LMFDB - Embedded newform 99.3.k.b.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21x^{14} + 227x^{12} - 1488x^{10} + 24225x^{8} - 62832x^{6} + 64372x^{4} + 7986x^{2} + 14641 $ x^16 - 21x^14 + 227x^12 - 1488x^10 + 24225x^8 - 62832x^6 + 64372x^4 + 7986*x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.4
Root			$1.83190 - 2.52140i$ of defining polynomial
Character	$\chi$	$=$	99.46
Dual form			99.3.k.b.28.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.96408 + 0.963089i) q^{2} +(4.62219 + 3.35821i) q^{4} +(0.439256 + 1.35189i) q^{5} +(2.23863 - 3.08121i) q^{7} +(3.13867 + 4.32000i) q^{8} +O(q^{10})$	\(q+(2.96408 + 0.963089i) q^{2} +(4.62219 + 3.35821i) q^{4} +(0.439256 + 1.35189i) q^{5} +(2.23863 - 3.08121i) q^{7} +(3.13867 + 4.32000i) q^{8} +4.43016i q^{10} +(0.450262 + 10.9908i) q^{11} +(-20.6093 - 6.69638i) q^{13} +(9.60298 - 6.97698i) q^{14} +(-1.91935 - 5.90715i) q^{16} +(16.1554 - 5.24922i) q^{17} +(-11.4850 - 15.8077i) q^{19} +(-2.50962 + 7.72381i) q^{20} +(-9.25049 + 33.0112i) q^{22} -4.82866 q^{23} +(18.5908 - 13.5070i) q^{25} +(-54.6386 - 39.6973i) q^{26} +(20.6948 - 6.72414i) q^{28} +(-26.7340 + 36.7963i) q^{29} +(-6.47773 + 19.9364i) q^{31} -40.7171i q^{32} +52.9416 q^{34} +(5.14880 + 1.67295i) q^{35} +(17.4008 + 12.6424i) q^{37} +(-18.8182 - 57.9164i) q^{38} +(-4.46150 + 6.14073i) q^{40} +(21.5764 + 29.6974i) q^{41} -10.0872i q^{43} +(-34.8282 + 52.3135i) q^{44} +(-14.3126 - 4.65043i) q^{46} +(53.7954 - 39.0846i) q^{47} +(10.6594 + 32.8063i) q^{49} +(68.1130 - 22.1313i) q^{50} +(-72.7723 - 100.162i) q^{52} +(-25.4792 + 78.4170i) q^{53} +(-14.6606 + 5.43647i) q^{55} +20.3372 q^{56} +(-114.680 + 83.3199i) q^{58} +(-51.7702 - 37.6132i) q^{59} +(10.3744 - 3.37084i) q^{61} +(-38.4011 + 52.8545i) q^{62} +(31.5368 - 97.0602i) q^{64} -30.8030i q^{65} +22.6034 q^{67} +(92.3014 + 29.9906i) q^{68} +(13.6503 + 9.91751i) q^{70} +(13.7276 + 42.2492i) q^{71} +(-41.1890 + 56.6919i) q^{73} +(39.4016 + 54.2316i) q^{74} -111.635i q^{76} +(34.8729 + 23.2170i) q^{77} +(132.665 + 43.1053i) q^{79} +(7.14273 - 5.18950i) q^{80} +(35.3531 + 108.806i) q^{82} +(106.716 - 34.6742i) q^{83} +(14.1928 + 19.5346i) q^{85} +(9.71487 - 29.8993i) q^{86} +(-46.0670 + 36.4415i) q^{88} -63.5921 q^{89} +(-66.7698 + 48.5111i) q^{91} +(-22.3190 - 16.2157i) q^{92} +(197.096 - 64.0404i) q^{94} +(16.3255 - 22.4701i) q^{95} +(31.2333 - 96.1262i) q^{97} +107.507i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) $ 16 * q - 4 * q^4 + 30 * q^7	$ 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) $ 16 * q - 4 * q^4 + 30 * q^7 - 30 * q^13 - 176 * q^16 + 90 * q^22 - 74 * q^25 - 50 * q^28 + 130 * q^31 + 328 * q^34 + 90 * q^37 + 450 * q^40 - 370 * q^46 - 54 * q^49 - 790 * q^52 - 476 * q^55 - 630 * q^58 + 210 * q^61 + 1104 * q^64 + 300 * q^67 + 268 * q^70 - 170 * q^73 + 30 * q^79 + 90 * q^82 - 610 * q^85 - 600 * q^88 - 402 * q^91 + 1030 * q^94 + 870 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	2.96408	+	0.963089i	1.48204	+	0.481545i	0.934722	−	0.355379i	$-0.115648\pi$
$2$	2.96408	+	0.963089i	1.48204	+	0.481545i	0.547320	+	0.836924i	$0.315648\pi$
$3$		0			0
$3$		0			0
$4$	4.62219	+	3.35821i	1.15555	+	0.839554i
$5$	0.439256	+	1.35189i	0.0878512	+	0.270378i	0.985325	−	0.170690i	$-0.0545997\pi$
$5$	0.439256	+	1.35189i	0.0878512	+	0.270378i	−0.897474	+	0.441068i	$0.854600\pi$
$6$		0			0
$7$	2.23863	−	3.08121i	0.319805	−	0.440174i	−0.618603	−	0.785704i	$-0.712301\pi$
$7$	2.23863	−	3.08121i	0.319805	−	0.440174i	0.938408	+	0.345530i	$0.112301\pi$
$8$	3.13867	+	4.32000i	0.392333	+	0.540001i
$9$		0			0
$10$			4.43016i			0.443016i
$11$	0.450262	+	10.9908i	0.0409329	+	0.999162i
$11$	0.450262	+	10.9908i	0.0409329	+	0.999162i
$12$		0			0
$13$	−20.6093	−	6.69638i	−1.58533	−	0.515106i	−0.621910	−	0.783089i	$-0.713643\pi$
$13$	−20.6093	−	6.69638i	−1.58533	−	0.515106i	−0.963424	+	0.267982i	$0.913643\pi$
$14$	9.60298	−	6.97698i	0.685927	−	0.498355i
$15$		0			0
$16$	−1.91935	−	5.90715i	−0.119959	−	0.369197i
$17$	16.1554	−	5.24922i	0.950320	−	0.308778i	0.207474	−	0.978240i	$-0.433476\pi$
$17$	16.1554	−	5.24922i	0.950320	−	0.308778i	0.742846	+	0.669463i	$0.233476\pi$
$18$		0			0
$19$	−11.4850	−	15.8077i	−0.604472	−	0.831985i	0.391636	−	0.920120i	$-0.371909\pi$
$19$	−11.4850	−	15.8077i	−0.604472	−	0.831985i	−0.996108	+	0.0881356i	$0.971909\pi$
$20$	−2.50962	+	7.72381i	−0.125481	+	0.386190i
$21$		0			0
$22$	−9.25049	+	33.0112i	−0.420477	+	1.50051i
$23$	−4.82866			−0.209942			−0.104971	−	0.994475i	$-0.533475\pi$
$23$	−4.82866			−0.209942			−0.104971	+	0.994475i	$0.533475\pi$
$24$		0			0
$25$	18.5908	−	13.5070i	0.743630	−	0.540279i
$26$	−54.6386	−	39.6973i	−2.10148	−	1.52682i
$27$		0			0
$28$	20.6948	−	6.72414i	0.739099	−	0.240148i
$29$	−26.7340	+	36.7963i	−0.921863	+	1.26884i	0.0410863	+	0.999156i	$0.486918\pi$
$29$	−26.7340	+	36.7963i	−0.921863	+	1.26884i	−0.962950	+	0.269681i	$0.913082\pi$
$30$		0			0
$31$	−6.47773	+	19.9364i	−0.208959	+	0.643110i	0.790569	+	0.612374i	$0.209785\pi$
$31$	−6.47773	+	19.9364i	−0.208959	+	0.643110i	−0.999528	+	0.0307360i	$0.990215\pi$
$32$		−	40.7171i		−	1.27241i
$33$		0			0
$34$	52.9416			1.55710
$35$	5.14880	+	1.67295i	0.147109	+	0.0477985i
$36$		0			0
$37$	17.4008	+	12.6424i	0.470291	+	0.341687i	0.797555	−	0.603247i	$-0.206127\pi$
$37$	17.4008	+	12.6424i	0.470291	+	0.341687i	−0.327264	+	0.944933i	$0.606127\pi$
$38$	−18.8182	−	57.9164i	−0.495215	−	1.52412i
$39$		0			0
$40$	−4.46150	+	6.14073i	−0.111537	+	0.153518i
$41$	21.5764	+	29.6974i	0.526254	+	0.724326i	0.986554	−	0.163437i	$-0.0522581\pi$
$41$	21.5764	+	29.6974i	0.526254	+	0.724326i	−0.460300	+	0.887763i	$0.652258\pi$
$42$		0			0
$43$		−	10.0872i		−	0.234586i	−0.993097	−	0.117293i	$-0.962578\pi$
$43$		−	10.0872i		−	0.234586i	0.993097	−	0.117293i	$-0.0374217\pi$
$44$	−34.8282	+	52.3135i	−0.791550	+	1.18894i
$45$		0			0
$46$	−14.3126	−	4.65043i	−0.311143	−	0.101096i
$47$	53.7954	−	39.0846i	1.14458	−	0.831588i	0.156831	−	0.987625i	$-0.449872\pi$
$47$	53.7954	−	39.0846i	1.14458	−	0.831588i	0.987751	+	0.156038i	$0.0498721\pi$
$48$		0			0
$49$	10.6594	+	32.8063i	0.217539	+	0.669517i
$50$	68.1130	−	22.1313i	1.36226	−	0.442625i
$51$		0			0
$52$	−72.7723	−	100.162i	−1.39947	−	1.92620i
$53$	−25.4792	+	78.4170i	−0.480740	+	1.47957i	0.357317	+	0.933983i	$0.383692\pi$
$53$	−25.4792	+	78.4170i	−0.480740	+	1.47957i	−0.838057	+	0.545583i	$0.816308\pi$
$54$		0			0
$55$	−14.6606	+	5.43647i	−0.266556	+	0.0988450i
$56$	20.3372			0.363164
$57$		0			0
$58$	−114.680	+	83.3199i	−1.97724	+	1.43655i
$59$	−51.7702	−	37.6132i	−0.877461	−	0.637512i	0.0551179	−	0.998480i	$-0.482447\pi$
$59$	−51.7702	−	37.6132i	−0.877461	−	0.637512i	−0.932578	+	0.360967i	$0.882447\pi$
$60$		0			0
$61$	10.3744	−	3.37084i	0.170072	−	0.0552596i	−0.222743	−	0.974877i	$-0.571501\pi$
$61$	10.3744	−	3.37084i	0.170072	−	0.0552596i	0.392815	+	0.919617i	$0.371501\pi$
$62$	−38.4011	+	52.8545i	−0.619372	+	0.852492i
$63$		0			0
$64$	31.5368	−	97.0602i	0.492762	−	1.51657i
$65$		−	30.8030i		−	0.473893i
$66$		0			0
$67$	22.6034			0.337364			0.168682	−	0.985671i	$-0.446049\pi$
$67$	22.6034			0.337364			0.168682	+	0.985671i	$0.446049\pi$
$68$	92.3014	+	29.9906i	1.35737	+	0.441038i
$69$		0			0
$70$	13.6503	+	9.91751i	0.195004	+	0.141679i
$71$	13.7276	+	42.2492i	0.193346	+	0.595059i	0.999992	+	0.00402327i	$0.00128065\pi$
$71$	13.7276	+	42.2492i	0.193346	+	0.595059i	−0.806646	+	0.591035i	$0.798719\pi$
$72$		0			0
$73$	−41.1890	+	56.6919i	−0.564234	+	0.776601i	−0.991857	−	0.127356i	$-0.959351\pi$
$73$	−41.1890	+	56.6919i	−0.564234	+	0.776601i	0.427624	+	0.903957i	$0.359351\pi$
$74$	39.4016	+	54.2316i	0.532454	+	0.732860i
$75$		0			0
$76$		−	111.635i		−	1.46888i
$77$	34.8729	+	23.2170i	0.452895	+	0.301519i
$78$		0			0
$79$	132.665	+	43.1053i	1.67930	+	0.545637i	0.984775	−	0.173834i	$-0.0556155\pi$
$79$	132.665	+	43.1053i	1.67930	+	0.545637i	0.694523	+	0.719471i	$0.255615\pi$
$80$	7.14273	−	5.18950i	0.0892842	−	0.0648688i
$81$		0			0
$82$	35.3531	+	108.806i	0.431135	+	1.32690i
$83$	106.716	−	34.6742i	1.28574	−	0.417762i	0.415141	−	0.909757i	$-0.363732\pi$
$83$	106.716	−	34.6742i	1.28574	−	0.417762i	0.870598	+	0.491996i	$0.163732\pi$
$84$		0			0
$85$	14.1928	+	19.5346i	0.166974	+	0.229819i
$86$	9.71487	−	29.8993i	0.112964	−	0.347666i
$87$		0			0
$88$	−46.0670	+	36.4415i	−0.523489	+	0.414108i
$89$	−63.5921			−0.714518			−0.357259	−	0.934005i	$-0.616289\pi$
$89$	−63.5921			−0.714518			−0.357259	+	0.934005i	$0.616289\pi$
$90$		0			0
$91$	−66.7698	+	48.5111i	−0.733734	+	0.533089i
$92$	−22.3190	−	16.2157i	−0.242598	−	0.176257i
$93$		0			0
$94$	197.096	−	64.0404i	2.09677	−	0.681280i
$95$	16.3255	−	22.4701i	0.171847	−	0.236527i
$96$		0			0
$97$	31.2333	−	96.1262i	0.321993	−	0.990992i	−0.650787	−	0.759260i	$-0.725561\pi$
$97$	31.2333	−	96.1262i	0.321993	−	0.990992i	0.972780	−	0.231732i	$-0.0744392\pi$
$98$			107.507i			1.09701i
$99$		0			0
$100$	131.289			1.31289
$101$	−125.715	−	40.8472i	−1.24470	−	0.404428i	−0.388682	−	0.921372i	$-0.627070\pi$
$101$	−125.715	−	40.8472i	−1.24470	−	0.404428i	−0.856019	+	0.516944i	$0.827070\pi$
$102$		0			0
$103$	−40.5805	−	29.4834i	−0.393985	−	0.286247i	0.373102	−	0.927791i	$-0.378294\pi$
$103$	−40.5805	−	29.4834i	−0.393985	−	0.286247i	−0.767087	+	0.641544i	$0.778294\pi$
$104$	−35.7575	−	110.050i	−0.343822	−	1.05817i
$105$		0			0
$106$	−151.045	+	207.896i	−1.42495	+	1.96128i
$107$	−93.5828	−	128.806i	−0.874606	−	1.20379i	−0.977886	−	0.209139i	$-0.932934\pi$
$107$	−93.5828	−	128.806i	−0.874606	−	1.20379i	0.103280	−	0.994652i	$-0.467066\pi$
$108$		0			0
$109$		−	93.4090i		−	0.856963i	−0.903551	−	0.428482i	$-0.859049\pi$
$109$		−	93.4090i		−	0.856963i	0.903551	−	0.428482i	$-0.140951\pi$
$110$	−48.6910	+	1.99474i	−0.442645	+	0.0181340i
$111$		0			0
$112$	−22.4979	−	7.31001i	−0.200874	−	0.0652680i
$113$	−31.1398	+	22.6244i	−0.275573	+	0.200216i	−0.716984	−	0.697089i	$-0.754478\pi$
$113$	−31.1398	+	22.6244i	−0.275573	+	0.200216i	0.441411	+	0.897305i	$0.354478\pi$
$114$		0			0
$115$	−2.12102	−	6.52783i	−0.0184437	−	0.0567637i
$116$	−247.139	+	80.3005i	−2.13051	+	0.692245i
$117$		0			0
$118$	−117.226	−	161.348i	−0.993443	−	1.36736i
$119$	19.9921	−	61.5295i	0.168001	−	0.517054i
$120$		0			0
$121$	−120.595	+	9.89747i	−0.996649	+	0.0817973i
$122$	33.9969			0.278663
$123$		0			0
$124$	−96.8920	+	70.3961i	−0.781387	+	0.567711i
$125$	55.1758	+	40.0875i	0.441406	+	0.320700i
$126$		0			0
$127$	−77.3128	+	25.1204i	−0.608762	+	0.197799i	−0.597144	−	0.802134i	$-0.703698\pi$
$127$	−77.3128	+	25.1204i	−0.608762	+	0.197799i	−0.0116175	+	0.999933i	$0.503698\pi$
$128$	91.2237	−	125.559i	0.712685	−	0.980927i
$129$		0			0
$130$	29.6661	−	91.3027i	0.228200	−	0.702329i
$131$		−	147.346i		−	1.12478i	−0.826874	−	0.562388i	$-0.809883\pi$
$131$		−	147.346i		−	1.12478i	0.826874	−	0.562388i	$-0.190117\pi$
$132$		0			0
$133$	−74.4176			−0.559531
$134$	66.9984	+	21.7691i	0.499988	+	0.162456i
$135$		0			0
$136$	73.3832	+	53.3160i	0.539582	+	0.392030i
$137$	65.5891	+	201.863i	0.478753	+	1.47345i	0.840829	+	0.541301i	$0.182068\pi$
$137$	65.5891	+	201.863i	0.478753	+	1.47345i	−0.362076	+	0.932149i	$0.617932\pi$
$138$		0			0
$139$	128.919	−	177.442i	0.927478	−	1.27656i	−0.0333579	−	0.999443i	$-0.510620\pi$
$139$	128.919	−	177.442i	0.927478	−	1.27656i	0.960835	−	0.277120i	$-0.0893799\pi$
$140$	18.1806	+	25.0235i	0.129861	+	0.178739i
$141$		0			0
$142$			138.451i			0.975007i
$143$	64.3188	−	229.528i	0.449782	−	1.60509i
$144$		0			0
$145$	−61.4876	−	19.9785i	−0.424053	−	0.137783i
$146$	−176.687	+	128.371i	−1.21019	+	0.879251i
$147$		0			0
$148$	37.9737	+	116.871i	0.256579	+	0.789669i
$149$	−43.9465	+	14.2791i	−0.294943	+	0.0958328i	−0.452751	−	0.891637i	$-0.649557\pi$
$149$	−43.9465	+	14.2791i	−0.294943	+	0.0958328i	0.157808	+	0.987470i	$0.449557\pi$
$150$		0			0
$151$	−94.3777	−	129.900i	−0.625018	−	0.860263i	0.372688	−	0.927957i	$-0.378436\pi$
$151$	−94.3777	−	129.900i	−0.625018	−	0.860263i	−0.997706	+	0.0676934i	$0.978436\pi$
$152$	32.2419	−	99.2303i	0.212118	−	0.652831i
$153$		0			0
$154$	81.0063	+	102.403i	0.526015	+	0.664953i
$155$	−29.7972			−0.192240
$156$		0			0
$157$	70.6280	−	51.3142i	0.449860	−	0.326842i	−0.339681	−	0.940541i	$-0.610319\pi$
$157$	70.6280	−	51.3142i	0.449860	−	0.326842i	0.789540	+	0.613699i	$0.210319\pi$
$158$	351.715	+	255.536i	2.22604	+	1.61731i
$159$		0			0
$160$	55.0450	−	17.8852i	0.344032	−	0.111783i
$161$	−10.8096	+	14.8781i	−0.0671404	+	0.0924109i
$162$		0			0
$163$	−47.8023	+	147.120i	−0.293266	+	0.902579i	0.690533	+	0.723301i	$0.257376\pi$
$163$	−47.8023	+	147.120i	−0.293266	+	0.902579i	−0.983798	+	0.179278i	$0.942624\pi$
$164$			209.725i			1.27881i
$165$		0			0
$166$	349.710			2.10669
$167$	−242.950	−	78.9391i	−1.45479	−	0.472689i	−0.528314	−	0.849049i	$-0.677176\pi$
$167$	−242.950	−	78.9391i	−1.45479	−	0.472689i	−0.926474	+	0.376360i	$0.877176\pi$
$168$		0			0
$169$	243.180	+	176.680i	1.43893	+	1.04545i
$170$	23.2549	+	71.5712i	0.136794	+	0.421007i
$171$		0			0
$172$	33.8750	−	46.6249i	0.196948	−	0.271075i
$173$	−19.3011	−	26.5657i	−0.111567	−	0.153559i	0.749582	−	0.661912i	$-0.230255\pi$
$173$	−19.3011	−	26.5657i	−0.111567	−	0.153559i	−0.861149	+	0.508353i	$0.830255\pi$
$174$		0			0
$175$		−	87.5193i		−	0.500110i
$176$	64.0599	−	23.7549i	0.363977	−	0.134971i
$177$		0			0
$178$	−188.492	−	61.2449i	−1.05895	−	0.344072i
$179$	134.387	−	97.6377i	0.750764	−	0.545462i	−0.145299	−	0.989388i	$-0.546415\pi$
$179$	134.387	−	97.6377i	0.750764	−	0.545462i	0.896064	+	0.443925i	$0.146415\pi$
$180$		0			0
$181$	−21.1750	−	65.1699i	−0.116989	−	0.360055i	0.875368	−	0.483458i	$-0.160619\pi$
$181$	−21.1750	−	65.1699i	−0.116989	−	0.360055i	−0.992357	+	0.123403i	$0.960619\pi$
$182$	−244.632	+	79.4856i	−1.34413	+	0.436734i
$183$		0			0
$184$	−15.1556	−	20.8598i	−0.0823672	−	0.113369i
$185$	−9.44776	+	29.0772i	−0.0510690	+	0.157174i
$186$		0			0
$187$	64.9672	+	175.197i	0.347418	+	0.936884i
$188$	379.907			2.02078
$189$		0			0
$190$	70.0307	−	50.8803i	0.368583	−	0.267791i
$191$	213.358	+	155.013i	1.11706	+	0.811588i	0.983760	−	0.179488i	$-0.0574441\pi$
$191$	213.358	+	155.013i	1.11706	+	0.811588i	0.133296	+	0.991076i	$0.457444\pi$
$192$		0			0
$193$	14.3528	−	4.66350i	0.0743667	−	0.0241632i	−0.271597	−	0.962411i	$-0.587552\pi$
$193$	14.3528	−	4.66350i	0.0743667	−	0.0241632i	0.345964	+	0.938248i	$0.387552\pi$
$194$	185.156	−	254.846i	0.954414	−	1.31364i
$195$		0			0
$196$	−60.9009	+	187.434i	−0.310719	+	0.956294i
$197$			205.342i			1.04234i	0.853452	+	0.521172i	$0.174505\pi$
$197$			205.342i			1.04234i	−0.853452	+	0.521172i	$0.825495\pi$
$198$		0			0
$199$	−104.559			−0.525420			−0.262710	−	0.964875i	$-0.584616\pi$
$199$	−104.559			−0.525420			−0.262710	+	0.964875i	$0.584616\pi$
$200$	116.700	+	37.9183i	0.583502	+	0.189591i
$201$		0			0
$202$	−333.290	−	242.149i	−1.64995	−	1.19876i
$203$	53.5294	+	164.747i	0.263692	+	0.811560i
$204$		0			0
$205$	−30.6701	+	42.2137i	−0.149610	+	0.205921i
$206$	−91.8887	−	126.474i	−0.446062	−	0.613951i
$207$		0			0
$208$			134.595i			0.647092i
$209$	168.568	−	133.346i	0.806544	−	0.638021i
$210$		0			0
$211$	−137.301	−	44.6117i	−0.650715	−	0.211430i	−0.0349854	−	0.999388i	$-0.511138\pi$
$211$	−137.301	−	44.6117i	−0.650715	−	0.211430i	−0.615729	+	0.787958i	$0.711138\pi$
$212$	−381.111	+	276.893i	−1.79769	+	1.30610i
$213$		0			0
$214$	−153.336	−	471.920i	−0.716523	−	2.20523i
$215$	13.6368	−	4.43086i	0.0634270	−	0.0206087i
$216$		0			0
$217$	46.9271	+	64.5896i	0.216254	+	0.297648i
$218$	89.9612	−	276.872i	0.412666	−	1.27006i
$219$		0			0
$220$	−86.0207	−	24.1049i	−0.391003	−	0.109568i
$221$	−368.104			−1.66563
$222$		0			0
$223$	151.491	−	110.065i	0.679333	−	0.493564i	−0.193804	−	0.981040i	$-0.562082\pi$
$223$	151.491	−	110.065i	0.679333	−	0.493564i	0.873136	+	0.487476i	$0.162082\pi$
$224$	−125.458	−	91.1506i	−0.560080	−	0.406922i
$225$		0			0
$226$	−114.090	+	37.0702i	−0.504824	+	0.164027i
$227$	−28.4905	+	39.2139i	−0.125509	+	0.172748i	−0.867147	−	0.498052i	$-0.834049\pi$
$227$	−28.4905	+	39.2139i	−0.125509	+	0.172748i	0.741638	+	0.670800i	$0.234049\pi$
$228$		0			0
$229$	−75.9858	+	233.860i	−0.331816	+	1.02122i	0.636454	+	0.771315i	$0.280401\pi$
$229$	−75.9858	+	233.860i	−0.331816	+	1.02122i	−0.968269	+	0.249909i	$0.919599\pi$
$230$		−	21.3918i		−	0.0930077i
$231$		0			0
$232$	−242.869			−1.04685
$233$	21.6263	+	7.02681i	0.0928167	+	0.0301580i	0.355057	−	0.934845i	$-0.384461\pi$
$233$	21.6263	+	7.02681i	0.0928167	+	0.0301580i	−0.262241	+	0.965003i	$0.584461\pi$
$234$		0			0
$235$	76.4681	+	55.5573i	0.325396	+	0.236414i
$236$	−112.978	−	347.711i	−0.478721	−	1.47335i
$237$		0			0
$238$	118.517	−	163.124i	0.497970	−	0.685396i
$239$	−36.2192	−	49.8514i	−0.151545	−	0.208583i	0.726494	−	0.687173i	$-0.241148\pi$
$239$	−36.2192	−	49.8514i	−0.151545	−	0.208583i	−0.878039	+	0.478589i	$0.841148\pi$
$240$		0			0
$241$		−	165.003i		−	0.684662i	−0.939579	−	0.342331i	$-0.888784\pi$
$241$		−	165.003i		−	0.684662i	0.939579	−	0.342331i	$-0.111216\pi$
$242$	−366.984	−	86.8064i	−1.51646	−	0.358704i
$243$		0			0
$244$	59.2723	+	19.2587i	0.242919	+	0.0789292i
$245$	−39.6684	+	28.8208i	−0.161912	+	0.117636i
$246$		0			0
$247$	130.843	+	402.694i	0.529730	+	1.63034i
$248$	−106.457	+	34.5899i	−0.429261	+	0.139475i
$249$		0			0
$250$	124.938	+	171.962i	0.499751	+	0.687848i
$251$	−13.7216	+	42.2307i	−0.0546677	+	0.168250i	−0.974662	−	0.223681i	$-0.928193\pi$
$251$	−13.7216	+	42.2307i	−0.0546677	+	0.168250i	0.919995	+	0.391931i	$0.128193\pi$
$252$		0			0
$253$	−2.17416	−	53.0708i	−0.00859354	−	0.209766i
$254$	−253.355			−0.997460
$255$		0			0
$256$	61.0617	−	44.3639i	0.238522	−	0.173297i
$257$	16.2405	+	11.7994i	0.0631928	+	0.0459122i	0.618933	−	0.785444i	$-0.287565\pi$
$257$	16.2405	+	11.7994i	0.0631928	+	0.0459122i	−0.555740	+	0.831356i	$0.687565\pi$
$258$		0			0
$259$	77.9079	−	25.3138i	0.300803	−	0.0977367i
$260$	103.443	−	142.377i	0.397858	−	0.547605i
$261$		0			0
$262$	141.907	−	436.745i	0.541629	−	1.66696i
$263$		−	212.968i		−	0.809765i	−0.914369	−	0.404883i	$-0.867312\pi$
$263$		−	212.968i		−	0.809765i	0.914369	−	0.404883i	$-0.132688\pi$
$264$		0			0
$265$	−117.203			−0.442276
$266$	−220.580	−	71.6708i	−0.829248	−	0.269439i
$267$		0			0
$268$	104.477	+	75.9071i	0.389840	+	0.283235i
$269$	126.349	+	388.861i	0.469698	+	1.44558i	0.852977	+	0.521948i	$0.174795\pi$
$269$	126.349	+	388.861i	0.469698	+	1.44558i	−0.383279	+	0.923632i	$0.625205\pi$
$270$		0			0
$271$	6.12668	−	8.43265i	0.0226077	−	0.0311168i	−0.797564	−	0.603235i	$-0.793878\pi$
$271$	6.12668	−	8.43265i	0.0226077	−	0.0311168i	0.820171	+	0.572118i	$0.193878\pi$
$272$	−62.0158	−	85.3575i	−0.227999	−	0.313814i
$273$		0			0
$274$			661.506i			2.41426i
$275$	156.823	+	198.245i	0.570265	+	0.720892i
$276$		0			0
$277$	414.941	+	134.823i	1.49798	+	0.486724i	0.939429	−	0.342745i	$-0.111357\pi$
$277$	414.941	+	134.823i	1.49798	+	0.486724i	0.558554	+	0.829468i	$0.311357\pi$
$278$	553.021	−	401.793i	1.98928	−	1.44530i
$279$		0			0
$280$	8.93324	+	27.4937i	0.0319044	+	0.0981917i
$281$	254.282	−	82.6212i	0.904918	−	0.294026i	0.180652	−	0.983547i	$-0.442179\pi$
$281$	254.282	−	82.6212i	0.904918	−	0.294026i	0.724265	+	0.689521i	$0.242179\pi$
$282$		0			0
$283$	196.923	+	271.041i	0.695840	+	0.957742i	0.999987	+	0.00511676i	$0.00162872\pi$
$283$	196.923	+	271.041i	0.695840	+	0.957742i	−0.304147	+	0.952625i	$0.598371\pi$
$284$	−78.4303	+	241.384i	−0.276163	+	0.849942i
$285$		0			0
$286$	411.702	−	618.395i	1.43952	−	2.16222i
$287$	139.806			0.487128
$288$		0			0
$289$	−0.361980	+	0.262994i	−0.00125253	+	0.000910014i
$290$	−163.013	−	118.436i	−0.562115	−	0.408401i
$291$		0			0
$292$	−380.767	+	123.719i	−1.30400	+	0.423694i
$293$	−158.442	+	218.076i	−0.540757	+	0.744288i	−0.988722	−	0.149763i	$-0.952149\pi$
$293$	−158.442	+	218.076i	−0.540757	+	0.744288i	0.447965	+	0.894051i	$0.352149\pi$
$294$		0			0
$295$	28.1086	−	86.5095i	0.0952835	−	0.293253i
$296$			114.852i			0.388013i
$297$		0			0
$298$	−144.013			−0.483266
$299$	99.5156	+	32.3346i	0.332828	+	0.108142i
$300$		0			0
$301$	−31.0808	−	22.5815i	−0.103259	−	0.0750217i
$302$	−154.638	−	475.928i	−0.512047	−	1.57592i
$303$		0			0
$304$	−71.3348	+	98.1839i	−0.234654	+	0.322973i
$305$	9.11402	+	12.5444i	0.0298820	+	0.0411291i
$306$		0			0
$307$		−	513.671i		−	1.67319i	−0.547819	−	0.836597i	$-0.684542\pi$
$307$		−	513.671i		−	1.67319i	0.547819	−	0.836597i	$-0.315458\pi$
$308$	83.2216	+	224.424i	0.270200	+	0.728649i
$309$		0			0
$310$	−88.3215	−	28.6974i	−0.284908	−	0.0925722i
$311$	−250.335	+	181.879i	−0.804935	+	0.584819i	−0.912358	−	0.409394i	$-0.865740\pi$
$311$	−250.335	+	181.879i	−0.804935	+	0.584819i	0.107423	+	0.994213i	$0.465740\pi$
$312$		0			0
$313$	−82.9976	−	255.440i	−0.265168	−	0.816103i	−0.991655	−	0.128923i	$-0.958848\pi$
$313$	−82.9976	−	255.440i	−0.265168	−	0.816103i	0.726487	−	0.687181i	$-0.241152\pi$
$314$	258.767	−	84.0787i	0.824100	−	0.267766i
$315$		0			0
$316$	468.443	+	644.757i	1.48242	+	2.04037i
$317$	−114.026	+	350.937i	−0.359705	+	1.10706i	0.593526	+	0.804815i	$0.297735\pi$
$317$	−114.026	+	350.937i	−0.359705	+	1.10706i	−0.953231	+	0.302243i	$0.902265\pi$
$318$		0			0
$319$	−416.457	−	277.260i	−1.30551	−	0.869154i
$320$	145.068			0.453336
$321$		0			0
$322$	−46.3696	+	33.6895i	−0.144005	+	0.104626i
$323$	−268.523	−	195.093i	−0.831340	−	0.604004i
$324$		0			0
$325$	−473.591	+	153.879i	−1.45720	+	0.473474i
$326$	−283.380	+	390.039i	−0.869264	+	1.19644i
$327$		0			0
$328$	−60.5716	+	186.420i	−0.184670	+	0.568355i
$329$		−	253.251i		−	0.769761i
$330$		0			0
$331$	−511.298			−1.54471			−0.772354	−	0.635192i	$-0.780921\pi$
$331$	−511.298			−1.54471			−0.772354	+	0.635192i	$0.780921\pi$
$332$	609.706	+	198.105i	1.83646	+	0.596703i
$333$		0			0
$334$	−644.097	−	467.964i	−1.92844	−	1.40109i
$335$	9.92868	+	30.5573i	0.0296379	+	0.0912160i
$336$		0			0
$337$	22.7778	−	31.3510i	0.0675900	−	0.0930296i	−0.773884	−	0.633328i	$-0.781689\pi$
$337$	22.7778	−	31.3510i	0.0675900	−	0.0930296i	0.841474	+	0.540298i	$0.181689\pi$
$338$	550.646	+	757.899i	1.62913	+	2.24230i
$339$		0			0
$340$			137.955i			0.405750i
$341$	−222.033	−	62.2187i	−0.651124	−	0.182459i
$342$		0			0
$343$	302.433	+	98.2665i	0.881729	+	0.286491i
$344$	43.5767	−	31.6604i	0.126677	−	0.0920359i
$345$		0			0
$346$	−31.6250	−	97.3318i	−0.0914018	−	0.281306i
$347$	385.558	−	125.275i	1.11112	−	0.361024i	0.304746	−	0.952434i	$-0.401428\pi$
$347$	385.558	−	125.275i	1.11112	−	0.361024i	0.806371	+	0.591410i	$0.201428\pi$
$348$		0			0
$349$	−127.851	−	175.972i	−0.366335	−	0.504217i	0.585565	−	0.810626i	$-0.300873\pi$
$349$	−127.851	−	175.972i	−0.366335	−	0.504217i	−0.951900	+	0.306408i	$0.900873\pi$
$350$	84.2889	−	259.415i	0.240825	−	0.741185i
$351$		0			0
$352$	447.512	−	18.3334i	1.27134	−	0.0520834i
$353$	417.749			1.18343			0.591713	−	0.806149i	$-0.298452\pi$
$353$	417.749			1.18343			0.591713	+	0.806149i	$0.298452\pi$
$354$		0			0
$355$	−51.0864	+	37.1164i	−0.143905	+	0.104553i
$356$	−293.934	−	213.556i	−0.825658	−	0.599876i
$357$		0			0
$358$	492.368	−	159.980i	1.37533	−	0.446871i
$359$	−192.130	+	264.444i	−0.535181	+	0.736613i	−0.987909	−	0.155036i	$-0.950451\pi$
$359$	−192.130	+	264.444i	−0.535181	+	0.736613i	0.452728	+	0.891649i	$0.350451\pi$
$360$		0			0
$361$	−6.42388	+	19.7707i	−0.0177947	+	0.0547664i
$362$		−	213.562i		−	0.589952i
$363$		0			0
$364$	−471.533			−1.29542
$365$	−94.7338	−	30.7809i	−0.259545	−	0.0843312i
$366$		0			0
$367$	1.26908	+	0.922044i	0.00345800	+	0.00251238i	0.589513	−	0.807759i	$-0.299320\pi$
$367$	1.26908	+	0.922044i	0.00345800	+	0.00251238i	−0.586055	+	0.810271i	$0.699320\pi$
$368$	9.26788	+	28.5236i	0.0251845	+	0.0775098i
$369$		0			0
$370$	−56.0079	+	77.0883i	−0.151373	+	0.208347i
$371$	184.581	+	254.054i	0.497523	+	0.684781i
$372$		0			0
$373$		−	294.158i		−	0.788627i	−0.918976	−	0.394314i	$-0.870982\pi$
$373$		−	294.158i		−	0.788627i	0.918976	−	0.394314i	$-0.129018\pi$
$374$	23.8376	+	581.869i	0.0637369	+	1.55580i
$375$		0			0
$376$	337.692	+	109.723i	0.898116	+	0.291815i
$377$	797.373	−	579.325i	2.11505	−	1.53667i
$378$		0			0
$379$	−4.42995	−	13.6340i	−0.0116885	−	0.0359736i	0.945042	−	0.326949i	$-0.106020\pi$
$379$	−4.42995	−	13.6340i	−0.0116885	−	0.0359736i	−0.956731	+	0.290975i	$0.906020\pi$
$380$	150.919	−	49.0364i	0.397154	−	0.129043i
$381$		0			0
$382$	483.118	+	664.955i	1.26471	+	1.74072i
$383$	−58.4266	+	179.819i	−0.152550	+	0.469500i	−0.997904	−	0.0647053i	$-0.979389\pi$
$383$	−58.4266	+	179.819i	−0.152550	+	0.469500i	0.845354	+	0.534206i	$0.179389\pi$
$384$		0			0
$385$	−16.0687	+	57.3426i	−0.0417368	+	0.148942i
$386$	47.0342			0.121850
$387$		0			0
$388$	467.179	−	339.425i	1.20407	−	0.874807i
$389$	−433.518	−	314.969i	−1.11444	−	0.809689i	−0.131084	−	0.991371i	$-0.541846\pi$
$389$	−433.518	−	314.969i	−1.11444	−	0.809689i	−0.983357	+	0.181683i	$0.941846\pi$
$390$		0			0
$391$	−78.0092	+	25.3467i	−0.199512	+	0.0648254i
$392$	−108.267	+	149.017i	−0.276192	+	0.380145i
$393$		0			0
$394$	−197.762	+	608.650i	−0.501935	+	1.54480i
$395$			198.282i			0.501981i
$396$		0			0
$397$	181.111			0.456199			0.228099	−	0.973638i	$-0.426749\pi$
$397$	181.111			0.456199			0.228099	+	0.973638i	$0.426749\pi$
$398$	−309.920	−	100.699i	−0.778694	−	0.253013i
$399$		0			0
$400$	−115.470	−	83.8937i	−0.288675	−	0.209734i
$401$	−191.776	−	590.226i	−0.478245	−	1.47189i	−0.841531	−	0.540208i	$-0.818346\pi$
$401$	−191.776	−	590.226i	−0.478245	−	1.47189i	0.363287	−	0.931677i	$-0.381654\pi$
$402$		0			0
$403$	267.003	−	367.499i	0.662539	−	0.911907i
$404$	−443.904	−	610.981i	−1.09877	−	1.51233i
$405$		0			0
$406$			539.877i			1.32975i
$407$	−131.115	+	196.940i	−0.322150	+	0.483883i
$408$		0			0
$409$	207.796	+	67.5172i	0.508060	+	0.165079i	0.551820	−	0.833963i	$-0.313934\pi$
$409$	207.796	+	67.5172i	0.508060	+	0.165079i	−0.0437599	+	0.999042i	$0.513934\pi$
$410$	−131.564	+	95.5870i	−0.320888	+	0.233139i
$411$		0			0
$412$	−88.5587	−	272.556i	−0.214948	−	0.661543i
$413$	−231.789	+	75.3128i	−0.561232	+	0.182355i
$414$		0			0
$415$	93.7516	+	129.038i	0.225907	+	0.310935i
$416$	−272.657	+	839.152i	−0.655425	+	2.01719i
$417$		0			0
$418$	628.074	−	232.904i	1.50257	−	0.557187i
$419$	−819.307			−1.95539			−0.977694	−	0.210035i	$-0.932642\pi$
$419$	−819.307			−1.95539			−0.977694	+	0.210035i	$0.932642\pi$
$420$		0			0
$421$	214.288	−	155.689i	0.508998	−	0.369809i	−0.303445	−	0.952849i	$-0.598137\pi$
$421$	214.288	−	155.689i	0.508998	−	0.369809i	0.812443	+	0.583040i	$0.198137\pi$
$422$	−364.006	−	264.466i	−0.862573	−	0.626696i
$423$		0			0
$424$	−418.733	+	136.054i	−0.987577	+	0.320883i
$425$	229.441	−	315.798i	0.539861	−	0.743055i
$426$		0			0
$427$	12.8381	−	39.5117i	0.0300659	−	0.0925334i
$428$		−	909.635i		−	2.12532i
$429$		0			0
$430$	44.6879			0.103925
$431$	80.8735	+	26.2774i	0.187642	+	0.0609684i	0.401330	−	0.915933i	$-0.368548\pi$
$431$	80.8735	+	26.2774i	0.187642	+	0.0609684i	−0.213689	+	0.976902i	$0.568548\pi$
$432$		0			0
$433$	318.990	+	231.760i	0.736698	+	0.535243i	0.891675	−	0.452676i	$-0.149530\pi$
$433$	318.990	+	231.760i	0.736698	+	0.535243i	−0.154977	+	0.987918i	$0.549530\pi$
$434$	76.8902	+	236.644i	0.177166	+	0.545262i
$435$		0			0
$436$	313.687	−	431.754i	0.719466	−	0.990261i
$437$	55.4571	+	76.3301i	0.126904	+	0.174668i
$438$		0			0
$439$			609.996i			1.38951i	0.719245	+	0.694756i	$0.244488\pi$
$439$			609.996i			1.38951i	−0.719245	+	0.694756i	$0.755512\pi$
$440$	−69.5002	−	46.2704i	−0.157955	−	0.105160i
$441$		0			0
$442$	−1091.09	−	354.517i	−2.46853	−	0.802074i
$443$	−136.683	+	99.3063i	−0.308541	+	0.224168i	−0.731270	−	0.682088i	$-0.761072\pi$
$443$	−136.683	+	99.3063i	−0.308541	+	0.224168i	0.422729	+	0.906256i	$0.361072\pi$
$444$		0			0
$445$	−27.9332	−	85.9696i	−0.0627713	−	0.193190i
$446$	555.035	−	180.342i	1.24447	−	0.404354i
$447$		0			0
$448$	−228.464	−	314.454i	−0.509964	−	0.701906i
$449$	209.322	−	644.227i	0.466196	−	1.43480i	−0.391276	−	0.920273i	$-0.627966\pi$
$449$	209.322	−	644.227i	0.466196	−	1.43480i	0.857472	−	0.514530i	$-0.172034\pi$
$450$		0			0
$451$	−316.682	+	250.513i	−0.702178	+	0.555462i
$452$	−219.911			−0.486530
$453$		0			0
$454$	−122.215	+	88.7943i	−0.269196	+	0.195582i
$455$	−94.9107	−	68.9567i	−0.208595	−	0.151553i
$456$		0			0
$457$	−545.057	+	177.100i	−1.19268	+	0.387527i	−0.837065	−	0.547104i	$-0.815730\pi$
$457$	−545.057	+	177.100i	−1.19268	+	0.387527i	−0.355620	+	0.934631i	$0.615730\pi$
$458$	−450.457	+	620.000i	−0.983530	+	1.35371i
$459$		0			0
$460$	12.1181	−	37.2957i	0.0263437	−	0.0810775i
$461$		−	333.147i		−	0.722661i	−0.932438	−	0.361330i	$-0.882323\pi$
$461$		−	333.147i		−	0.722661i	0.932438	−	0.361330i	$-0.117677\pi$
$462$		0			0
$463$	35.2648			0.0761659			0.0380829	−	0.999275i	$-0.487875\pi$
$463$	35.2648			0.0761659			0.0380829	+	0.999275i	$0.487875\pi$
$464$	268.673	+	87.2971i	0.579036	+	0.188140i
$465$		0			0
$466$	57.3347	+	41.6561i	0.123036	+	0.0893907i
$467$	1.63484	+	5.03152i	0.00350073	+	0.0107741i	0.952792	−	0.303625i	$-0.0981970\pi$
$467$	1.63484	+	5.03152i	0.00350073	+	0.0107741i	−0.949291	+	0.314399i	$0.898197\pi$
$468$		0			0
$469$	50.6007	−	69.6459i	0.107891	−	0.148499i
$470$	173.151	+	238.322i	0.368407	+	0.507069i
$471$		0			0
$472$		−	341.703i		−	0.723947i
$473$	110.866	−	4.54188i	0.234389	−	0.00960229i
$474$		0			0
$475$	−427.029	−	138.750i	−0.899008	−	0.292105i
$476$	299.036	−	217.263i	0.628228	−	0.456434i
$477$		0			0
$478$	−59.3453	−	182.646i	−0.124153	−	0.382105i
$479$	−118.584	+	38.5304i	−0.247566	+	0.0804392i	−0.430172	−	0.902747i	$-0.641547\pi$
$479$	−118.584	+	38.5304i	−0.247566	+	0.0804392i	0.182605	+	0.983186i	$0.441547\pi$
$480$		0			0
$481$	−273.960	−	377.074i	−0.569564	−	0.783937i
$482$	158.913	−	489.084i	0.329695	−	1.01470i
$483$		0			0
$484$	−590.648	−	359.234i	−1.22035	−	0.742220i
$485$	143.672			0.296230
$486$		0			0
$487$	537.148	−	390.261i	1.10297	−	0.801357i	0.121430	−	0.992600i	$-0.461252\pi$
$487$	537.148	−	390.261i	1.10297	−	0.801357i	0.981543	+	0.191243i	$0.0612520\pi$
$488$	47.1237	+	34.2374i	0.0965651	+	0.0701586i
$489$		0			0
$490$	−145.337	+	47.2230i	−0.296607	+	0.0963735i
$491$	172.912	−	237.993i	0.352164	−	0.484712i	−0.595781	−	0.803147i	$-0.703157\pi$
$491$	172.912	−	237.993i	0.352164	−	0.484712i	0.947945	+	0.318435i	$0.103157\pi$
$492$		0			0
$493$	−238.749	+	734.793i	−0.484277	+	1.49045i
$494$			1319.63i			2.67132i
$495$		0			0
$496$	130.200			0.262500
$497$	160.910	+	52.2828i	0.323762	+	0.105197i
$498$		0			0
$499$	519.487	+	377.430i	1.04106	+	0.756372i	0.970492	−	0.241135i	$-0.0775198\pi$
$499$	519.487	+	377.430i	1.04106	+	0.756372i	0.0705651	+	0.997507i	$0.477520\pi$
$500$	120.410	+	370.584i	0.240820	+	0.741168i
$501$		0			0
$502$	−81.3439	+	111.960i	−0.162040	+	0.223028i
$503$	−129.664	−	178.467i	−0.257780	−	0.354804i	0.660437	−	0.750882i	$-0.270371\pi$
$503$	−129.664	−	178.467i	−0.257780	−	0.354804i	−0.918217	+	0.396077i	$0.870371\pi$
$504$		0			0
$505$		−	187.895i		−	0.372070i
$506$	44.6675	−	159.400i	0.0882757	−	0.315020i
$507$		0			0
$508$	−441.714	−	143.521i	−0.869515	−	0.282523i
$509$	−553.286	+	401.986i	−1.08701	+	0.789756i	−0.978891	−	0.204382i	$-0.934482\pi$
$509$	−553.286	+	401.986i	−1.08701	+	0.789756i	−0.108115	+	0.994138i	$0.534482\pi$
$510$		0			0
$511$	82.4726	+	253.825i	0.161395	+	0.496721i
$512$	−366.694	+	119.146i	−0.716199	+	0.232707i
$513$		0			0
$514$	36.7744	+	50.6156i	0.0715455	+	0.0984740i
$515$	22.0332	−	67.8112i	0.0427829	−	0.131672i
$516$		0			0
$517$	453.793	+	573.655i	0.877742	+	1.10958i
$518$	255.305			0.492867
$519$		0			0
$520$	133.069	−	96.6804i	0.255902	−	0.185924i
$521$	235.869	+	171.369i	0.452724	+	0.328923i	0.790670	−	0.612242i	$-0.209732\pi$
$521$	235.869	+	171.369i	0.452724	+	0.328923i	−0.337947	+	0.941165i	$0.609732\pi$
$522$		0			0
$523$	324.889	−	105.563i	0.621202	−	0.201841i	0.0185283	−	0.999828i	$-0.494102\pi$
$523$	324.889	−	105.563i	0.621202	−	0.201841i	0.602674	+	0.797987i	$0.294102\pi$
$524$	494.818	−	681.058i	0.944309	−	1.29973i
$525$		0			0
$526$	205.107	−	631.256i	0.389938	−	1.20011i
$527$			356.084i			0.675682i
$528$		0			0
$529$	−505.684			−0.955924
$530$	−347.400	−	112.877i	−0.655472	−	0.212976i
$531$		0			0
$532$	−343.972	−	249.910i	−0.646564	−	0.469756i
$533$	−245.811	−	756.527i	−0.461183	−	1.41938i
$534$		0			0
$535$	133.025	−	183.093i	0.248644	−	0.342229i
$536$	70.9445	+	97.6468i	0.132359	+	0.182177i
$537$		0			0
$538$			1274.30i			2.36859i
$539$	−355.768	+	131.927i	−0.660052	+	0.244762i
$540$		0			0
$541$	365.820	+	118.862i	0.676192	+	0.219708i	0.626928	−	0.779078i	$-0.284312\pi$
$541$	365.820	+	118.862i	0.676192	+	0.219708i	0.0492647	+	0.998786i	$0.484312\pi$
$542$	26.2814	−	19.0945i	0.0484896	−	0.0352298i
$543$		0			0
$544$	−213.733	−	657.802i	−0.392891	−	1.20919i
$545$	126.279	−	41.0305i	0.231704	−	0.0752853i
$546$		0			0
$547$	317.755	+	437.353i	0.580906	+	0.799548i	0.993794	−	0.111234i	$-0.0354802\pi$
$547$	317.755	+	437.353i	0.580906	+	0.799548i	−0.412889	+	0.910781i	$0.635480\pi$
$548$	−374.733	+	1153.31i	−0.683819	+	2.10458i
$549$		0			0
$550$	273.908	+	738.650i	0.498015	+	1.34300i
$551$	888.704			1.61289
$552$		0			0
$553$	429.804	−	312.271i	0.777223	−	0.564685i
$554$	1100.07	+	799.251i	1.98569	+	1.44269i
$555$		0			0
$556$	1191.78	−	387.232i	2.14349	−	0.696461i
$557$	12.3540	−	17.0038i	0.0221795	−	0.0305274i	−0.797783	−	0.602944i	$-0.793994\pi$
$557$	12.3540	−	17.0038i	0.0221795	−	0.0305274i	0.819963	+	0.572417i	$0.193994\pi$
$558$		0			0
$559$	−67.5477	+	207.891i	−0.120837	+	0.371897i
$560$		−	33.6257i		−	0.0600459i
$561$		0			0
$562$	833.284			1.48271
$563$	2.65747	+	0.863465i	0.00472020	+	0.00153368i	0.311376	−	0.950287i	$-0.399210\pi$
$563$	2.65747	+	0.863465i	0.00472020	+	0.00153368i	−0.306656	+	0.951820i	$0.599210\pi$
$564$		0			0
$565$	−44.2641	−	32.1597i	−0.0783435	−	0.0569199i
$566$	322.659	+	993.043i	0.570069	+	1.75449i
$567$		0			0
$568$	−139.430	+	191.909i	−0.245476	+	0.337868i
$569$	−186.763	−	257.058i	−0.328231	−	0.451771i	0.612727	−	0.790295i	$-0.290073\pi$
$569$	−186.763	−	257.058i	−0.328231	−	0.451771i	−0.940958	+	0.338524i	$0.890073\pi$
$570$		0			0
$571$		−	684.355i		−	1.19852i	−0.800554	−	0.599260i	$-0.795462\pi$
$571$		−	684.355i		−	1.19852i	0.800554	−	0.599260i	$-0.204538\pi$
$572$	1068.10	−	844.924i	1.86730	−	1.47714i
$573$		0			0
$574$	414.396	+	134.645i	0.721944	+	0.234574i
$575$	−89.7685	+	65.2206i	−0.156119	+	0.113427i
$576$		0			0
$577$	202.491	+	623.203i	0.350938	+	1.08007i	0.958328	+	0.285671i	$0.0922165\pi$
$577$	202.491	+	623.203i	0.350938	+	1.08007i	−0.607390	+	0.794404i	$0.707784\pi$
$578$	−1.32623	+	0.430917i	−0.00229451	+	0.000745531i
$579$		0			0
$580$	−217.115	−	298.833i	−0.374336	−	0.515230i
$581$	132.060	−	406.439i	0.227298	−	0.699550i
$582$		0			0
$583$	−873.336	−	244.728i	−1.49800	−	0.419774i
$584$	−374.188			−0.640733
$585$		0			0
$586$	−679.662	+	493.803i	−1.15983	+	0.842668i
$587$	828.411	+	601.876i	1.41126	+	1.02534i	0.993137	+	0.116953i	$0.0373126\pi$
$587$	828.411	+	601.876i	1.41126	+	1.02534i	0.418125	+	0.908389i	$0.362687\pi$
$588$		0			0
$589$	389.545	−	126.571i	0.661367	−	0.214891i
$590$	166.633	−	229.350i	0.282428	−	0.388729i
$591$		0			0
$592$	41.2824	−	127.054i	0.0697337	−	0.214618i
$593$			168.317i			0.283839i	0.989878	+	0.141920i	$0.0453275\pi$
$593$			168.317i			0.283839i	−0.989878	+	0.141920i	$0.954673\pi$
$594$		0			0
$595$	91.9628			0.154559
$596$	−251.081	−	81.5812i	−0.421277	−	0.136881i
$597$		0			0
$598$	263.831	+	191.685i	0.441190	+	0.320543i
$599$	−22.4285	−	69.0277i	−0.0374432	−	0.115238i	0.930588	−	0.366068i	$-0.119296\pi$
$599$	−22.4285	−	69.0277i	−0.0374432	−	0.115238i	−0.968031	+	0.250830i	$0.919296\pi$
$600$		0			0
$601$	−209.484	+	288.330i	−0.348559	+	0.479750i	−0.946917	−	0.321479i	$-0.895820\pi$
$601$	−209.484	+	288.330i	−0.348559	+	0.479750i	0.598358	+	0.801229i	$0.295820\pi$
$602$	−70.3781	−	96.8672i	−0.116907	−	0.160909i
$603$		0			0
$604$		−	917.361i		−	1.51881i
$605$	−66.3522	−	158.683i	−0.109673	−	0.262286i
$606$		0			0
$607$	−189.801	−	61.6702i	−0.312688	−	0.101598i	0.148469	−	0.988917i	$-0.452565\pi$
$607$	−189.801	−	61.6702i	−0.312688	−	0.101598i	−0.461157	+	0.887319i	$0.652565\pi$
$608$	−643.643	+	467.634i	−1.05862	+	0.769135i
$609$		0			0
$610$	14.9334	+	45.9602i	0.0244809	+	0.0753445i
$611$	−1370.41	+	445.274i	−2.24290	+	0.728763i
$612$		0			0
$613$	−225.432	−	310.280i	−0.367752	−	0.506167i	0.584536	−	0.811368i	$-0.301276\pi$
$613$	−225.432	−	310.280i	−0.367752	−	0.506167i	−0.952288	+	0.305201i	$0.901276\pi$
$614$	494.711	−	1522.56i	0.805718	−	2.47974i
$615$		0			0
$616$	9.15707	+	223.522i	0.0148654	+	0.362860i
$617$	196.438			0.318376			0.159188	−	0.987248i	$-0.449112\pi$
$617$	196.438			0.318376			0.159188	+	0.987248i	$0.449112\pi$
$618$		0			0
$619$	−884.074	+	642.317i	−1.42823	+	1.03767i	−0.437886	+	0.899030i	$0.644273\pi$
$619$	−884.074	+	642.317i	−1.42823	+	1.03767i	−0.990343	+	0.138639i	$0.955727\pi$
$620$	−137.728	−	100.065i	−0.222142	−	0.161396i
$621$		0			0
$622$	−917.179	+	298.009i	−1.47456	+	0.479115i
$623$	−142.359	+	195.941i	−0.228506	+	0.314512i
$624$		0			0
$625$	147.568	−	454.168i	0.236109	−	0.726669i
$626$		−	837.081i		−	1.33719i
$627$		0			0
$628$	498.780			0.794235
$629$	347.480	+	112.903i	0.552432	+	0.179496i
$630$		0			0
$631$	−647.545	−	470.469i	−1.02622	−	0.745593i	−0.0586718	−	0.998277i	$-0.518687\pi$
$631$	−647.545	−	470.469i	−1.02622	−	0.745593i	−0.967549	+	0.252684i	$0.918687\pi$
$632$	230.175	+	708.405i	0.364200	+	1.12089i
$633$		0			0
$634$	−675.968	+	930.390i	−1.06620	+	1.46749i
$635$	−67.9202	−	93.4841i	−0.106961	−	0.147219i
$636$		0			0
$637$		−	747.497i		−	1.17346i
$638$	−967.387	−	1222.91i	−1.51628	−	1.91678i
$639$		0			0
$640$	209.812	+	68.1722i	0.327832	+	0.106519i
$641$	−252.179	+	183.219i	−0.393415	+	0.285833i	−0.766854	−	0.641822i	$-0.778179\pi$
$641$	−252.179	+	183.219i	−0.393415	+	0.285833i	0.373438	+	0.927655i	$0.378179\pi$
$642$		0			0
$643$	−3.12104	−	9.60557i	−0.00485387	−	0.0149387i	0.948600	−	0.316477i	$-0.102500\pi$
$643$	−3.12104	−	9.60557i	−0.00485387	−	0.0149387i	−0.953454	+	0.301538i	$0.902500\pi$
$644$	−99.9280	+	32.4686i	−0.155168	+	0.0504171i
$645$		0			0
$646$	−608.032	−	836.884i	−0.941226	−	1.29549i
$647$	−107.487	+	330.811i	−0.166131	+	0.511299i	−0.999118	−	0.0419938i	$-0.986629\pi$
$647$	−107.487	+	330.811i	−0.166131	+	0.511299i	0.832987	+	0.553293i	$0.186629\pi$
$648$		0			0
$649$	390.089	−	585.930i	0.601061	−	0.902820i
$650$	−1551.96			−2.38764
$651$		0			0
$652$	−715.013	+	519.487i	−1.09665	+	0.796760i
$653$	386.475	+	280.791i	0.591846	+	0.430001i	0.842975	−	0.537952i	$-0.180802\pi$
$653$	386.475	+	280.791i	0.591846	+	0.430001i	−0.251130	+	0.967953i	$0.580802\pi$
$654$		0			0
$655$	199.195	−	64.7224i	0.304115	−	0.0988129i
$656$	134.014	−	184.455i	0.204290	−	0.281181i
$657$		0			0
$658$	243.904	−	750.658i	0.370674	−	1.14082i
$659$			813.433i			1.23434i	0.786828	+	0.617172i	$0.211722\pi$
$659$			813.433i			1.23434i	−0.786828	+	0.617172i	$0.788278\pi$
$660$		0			0
$661$	−1010.49			−1.52873			−0.764364	−	0.644784i	$-0.776947\pi$
$661$	−1010.49			−1.52873			−0.764364	+	0.644784i	$0.776947\pi$
$662$	−1515.53	−	492.426i	−2.28932	−	0.743846i
$663$		0			0
$664$	484.740	+	352.184i	0.730030	+	0.530398i
$665$	−32.6884	−	100.604i	−0.0491555	−	0.151285i
$666$		0			0
$667$	129.090	−	177.677i	0.193538	−	0.266382i
$668$	−857.863	−	1180.75i	−1.28423	−	1.76759i
$669$		0			0
$670$			100.137i			0.149458i
$671$	41.7193	+	112.505i	0.0621749	+	0.167667i
$672$		0			0
$673$	257.551	+	83.6834i	0.382691	+	0.124344i	0.494044	−	0.869437i	$-0.335518\pi$
$673$	257.551	+	83.6834i	0.382691	+	0.124344i	−0.111353	+	0.993781i	$0.535518\pi$
$674$	97.7092	−	70.9899i	0.144969	−	0.105326i
$675$		0			0
$676$	530.691	+	1633.30i	0.785045	+	2.41612i
$677$	−780.683	+	253.659i	−1.15315	+	0.374681i	−0.822329	−	0.569012i	$-0.807326\pi$
$677$	−780.683	+	253.659i	−1.15315	+	0.374681i	−0.330821	+	0.943694i	$0.607326\pi$
$678$		0			0
$679$	−226.266	−	311.428i	−0.333234	−	0.458657i
$680$	−39.8434	+	122.626i	−0.0585933	+	0.180332i
$681$		0			0
$682$	−598.203	−	398.259i	−0.877131	−	0.583958i
$683$	810.930			1.18731			0.593653	−	0.804721i	$-0.297685\pi$
$683$	810.930			1.18731			0.593653	+	0.804721i	$0.297685\pi$
$684$		0			0
$685$	−244.086	+	177.339i	−0.356330	+	0.258889i
$686$	801.798	+	582.540i	1.16880	+	0.849184i
$687$		0			0
$688$	−59.5866	+	19.3608i	−0.0866084	+	0.0281408i
$689$	1050.22	−	1445.50i	1.52427	−	2.09797i
$690$		0			0
$691$	21.4328	−	65.9633i	0.0310171	−	0.0954607i	−0.934350	−	0.356358i	$-0.884018\pi$
$691$	21.4328	−	65.9633i	0.0310171	−	0.0954607i	0.965367	+	0.260897i	$0.0840184\pi$
$692$		−	187.609i		−	0.271112i
$693$		0			0
$694$	1263.48			1.82057
$695$	296.511	+	96.3424i	0.426635	+	0.138622i
$696$		0			0
$697$	504.464	+	366.515i	0.723765	+	0.525846i
$698$	−209.485	−	644.727i	−0.300121	−	0.923678i
$699$		0			0
$700$	293.909	−	404.530i	0.419869	−	0.577901i
$701$	75.8101	+	104.344i	0.108146	+	0.148850i	0.859659	−	0.510868i	$-0.170676\pi$
$701$	75.8101	+	104.344i	0.108146	+	0.148850i	−0.751514	+	0.659718i	$0.770676\pi$
$702$		0			0
$703$		−	420.264i		−	0.597815i
$704$	1080.97	+	302.911i	1.53546	+	0.430272i
$705$		0			0
$706$	1238.24	+	402.330i	1.75389	+	0.569872i
$707$	−407.289	+	295.913i	−0.576080	+	0.418547i
$708$		0			0
$709$	−133.448	−	410.711i	−0.188220	−	0.579282i	0.811769	−	0.583979i	$-0.198505\pi$
$709$	−133.448	−	410.711i	−0.188220	−	0.579282i	−0.999989	+	0.00469673i	$0.998505\pi$
$710$	−187.171	+	60.8154i	−0.263621	+	0.0856556i
$711$		0			0
$712$	−199.594	−	274.718i	−0.280329	−	0.385840i
$713$	31.2788	−	96.2661i	0.0438692	−	0.135016i
$714$		0			0
$715$	338.549	−	13.8694i	0.473495	−	0.0193978i
$716$	949.049			1.32549
$717$		0			0
$718$	−824.172	+	598.796i	−1.14787	+	0.833978i
$719$	−441.321	−	320.639i	−0.613799	−	0.445951i	0.236951	−	0.971522i	$-0.423852\pi$
$719$	−441.321	−	320.639i	−0.613799	−	0.445951i	−0.850750	+	0.525571i	$0.823852\pi$
$720$		0			0
$721$	−181.690	+	59.0345i	−0.251997	+	0.0818787i
$722$	−38.0818	+	52.4151i	−0.0527449	+	0.0725971i
$723$		0			0
$724$	120.980	−	372.338i	0.167099	−	0.514278i
$725$			1045.17i			1.44161i
$726$		0			0
$727$	1092.98			1.50341			0.751705	−	0.659500i	$-0.229232\pi$
$727$	1092.98			1.50341			0.751705	+	0.659500i	$0.229232\pi$
$728$	−419.136	−	136.186i	−0.575736	−	0.187068i
$729$		0			0
$730$	−251.154	−	182.474i	−0.344047	−	0.249965i
$731$	−52.9499	−	162.963i	−0.0724349	−	0.222932i
$732$		0			0
$733$	−810.014	+	1114.89i	−1.10507	+	1.52099i	−0.276576	+	0.960992i	$0.589200\pi$
$733$	−810.014	+	1114.89i	−1.10507	+	1.52099i	−0.828491	+	0.560003i	$0.810800\pi$
$734$	2.87366	+	3.95526i	0.00391507	+	0.00538864i
$735$		0			0
$736$			196.609i			0.267132i
$737$	10.1775	+	248.429i	0.0138093	+	0.337081i
$738$		0			0
$739$	444.744	+	144.506i	0.601819	+	0.195543i	0.594052	−	0.804427i	$-0.297528\pi$
$739$	444.744	+	144.506i	0.601819	+	0.195543i	0.00776749	+	0.999970i	$0.497528\pi$
$740$	−141.317	+	102.673i	−0.190969	+	0.138747i
$741$		0			0
$742$	302.437	+	930.805i	0.407597	+	1.25445i
$743$	−315.622	+	102.552i	−0.424793	+	0.138024i	−0.513609	−	0.858024i	$-0.671692\pi$
$743$	−315.622	+	102.552i	−0.424793	+	0.138024i	0.0888156	+	0.996048i	$0.471692\pi$
$744$		0			0
$745$	−38.6076	−	53.1388i	−0.0518222	−	0.0713272i
$746$	283.300	−	871.909i	0.379759	−	1.16878i
$747$		0			0
$748$	−288.060	+	1027.97i	−0.385107	+	1.37429i
$749$	−606.376			−0.809580
$750$		0			0
$751$	−197.033	+	143.153i	−0.262361	+	0.190616i	−0.711187	−	0.703003i	$-0.751842\pi$
$751$	−197.033	+	143.153i	−0.262361	+	0.190616i	0.448826	+	0.893619i	$0.351842\pi$
$752$	−334.131	−	242.760i	−0.444323	−	0.322819i
$753$		0			0
$754$	2921.42	−	949.227i	3.87456	−	1.25892i
$755$	134.154	−	184.648i	0.177688	−	0.244566i
$756$		0			0
$757$	435.074	−	1339.02i	0.574735	−	1.76885i	−0.0623449	−	0.998055i	$-0.519858\pi$
$757$	435.074	−	1339.02i	0.574735	−	1.76885i	0.637080	−	0.770798i	$-0.280142\pi$
$758$		−	44.6787i		−	0.0589429i
$759$		0			0
$760$	148.311			0.195146
$761$	700.198	+	227.508i	0.920103	+	0.298959i	0.730509	−	0.682903i	$-0.239283\pi$
$761$	700.198	+	227.508i	0.920103	+	0.298959i	0.189594	+	0.981863i	$0.439283\pi$
$762$		0			0
$763$	−287.813	−	209.108i	−0.377213	−	0.274061i
$764$	465.610	+	1433.00i	0.609438	+	1.87566i
$765$		0			0
$766$	−346.363	+	476.728i	−0.452171	+	0.622360i
$767$	815.077	+	1121.86i	1.06268	+	1.46266i
$768$		0			0
$769$			676.556i			0.879787i	0.898050	+	0.439894i	$0.144984\pi$
$769$			676.556i			0.879787i	−0.898050	+	0.439894i	$0.855016\pi$
$770$	−102.855	+	154.493i	−0.133578	+	0.200640i
$771$		0			0
$772$	82.0022	+	26.6441i	0.106220	+	0.0345131i
$773$	−477.661	+	347.041i	−0.617932	+	0.448954i	−0.852198	−	0.523219i	$-0.824731\pi$
$773$	−477.661	+	347.041i	−0.617932	+	0.448954i	0.234267	+	0.972172i	$0.424731\pi$
$774$		0			0
$775$	148.855	+	458.127i	0.192070	+	0.591132i
$776$	513.297	−	166.780i	0.661465	−	0.214923i
$777$		0			0
$778$	−981.639	−	1351.11i	−1.26175	−	1.73665i
$779$	221.643	−	682.147i	0.284522	−	0.875670i
$780$		0			0
$781$	−458.170	+	169.900i	−0.586646	+	0.217542i
$782$	−255.637			−0.326901
$783$		0			0
$784$	173.333	−	125.934i	0.221088	−	0.160630i
$785$	100.395	+	72.9413i	0.127892	+	0.0929188i
$786$		0			0
$787$	−873.933	+	283.958i	−1.11046	+	0.360811i	−0.806120	−	0.591752i	$-0.798436\pi$
$787$	−873.933	+	283.958i	−1.11046	+	0.360811i	−0.304341	+	0.952563i	$0.598436\pi$
$788$	−689.581	+	949.127i	−0.875103	+	1.20448i
$789$		0			0
$790$	−190.964	+	587.726i	−0.241726	+	0.743956i
$791$			146.596i			0.185330i
$792$		0			0
$793$	−236.381			−0.298085
$794$	536.828	+	174.426i	0.676106	+	0.219680i
$795$		0			0
$796$	−483.289	−	351.130i	−0.607147	−	0.441118i
$797$	36.1517	+	111.264i	0.0453598	+	0.139603i	0.971171	−	0.238382i	$-0.0766171\pi$
$797$	36.1517	+	111.264i	0.0453598	+	0.139603i	−0.925812	+	0.377985i	$0.876617\pi$
$798$		0			0
$799$	663.924	−	913.813i	0.830944	−	1.14370i
$800$	−549.964	−	756.961i	−0.687455	−	0.946201i
$801$		0			0
$802$		−	1934.18i		−	2.41169i
$803$	−641.634	−	427.174i	−0.799046	−	0.531972i
$804$		0			0
$805$	−24.8618	−	8.07810i	−0.0308843	−	0.0100349i
$806$	1145.35	−	832.149i	1.42104	−	1.03244i
$807$		0			0
$808$	−218.117	−	671.295i	−0.269947	−	0.830810i
$809$	731.663	−	237.732i	0.904404	−	0.293859i	0.180351	−	0.983602i	$-0.442277\pi$
$809$	731.663	−	237.732i	0.904404	−	0.293859i	0.724054	+	0.689744i	$0.242277\pi$
$810$		0			0
$811$	502.546	+	691.695i	0.619662	+	0.852892i	0.997328	−	0.0730500i	$-0.0232733\pi$
$811$	502.546	+	691.695i	0.619662	+	0.852892i	−0.377666	+	0.925942i	$0.623273\pi$
$812$	−305.832	+	941.253i	−0.376640	+	1.15918i
$813$		0			0
$814$	−578.307	+	457.473i	−0.710451	+	0.562006i
$815$	−219.888			−0.269802
$816$		0			0
$817$	−159.455	+	115.851i	−0.195172	+	0.141801i
$818$	550.901	+	400.253i	0.673473	+	0.489307i
$819$		0			0
$820$	−283.525	+	92.1230i	−0.345763	+	0.112345i
$821$	−441.221	+	607.288i	−0.537419	+	0.739694i	−0.988238	−	0.152922i	$-0.951132\pi$
$821$	−441.221	+	607.288i	−0.537419	+	0.739694i	0.450819	+	0.892615i	$0.351132\pi$
$822$		0			0
$823$	−399.433	+	1229.33i	−0.485337	+	1.49371i	0.346154	+	0.938178i	$0.387487\pi$
$823$	−399.433	+	1229.33i	−0.485337	+	1.49371i	−0.831492	+	0.555537i	$0.812513\pi$
$824$		−	267.846i		−	0.325056i
$825$		0			0
$826$	−759.575			−0.919582
$827$	569.808	+	185.142i	0.689005	+	0.223871i	0.632534	−	0.774533i	$-0.282015\pi$
$827$	569.808	+	185.142i	0.689005	+	0.223871i	0.0564717	+	0.998404i	$0.482015\pi$
$828$		0			0
$829$	790.284	+	574.175i	0.953298	+	0.692611i	0.951585	−	0.307387i	$-0.0994546\pi$
$829$	790.284	+	574.175i	0.953298	+	0.692611i	0.00171336	+	0.999999i	$0.499455\pi$
$830$	153.612	+	472.771i	0.185075	+	0.569603i
$831$		0			0
$832$	−1299.90	+	1789.16i	−1.56238	+	2.15044i
$833$	344.416	+	474.047i	0.413464	+	0.569084i
$834$		0			0
$835$		−	363.116i		−	0.434869i
$836$	1226.96	−	50.2651i	1.46765	−	0.0601257i
$837$		0			0
$838$	−2428.50	−	789.066i	−2.89797	−	0.941606i
$839$	326.638	−	237.316i	0.389318	−	0.282856i	−0.375858	−	0.926677i	$-0.622652\pi$
$839$	326.638	−	237.316i	0.389318	−	0.282856i	0.765176	+	0.643821i	$0.222652\pi$
$840$		0			0
$841$	−379.372	−	1167.59i	−0.451096	−	1.38833i
$842$	785.111	−	255.098i	0.932436	−	0.302967i
$843$		0			0
$844$	−484.814	−	667.289i	−0.574424	−	0.790627i
$845$	−132.034	+	406.360i	−0.156254	+	0.480900i
$846$		0			0
$847$	−239.471	+	393.734i	−0.282728	+	0.464858i
$848$	512.124			0.603920
$849$		0			0
$850$	984.224	−	715.080i	1.15791	−	0.841271i
$851$	−84.0225	−	61.0459i	−0.0987338	−	0.0717343i
$852$		0			0
$853$	693.341	−	225.280i	0.812826	−	0.264103i	0.127032	−	0.991899i	$-0.459455\pi$
$853$	693.341	−	225.280i	0.812826	−	0.264103i	0.685794	+	0.727795i	$0.259455\pi$
$854$	76.1067	−	104.752i	0.0891179	−	0.122660i
$855$		0			0
$856$	262.716	−	808.557i	0.306911	−	0.944575i
$857$		−	999.714i		−	1.16653i	−0.812283	−	0.583264i	$-0.801775\pi$
$857$		−	999.714i		−	1.16653i	0.812283	−	0.583264i	$-0.198225\pi$
$858$		0			0
$859$	1116.47			1.29973			0.649864	−	0.760050i	$-0.274826\pi$
$859$	1116.47			1.29973			0.649864	+	0.760050i	$0.274826\pi$
$860$	77.9116	+	25.3150i	0.0905949	+	0.0294361i
$861$		0			0
$862$	214.408	+	155.777i	0.248734	+	0.180716i
$863$	−452.481	−	1392.59i	−0.524311	−	1.61366i	−0.765674	−	0.643229i	$-0.777594\pi$
$863$	−452.481	−	1392.59i	−0.524311	−	1.61366i	0.241362	−	0.970435i	$-0.422406\pi$
$864$		0			0
$865$	27.4359	−	37.7622i	0.0317178	−	0.0436557i
$866$	722.308	+	994.172i	0.834074	+	1.14800i
$867$		0			0
$868$			456.136i			0.525502i
$869$	−414.027	+	1477.50i	−0.476441	+	1.70023i
$870$		0			0
$871$	−465.841	−	151.361i	−0.534835	−	0.173778i
$872$	403.527	−	293.180i	0.462761	−	0.336215i
$873$		0			0
$874$	90.8667	+	279.659i	0.103966	+	0.319976i
$875$	247.037	−	80.2671i	0.282328	−	0.0917338i
$876$		0			0
$877$	−143.835	−	197.971i	−0.164008	−	0.225737i	0.719101	−	0.694905i	$-0.244554\pi$
$877$	−143.835	−	197.971i	−0.164008	−	0.225737i	−0.883109	+	0.469168i	$0.844554\pi$
$878$	−587.480	+	1808.08i	−0.669112	+	2.05932i
$879$		0			0
$880$	60.2528	+	76.1676i	0.0684691	+	0.0865541i
$881$	1021.52			1.15950			0.579748	−	0.814796i	$-0.303151\pi$
$881$	1021.52			1.15950			0.579748	+	0.814796i	$0.303151\pi$
$882$		0			0
$883$	−291.741	+	211.963i	−0.330398	+	0.240048i	−0.740600	−	0.671947i	$-0.765458\pi$
$883$	−291.741	+	211.963i	−0.330398	+	0.240048i	0.410201	+	0.911995i	$0.365458\pi$
$884$	−1701.44	−	1236.17i	−1.92471	−	1.39838i
$885$		0			0
$886$	−500.782	+	162.714i	−0.565217	+	0.183650i
$887$	80.1825	−	110.362i	0.0903974	−	0.124421i	−0.761423	−	0.648256i	$-0.775499\pi$
$887$	80.1825	−	110.362i	0.0903974	−	0.124421i	0.851820	+	0.523834i	$0.175499\pi$
$888$		0			0
$889$	−95.6735	+	294.453i	−0.107619	+	0.331218i
$890$		−	281.723i		−	0.316543i
$891$		0			0
$892$	1069.84			1.19937
$893$	−1235.68	−	401.496i	−1.38374	−	0.449603i
$894$		0			0
$895$	191.026	+	138.788i	0.213437	+	0.155071i
$896$	−182.657	−	562.160i	−0.203858	−	0.627411i
$897$		0			0
$898$	1240.90	−	1707.95i	1.38184	−	1.90195i
$899$	−560.409	−	771.337i	−0.623369	−	0.857994i
$900$		0			0
$901$			1400.61i			1.55450i
$902$	−1179.94	+	437.549i	−1.30814	+	0.485087i
$903$		0			0
$904$	−195.475	−	63.5137i	−0.216233	−	0.0702585i
$905$	78.8014	−	57.2526i	0.0870734	−	0.0632625i
$906$		0			0
$907$	217.827	+	670.403i	0.240162	+	0.739143i	0.996395	+	0.0848399i	$0.0270379\pi$
$907$	217.827	+	670.403i	0.240162	+	0.739143i	−0.756233	+	0.654303i	$0.772962\pi$
$908$	−263.377	+	85.5764i	−0.290063	+	0.0942471i
$909$		0			0
$910$	−214.912	−	295.801i	−0.236167	−	0.325056i
$911$	59.3128	−	182.546i	0.0651074	−	0.200380i	−0.913211	−	0.407487i	$-0.866405\pi$
$911$	59.3128	−	182.546i	0.0651074	−	0.200380i	0.978318	+	0.207108i	$0.0664050\pi$
$912$		0			0
$913$	429.147	+	1157.28i	0.470041	+	1.26756i
$914$	−1786.16			−1.95422
$915$		0			0
$916$	−1136.57	+	825.769i	−1.24080	+	0.901494i
$917$	−454.003	−	329.853i	−0.495096	−	0.359708i
$918$		0			0
$919$	348.974	−	113.389i	0.379733	−	0.123383i	−0.112930	−	0.993603i	$-0.536024\pi$
$919$	348.974	−	113.389i	0.379733	−	0.123383i	0.492663	+	0.870220i	$0.336024\pi$
$920$	21.5431	−	29.6515i	0.0234164	−	0.0322299i
$921$		0			0
$922$	320.850	−	987.475i	0.347993	−	1.07101i
$923$		−	962.653i		−	1.04296i
$924$		0			0
$925$	494.254			0.534329
$926$	104.528	+	33.9631i	0.112881	+	0.0366773i
$927$		0			0
$928$	1498.24	+	1088.53i	1.61448	+	1.17299i
$929$	−201.875	−	621.308i	−0.217304	−	0.668792i	−0.998982	−	0.0451102i	$-0.985636\pi$
$929$	−201.875	−	621.308i	−0.217304	−	0.668792i	0.781678	−	0.623682i	$-0.214364\pi$
$930$		0			0
$931$	396.170	−	545.281i	0.425532	−	0.585694i
$932$	76.3632	+	105.105i	0.0819347	+	0.112773i
$933$		0			0
$934$			16.4883i			0.0176535i
$935$	−208.311	+	164.785i	−0.222792	+	0.176241i
$936$		0			0
$937$	−338.118	−	109.861i	−0.360851	−	0.117248i	0.122980	−	0.992409i	$-0.460755\pi$
$937$	−338.118	−	109.861i	−0.360851	−	0.117248i	−0.483831	+	0.875162i	$0.660755\pi$
$938$	217.060	−	157.703i	0.231407	−	0.168127i
$939$		0			0
$940$	166.876	+	513.593i	0.177528	+	0.546375i
$941$	−300.119	+	97.5145i	−0.318936	+	0.103629i	−0.464110	−	0.885778i	$-0.653626\pi$
$941$	−300.119	+	97.5145i	−0.318936	+	0.103629i	0.145174	+	0.989406i	$0.453626\pi$
$942$		0			0
$943$	−104.185	−	143.399i	−0.110483	−	0.152066i
$944$	−122.822	+	378.007i	−0.130108	+	0.400431i
$945$		0			0
$946$	332.991	+	93.3115i	0.351999	+	0.0986380i
$947$	548.676			0.579383			0.289691	−	0.957120i	$-0.406447\pi$
$947$	548.676			0.579383			0.289691	+	0.957120i	$0.406447\pi$
$948$		0			0
$949$	1228.51	−	892.564i	1.29453	−	0.940531i
$950$	−1132.12	−	822.533i	−1.19171	−	0.865825i
$951$		0			0
$952$	328.556	−	106.754i	0.345122	−	0.112137i
$953$	−982.505	+	1352.30i	−1.03096	+	1.41900i	−0.126737	+	0.991936i	$0.540450\pi$
$953$	−982.505	+	1352.30i	−1.03096	+	1.41900i	−0.904224	+	0.427059i	$0.859550\pi$
$954$		0			0
$955$	−115.843	+	356.527i	−0.121301	+	0.373327i
$956$		−	352.054i		−	0.368258i
$957$		0			0
$958$	−388.602			−0.405639
$959$	768.812	+	249.802i	0.801681	+	0.260482i
$960$		0			0
$961$	421.966	+	306.577i	0.439091	+	0.319018i
$962$	−448.885	−	1381.53i	−0.466617	−	1.43610i
$963$		0			0
$964$	554.117	−	762.677i	0.574810	−	0.791158i
$965$	12.6091	+	17.3549i	0.0130664	+	0.0179844i
$966$		0			0
$967$			562.236i			0.581423i	0.956811	+	0.290711i	$0.0938919\pi$
$967$			562.236i			0.581423i	−0.956811	+	0.290711i	$0.906108\pi$
$968$	−421.263	−	489.904i	−0.435189	−	0.506099i
$969$		0			0
$970$	425.855	+	138.369i	0.439026	+	0.142648i
$971$	450.923	−	327.615i	0.464390	−	0.337399i	−0.330861	−	0.943680i	$-0.607339\pi$
$971$	450.923	−	327.615i	0.464390	−	0.337399i	0.795251	+	0.606280i	$0.207339\pi$
$972$		0			0
$973$	−258.135	−	794.457i	−0.265298	−	0.816502i
$974$	1968.01	−	639.444i	2.02054	−	0.656513i
$975$		0			0
$976$	−39.8241	−	54.8131i	−0.0408033	−	0.0561610i
$977$	132.647	−	408.247i	0.135770	−	0.417857i	−0.859939	−	0.510397i	$-0.829498\pi$
$977$	132.647	−	408.247i	0.135770	−	0.417857i	0.995709	+	0.0925396i	$0.0294985\pi$
$978$		0			0
$979$	−28.6331	−	698.927i	−0.0292473	−	0.713919i
$980$	−280.141			−0.285858
$981$		0			0
$982$	741.735	−	538.902i	0.755331	−	0.548780i
$983$	−1060.27	−	770.334i	−1.07861	−	0.783657i	−0.101171	−	0.994869i	$-0.532259\pi$
$983$	−1060.27	−	770.334i	−1.07861	−	0.783657i	−0.977440	+	0.211212i	$0.932259\pi$
$984$		0			0
$985$	−277.600	+	90.1976i	−0.281827	+	0.0915712i
$986$	−1415.34	+	1948.05i	−1.43544	+	1.97571i
$987$		0			0
$988$	−747.551	+	2300.73i	−0.756631	+	2.32867i
$989$			48.7077i			0.0492494i
$990$		0			0
$991$	33.4939			0.0337981			0.0168990	−	0.999857i	$-0.494621\pi$
$991$	33.4939			0.0337981			0.0168990	+	0.999857i	$0.494621\pi$
$992$	811.751	+	263.754i	0.818298	+	0.265881i
$993$		0			0
$994$	426.597	+	309.941i	0.429172	+	0.311812i
$995$	−45.9280	−	141.352i	−0.0461588	−	0.142062i
$996$		0			0
$997$	−544.125	+	748.924i	−0.545762	+	0.751177i	−0.989430	−	0.145014i	$-0.953677\pi$
$997$	−544.125	+	748.924i	−0.545762	+	0.751177i	0.443667	+	0.896192i	$0.353677\pi$
$998$	1176.31	+	1619.05i	1.17866	+	1.62229i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.b.46.4	yes	16
3.2	odd	2	inner	99.3.k.b.46.1	yes	16
11.4	even	5		1089.3.c.l.604.14		16
11.6	odd	10	inner	99.3.k.b.28.4	yes	16
11.7	odd	10		1089.3.c.l.604.4		16
33.17	even	10	inner	99.3.k.b.28.1	✓	16
33.26	odd	10		1089.3.c.l.604.3		16
33.29	even	10		1089.3.c.l.604.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.k.b.28.1	✓	16	33.17	even	10	inner
99.3.k.b.28.4	yes	16	11.6	odd	10	inner
99.3.k.b.46.1	yes	16	3.2	odd	2	inner
99.3.k.b.46.4	yes	16	1.1	even	1	trivial
1089.3.c.l.604.3		16	33.26	odd	10
1089.3.c.l.604.4		16	11.7	odd	10
1089.3.c.l.604.13		16	33.29	even	10
1089.3.c.l.604.14		16	11.4	even	5

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.96408 + 0.963089i) q^{2} +(4.62219 + 3.35821i) q^{4} +(0.439256 + 1.35189i) q^{5} +(2.23863 - 3.08121i) q^{7} +(3.13867 + 4.32000i) q^{8} +O(q^{10})\)	\(q+(2.96408 + 0.963089i) q^{2} +(4.62219 + 3.35821i) q^{4} +(0.439256 + 1.35189i) q^{5} +(2.23863 - 3.08121i) q^{7} +(3.13867 + 4.32000i) q^{8} +4.43016i q^{10} +(0.450262 + 10.9908i) q^{11} +(-20.6093 - 6.69638i) q^{13} +(9.60298 - 6.97698i) q^{14} +(-1.91935 - 5.90715i) q^{16} +(16.1554 - 5.24922i) q^{17} +(-11.4850 - 15.8077i) q^{19} +(-2.50962 + 7.72381i) q^{20} +(-9.25049 + 33.0112i) q^{22} -4.82866 q^{23} +(18.5908 - 13.5070i) q^{25} +(-54.6386 - 39.6973i) q^{26} +(20.6948 - 6.72414i) q^{28} +(-26.7340 + 36.7963i) q^{29} +(-6.47773 + 19.9364i) q^{31} -40.7171i q^{32} +52.9416 q^{34} +(5.14880 + 1.67295i) q^{35} +(17.4008 + 12.6424i) q^{37} +(-18.8182 - 57.9164i) q^{38} +(-4.46150 + 6.14073i) q^{40} +(21.5764 + 29.6974i) q^{41} -10.0872i q^{43} +(-34.8282 + 52.3135i) q^{44} +(-14.3126 - 4.65043i) q^{46} +(53.7954 - 39.0846i) q^{47} +(10.6594 + 32.8063i) q^{49} +(68.1130 - 22.1313i) q^{50} +(-72.7723 - 100.162i) q^{52} +(-25.4792 + 78.4170i) q^{53} +(-14.6606 + 5.43647i) q^{55} +20.3372 q^{56} +(-114.680 + 83.3199i) q^{58} +(-51.7702 - 37.6132i) q^{59} +(10.3744 - 3.37084i) q^{61} +(-38.4011 + 52.8545i) q^{62} +(31.5368 - 97.0602i) q^{64} -30.8030i q^{65} +22.6034 q^{67} +(92.3014 + 29.9906i) q^{68} +(13.6503 + 9.91751i) q^{70} +(13.7276 + 42.2492i) q^{71} +(-41.1890 + 56.6919i) q^{73} +(39.4016 + 54.2316i) q^{74} -111.635i q^{76} +(34.8729 + 23.2170i) q^{77} +(132.665 + 43.1053i) q^{79} +(7.14273 - 5.18950i) q^{80} +(35.3531 + 108.806i) q^{82} +(106.716 - 34.6742i) q^{83} +(14.1928 + 19.5346i) q^{85} +(9.71487 - 29.8993i) q^{86} +(-46.0670 + 36.4415i) q^{88} -63.5921 q^{89} +(-66.7698 + 48.5111i) q^{91} +(-22.3190 - 16.2157i) q^{92} +(197.096 - 64.0404i) q^{94} +(16.3255 - 22.4701i) q^{95} +(31.2333 - 96.1262i) q^{97} +107.507i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) \) 16 * q - 4 * q^4 + 30 * q^7	\( 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) \) 16 * q - 4 * q^4 + 30 * q^7 - 30 * q^13 - 176 * q^16 + 90 * q^22 - 74 * q^25 - 50 * q^28 + 130 * q^31 + 328 * q^34 + 90 * q^37 + 450 * q^40 - 370 * q^46 - 54 * q^49 - 790 * q^52 - 476 * q^55 - 630 * q^58 + 210 * q^61 + 1104 * q^64 + 300 * q^67 + 268 * q^70 - 170 * q^73 + 30 * q^79 + 90 * q^82 - 610 * q^85 - 600 * q^88 - 402 * q^91 + 1030 * q^94 + 870 * q^97

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