627339i	$-0.215856\pi$
$41$	408.886			1.55749			0.778746	+	0.627339i	$0.215856\pi$
$42$		0			0
$43$	129.530			0.459377			0.229688	−	0.973264i	$-0.426229\pi$
$43$	129.530			0.459377			0.229688	+	0.973264i	$0.426229\pi$
$44$	−288.783	+	166.729i	−0.989448	+	0.571258i
$45$		0			0
$46$	−14.7925	+	25.6214i	−0.0474139	+	0.0821234i
$47$	257.340	+	445.726i	0.798658	+	1.38332i	0.920490	+	0.390766i	$0.127790\pi$
$47$	257.340	+	445.726i	0.798658	+	1.38332i	−0.121832	+	0.992551i	$0.538877\pi$
$48$		0			0
$49$		0			0
$50$			13.3051i			0.0376324i
$51$		0			0
$52$	440.204	+	254.152i	1.17395	+	0.677779i
$53$	−378.958	−	218.792i	−0.982150	−	0.567045i	−0.0792314	−	0.996856i	$-0.525247\pi$
$53$	−378.958	−	218.792i	−0.982150	−	0.567045i	−0.902919	+	0.429812i	$0.858580\pi$
$54$		0			0
$55$		−	530.475i		−	1.30053i
$56$		0			0
$57$		0			0
$58$	64.6241	+	111.932i	0.146303	+	0.253404i
$59$	−303.953	+	526.462i	−0.670701	+	1.16169i	0.307005	+	0.951708i	$0.400673\pi$
$59$	−303.953	+	526.462i	−0.670701	+	1.16169i	−0.977706	+	0.209980i	$0.932660\pi$
$60$		0			0
$61$	21.2342	−	12.2596i	0.0445699	−	0.0257324i	−0.477549	−	0.878605i	$-0.658475\pi$
$61$	21.2342	−	12.2596i	0.0445699	−	0.0257324i	0.522119	+	0.852872i	$0.325142\pi$
$62$	118.926			0.243607
$63$		0			0
$64$	360.888			0.704860
$65$	−700.289	+	404.312i	−1.33631	+	0.771519i
$66$		0			0
$67$	−220.750	+	382.350i	−0.402520	+	0.697186i	−0.994029	−	0.109113i	$-0.965199\pi$
$67$	−220.750	+	382.350i	−0.402520	+	0.697186i	0.591509	+	0.806298i	$0.298532\pi$
$68$	−149.622	−	259.153i	−0.266829	−	0.462161i
$69$		0			0
$70$		0			0
$71$			1150.89i			1.92373i	0.273518	+	0.961867i	$0.411813\pi$
$71$			1150.89i			1.92373i	−0.273518	+	0.961867i	$0.588187\pi$
$72$		0			0
$73$	−454.730	−	262.539i	−0.729070	−	0.420929i	0.0890117	−	0.996031i	$-0.471629\pi$
$73$	−454.730	−	262.539i	−0.729070	−	0.420929i	−0.818082	+	0.575102i	$0.804962\pi$
$74$	228.060	+	131.671i	0.358263	+	0.206843i
$75$		0			0
$76$		−	439.517i		−	0.663369i
$77$		0			0
$78$		0			0
$79$	75.9251	+	131.506i	0.108130	+	0.187286i	0.915013	−	0.403425i	$-0.132181\pi$
$79$	75.9251	+	131.506i	0.108130	+	0.187286i	−0.806883	+	0.590711i	$0.798847\pi$
$80$	−327.820	+	567.800i	−0.458142	+	0.793525i
$81$		0			0
$82$	226.995	−	131.055i	0.305700	−	0.176496i
$83$	1302.05			1.72191			0.860956	−	0.508680i	$-0.169866\pi$
$83$	1302.05			1.72191			0.860956	+	0.508680i	$0.169866\pi$
$84$		0			0
$85$	476.047			0.607466
$86$	71.9094	−	41.5169i	0.0901650	−	0.0520568i
$87$		0			0
$88$	−219.546	+	380.266i	−0.265951	+	0.460641i
$89$	−291.595	−	505.057i	−0.347292	−	0.601528i	0.638475	−	0.769642i	$-0.279565\pi$
$89$	−291.595	−	505.057i	−0.347292	−	0.601528i	−0.985767	+	0.168115i	$0.946232\pi$
$90$		0			0
$91$		0			0
$92$		−	350.250i		−	0.396914i
$93$		0			0
$94$	285.727	+	164.965i	0.313516	+	0.181009i
$95$	605.522	+	349.598i	0.653950	+	0.377558i
$96$		0			0
$97$		−	1091.84i		−	1.14288i	−0.820643	−	0.571441i	$-0.806384\pi$
$97$		−	1091.84i		−	1.14288i	0.820643	−	0.571441i	$-0.193616\pi$
$98$		0			0
$99$		0			0
$100$	−78.7576	−	136.412i	−0.0787576	−	0.136412i
$101$	−78.3866	+	135.770i	−0.0772254	+	0.133758i	−0.902052	−	0.431628i	$-0.857939\pi$
$101$	−78.3866	+	135.770i	−0.0772254	+	0.133758i	0.824826	+	0.565386i	$0.191273\pi$
$102$		0			0
$103$	−208.779	+	120.539i	−0.199725	+	0.115311i	−0.596527	−	0.802593i	$-0.703453\pi$
$103$	−208.779	+	120.539i	−0.199725	+	0.115311i	0.396802	+	0.917904i	$0.370120\pi$
$104$	669.326			0.631085
$105$		0			0
$106$	−280.507			−0.257031
$107$	−11.1175	+	6.41871i	−0.0100446	+	0.00579926i	−0.505014	−	0.863111i	$-0.668513\pi$
$107$	−11.1175	+	6.41871i	−0.0100446	+	0.00579926i	0.494969	+	0.868910i	$0.335179\pi$
$108$		0			0
$109$	1033.20	−	1789.56i	0.907915	−	1.57256i	0.0909595	−	0.995855i	$-0.471007\pi$
$109$	1033.20	−	1789.56i	0.907915	−	1.57256i	0.816956	−	0.576701i	$-0.195660\pi$
$110$	−170.027	−	294.496i	−0.147377	−	0.255264i
$111$		0			0
$112$		0			0
$113$			87.2159i			0.0726069i	0.999341	+	0.0363035i	$0.0115583\pi$
$113$			87.2159i			0.0726069i	−0.999341	+	0.0363035i	$0.988442\pi$
$114$		0			0
$115$	482.539	+	278.594i	0.391278	+	0.225905i
$116$	−1325.14	−	765.067i	−1.06065	−	0.612368i
$117$		0			0
$118$			389.691i			0.304016i
$119$		0			0
$120$		0			0
$121$	299.829	+	519.320i	0.225266	+	0.390173i
$122$	7.85885	−	13.6119i	0.00583202	−	0.0101014i
$123$		0			0
$124$	−1219.31	+	703.966i	−0.883039	+	0.509823i
$125$	−1258.54			−0.900535
$126$		0			0
$127$	1933.38			1.35086			0.675432	−	0.737423i	$-0.263957\pi$
$127$	1933.38			1.35086			0.675432	+	0.737423i	$0.263957\pi$
$128$	995.415	−	574.703i	0.687368	−	0.396852i
$129$		0			0
$130$	−259.179	+	448.912i	−0.174858	+	0.302863i
$131$	677.042	+	1172.67i	0.451553	+	0.782112i	0.998483	−	0.0550661i	$-0.0175370\pi$
$131$	677.042	+	1172.67i	0.451553	+	0.782112i	−0.546930	+	0.837178i	$0.684204\pi$
$132$		0			0
$133$		0			0
$134$			283.018i			0.182455i
$135$		0			0
$136$	−341.249	−	197.020i	−0.215161	−	0.124223i
$137$	−53.9293	−	31.1361i	−0.0336313	−	0.0194171i	0.483090	−	0.875571i	$-0.339514\pi$
$137$	−53.9293	−	31.1361i	−0.0336313	−	0.0194171i	−0.516721	+	0.856154i	$0.672848\pi$
$138$		0			0
$139$			2355.95i			1.43762i	0.695208	+	0.718808i	$0.255312\pi$
$139$			2355.95i			1.43762i	−0.695208	+	0.718808i	$0.744688\pi$
$140$		0			0
$141$		0			0
$142$	368.881	+	638.920i	0.217998	+	0.377584i
$143$	1471.49	−	2548.69i	0.860504	−	1.49044i
$144$		0			0
$145$	2108.07	−	1217.09i	1.20735	−	0.697062i
$146$	−336.594			−0.190799
$147$		0			0
$148$	−3117.63			−1.73154
$149$	−310.258	+	179.128i	−0.170586	+	0.0984881i	−0.582862	−	0.812571i	$-0.698067\pi$
$149$	−310.258	+	179.128i	−0.170586	+	0.0984881i	0.412276	+	0.911059i	$0.364734\pi$
$150$		0			0
$151$	−230.159	+	398.648i	−0.124040	+	0.214844i	−0.921357	−	0.388716i	$-0.872919\pi$
$151$	−230.159	+	398.648i	−0.124040	+	0.214844i	0.797317	+	0.603561i	$0.206252\pi$
$152$	−289.374	−	501.211i	−0.154417	−	0.267458i
$153$		0			0
$154$		0			0
$155$		−	2239.78i		−	1.16067i
$156$		0			0
$157$	−652.641	−	376.803i	−0.331761	−	0.191542i	0.324862	−	0.945762i	$-0.394682\pi$
$157$	−652.641	−	376.803i	−0.331761	−	0.191542i	−0.656623	+	0.754219i	$0.728016\pi$
$158$	84.3003	+	48.6708i	0.0424467	+	0.0245066i
$159$		0			0
$160$			1385.46i			0.684566i
$161$		0			0
$162$		0			0
$163$	−1206.86	−	2090.34i	−0.579929	−	1.00447i	−0.995487	−	0.0948996i	$-0.969747\pi$
$163$	−1206.86	−	2090.34i	−0.579929	−	1.00447i	0.415558	−	0.909567i	$-0.363586\pi$
$164$	−1551.53	+	2687.33i	−0.738745	+	1.27954i
$165$		0			0
$166$	722.839	−	417.332i	0.337971	−	0.195128i
$167$	−2912.06			−1.34935			−0.674676	−	0.738114i	$-0.735717\pi$
$167$	−2912.06			−1.34935			−0.674676	+	0.738114i	$0.735717\pi$
$168$		0			0
$169$	−2289.10			−1.04192
$170$	264.280	−	152.582i	0.119231	−	0.0688383i
$171$		0			0
$172$	−491.508	+	851.316i	−0.217890	+	0.377397i
$173$	869.770	+	1506.49i	0.382239	+	0.662057i	0.991382	−	0.131003i	$-0.0418198\pi$
$173$	869.770	+	1506.49i	0.382239	+	0.662057i	−0.609143	+	0.793060i	$0.708486\pi$
$174$		0			0
$175$		0			0
$176$		−	2386.19i		−	1.02197i
$177$		0			0
$178$	−323.761	−	186.923i	−0.136331	−	0.0787106i
$179$	2283.30	+	1318.26i	0.953418	+	0.550456i	0.894141	−	0.447785i	$-0.147787\pi$
$179$	2283.30	+	1318.26i	0.953418	+	0.550456i	0.0592772	+	0.998242i	$0.481120\pi$
$180$		0			0
$181$		−	208.975i		−	0.0858175i	−0.999079	−	0.0429087i	$-0.986338\pi$
$181$		−	208.975i		−	0.0858175i	0.999079	−	0.0429087i	$-0.0136625\pi$
$182$		0			0
$183$		0			0
$184$	−230.602	−	399.414i	−0.0923924	−	0.160028i
$185$	2479.81	−	4295.15i	0.985509	−	1.70695i
$186$		0			0
$187$	−1500.45	+	866.284i	−0.586757	+	0.338765i
$188$	−3905.95			−1.51527
$189$		0			0
$190$	448.211			0.171140
$191$	667.111	−	385.157i	0.252725	−	0.145911i	−0.368286	−	0.929712i	$-0.620055\pi$
$191$	667.111	−	385.157i	0.252725	−	0.145911i	0.621011	+	0.783802i	$0.286722\pi$
$192$		0			0
$193$	−430.418	+	745.506i	−0.160529	+	0.278045i	−0.935059	−	0.354493i	$-0.884654\pi$
$193$	−430.418	+	745.506i	−0.160529	+	0.278045i	0.774529	+	0.632538i	$0.217987\pi$
$194$	−349.955	−	606.140i	−0.129512	−	0.224321i
$195$		0			0
$196$		0			0
$197$			1034.13i			0.374003i	0.982360	+	0.187001i	$0.0598769\pi$
$197$			1034.13i			0.374003i	−0.982360	+	0.187001i	$0.940123\pi$
$198$		0			0
$199$	−4469.63	−	2580.54i	−1.59218	−	0.919246i	−0.992932	−	0.118682i	$-0.962133\pi$
$199$	−4469.63	−	2580.54i	−1.59218	−	0.919246i	−0.599248	−	0.800564i	$-0.704534\pi$
$200$	−179.626	−	103.707i	−0.0635072	−	0.0366659i
$201$		0			0
$202$			100.498i			0.0350049i
$203$		0			0
$204$		0			0
$205$	−2468.22	−	4275.09i	−0.840918	−	1.45651i
$206$	−77.2699	+	133.835i	−0.0261342	+	0.0452658i
$207$		0			0
$208$	−3150.05	+	1818.68i	−1.05008	+	0.606264i
$209$	−2544.72			−0.842209
$210$		0			0
$211$	136.191			0.0444349			0.0222174	−	0.999753i	$-0.492927\pi$
$211$	136.191			0.0444349			0.0222174	+	0.999753i	$0.492927\pi$
$212$	2875.94	−	1660.43i	0.931701	−	0.537918i
$213$		0			0
$214$	−4.11463	+	7.12675i	−0.00131435	+	0.00227652i
$215$	−781.906	−	1354.30i	−0.248026	−	0.429593i
$216$		0			0
$217$		0			0
$218$		−	1324.64i		−	0.411541i
$219$		0			0
$220$	3486.46	+	2012.91i	1.06844	+	0.616865i
$221$	2287.19	+	1320.51i	0.696168	+	0.401933i
$222$		0			0
$223$			2544.16i			0.763989i	0.924165	+	0.381994i	$0.124763\pi$
$223$			2544.16i			0.763989i	−0.924165	+	0.381994i	$0.875237\pi$
$224$		0			0
$225$		0			0
$226$	27.9543	+	48.4183i	0.00822785	+	0.0142511i
$227$	2219.10	−	3843.59i	0.648840	−	1.12382i	−0.334560	−	0.942374i	$-0.608588\pi$
$227$	2219.10	−	3843.59i	0.648840	−	1.12382i	0.983400	−	0.181449i	$-0.0580789\pi$
$228$		0			0
$229$	2692.24	−	1554.36i	0.776892	−	0.448539i	−0.0584360	−	0.998291i	$-0.518611\pi$
$229$	2692.24	−	1554.36i	0.776892	−	0.448539i	0.835328	+	0.549753i	$0.185278\pi$
$230$	357.179			0.102398
$231$		0			0
$232$	−2014.86			−0.570181
$233$	3973.34	−	2294.01i	1.11718	−	0.645002i	0.176498	−	0.984301i	$-0.443523\pi$
$233$	3973.34	−	2294.01i	1.11718	−	0.645002i	0.940679	+	0.339299i	$0.110190\pi$
$234$		0			0
$235$	3106.85	−	5381.22i	0.862419	−	1.49375i
$236$	−2306.72	−	3995.36i	−0.636249	−	1.10202i
$237$		0			0
$238$		0			0
$239$		−	738.555i		−	0.199888i	−0.994993	−	0.0999439i	$-0.968134\pi$
$239$		−	738.555i		−	0.199888i	0.994993	−	0.0999439i	$-0.0318663\pi$
$240$		0			0
$241$	−216.280	−	124.870i	−0.0578085	−	0.0333757i	0.470817	−	0.882231i	$-0.343959\pi$
$241$	−216.280	−	124.870i	−0.0578085	−	0.0333757i	−0.528626	+	0.848855i	$0.677292\pi$
$242$	332.903	+	192.202i	0.0884291	+	0.0510545i
$243$		0			0
$244$			186.078i			0.0488213i
$245$		0			0
$246$		0			0
$247$	1939.51	+	3359.32i	0.499627	+	0.865379i
$248$	−926.972	+	1605.56i	−0.237350	+	0.411102i
$249$		0			0
$250$	−698.682	+	403.384i	−0.176754	+	0.102049i
$251$	4098.68			1.03070			0.515351	−	0.856979i	$-0.327662\pi$
$251$	4098.68			1.03070			0.515351	+	0.856979i	$0.327662\pi$
$252$		0			0
$253$	−2027.88			−0.503920
$254$	1073.32	−	619.684i	0.265143	−	0.153080i
$255$		0			0
$256$	−1075.15	+	1862.21i	−0.262487	+	0.454641i
$257$	1337.52	+	2316.66i	0.324640	+	0.562293i	0.981439	−	0.191773i	$-0.0614236\pi$
$257$	1337.52	+	2316.66i	0.324640	+	0.562293i	−0.656800	+	0.754065i	$0.728090\pi$
$258$		0			0
$259$		0			0
$260$		−	6136.71i		−	1.46378i
$261$		0			0
$262$	751.726	+	434.009i	0.177259	+	0.102340i
$263$	1632.27	+	942.393i	0.382700	+	0.220952i	0.678993	−	0.734145i	$-0.262417\pi$
$263$	1632.27	+	942.393i	0.382700	+	0.220952i	−0.296292	+	0.955097i	$0.595750\pi$
$264$		0			0
$265$			5282.91i			1.22463i
$266$		0			0
$267$		0			0
$268$	−1675.28	−	2901.68i	−0.381844	−	0.661374i
$269$	603.608	−	1045.48i	0.136813	−	0.236967i	−0.789476	−	0.613782i	$-0.789647\pi$
$269$	603.608	−	1045.48i	0.136813	−	0.236967i	0.926289	+	0.376815i	$0.122981\pi$
$270$		0			0
$271$	−3938.31	+	2273.78i	−0.882786	+	0.509677i	−0.871576	−	0.490260i	$-0.836902\pi$
$271$	−3938.31	+	2273.78i	−0.882786	+	0.509677i	−0.0112103	+	0.999937i	$0.503568\pi$
$272$	2141.36			0.477350
$273$		0			0
$274$	−39.9188			−0.00880140
$275$	−789.800	+	455.991i	−0.173188	+	0.0999903i
$276$		0			0
$277$	2136.36	−	3700.29i	0.463400	−	0.802632i	−0.535728	−	0.844391i	$-0.679963\pi$
$277$	2136.36	−	3700.29i	0.463400	−	0.802632i	0.999128	+	0.0417588i	$0.0132961\pi$
$278$	755.125	+	1307.91i	0.162911	+	0.282171i
$279$		0			0
$280$		0			0
$281$			8218.49i			1.74475i	0.488840	+	0.872374i	$0.337420\pi$
$281$			8218.49i			1.74475i	−0.488840	+	0.872374i	$0.662580\pi$
$282$		0			0
$283$	−4172.42	−	2408.95i	−0.876411	−	0.505996i	−0.00693786	−	0.999976i	$-0.502208\pi$
$283$	−4172.42	−	2408.95i	−0.876411	−	0.505996i	−0.869473	+	0.493980i	$0.835542\pi$
$284$	−7564.01	−	4367.08i	−1.58043	−	0.912460i
$285$		0			0
$286$		−	1886.56i		−	0.390051i
$287$		0			0
$288$		0			0
$289$	1679.10	+	2908.28i	0.341767	+	0.591957i
$290$	780.201	−	1351.35i	0.157983	−	0.273634i
$291$		0			0
$292$	3450.98	−	1992.42i	0.691621	−	0.399307i
$293$	−6857.68			−1.36734			−0.683669	−	0.729792i	$-0.739617\pi$
$293$	−6857.68			−1.36734			−0.683669	+	0.729792i	$0.739617\pi$
$294$		0			0
$295$	7339.21			1.44849
$296$	−3555.25	+	2052.62i	−0.698123	+	0.403062i
$297$		0			0
$298$	−114.828	+	198.887i	−0.0223214	+	0.0386618i
$299$	1545.59	+	2677.04i	0.298942	+	0.517783i
$300$		0			0
$301$		0			0
$302$			295.081i			0.0562253i
$303$		0			0
$304$	2723.77	+	1572.57i	0.513877	+	0.296687i
$305$	−256.359	−	148.009i	−0.0481281	−	0.0277868i
$306$		0			0
$307$		−	7537.04i		−	1.40118i	−0.713565	−	0.700589i	$-0.752921\pi$
$307$		−	7537.04i		−	1.40118i	0.713565	−	0.700589i	$-0.247079\pi$
$308$		0			0
$309$		0			0
$310$	−717.892	−	1243.43i	−0.131527	−	0.227812i
$311$	−2793.76	+	4838.93i	−0.509388	+	0.882285i	0.490553	+	0.871411i	$0.336795\pi$
$311$	−2793.76	+	4838.93i	−0.509388	+	0.882285i	−0.999941	+	0.0108742i	$0.996539\pi$
$312$		0			0
$313$	3655.95	−	2110.76i	0.660212	−	0.381174i	−0.132146	−	0.991230i	$-0.542187\pi$
$313$	3655.95	−	2110.76i	0.660212	−	0.381174i	0.792358	+	0.610057i	$0.208853\pi$
$314$	−483.089			−0.0868226
$315$		0			0
$316$	−1152.40			−0.205151
$317$	−7158.31	+	4132.85i	−1.26830	+	0.732252i	−0.974666	−	0.223666i	$-0.928197\pi$
$317$	−7158.31	+	4132.85i	−1.26830	+	0.732252i	−0.293632	+	0.955918i	$0.594864\pi$
$318$		0			0
$319$	−4429.59	+	7672.28i	−0.777459	+	1.34660i
$320$	−2178.49	−	3773.25i	−0.380566	−	0.659161i
$321$		0			0
$322$		0			0
$323$		−	2283.62i		−	0.393387i
$324$		0			0
$325$	1203.92	+	695.086i	0.205482	+	0.118635i
$326$	−1339.99	−	773.641i	−0.227653	−	0.131436i
$327$		0			0
$328$			4086.07i			0.687851i
$329$		0			0
$330$		0			0
$331$	3654.72	+	6330.16i	0.606893	+	1.05117i	0.991749	+	0.128193i	$0.0409178\pi$
$331$	3654.72	+	6330.16i	0.606893	+	1.05117i	−0.384856	+	0.922977i	$0.625749\pi$
$332$	−4940.68	+	8557.51i	−0.816732	+	1.41462i
$333$		0			0
$334$	−1616.64	+	933.369i	−0.264846	+	0.152909i
$335$	5330.19			0.869311
$336$		0			0
$337$	127.665			0.0206361			0.0103180	−	0.999947i	$-0.496716\pi$
$337$	127.665			0.0206361			0.0103180	+	0.999947i	$0.496716\pi$
$338$	−1270.80	+	733.698i	−0.204505	+	0.118071i
$339$		0			0
$340$	−1806.38	+	3128.74i	−0.288131	+	0.499058i
$341$	4075.83	+	7059.54i	0.647268	+	1.12110i
$342$		0			0
$343$		0			0
$344$			1294.42i			0.202879i
$345$		0			0
$346$	965.713	+	557.555i	0.150049	+	0.0866310i
$347$	4477.85	+	2585.29i	0.692748	+	0.399958i	0.804641	−	0.593762i	$-0.202358\pi$
$347$	4477.85	+	2585.29i	0.692748	+	0.399958i	−0.111893	+	0.993720i	$0.535691\pi$
$348$		0			0
$349$		−	11271.1i		−	1.72874i	−0.502855	−	0.864370i	$-0.667717\pi$
$349$		−	11271.1i		−	1.72874i	0.502855	−	0.864370i	$-0.332283\pi$
$350$		0			0
$351$		0			0
$352$	−2521.19	−	4366.83i	−0.381761	−	0.661229i
$353$	−828.962	+	1435.80i	−0.124989	+	0.216488i	−0.921729	−	0.387835i	$-0.873223\pi$
$353$	−828.962	+	1435.80i	−0.124989	+	0.216488i	0.796740	+	0.604323i	$0.206556\pi$
$354$		0			0
$355$	12033.0	−	6947.28i	1.79901	−	1.03866i
$356$	4425.87			0.658906
$357$		0			0
$358$	1690.11			0.249512
$359$	247.512	−	142.901i	0.0363878	−	0.0210085i	−0.481696	−	0.876339i	$-0.659979\pi$
$359$	247.512	−	142.901i	0.0363878	−	0.0210085i	0.518084	+	0.855330i	$0.326646\pi$
$360$		0			0
$361$	−1752.46	+	3035.35i	−0.255498	+	0.442535i
$362$	−66.9803	−	116.013i	−0.00972488	−	0.0168440i
$363$		0			0
$364$		0			0
$365$			6339.22i			0.909068i
$366$		0			0
$367$	−3815.77	−	2203.04i	−0.542729	−	0.313345i	0.203455	−	0.979084i	$-0.434783\pi$
$367$	−3815.77	−	2203.04i	−0.542729	−	0.313345i	−0.746184	+	0.665739i	$0.768116\pi$
$368$	2170.56	+	1253.18i	0.307469	+	0.177517i
$369$		0			0
$370$		−	3179.30i		−	0.446713i
$371$		0			0
$372$		0			0
$373$	6272.53	+	10864.3i	0.870722	+	1.50813i	0.861251	+	0.508179i	$0.169681\pi$
$373$	6272.53	+	10864.3i	0.870722	+	1.50813i	0.00947025	+	0.999955i	$0.496985\pi$
$374$	−555.320	+	961.843i	−0.0767779	+	0.132983i
$375$		0			0
$376$	−4454.22	+	2571.65i	−0.610928	+	0.352720i
$377$	13504.4			1.84486
$378$		0			0
$379$	4695.85			0.636437			0.318219	−	0.948017i	$-0.396915\pi$
$379$	4695.85			0.636437			0.318219	+	0.948017i	$0.396915\pi$
$380$	−4595.35	+	2653.13i	−0.620359	+	0.358164i
$381$		0			0
$382$	246.900	−	427.643i	0.0330693	−	0.0572778i
$383$	−3595.01	−	6226.74i	−0.479625	−	0.830735i	0.520102	−	0.854104i	$-0.325894\pi$
$383$	−3595.01	−	6226.74i	−0.479625	−	0.830735i	−0.999727	+	0.0233693i	$0.992561\pi$
$384$		0			0
$385$		0			0
$386$			551.828i			0.0727651i
$387$		0			0
$388$	7175.94	+	4143.03i	0.938925	+	0.542089i
$389$	−7956.88	−	4593.91i	−1.03709	−	0.598767i	−0.118086	−	0.993003i	$-0.537676\pi$
$389$	−7956.88	−	4593.91i	−1.03709	−	0.598767i	−0.919009	+	0.394237i	$0.871009\pi$
$390$		0			0
$391$		−	1819.81i		−	0.235376i
$392$		0			0
$393$		0			0
$394$	331.457	+	574.101i	0.0423822	+	0.0734080i
$395$	916.638	−	1587.66i	0.116762	−	0.202238i
$396$		0			0
$397$	−10350.6	+	5975.91i	−1.30851	+	0.755471i	−0.981848	−	0.189668i	$-0.939259\pi$
$397$	−10350.6	+	5975.91i	−1.30851	+	0.755471i	−0.326667	+	0.945140i	$0.605925\pi$
$398$	−3308.45			−0.416677
$399$		0			0
$400$	1127.16			0.140895
$401$	−5927.66	+	3422.34i	−0.738188	+	0.426193i	−0.821410	−	0.570338i	$-0.806812\pi$
$401$	−5927.66	+	3422.34i	−0.738188	+	0.426193i	0.0832223	+	0.996531i	$0.473479\pi$
$402$		0			0
$403$	6212.94	−	10761.1i	0.767962	−	1.33015i
$404$	−594.882	−	1030.37i	−0.0732586	−	0.126888i
$405$		0			0
$406$		0			0
$407$			18050.5i			2.19835i
$408$		0			0
$409$	4474.70	+	2583.47i	0.540977	+	0.312333i	0.745475	−	0.666534i	$-0.232223\pi$
$409$	4474.70	+	2583.47i	0.540977	+	0.312333i	−0.204498	+	0.978867i	$0.565556\pi$
$410$	−2740.49	−	1582.22i	−0.330105	−	0.190586i
$411$		0			0
$412$		−	1829.56i		−	0.218776i
$413$		0			0
$414$		0			0
$415$	−7859.78	−	13613.5i	−0.929690	−	1.61027i
$416$	−3843.15	+	6656.53i	−0.452947	+	0.784527i
$417$		0			0
$418$	−1412.71	+	815.629i	−0.165306	+	0.0954395i
$419$	13900.4			1.62071			0.810356	−	0.585938i	$-0.199274\pi$
$419$	13900.4			1.62071			0.810356	+	0.585938i	$0.199274\pi$
$420$		0			0
$421$	7800.31			0.903003			0.451501	−	0.892270i	$-0.350889\pi$
$421$	7800.31			0.903003			0.451501	+	0.892270i	$0.350889\pi$
$422$	75.6069	−	43.6517i	0.00872153	−	0.00503538i
$423$		0			0
$424$	2186.42	−	3787.00i	0.250430	−	0.433757i
$425$	−409.206	−	708.765i	−0.0467044	−	0.0808945i
$426$		0			0
$427$		0			0
$428$		−	97.4241i		−	0.0110027i
$429$		0			0
$430$	−868.157	−	501.231i	−0.0973634	−	0.0562128i
$431$	1806.23	+	1042.83i	0.201863	+	0.116546i	0.597524	−	0.801851i	$-0.296151\pi$
$431$	1806.23	+	1042.83i	0.201863	+	0.116546i	−0.395661	+	0.918397i	$0.629485\pi$
$432$		0			0
$433$			1186.95i			0.131735i	0.997828	+	0.0658674i	$0.0209814\pi$
$433$			1186.95i			0.131735i	−0.997828	+	0.0658674i	$0.979019\pi$
$434$		0			0
$435$		0			0
$436$	7841.04	+	13581.1i	0.861279	+	1.49178i
$437$	1336.43	−	2314.76i	0.146293	−	0.253387i
$438$		0			0
$439$	−7527.93	+	4346.25i	−0.818425	+	0.472518i	−0.849873	−	0.526988i	$-0.823321\pi$
$439$	−7527.93	+	4346.25i	−0.818425	+	0.472518i	0.0314484	+	0.999505i	$0.489988\pi$
$440$	5301.13			0.574367
$441$		0			0
$442$	1692.99			0.182189
$443$	5853.20	−	3379.34i	0.627751	−	0.362432i	−0.152130	−	0.988361i	$-0.548613\pi$
$443$	5853.20	−	3379.34i	0.627751	−	0.362432i	0.779881	+	0.625928i	$0.215280\pi$
$444$		0			0
$445$	−3520.40	+	6097.52i	−0.375018	+	0.649551i
$446$	815.451	+	1412.40i	0.0865756	+	0.149953i
$447$		0			0
$448$		0			0
$449$		−	6721.89i		−	0.706516i	−0.935526	−	0.353258i	$-0.885074\pi$
$449$		−	6721.89i		−	0.706516i	0.935526	−	0.353258i	$-0.114926\pi$
$450$		0			0
$451$	15559.1	+	8983.06i	1.62450	+	0.937907i
$452$	−573.212	−	330.944i	−0.0596496	−	0.0344387i
$453$		0			0
$454$		−	2845.05i		−	0.294107i
$455$		0			0
$456$		0			0
$457$	1650.93	+	2859.50i	0.168988	+	0.292695i	0.938064	−	0.346461i	$-0.112617\pi$
$457$	1650.93	+	2859.50i	0.168988	+	0.292695i	−0.769077	+	0.639157i	$0.779284\pi$
$458$	996.406	−	1725.83i	0.101657	−	0.176075i
$459$		0			0
$460$	−3662.02	+	2114.27i	−0.371180	+	0.214301i
$461$	7241.19			0.731574			0.365787	−	0.930699i	$-0.380800\pi$
$461$	7241.19			0.731574			0.365787	+	0.930699i	$0.380800\pi$
$462$		0			0
$463$	−7585.65			−0.761415			−0.380707	−	0.924696i	$-0.624319\pi$
$463$	−7585.65			−0.761415			−0.380707	+	0.924696i	$0.624319\pi$
$464$	9482.52	−	5474.74i	0.948739	−	0.547755i
$465$		0			0
$466$	1470.54	−	2547.06i	0.146184	−	0.253198i
$467$	1024.28	+	1774.11i	0.101495	+	0.175794i	0.912301	−	0.409521i	$-0.134304\pi$
$467$	1024.28	+	1774.11i	0.101495	+	0.175794i	−0.810806	+	0.585315i	$0.800971\pi$
$468$		0			0
$469$		0			0
$470$		−	3983.21i		−	0.390919i
$471$		0			0
$472$	−5261.03	−	3037.46i	−0.513048	−	0.296208i
$473$	4928.96	+	2845.74i	0.479141	+	0.276632i
$474$		0			0
$475$		−	1202.04i		−	0.116113i
$476$		0			0
$477$		0			0
$478$	−236.721	−	410.012i	−0.0226514	−	0.0392333i
$479$	−1648.52	+	2855.32i	−0.157250	+	0.272365i	−0.933876	−	0.357597i	$-0.883596\pi$
$479$	−1648.52	+	2855.32i	−0.157250	+	0.272365i	0.776626	+	0.629962i	$0.216929\pi$
$480$		0			0
$481$	23828.7	−	13757.5i	2.25883	−	1.30413i
$482$	−160.092			−0.0151286
$483$		0			0
$484$	−4550.85			−0.427390
$485$	−11415.7	+	6590.86i	−1.06878	+	0.617063i
$486$		0			0
$487$	589.853	−	1021.66i	0.0548846	−	0.0950630i	−0.837278	−	0.546778i	$-0.815854\pi$
$487$	589.853	−	1021.66i	0.0548846	−	0.0950630i	0.892162	+	0.451715i	$0.149188\pi$
$488$	122.512	+	212.197i	0.0113645	+	0.0196839i
$489$		0			0
$490$		0			0
$491$			7573.80i			0.696132i	0.937470	+	0.348066i	$0.113162\pi$
$491$			7573.80i			0.696132i	−0.937470	+	0.348066i	$0.886838\pi$
$492$		0			0
$493$	−6885.08	−	3975.10i	−0.628983	−	0.363143i
$494$	2153.45	+	1243.30i	0.196130	+	0.113236i
$495$		0			0
$496$		−	10075.0i		−	0.912059i
$497$		0			0
$498$		0			0
$499$	909.766	+	1575.76i	0.0816167	+	0.141364i	0.903945	−	0.427650i	$-0.140658\pi$
$499$	909.766	+	1575.76i	0.0816167	+	0.141364i	−0.822328	+	0.569014i	$0.807325\pi$
$500$	4775.56	−	8271.51i	0.427139	−	0.739826i
$501$		0			0
$502$	2275.40	−	1313.70i	0.202303	−	0.116800i
$503$	−15635.9			−1.38602			−0.693012	−	0.720926i	$-0.743717\pi$
$503$	−15635.9			−1.38602			−0.693012	+	0.720926i	$0.743717\pi$
$504$		0			0
$505$	1892.71			0.166781
$506$	−1125.79	+	649.973i	−0.0989078	+	0.0571044i
$507$		0			0
$508$	−7336.28	+	12706.8i	−0.640737	+	1.10979i
$509$	1646.90	+	2852.51i	0.143413	+	0.248399i	0.928780	−	0.370632i	$-0.120859\pi$
$509$	1646.90	+	2852.51i	0.143413	+	0.248399i	−0.785367	+	0.619031i	$0.787526\pi$
$510$		0			0
$511$		0			0
$512$			10573.7i			0.912685i
$513$		0			0
$514$	1485.06	+	857.403i	0.127439	+	0.0735767i
$515$	2520.58	+	1455.26i	0.215670	+	0.124517i
$516$		0			0
$517$			22614.7i			1.92378i
$518$		0			0
$519$		0			0
$520$	−4040.36	−	6998.11i	−0.340734	−	0.590168i
$521$	−1649.02	+	2856.19i	−0.138666	+	0.240176i	−0.926992	−	0.375081i	$-0.877615\pi$
$521$	−1649.02	+	2856.19i	−0.138666	+	0.240176i	0.788326	+	0.615258i	$0.210948\pi$
$522$		0			0
$523$	−15438.1	+	8913.21i	−1.29075	+	0.745215i	−0.978787	−	0.204879i	$-0.934320\pi$
$523$	−15438.1	+	8913.21i	−1.29075	+	0.745215i	−0.311963	+	0.950094i	$0.600987\pi$
$524$	−10276.2			−0.856716
$525$		0			0
$526$	1208.22			0.100154
$527$	−6335.22	+	3657.64i	−0.523655	+	0.302333i
$528$		0			0
$529$	−5018.50	+	8692.30i	−0.412468	+	0.714416i
$530$	1693.27	+	2932.83i	0.138776	+	0.240366i
$531$		0			0
$532$		0			0
$533$		−	27386.5i		−	2.22559i
$534$		0			0
$535$	134.221	+	77.4926i	0.0108465	+	0.00626224i
$536$	−3820.89	−	2205.99i	−0.307905	−	0.177769i
$537$		0			0
$538$		−	773.871i		−	0.0620148i
$539$		0			0
$540$		0			0
$541$	−5209.12	−	9022.46i	−0.413969	−	0.717016i	0.581350	−	0.813653i	$-0.302525\pi$
$541$	−5209.12	−	9022.46i	−0.413969	−	0.717016i	−0.995320	+	0.0966374i	$0.969191\pi$
$542$	−1457.58	+	2524.60i	−0.115514	+	0.200076i
$543$		0			0
$544$	3918.78	−	2262.51i	0.308854	−	0.178317i
$545$	−24947.5			−1.96080
$546$		0			0
$547$	−996.607			−0.0779010			−0.0389505	−	0.999241i	$-0.512401\pi$
$547$	−996.607			−0.0779010			−0.0389505	+	0.999241i	$0.512401\pi$
$548$	409.274	−	236.294i	0.0319038	−	0.0184197i
$549$		0			0
$550$	−292.308	+	506.292i	−0.0226619	+	0.0392515i
$551$	−5838.45	−	10112.5i	−0.451409	−	0.781863i
$552$		0			0
$553$		0			0
$554$		−	2738.98i		−	0.210051i
$555$		0			0
$556$	−15484.1	−	8939.72i	−1.18106	−	0.681886i
$557$	−9645.26	−	5568.69i	−0.733722	−	0.423614i	0.0860606	−	0.996290i	$-0.472572\pi$
$557$	−9645.26	−	5568.69i	−0.733722	−	0.423614i	−0.819782	+	0.572676i	$0.805905\pi$
$558$		0			0
$559$		−	8675.73i		−	0.656430i
$560$		0			0
$561$		0			0
$562$	2634.18	+	4562.53i	0.197716	+	0.342453i
$563$	2095.75	−	3629.94i	0.156883	−	0.271730i	−0.776860	−	0.629673i	$-0.783189\pi$
$563$	2095.75	−	3629.94i	0.156883	−	0.271730i	0.933743	+	0.357944i	$0.116522\pi$
$564$		0			0
$565$	911.882	−	526.476i	0.0678994	−	0.0392018i
$566$	−3088.45			−0.229359
$567$		0			0
$568$	−11501.0			−0.849598
$569$	2596.22	−	1498.93i	0.191281	−	0.110436i	−0.401301	−	0.915946i	$-0.631442\pi$
$569$	2596.22	−	1498.93i	0.191281	−	0.110436i	0.592582	+	0.805510i	$0.298109\pi$
$570$		0			0
$571$	−881.110	+	1526.13i	−0.0645768	+	0.111850i	−0.896506	−	0.443031i	$-0.853903\pi$
$571$	−881.110	+	1526.13i	−0.0645768	+	0.111850i	0.831929	+	0.554881i	$0.187236\pi$
$572$	11167.2	+	19342.2i	0.816303	+	1.41388i
$573$		0			0
$574$		0			0
$575$		−	957.907i		−	0.0694739i
$576$		0			0
$577$	−13336.8	−	7700.03i	−0.962253	−	0.555557i	−0.0653874	−	0.997860i	$-0.520828\pi$
$577$	−13336.8	−	7700.03i	−0.962253	−	0.555557i	−0.896866	+	0.442303i	$0.854162\pi$
$578$	1864.32	+	1076.36i	0.134162	+	0.0774583i
$579$		0			0
$580$			18473.2i			1.32251i
$581$		0			0
$582$		0			0
$583$	−9613.55	−	16651.2i	−0.682937	−	1.18288i
$584$	2623.59	−	4544.20i	0.185899	−	0.321987i
$585$		0			0
$586$	−3807.07	+	2198.02i	−0.268377	+	0.154947i
$587$	−2642.97			−0.185838			−0.0929190	−	0.995674i	$-0.529620\pi$
$587$	−2642.97			−0.185838			−0.0929190	+	0.995674i	$0.529620\pi$
$588$		0			0
$589$	−10744.3			−0.751635
$590$	4074.40	−	2352.35i	0.284305	−	0.164144i
$591$		0			0
$592$	11154.7	−	19320.5i	0.774418	−	1.34133i
$593$	600.950	+	1040.88i	0.0416156	+	0.0720803i	0.886083	−	0.463527i	$-0.153416\pi$
$593$	600.950	+	1040.88i	0.0416156	+	0.0720803i	−0.844467	+	0.535607i	$0.820083\pi$
$594$		0			0
$595$		0			0
$596$		−	2718.83i		−	0.186858i
$597$		0			0
$598$	1716.08	+	990.780i	0.117351	+	0.0677525i
$599$	8533.05	+	4926.56i	0.582055	+	0.336049i	0.761950	−	0.647636i	$-0.224242\pi$
$599$	8533.05	+	4926.56i	0.582055	+	0.336049i	−0.179895	+	0.983686i	$0.557576\pi$
$600$		0			0
$601$			7573.82i			0.514047i	0.966405	+	0.257024i	$0.0827418\pi$
$601$			7573.82i			0.514047i	−0.966405	+	0.257024i	$0.917258\pi$
$602$		0			0
$603$		0			0
$604$	−1746.70	−	3025.37i	−0.117669	−	0.203809i
$605$	3619.82	−	6269.71i	0.243250	−	0.421322i
$606$		0			0
$607$	17144.7	−	9898.52i	1.14643	−	0.661892i	0.198416	−	0.980118i	$-0.436420\pi$
$607$	17144.7	−	9898.52i	1.14643	−	0.661892i	0.948015	+	0.318226i	$0.103087\pi$
$608$	6646.14			0.443317
$609$		0			0
$610$	−189.759			−0.0125952
$611$	29854.0	−	17236.2i	1.97670	−	1.14125i
$612$		0			0
$613$	5263.87	−	9117.28i	0.346828	−	0.600724i	−0.638856	−	0.769326i	$-0.720592\pi$
$613$	5263.87	−	9117.28i	0.346828	−	0.600724i	0.985684	+	0.168603i	$0.0539254\pi$
$614$	−2415.76	−	4184.22i	−0.158782	−	0.275019i
$615$		0			0
$616$		0			0
$617$		−	23133.1i		−	1.50940i	−0.656067	−	0.754702i	$-0.727781\pi$
$617$		−	23133.1i		−	1.50940i	0.656067	−	0.754702i	$-0.272219\pi$
$618$		0			0
$619$	14154.6	+	8172.19i	0.919101	+	0.530643i	0.883348	−	0.468718i	$-0.155284\pi$
$619$	14154.6	+	8172.19i	0.919101	+	0.530643i	0.0357526	+	0.999361i	$0.488617\pi$
$620$	14720.6	+	8498.93i	0.953537	+	0.550525i
$621$		0			0
$622$			3581.81i			0.230896i
$623$		0			0
$624$		0			0
$625$	8894.32	+	15405.4i	0.569237	+	0.985947i
$626$	1353.08	−	2343.60i	0.0863896	−	0.149631i
$627$		0			0
$628$	4952.94	−	2859.58i	0.314720	−	0.181703i
$629$	−16198.4			−1.02683
$630$		0			0
$631$	−11124.2			−0.701819			−0.350909	−	0.936409i	$-0.614127\pi$
$631$	−11124.2			−0.701819			−0.350909	+	0.936409i	$0.614127\pi$
$632$	−1314.16	+	758.733i	−0.0827130	+	0.0477544i
$633$		0			0
$634$	−2649.31	+	4588.74i	−0.165958	+	0.287448i
$635$	−11670.8	−	20214.4i	−0.729355	−	1.26328i
$636$		0			0
$637$		0			0
$638$			5679.07i			0.352408i
$639$		0			0
$640$	−12017.6	−	6938.35i	−0.742244	−	0.428535i
$641$	−3102.69	−	1791.34i	−0.191184	−	0.110380i	0.401353	−	0.915924i	$-0.368540\pi$
$641$	−3102.69	−	1791.34i	−0.191184	−	0.110380i	−0.592537	+	0.805543i	$0.701873\pi$
$642$		0			0
$643$			14145.6i			0.867570i	0.901016	+	0.433785i	$0.142822\pi$
$643$			14145.6i			0.867570i	−0.901016	+	0.433785i	$0.857178\pi$
$644$		0			0
$645$		0			0
$646$	−731.943	−	1267.76i	−0.0445788	−	0.0772128i
$647$	11957.3	−	20710.6i	0.726568	−	1.25845i	−0.231758	−	0.972773i	$-0.574448\pi$
$647$	11957.3	−	20710.6i	0.726568	−	1.25845i	0.958326	−	0.285678i	$-0.0922189\pi$
$648$		0			0
$649$	−23132.4	+	13355.5i	−1.39911	+	0.807779i
$650$	891.152			0.0537751
$651$		0			0
$652$	18317.9			1.10028
$653$	22006.3	−	12705.3i	1.31879	−	0.761406i	0.335259	−	0.942126i	$-0.391176\pi$
$653$	22006.3	−	12705.3i	1.31879	−	0.761406i	0.983534	+	0.180721i	$0.0578430\pi$
$654$		0			0
$655$	8173.87	−	14157.6i	0.487603	−	0.844552i
$656$	−11102.6	−	19230.2i	−0.660798	−	1.14453i
$657$		0			0
$658$		0			0
$659$		−	14977.5i		−	0.885342i	−0.896684	−	0.442671i	$-0.854031\pi$
$659$		−	14977.5i		−	0.885342i	0.896684	−	0.442671i	$-0.145969\pi$
$660$		0			0
$661$	88.5773	+	51.1401i	0.00521219	+	0.00300926i	0.502604	−	0.864517i	$-0.332375\pi$
$661$	88.5773	+	51.1401i	0.00521219	+	0.00300926i	−0.497392	+	0.867526i	$0.665709\pi$
$662$	4057.87	+	2342.81i	0.238238	+	0.137547i
$663$		0			0
$664$			13011.6i			0.760465i
$665$		0			0
$666$		0			0
$667$	−4652.65	−	8058.63i	−0.270092	−	0.467813i
$668$	11049.9	−	19139.0i	0.640021	−	1.10855i
$669$		0			0
$670$	2959.08	−	1708.42i	0.170626	−	0.0985108i
$671$	1077.35			0.0619833
$672$		0			0
$673$	7778.89			0.445549			0.222774	−	0.974870i	$-0.428489\pi$
$673$	7778.89			0.445549			0.222774	+	0.974870i	$0.428489\pi$
$674$	70.8738	−	40.9190i	0.00405038	−	0.00233849i
$675$		0			0
$676$	8686.06	−	15044.7i	0.494200	−	0.855979i
$677$	10208.1	+	17680.9i	0.579510	+	1.00374i	0.995536	+	0.0943875i	$0.0300893\pi$
$677$	10208.1	+	17680.9i	0.579510	+	1.00374i	−0.416026	+	0.909353i	$0.636577\pi$
$678$		0			0
$679$		0			0
$680$			4757.22i			0.268281i
$681$		0			0
$682$	4525.43	+	2612.76i	0.254088	+	0.146697i
$683$	−23214.1	−	13402.7i	−1.30053	−	0.750863i	−0.320038	−	0.947405i	$-0.603696\pi$
$683$	−23214.1	−	13402.7i	−1.30053	−	0.750863i	−0.980495	+	0.196542i	$0.937029\pi$
$684$		0			0
$685$			751.808i			0.0419345i
$686$		0			0
$687$		0			0
$688$	−3517.18	−	6091.93i	−0.194900	−	0.337576i
$689$	−14654.3	+	25382.0i	−0.810282	+	1.40345i
$690$		0			0
$691$	−28328.7	+	16355.6i	−1.55959	+	0.900429i	−0.562293	+	0.826938i	$0.690081\pi$
$691$	−28328.7	+	16355.6i	−1.55959	+	0.900429i	−0.997296	+	0.0734905i	$0.976586\pi$
$692$	−13201.5			−0.725210
$693$		0			0
$694$	3314.53			0.181294
$695$	24632.5	−	14221.6i	1.34441	−	0.776195i
$696$		0			0
$697$	−8061.38	+	13962.7i	−0.438087	+	0.758789i
$698$	−3612.61	−	6257.23i	−0.195902	−	0.339312i
$699$		0			0
$700$		0			0
$701$		−	503.993i		−	0.0271548i	−0.999908	−	0.0135774i	$-0.995678\pi$
$701$		−	503.993i		−	0.0271548i	0.999908	−	0.0135774i	$-0.00432196\pi$
$702$		0			0
$703$	−20604.1	−	11895.8i	−1.10540	−	0.638204i
$704$	13732.7	+	7928.59i	0.735186	+	0.424460i
$705$		0			0
$706$			1062.79i			0.0566553i
$707$		0			0
$708$		0			0
$709$	−6893.77	−	11940.4i	−0.365163	−	0.632482i	0.623639	−	0.781713i	$-0.285654\pi$
$709$	−6893.77	−	11940.4i	−0.365163	−	0.632482i	−0.988802	+	0.149231i	$0.952320\pi$
$710$	4453.47	−	7713.63i	0.235402	−	0.407729i
$711$		0			0
$712$	5047.13	−	2913.96i	0.265659	−	0.153378i
$713$	−8562.15			−0.449726
$714$		0			0
$715$	−35530.4			−1.85841
$716$	−17328.1	+	10004.4i	−0.904445	+	0.522182i
$717$		0			0
$718$	91.6051	−	158.665i	0.00476138	−	0.00824695i
$719$	−16111.5	−	27906.0i	−0.835688	−	1.44745i	−0.893469	−	0.449124i	$-0.851736\pi$
$719$	−16111.5	−	27906.0i	−0.835688	−	1.44745i	0.0577818	−	0.998329i	$-0.481597\pi$
$720$		0			0
$721$		0			0
$722$			2246.78i			0.115813i
$723$		0			0
$724$	1373.45	+	792.962i	0.0705026	+	0.0407047i
$725$	−3624.14	−	2092.40i	−0.185652	−	0.107186i
$726$		0			0
$727$		−	33807.4i		−	1.72469i	−0.506325	−	0.862343i	$-0.668996\pi$
$727$		−	33807.4i		−	1.72469i	0.506325	−	0.862343i	$-0.331004\pi$
$728$		0			0
$729$		0			0
$730$	2031.84	+	3519.25i	0.103016	+	0.178429i
$731$	−2553.76	+	4423.23i	−0.129212	+	0.223802i
$732$		0			0
$733$	14239.9	−	8221.39i	0.717546	−	0.414275i	−0.0963028	−	0.995352i	$-0.530702\pi$
$733$	14239.9	−	8221.39i	0.717546	−	0.414275i	0.813849	+	0.581077i	$0.197368\pi$
$734$	−2824.46			−0.142034
$735$		0			0
$736$	5296.30			0.265250
$737$	−16800.2	+	9699.58i	−0.839677	+	0.484788i
$738$		0			0
$739$	10102.7	−	17498.4i	0.502888	−	0.871028i	−0.497106	−	0.867690i	$-0.665604\pi$
$739$	10102.7	−	17498.4i	0.502888	−	0.871028i	0.999994	−	0.00333840i	$-0.00106265\pi$
$740$	18819.4	+	32596.2i	0.934887	+	1.61927i
$741$		0			0
$742$		0			0
$743$		−	14573.9i		−	0.719601i	−0.933029	−	0.359800i	$-0.882845\pi$
$743$		−	14573.9i		−	0.719601i	0.933029	−	0.359800i	$-0.117155\pi$
$744$		0			0
$745$	3745.73	+	2162.60i	0.184205	+	0.106351i
$746$	6964.45	+	4020.92i	0.341805	+	0.197341i
$747$		0			0
$748$		−	13148.6i		−	0.642727i
$749$		0			0
$750$		0			0
$751$	−1344.53	−	2328.79i	−0.0653297	−	0.113154i	0.831510	−	0.555509i	$-0.187477\pi$
$751$	−1344.53	−	2328.79i	−0.0653297	−	0.113154i	−0.896840	+	0.442355i	$0.854143\pi$
$752$	13975.3	−	24205.9i	0.677694	−	1.17380i
$753$		0			0
$754$	7497.03	−	4328.41i	0.362103	−	0.209060i
$755$	5557.39			0.267886
$756$		0			0
$757$	11192.8			0.537395			0.268697	−	0.963225i	$-0.413407\pi$
$757$	11192.8			0.537395			0.268697	+	0.963225i	$0.413407\pi$
$758$	2606.92	−	1505.11i	0.124918	−	0.0721214i
$759$		0			0
$760$	−3493.60	+	6051.09i	−0.166745	+	0.288810i
$761$	14531.7	+	25169.6i	0.692212	+	1.19895i	0.971112	+	0.238626i	$0.0766970\pi$
$761$	14531.7	+	25169.6i	0.692212	+	1.19895i	−0.278900	+	0.960320i	$0.589970\pi$
$762$		0			0
$763$		0			0
$764$			5845.96i			0.276832i
$765$		0			0
$766$	−3991.57	−	2304.54i	−0.188279	−	0.108703i
$767$	35261.6	+	20358.3i	1.66000	+	0.958403i
$768$		0			0
$769$			40870.3i			1.91654i	0.285861	+	0.958271i	$0.407720\pi$
$769$			40870.3i			1.91654i	−0.285861	+	0.958271i	$0.592280\pi$
$770$		0			0
$771$		0			0
$772$	−3266.48	−	5657.70i	−0.152284	−	0.263763i
$773$	−20145.8	+	34893.5i	−0.937378	+	1.62359i	−0.167042	+	0.985950i	$0.553421\pi$
$773$	−20145.8	+	34893.5i	−0.937378	+	1.62359i	−0.770337	+	0.637637i	$0.779912\pi$
$774$		0			0
$775$	−3334.71	+	1925.29i	−0.154563	+	0.0892369i
$776$	10911.0			0.504743
$777$		0			0
$778$	−5889.73			−0.271410
$779$	−20507.8	+	11840.2i	−0.943220	+	0.544568i
$780$		0			0
$781$	−25284.6	+	43794.1i	−1.15845	+	2.00650i
$782$	−583.284	−	1010.28i	−0.0266729	−	0.0461988i
$783$		0			0
$784$		0			0
$785$			9098.22i			0.413668i
$786$		0			0
$787$	−4331.01	−	2500.51i	−0.196167	−	0.113257i	0.398699	−	0.917082i	$-0.369462\pi$
$787$	−4331.01	−	2500.51i	−0.196167	−	0.113257i	−0.594867	+	0.803824i	$0.702795\pi$
$788$	−6796.62	−	3924.03i	−0.307259	−	0.177396i
$789$		0			0
$790$		−	1175.20i		−	0.0529262i
$791$		0			0
$792$		0			0
$793$	−821.126	−	1422.23i	−0.0367706	−	0.0636885i
$794$	−3830.78	+	6635.10i	−0.171221	+	0.296563i
$795$		0			0
$796$	33920.4	−	19583.9i	1.51040	−	0.872028i
$797$	−8762.59			−0.389444			−0.194722	−	0.980858i	$-0.562380\pi$
$797$	−8762.59			−0.389444			−0.194722	+	0.980858i	$0.562380\pi$
$798$		0			0
$799$	−20294.4			−0.898577
$800$	2062.75	−	1190.93i	0.0911617	−	0.0526322i
$801$		0			0
$802$	−2193.85	+	3799.85i	−0.0965927	+	0.167304i
$803$	−11535.8	−	19980.5i	−0.506959	−	0.878078i
$804$		0			0
$805$		0			0
$806$		−	7965.46i		−	0.348103i
$807$		0			0
$808$	−1356.77	−	783.331i	−0.0590730	−	0.0341058i
$809$	−33466.5	−	19321.9i	−1.45441	−	0.839705i	−0.455684	−	0.890141i	$-0.650605\pi$
$809$	−33466.5	−	19321.9i	−1.45441	−	0.839705i	−0.998727	+	0.0504366i	$0.983939\pi$
$810$		0			0
$811$		−	3577.67i		−	0.154906i	−0.996996	−	0.0774530i	$-0.975321\pi$
$811$		−	3577.67i		−	0.154906i	0.996996	−	0.0774530i	$-0.0246788\pi$
$812$		0			0
$813$		0			0
$814$	5785.51	+	10020.8i	0.249118	+	0.431485i
$815$	−14570.3	+	25236.5i	−0.626228	+	1.08466i
$816$		0			0
$817$	−6496.64	+	3750.84i	−0.278199	+	0.160618i
$818$	3312.20			0.141575
$819$		0			0
$820$	37463.0			1.59545
$821$	−18194.3	+	10504.5i	−0.773431	+	0.446541i	−0.834097	−	0.551617i	$-0.814011\pi$
$821$	−18194.3	+	10504.5i	−0.773431	+	0.446541i	0.0606661	+	0.998158i	$0.480678\pi$
$822$		0			0
$823$	−15654.6	+	27114.6i	−0.663044	+	1.14843i	0.316767	+	0.948503i	$0.397403\pi$
$823$	−15654.6	+	27114.6i	−0.663044	+	1.14843i	−0.979812	+	0.199923i	$0.935931\pi$
$824$	−1204.57	−	2086.37i	−0.0509260	−	0.0882065i
$825$		0			0
$826$		0			0
$827$			27813.3i			1.16949i	0.811219	+	0.584743i	$0.198805\pi$
$827$			27813.3i			1.16949i	−0.811219	+	0.584743i	$0.801195\pi$
$828$		0			0
$829$	30364.1	+	17530.7i	1.27212	+	0.734460i	0.975387	−	0.220500i	$-0.0707688\pi$
$829$	30364.1	+	17530.7i	1.27212	+	0.734460i	0.296735	+	0.954960i	$0.404102\pi$
$830$	−8726.79	−	5038.41i	−0.364953	−	0.210706i
$831$		0			0
$832$		−	24171.7i		−	1.00722i
$833$		0			0
$834$		0			0
$835$	17578.5	+	30446.9i	0.728539	+	1.26187i
$836$	9656.02	−	16724.7i	0.399474	−	0.691909i
$837$		0			0
$838$	7716.86	−	4455.33i	0.318108	−	0.183660i
$839$	4808.56			0.197866			0.0989332	−	0.995094i	$-0.468457\pi$
$839$	4808.56			0.197866			0.0989332	+	0.995094i	$0.468457\pi$
$840$		0			0
$841$	−16263.0			−0.666816
$842$	4330.38	−	2500.15i	0.177238	−	0.102329i
$843$		0			0
$844$	−516.780	+	895.090i	−0.0210762	+	0.0365051i
$845$	13818.0	+	23933.6i	0.562550	+	0.974366i
$846$		0			0
$847$		0			0
$848$			23763.7i			0.962320i
$849$		0			0
$850$	−454.345	−	262.316i	−0.0183340	−	0.0105851i
$851$	−16419.3	−	9479.71i	−0.661396	−	0.381857i
$852$		0			0
$853$		−	9486.81i		−	0.380800i	−0.981707	−	0.190400i	$-0.939022\pi$
$853$		−	9486.81i		−	0.380800i	0.981707	−	0.190400i	$-0.0609784\pi$
$854$		0			0
$855$		0			0
$856$	−64.1433	−	111.099i	−0.00256118	−	0.00443610i
$857$	11262.4	−	19507.0i	0.448909	−	0.777533i	−0.549406	−	0.835555i	$-0.685146\pi$
$857$	11262.4	−	19507.0i	0.448909	−	0.777533i	0.998315	+	0.0580220i	$0.0184793\pi$
$858$		0			0
$859$	−23940.7	+	13822.2i	−0.950927	+	0.549018i	−0.893369	−	0.449324i	$-0.851665\pi$
$859$	−23940.7	+	13822.2i	−0.950927	+	0.549018i	−0.0575581	+	0.998342i	$0.518331\pi$
$860$	11867.9			0.470571
$861$		0			0
$862$	1336.98			0.0528280
$863$	−17457.3	+	10079.0i	−0.688591	+	0.397558i	−0.803084	−	0.595866i	$-0.796809\pi$
$863$	−17457.3	+	10079.0i	−0.688591	+	0.397558i	0.114493	+	0.993424i	$0.463476\pi$
$864$		0			0
$865$	10500.7	−	18187.7i	0.412755	−	0.714913i
$866$	380.439	+	658.940i	0.0149282	+	0.0258565i
$867$		0			0
$868$		0			0
$869$			6672.18i			0.260458i
$870$		0			0
$871$	25609.1	+	14785.4i	0.996249	+	0.575184i
$872$	17883.4	+	10325.0i	0.694503	+	0.400972i
$873$		0			0
$874$		−	1713.40i		−	0.0663120i
$875$		0			0
$876$		0			0
$877$	15486.6	+	26823.5i	0.596288	+	1.03280i	0.993364	+	0.115015i	$0.0366916\pi$
$877$	15486.6	+	26823.5i	0.596288	+	1.03280i	−0.397076	+	0.917786i	$0.629975\pi$
$878$	−2786.11	+	4825.68i	−0.107092	+	0.185488i
$879$		0			0
$880$	−24948.7	+	14404.2i	−0.955706	+	0.551777i
$881$	10973.0			0.419626			0.209813	−	0.977741i	$-0.432714\pi$
$881$	10973.0			0.419626			0.209813	+	0.977741i	$0.432714\pi$
$882$		0			0
$883$	42025.5			1.60167			0.800833	−	0.598888i	$-0.204390\pi$
$883$	42025.5			1.60167			0.800833	+	0.598888i	$0.204390\pi$
$884$	−17357.7	+	10021.4i	−0.660409	+	0.381287i
$885$		0			0
$886$	2166.29	−	3752.12i	0.0821420	−	0.142274i
$887$	−2340.56	−	4053.97i	−0.0886002	−	0.153460i	0.818319	−	0.574764i	$-0.194906\pi$
$887$	−2340.56	−	4053.97i	−0.0886002	−	0.153460i	−0.906920	+	0.421304i	$0.861573\pi$
$888$		0			0
$889$		0			0
$890$			4513.42i			0.169989i
$891$		0			0
$892$	−16721.1	−	9653.90i	−0.627648	−	0.362373i
$893$	−25814.0	−	14903.7i	−0.967337	−	0.558492i
$894$		0			0
$895$		−	31830.6i		−	1.18880i
$896$		0			0
$897$		0			0
$898$	−2154.49	−	3731.69i	−0.0800627	−	0.138673i
$899$	−18702.7	+	32394.0i	−0.693848	+	1.20178i
$900$		0			0
$901$	14942.7	−	8627.17i	0.552512	−	0.318993i
$902$	11517.0			0.425136
$903$		0			0
$904$	−871.564			−0.0320661
$905$	−2184.93	+	1261.47i	−0.0802535	+	0.0463344i
$906$		0			0
$907$	24203.3	−	41921.3i	0.886060	−	1.53470i	0.0415653	−	0.999136i	$-0.486766\pi$
$907$	24203.3	−	41921.3i	0.886060	−	1.53470i	0.844494	−	0.535564i	$-0.179901\pi$
$908$	16840.9	+	29169.3i	0.615512	+	1.06610i
$909$		0			0
$910$		0			0
$911$		−	20920.5i		−	0.760842i	−0.924813	−	0.380421i	$-0.875779\pi$
$911$		−	20920.5i		−	0.760842i	0.924813	−	0.380421i	$-0.124221\pi$
$912$		0			0
$913$	49546.3	+	28605.6i	1.79600	+	1.03692i
$914$	1833.05	+	1058.31i	0.0663367	+	0.0382995i
$915$		0			0
$916$			23592.4i			0.850998i
$917$		0			0
$918$		0			0
$919$	−16735.7	−	28987.1i	−0.600717	−	1.04047i	−0.992713	−	0.120506i	$-0.961548\pi$
$919$	−16735.7	−	28987.1i	−0.600717	−	1.04047i	0.391995	−	0.919967i	$-0.371785\pi$
$920$	−2784.04	+	4822.10i	−0.0997686	+	0.172804i
$921$		0			0
$922$	4019.98	−	2320.94i	0.143591	−	0.0829023i
$923$	77084.5			2.74893
$924$		0			0
$925$	−8526.48			−0.303080
$926$	−4211.21	+	2431.34i	−0.149448	+	0.0862838i
$927$		0			0
$928$	11568.9	−	20038.0i	0.409234	−	0.708814i
$929$	−4685.49	−	8115.50i	−0.165475	−	0.286610i	0.771349	−	0.636412i	$-0.219582\pi$
$929$	−4685.49	−	8115.50i	−0.165475	−	0.286610i	−0.936824	+	0.349802i	$0.886249\pi$
$930$		0			0
$931$		0			0
$932$			34818.8i			1.22374i
$933$		0			0
$934$	1137.27	+	656.602i	0.0398421	+	0.0230029i
$935$	18114.8	+	10458.6i	0.633601	+	0.365810i
$936$		0			0
$937$		−	29702.0i		−	1.03556i	−0.855513	−	0.517781i	$-0.826758\pi$
$937$		−	29702.0i		−	1.03556i	0.855513	−	0.517781i	$-0.173242\pi$
$938$		0			0
$939$		0			0
$940$	23578.1	+	40838.5i	0.818120	+	1.41703i
$941$	2451.67	−	4246.41i	0.0849331	−	0.147108i	−0.820430	−	0.571748i	$-0.806266\pi$
$941$	2451.67	−	4246.41i	0.0849331	−	0.147108i	0.905363	+	0.424639i	$0.139599\pi$
$942$		0			0
$943$	−16342.6	+	9435.42i	−0.564358	+	0.325832i
$944$	33013.3			1.13823
$945$		0			0
$946$	3648.44			0.125392
$947$	18190.4	−	10502.3i	0.624192	−	0.360378i	−0.154307	−	0.988023i	$-0.549315\pi$
$947$	18190.4	−	10502.3i	0.624192	−	0.360378i	0.778499	+	0.627645i	$0.215981\pi$
$948$		0			0
$949$	−17584.4	+	30457.1i	−0.601489	+	1.04181i
$950$	−385.278	−	667.321i	−0.0131580	−	0.0227903i
$951$		0			0
$952$		0			0
$953$		−	4598.25i		−	0.156298i	−0.996942	−	0.0781489i	$-0.975099\pi$
$953$		−	4598.25i		−	0.156298i	0.996942	−	0.0781489i	$-0.0249010\pi$
$954$		0			0
$955$	−8053.98	−	4649.97i	−0.272901	−	0.157560i
$956$	4854.03	+	2802.47i	0.164216	+	0.0948102i
$957$		0			0
$958$			2113.52i			0.0712785i
$959$		0			0
$960$		0			0
$961$	2313.53	+	4007.15i	0.0776587	+	0.134509i
$962$	8819.08	−	15275.1i	0.295570	−	0.511942i
$963$		0			0
$964$	1641.37	−	947.644i	0.0548391	−	0.0316614i
$965$	10392.8			0.346691
$966$		0			0
$967$	52408.6			1.74286			0.871431	−	0.490518i	$-0.163192\pi$
$967$	52408.6			1.74286			0.871431	+	0.490518i	$0.163192\pi$
$968$	−5189.65	+	2996.25i	−0.172316	+	0.0994866i
$969$		0			0
$970$	−4224.98	+	7317.89i	−0.139852	+	0.242230i
$971$	−24356.2	−	42186.1i	−0.804971	−	1.39425i	−0.916311	−	0.400468i	$-0.868847\pi$
$971$	−24356.2	−	42186.1i	−0.804971	−	1.39425i	0.111339	−	0.993782i	$-0.464486\pi$
$972$		0			0
$973$		0			0
$974$		−	756.236i		−	0.0248782i
$975$		0			0
$976$	−1153.16	−	665.776i	−0.0378193	−	0.0218350i
$977$	−10094.1	−	5827.83i	−0.330541	−	0.190838i	0.325540	−	0.945528i	$-0.394454\pi$
$977$	−10094.1	−	5827.83i	−0.330541	−	0.190838i	−0.656081	+	0.754690i	$0.727787\pi$
$978$		0			0
$979$		−	25624.9i		−	0.836544i
$980$		0			0
$981$		0			0
$982$	2427.54	+	4204.63i	0.0788860	+	0.136635i
$983$	−20228.6	+	35036.9i	−0.656350	+	1.13683i	0.325204	+	0.945644i	$0.394567\pi$
$983$	−20228.6	+	35036.9i	−0.656350	+	1.13683i	−0.981554	+	0.191187i	$0.938766\pi$
$984$		0			0
$985$	10812.3	−	6242.47i	0.349754	−	0.201931i
$986$	−5096.38			−0.164606
$987$		0			0
$988$	−29438.1			−0.947925
$989$	−5177.16	+	2989.04i	−0.166455	+	0.0961030i
$990$		0			0
$991$	−4830.44	+	8366.57i	−0.154838	+	0.268187i	−0.933000	−	0.359877i	$-0.882819\pi$
$991$	−4830.44	+	8366.57i	−0.154838	+	0.268187i	0.778162	+	0.628063i	$0.216152\pi$
$992$	−10645.0	−	18437.7i	−0.340705	−	0.590118i
$993$		0			0
$994$		0			0
$995$			62309.4i			1.98527i
$996$		0			0
$997$	4327.53	+	2498.50i	0.137467	+	0.0793665i	0.567156	−	0.823610i	$-0.308044\pi$
$997$	4327.53	+	2498.50i	0.137467	+	0.0793665i	−0.429689	+	0.902977i	$0.641377\pi$
$998$	1010.12	+	583.194i	0.0320389	+	0.0184977i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.d.80.13		48
3.2	odd	2	inner	441.4.p.d.80.12		48
7.2	even	3	inner	441.4.p.d.215.11		48
7.3	odd	6		441.4.c.b.440.6	yes	24
7.4	even	3		441.4.c.b.440.20	yes	24
7.5	odd	6	inner	441.4.p.d.215.12		48
7.6	odd	2	inner	441.4.p.d.80.14		48
21.2	odd	6	inner	441.4.p.d.215.14		48
21.5	even	6	inner	441.4.p.d.215.13		48
21.11	odd	6		441.4.c.b.440.5	✓	24
21.17	even	6		441.4.c.b.440.19	yes	24
21.20	even	2	inner	441.4.p.d.80.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.4.c.b.440.5	✓	24	21.11	odd	6
441.4.c.b.440.6	yes	24	7.3	odd	6
441.4.c.b.440.19	yes	24	21.17	even	6
441.4.c.b.440.20	yes	24	7.4	even	3
441.4.p.d.80.11		48	21.20	even	2	inner
441.4.p.d.80.12		48	3.2	odd	2	inner
441.4.p.d.80.13		48	1.1	even	1	trivial
441.4.p.d.80.14		48	7.6	odd	2	inner
441.4.p.d.215.11		48	7.2	even	3	inner
441.4.p.d.215.12		48	7.5	odd	6	inner
441.4.p.d.215.13		48	21.5	even	6	inner
441.4.p.d.215.14		48	21.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.555155 - 0.320519i) q^{2} +(-3.79454 + 6.57233i) q^{4} +(-6.03646 - 10.4555i) q^{5} +9.99318i q^{8} +O(q^{10})\)	\(q+(0.555155 - 0.320519i) q^{2} +(-3.79454 + 6.57233i) q^{4} +(-6.03646 - 10.4555i) q^{5} +9.99318i q^{8} +(-6.70234 - 3.86960i) q^{10} +(38.0525 + 21.9696i) q^{11} -66.9783i q^{13} +(-27.1533 - 47.0309i) q^{16} +(-19.7155 + 34.1482i) q^{17} +(-50.1554 + 28.9572i) q^{19} +91.6223 q^{20} +28.1667 q^{22} +(-39.9687 + 23.0759i) q^{23} +(-10.3778 + 17.9748i) q^{25} +(-21.4678 - 37.1833i) q^{26} +201.623i q^{29} +(160.666 + 92.7605i) q^{31} +(-99.3833 - 57.3790i) q^{32} +25.2767i q^{34} +(205.402 + 355.767i) q^{37} +(-18.5626 + 32.1515i) q^{38} +(104.483 - 60.3234i) q^{40} +408.886 q^{41} +129.530 q^{43} +(-288.783 + 166.729i) q^{44} +(-14.7925 + 25.6214i) q^{46} +(257.340 + 445.726i) q^{47} +13.3051i q^{50} +(440.204 + 254.152i) q^{52} +(-378.958 - 218.792i) q^{53} -530.475i q^{55} +(64.6241 + 111.932i) q^{58} +(-303.953 + 526.462i) q^{59} +(21.2342 - 12.2596i) q^{61} +118.926 q^{62} +360.888 q^{64} +(-700.289 + 404.312i) q^{65} +(-220.750 + 382.350i) q^{67} +(-149.622 - 259.153i) q^{68} +1150.89i q^{71} +(-454.730 - 262.539i) q^{73} +(228.060 + 131.671i) q^{74} -439.517i q^{76} +(75.9251 + 131.506i) q^{79} +(-327.820 + 567.800i) q^{80} +(226.995 - 131.055i) q^{82} +1302.05 q^{83} +476.047 q^{85} +(71.9094 - 41.5169i) q^{86} +(-219.546 + 380.266i) q^{88} +(-291.595 - 505.057i) q^{89} -350.250i q^{92} +(285.727 + 164.965i) q^{94} +(605.522 + 349.598i) q^{95} -1091.84i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4}+O(q^{10}) \) 48 * q + 96 * q^4	\( 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) \) 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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