LMFDB - Embedded newform 441.4.p.d.80.14

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			80.14
Character	$\chi$	$=$	441.80
Dual form			441.4.p.d.215.14

$q$-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	$0.0148780\pi$
$5$	6.03646	+	10.4555i	0.539918	+	0.935165i	−0.458990	+	0.888441i	$0.651789\pi$
$6$		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	$0.253336\pi$
$13$			66.9783i			1.42896i	−0.699657	+	0.714479i	$0.746664\pi$
$14$		0			0
$15$		0			0
$16$	−27.1533	−	47.0309i	−0.424270	−	0.734857i
$17$	19.7155	−	34.1482i	0.281277	−	0.487186i	−0.690423	−	0.723406i	$-0.742575\pi$
$17$	19.7155	−	34.1482i	0.281277	−	0.487186i	0.971700	+	0.236220i	$0.0759087\pi$
$18$		0			0
$19$	50.1554	−	28.9572i	0.605601	−	0.349644i	−0.165641	−	0.986186i	$-0.552969\pi$
$19$	50.1554	−	28.9572i	0.605601	−	0.349644i	0.771242	+	0.636542i	$0.219636\pi$
$20$	−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	−0.0437720	−	0.999042i	$-0.513938\pi$
$31$	−160.666	−	92.7605i	−0.930853	−	0.537428i	−0.887081	+	0.461613i	$0.847271\pi$
$32$	−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	$-0.784144\pi$
$41$	−408.886			−1.55749			−0.778746	+	0.627339i	$0.784144\pi$
$42$		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	$-0.872210\pi$
$47$	−257.340	−	445.726i	−0.798658	−	1.38332i	0.121832	−	0.992551i	$-0.461123\pi$
$48$		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	$-0.599327\pi$
$59$	303.953	−	526.462i	0.670701	−	1.16169i	0.977706	−	0.209980i	$-0.0673398\pi$
$60$		0			0
$61$	−21.2342	+	12.2596i	−0.0445699	+	0.0257324i	−0.522119	−	0.852872i	$-0.674858\pi$
$61$	−21.2342	+	12.2596i	−0.0445699	+	0.0257324i	0.477549	+	0.878605i	$0.341525\pi$
$62$	−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	0.818082	−	0.575102i	$-0.195038\pi$
$73$	454.730	+	262.539i	0.729070	+	0.420929i	−0.0890117	+	0.996031i	$0.528371\pi$
$74$	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	$-0.830134\pi$
$83$	−1302.05			−1.72191			−0.860956	+	0.508680i	$0.830134\pi$
$84$		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	0.985767	−	0.168115i	$-0.0537679\pi$
$89$	291.595	+	505.057i	0.347292	+	0.601528i	−0.638475	+	0.769642i	$0.720435\pi$
$90$		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	$0.193616\pi$
$97$			1091.84i			1.14288i	−0.820643	+	0.571441i	$0.806384\pi$
$98$		0			0
$99$		0			0
$100$	−78.7576	−	136.412i	−0.0787576	−	0.136412i
$101$	78.3866	−	135.770i	0.0772254	−	0.133758i	−0.824826	−	0.565386i	$-0.808727\pi$
$101$	78.3866	−	135.770i	0.0772254	−	0.133758i	0.902052	+	0.431628i	$0.142061\pi$
$102$		0			0
$103$	208.779	−	120.539i	0.199725	−	0.115311i	−0.396802	−	0.917904i	$-0.629880\pi$
$103$	208.779	−	120.539i	0.199725	−	0.115311i	0.596527	+	0.802593i	$0.296547\pi$
$104$	−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	0.546930	−	0.837178i	$-0.315796\pi$
$131$	−677.042	−	1172.67i	−0.451553	−	0.782112i	−0.998483	+	0.0550661i	$0.982463\pi$
$132$		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	$-0.744688\pi$
$139$		−	2355.95i		−	1.43762i	0.695208	−	0.718808i	$-0.255312\pi$
$140$		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	0.656623	−	0.754219i	$-0.271984\pi$
$157$	652.641	+	376.803i	0.331761	+	0.191542i	−0.324862	+	0.945762i	$0.605318\pi$
$158$	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	$-0.264283\pi$
$167$	2912.06			1.34935			0.674676	+	0.738114i	$0.264283\pi$
$168$		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	0.609143	−	0.793060i	$-0.291514\pi$
$173$	−869.770	−	1506.49i	−0.382239	−	0.662057i	−0.991382	+	0.131003i	$0.958180\pi$
$174$		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	$0.0136625\pi$
$181$			208.975i			0.0858175i	−0.999079	+	0.0429087i	$0.986338\pi$
$182$		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	$0.0378670\pi$
$199$	4469.63	+	2580.54i	1.59218	+	0.919246i	0.599248	+	0.800564i	$0.295466\pi$
$200$	−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	$-0.875237\pi$
$223$		−	2544.16i		−	0.763989i	0.924165	−	0.381994i	$-0.124763\pi$
$224$		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	$0.391412\pi$
$227$	−2219.10	+	3843.59i	−0.648840	+	1.12382i	−0.983400	+	0.181449i	$0.941921\pi$
$228$		0			0
$229$	−2692.24	+	1554.36i	−0.776892	+	0.448539i	−0.835328	−	0.549753i	$-0.814722\pi$
$229$	−2692.24	+	1554.36i	−0.776892	+	0.448539i	0.0584360	+	0.998291i	$0.481389\pi$
$230$	−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	0.528626	−	0.848855i	$-0.322708\pi$
$241$	216.280	+	124.870i	0.0578085	+	0.0333757i	−0.470817	+	0.882231i	$0.656041\pi$
$242$	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	$-0.672338\pi$
$251$	−4098.68			−1.03070			−0.515351	+	0.856979i	$0.672338\pi$
$252$		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	0.656800	−	0.754065i	$-0.271910\pi$
$257$	−1337.52	−	2316.66i	−0.324640	−	0.562293i	−0.981439	+	0.191773i	$0.938576\pi$
$258$		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	−0.926289	−	0.376815i	$-0.877019\pi$
$269$	−603.608	+	1045.48i	−0.136813	+	0.236967i	0.789476	+	0.613782i	$0.210353\pi$
$270$		0			0
$271$	3938.31	−	2273.78i	0.882786	−	0.509677i	0.0112103	−	0.999937i	$-0.496432\pi$
$271$	3938.31	−	2273.78i	0.882786	−	0.509677i	0.871576	+	0.490260i	$0.163098\pi$
$272$	−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	0.869473	−	0.493980i	$-0.164458\pi$
$283$	4172.42	+	2408.95i	0.876411	+	0.505996i	0.00693786	+	0.999976i	$0.497792\pi$
$284$	−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	$-0.260383\pi$
$293$	6857.68			1.36734			0.683669	+	0.729792i	$0.260383\pi$
$294$		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	$0.247079\pi$
$307$			7537.04i			1.40118i	−0.713565	+	0.700589i	$0.752921\pi$
$308$		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	$-0.663205\pi$
$311$	2793.76	−	4838.93i	0.509388	−	0.882285i	0.999941	−	0.0108742i	$-0.00346142\pi$
$312$		0			0
$313$	−3655.95	+	2110.76i	−0.660212	+	0.381174i	−0.792358	−	0.610057i	$-0.791147\pi$
$313$	−3655.95	+	2110.76i	−0.660212	+	0.381174i	0.132146	+	0.991230i	$0.457813\pi$
$314$	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	$0.332283\pi$
$349$			11271.1i			1.72874i	−0.502855	+	0.864370i	$0.667717\pi$
$350$		0			0
$351$		0			0
$352$	−2521.19	−	4366.83i	−0.381761	−	0.661229i
$353$	828.962	−	1435.80i	0.124989	−	0.216488i	−0.796740	−	0.604323i	$-0.793444\pi$
$353$	828.962	−	1435.80i	0.124989	−	0.216488i	0.921729	+	0.387835i	$0.126777\pi$
$354$		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	0.746184	−	0.665739i	$-0.231884\pi$
$367$	3815.77	+	2203.04i	0.542729	+	0.313345i	−0.203455	+	0.979084i	$0.565217\pi$
$368$	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	0.999727	−	0.0233693i	$-0.00743934\pi$
$383$	3595.01	+	6226.74i	0.479625	+	0.830735i	−0.520102	+	0.854104i	$0.674106\pi$
$384$		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	0.326667	−	0.945140i	$-0.394075\pi$
$397$	10350.6	−	5975.91i	1.30851	−	0.755471i	0.981848	+	0.189668i	$0.0607412\pi$
$398$	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	0.204498	−	0.978867i	$-0.434444\pi$
$409$	−4474.70	−	2583.47i	−0.540977	−	0.312333i	−0.745475	+	0.666534i	$0.767777\pi$
$410$	−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	$-0.800726\pi$
$419$	−13900.4			−1.62071			−0.810356	+	0.585938i	$0.800726\pi$
$420$		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	$-0.979019\pi$
$433$		−	1186.95i		−	0.131735i	0.997828	−	0.0658674i	$-0.0209814\pi$
$434$		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	−0.0314484	−	0.999505i	$-0.510012\pi$
$439$	7527.93	−	4346.25i	0.818425	−	0.472518i	0.849873	+	0.526988i	$0.176679\pi$
$440$	−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	$-0.619200\pi$
$461$	−7241.19			−0.731574			−0.365787	+	0.930699i	$0.619200\pi$
$462$		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	0.810806	−	0.585315i	$-0.199029\pi$
$467$	−1024.28	−	1774.11i	−0.101495	−	0.175794i	−0.912301	+	0.409521i	$0.865696\pi$
$468$		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	−0.776626	−	0.629962i	$-0.783071\pi$
$479$	1648.52	−	2855.32i	0.157250	−	0.272365i	0.933876	+	0.357597i	$0.116404\pi$
$480$		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	$-0.256283\pi$
$503$	15635.9			1.38602			0.693012	+	0.720926i	$0.256283\pi$
$504$		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	0.785367	−	0.619031i	$-0.212474\pi$
$509$	−1646.90	−	2852.51i	−0.143413	−	0.248399i	−0.928780	+	0.370632i	$0.879141\pi$
$510$		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	−0.788326	−	0.615258i	$-0.789052\pi$
$521$	1649.02	−	2856.19i	0.138666	−	0.240176i	0.926992	+	0.375081i	$0.122385\pi$
$522$		0			0
$523$	15438.1	−	8913.21i	1.29075	−	0.745215i	0.311963	−	0.950094i	$-0.399013\pi$
$523$	15438.1	−	8913.21i	1.29075	−	0.745215i	0.978787	+	0.204879i	$0.0656801\pi$
$524$	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	−0.933743	−	0.357944i	$-0.883478\pi$
$563$	−2095.75	+	3629.94i	−0.156883	+	0.271730i	0.776860	+	0.629673i	$0.216811\pi$
$564$		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	0.896866	−	0.442303i	$-0.145838\pi$
$577$	13336.8	+	7700.03i	0.962253	+	0.555557i	0.0653874	+	0.997860i	$0.479172\pi$
$578$	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	$-0.470380\pi$
$587$	2642.97			0.185838			0.0929190	+	0.995674i	$0.470380\pi$
$588$		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	0.844467	−	0.535607i	$-0.179917\pi$
$593$	−600.950	−	1040.88i	−0.0416156	−	0.0720803i	−0.886083	+	0.463527i	$0.846584\pi$
$594$		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	$-0.917258\pi$
$601$		−	7573.82i		−	0.514047i	0.966405	−	0.257024i	$-0.0827418\pi$
$602$		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	−0.948015	−	0.318226i	$-0.896913\pi$
$607$	−17144.7	+	9898.52i	−1.14643	+	0.661892i	−0.198416	+	0.980118i	$0.563580\pi$
$608$	−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	−0.0357526	−	0.999361i	$-0.511383\pi$
$619$	−14154.6	−	8172.19i	−0.919101	−	0.530643i	−0.883348	+	0.468718i	$0.844716\pi$
$620$	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	$-0.857178\pi$
$643$		−	14145.6i		−	0.867570i	0.901016	−	0.433785i	$-0.142822\pi$
$644$		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	$0.425552\pi$
$647$	−11957.3	+	20710.6i	−0.726568	+	1.25845i	−0.958326	+	0.285678i	$0.907781\pi$
$648$		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	0.497392	−	0.867526i	$-0.334291\pi$
$661$	−88.5773	−	51.1401i	−0.00521219	−	0.00300926i	−0.502604	+	0.864517i	$0.667625\pi$
$662$	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	$-0.969911\pi$
$677$	−10208.1	−	17680.9i	−0.579510	−	1.00374i	0.416026	−	0.909353i	$-0.363423\pi$
$678$		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	$-0.309919\pi$
$691$	28328.7	−	16355.6i	1.55959	−	0.900429i	0.997296	−	0.0734905i	$-0.0234139\pi$
$692$	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	$0.148264\pi$
$719$	16111.5	+	27906.0i	0.835688	+	1.44745i	−0.0577818	+	0.998329i	$0.518403\pi$
$720$		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	$0.331004\pi$
$727$			33807.4i			1.72469i	−0.506325	+	0.862343i	$0.668996\pi$
$728$		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	−0.813849	−	0.581077i	$-0.802632\pi$
$733$	−14239.9	+	8221.39i	−0.717546	+	0.414275i	0.0963028	+	0.995352i	$0.469298\pi$
$734$	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	$-0.923303\pi$
$761$	−14531.7	−	25169.6i	−0.692212	−	1.19895i	0.278900	−	0.960320i	$-0.410030\pi$
$762$		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	$-0.592280\pi$
$769$		−	40870.3i		−	1.91654i	0.285861	−	0.958271i	$-0.407720\pi$
$770$		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	$-0.446579\pi$
$773$	20145.8	−	34893.5i	0.937378	−	1.62359i	0.770337	−	0.637637i	$-0.220088\pi$
$774$		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	0.594867	−	0.803824i	$-0.297205\pi$
$787$	4331.01	+	2500.51i	0.196167	+	0.113257i	−0.398699	+	0.917082i	$0.630538\pi$
$788$	−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	$-0.437620\pi$
$797$	8762.59			0.389444			0.194722	+	0.980858i	$0.437620\pi$
$798$		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	$0.0246788\pi$
$811$			3577.67i			0.154906i	−0.996996	+	0.0774530i	$0.975321\pi$
$812$		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	−0.296735	−	0.954960i	$-0.595898\pi$
$829$	−30364.1	−	17530.7i	−1.27212	−	0.734460i	−0.975387	+	0.220500i	$0.929231\pi$
$830$	−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	$-0.531543\pi$
$839$	−4808.56			−0.197866			−0.0989332	+	0.995094i	$0.531543\pi$
$840$		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	$0.0609784\pi$
$853$			9486.81i			0.380800i	−0.981707	+	0.190400i	$0.939022\pi$
$854$		0			0
$855$		0			0
$856$	−64.1433	−	111.099i	−0.00256118	−	0.00443610i
$857$	−11262.4	+	19507.0i	−0.448909	+	0.777533i	−0.998315	−	0.0580220i	$-0.981521\pi$
$857$	−11262.4	+	19507.0i	−0.448909	+	0.777533i	0.549406	+	0.835555i	$0.314854\pi$
$858$		0			0
$859$	23940.7	−	13822.2i	0.950927	−	0.549018i	0.0575581	−	0.998342i	$-0.481669\pi$
$859$	23940.7	−	13822.2i	0.950927	−	0.549018i	0.893369	+	0.449324i	$0.148335\pi$
$860$	−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	$-0.567286\pi$
$881$	−10973.0			−0.419626			−0.209813	+	0.977741i	$0.567286\pi$
$882$		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	0.906920	−	0.421304i	$-0.138427\pi$
$887$	2340.56	+	4053.97i	0.0886002	+	0.153460i	−0.818319	+	0.574764i	$0.805094\pi$
$888$		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	0.936824	−	0.349802i	$-0.113751\pi$
$929$	4685.49	+	8115.50i	0.165475	+	0.286610i	−0.771349	+	0.636412i	$0.780418\pi$
$930$		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	$0.173242\pi$
$937$			29702.0i			1.03556i	−0.855513	+	0.517781i	$0.826758\pi$
$938$		0			0
$939$		0			0
$940$	23578.1	+	40838.5i	0.818120	+	1.41703i
$941$	−2451.67	+	4246.41i	−0.0849331	+	0.147108i	−0.905363	−	0.424639i	$-0.860401\pi$
$941$	−2451.67	+	4246.41i	−0.0849331	+	0.147108i	0.820430	+	0.571748i	$0.193734\pi$
$942$		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	$0.131153\pi$
$971$	24356.2	+	42186.1i	0.804971	+	1.39425i	−0.111339	+	0.993782i	$0.535514\pi$
$972$		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	$-0.605433\pi$
$983$	20228.6	−	35036.9i	0.656350	−	1.13683i	0.981554	−	0.191187i	$-0.0612337\pi$
$984$		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	0.429689	−	0.902977i	$-0.358623\pi$
$997$	−4327.53	−	2498.50i	−0.137467	−	0.0793665i	−0.567156	+	0.823610i	$0.691956\pi$
$998$	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.80.14		48
3.2	odd	2	inner	441.4.p.d.80.11		48
7.2	even	3	inner	441.4.p.d.215.12		48
7.3	odd	6		441.4.c.b.440.20	yes	24
7.4	even	3		441.4.c.b.440.6	yes	24
7.5	odd	6	inner	441.4.p.d.215.11		48
7.6	odd	2	inner	441.4.p.d.80.13		48
21.2	odd	6	inner	441.4.p.d.215.13		48
21.5	even	6	inner	441.4.p.d.215.14		48
21.11	odd	6		441.4.c.b.440.19	yes	24
21.17	even	6		441.4.c.b.440.5	✓	24
21.20	even	2	inner	441.4.p.d.80.12		48

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