LMFDB - Embedded newform 99.3.k.b.46.1

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			46.1
Root			$-1.83190 + 2.52140i$ of defining polynomial
Character	$\chi$	$=$	99.46
Dual form			99.3.k.b.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.96408 - 0.963089i) q^{2} +(4.62219 + 3.35821i) q^{4} +(-0.439256 - 1.35189i) q^{5} +(2.23863 - 3.08121i) q^{7} +(-3.13867 - 4.32000i) q^{8} +O(q^{10})$	\(q+(-2.96408 - 0.963089i) q^{2} +(4.62219 + 3.35821i) q^{4} +(-0.439256 - 1.35189i) q^{5} +(2.23863 - 3.08121i) q^{7} +(-3.13867 - 4.32000i) q^{8} +4.43016i q^{10} +(-0.450262 - 10.9908i) q^{11} +(-20.6093 - 6.69638i) q^{13} +(-9.60298 + 6.97698i) q^{14} +(-1.91935 - 5.90715i) q^{16} +(-16.1554 + 5.24922i) q^{17} +(-11.4850 - 15.8077i) q^{19} +(2.50962 - 7.72381i) q^{20} +(-9.25049 + 33.0112i) q^{22} +4.82866 q^{23} +(18.5908 - 13.5070i) q^{25} +(54.6386 + 39.6973i) q^{26} +(20.6948 - 6.72414i) q^{28} +(26.7340 - 36.7963i) q^{29} +(-6.47773 + 19.9364i) q^{31} +40.7171i q^{32} +52.9416 q^{34} +(-5.14880 - 1.67295i) q^{35} +(17.4008 + 12.6424i) q^{37} +(18.8182 + 57.9164i) q^{38} +(-4.46150 + 6.14073i) q^{40} +(-21.5764 - 29.6974i) q^{41} -10.0872i q^{43} +(34.8282 - 52.3135i) q^{44} +(-14.3126 - 4.65043i) q^{46} +(-53.7954 + 39.0846i) q^{47} +(10.6594 + 32.8063i) q^{49} +(-68.1130 + 22.1313i) q^{50} +(-72.7723 - 100.162i) q^{52} +(25.4792 - 78.4170i) q^{53} +(-14.6606 + 5.43647i) q^{55} -20.3372 q^{56} +(-114.680 + 83.3199i) q^{58} +(51.7702 + 37.6132i) q^{59} +(10.3744 - 3.37084i) q^{61} +(38.4011 - 52.8545i) q^{62} +(31.5368 - 97.0602i) q^{64} +30.8030i q^{65} +22.6034 q^{67} +(-92.3014 - 29.9906i) q^{68} +(13.6503 + 9.91751i) q^{70} +(-13.7276 - 42.2492i) q^{71} +(-41.1890 + 56.6919i) q^{73} +(-39.4016 - 54.2316i) q^{74} -111.635i q^{76} +(-34.8729 - 23.2170i) q^{77} +(132.665 + 43.1053i) q^{79} +(-7.14273 + 5.18950i) q^{80} +(35.3531 + 108.806i) q^{82} +(-106.716 + 34.6742i) q^{83} +(14.1928 + 19.5346i) q^{85} +(-9.71487 + 29.8993i) q^{86} +(-46.0670 + 36.4415i) q^{88} +63.5921 q^{89} +(-66.7698 + 48.5111i) q^{91} +(22.3190 + 16.2157i) q^{92} +(197.096 - 64.0404i) q^{94} +(-16.3255 + 22.4701i) q^{95} +(31.2333 - 96.1262i) q^{97} -107.507i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.547320	−	0.836924i	$-0.684352\pi$
$2$	−2.96408	−	0.963089i	−1.48204	−	0.481545i	−0.934722	+	0.355379i	$0.884352\pi$
$3$		0			0
$3$		0			0
$4$	4.62219	+	3.35821i	1.15555	+	0.839554i
$5$	−0.439256	−	1.35189i	−0.0878512	−	0.270378i	0.897474	−	0.441068i	$-0.145400\pi$
$5$	−0.439256	−	1.35189i	−0.0878512	−	0.270378i	−0.985325	+	0.170690i	$0.945400\pi$
$6$		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	−0.742846	−	0.669463i	$-0.766524\pi$
$17$	−16.1554	+	5.24922i	−0.950320	+	0.308778i	−0.207474	+	0.978240i	$0.566524\pi$
$18$		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	$-0.466525\pi$
$23$	4.82866			0.209942			0.104971	+	0.994475i	$0.466525\pi$
$24$		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	$-0.513082\pi$
$29$	26.7340	−	36.7963i	0.921863	−	1.26884i	0.962950	−	0.269681i	$-0.0869181\pi$
$30$		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	0.460300	−	0.887763i	$-0.347742\pi$
$41$	−21.5764	−	29.6974i	−0.526254	−	0.724326i	−0.986554	+	0.163437i	$0.947742\pi$
$42$		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	−0.987751	−	0.156038i	$-0.950128\pi$
$47$	−53.7954	+	39.0846i	−1.14458	+	0.831588i	−0.156831	+	0.987625i	$0.550128\pi$
$48$		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	$-0.616308\pi$
$53$	25.4792	−	78.4170i	0.480740	−	1.47957i	0.838057	−	0.545583i	$-0.183692\pi$
$54$		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	0.932578	−	0.360967i	$-0.117553\pi$
$59$	51.7702	+	37.6132i	0.877461	+	0.637512i	−0.0551179	+	0.998480i	$0.517553\pi$
$60$		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	$-0.998719\pi$
$71$	−13.7276	−	42.2492i	−0.193346	−	0.595059i	0.806646	−	0.591035i	$-0.201281\pi$
$72$		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	−0.870598	−	0.491996i	$-0.836268\pi$
$83$	−106.716	+	34.6742i	−1.28574	+	0.417762i	−0.415141	+	0.909757i	$0.636268\pi$
$84$		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	$-0.383711\pi$
$89$	63.5921			0.714518			0.357259	+	0.934005i	$0.383711\pi$
$90$		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	0.856019	−	0.516944i	$-0.172930\pi$
$101$	125.715	+	40.8472i	1.24470	+	0.404428i	0.388682	+	0.921372i	$0.372930\pi$
$102$		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	$0.0670662\pi$
$107$	93.5828	+	128.806i	0.874606	+	1.20379i	−0.103280	+	0.994652i	$0.532934\pi$
$108$		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	−0.441411	−	0.897305i	$-0.645522\pi$
$113$	31.1398	−	22.6244i	0.275573	−	0.200216i	0.716984	+	0.697089i	$0.245522\pi$
$114$		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	$0.190117\pi$
$131$			147.346i			1.12478i	−0.826874	+	0.562388i	$0.809883\pi$
$132$		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	$-0.817932\pi$
$137$	−65.5891	−	201.863i	−0.478753	−	1.47345i	0.362076	−	0.932149i	$-0.382068\pi$
$138$		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	−0.157808	−	0.987470i	$-0.550443\pi$
$149$	43.9465	−	14.2791i	0.294943	−	0.0958328i	0.452751	+	0.891637i	$0.350443\pi$
$150$		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	0.926474	−	0.376360i	$-0.122824\pi$
$167$	242.950	+	78.9391i	1.45479	+	0.472689i	0.528314	+	0.849049i	$0.322824\pi$
$168$		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	0.861149	−	0.508353i	$-0.169745\pi$
$173$	19.3011	+	26.5657i	0.111567	+	0.153559i	−0.749582	+	0.661912i	$0.769745\pi$
$174$		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	−0.896064	−	0.443925i	$-0.853585\pi$
$179$	−134.387	+	97.6377i	−0.750764	+	0.545462i	0.145299	+	0.989388i	$0.453585\pi$
$180$		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	−0.133296	−	0.991076i	$-0.542556\pi$
$191$	−213.358	−	155.013i	−1.11706	−	0.811588i	−0.983760	+	0.179488i	$0.942556\pi$
$192$		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	$-0.825495\pi$
$197$		−	205.342i		−	1.04234i	0.853452	−	0.521172i	$-0.174505\pi$
$198$		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	−0.741638	−	0.670800i	$-0.765951\pi$
$227$	28.4905	−	39.2139i	0.125509	−	0.172748i	0.867147	+	0.498052i	$0.165951\pi$
$228$		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	0.262241	−	0.965003i	$-0.415539\pi$
$233$	−21.6263	−	7.02681i	−0.0928167	−	0.0301580i	−0.355057	+	0.934845i	$0.615539\pi$
$234$		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	0.878039	−	0.478589i	$-0.158852\pi$
$239$	36.2192	+	49.8514i	0.151545	+	0.208583i	−0.726494	+	0.687173i	$0.758852\pi$
$240$		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	−0.919995	−	0.391931i	$-0.871807\pi$
$251$	13.7216	−	42.2307i	0.0546677	−	0.168250i	0.974662	+	0.223681i	$0.0718073\pi$
$252$		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	0.555740	−	0.831356i	$-0.312435\pi$
$257$	−16.2405	−	11.7994i	−0.0631928	−	0.0459122i	−0.618933	+	0.785444i	$0.712435\pi$
$258$		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	$0.132688\pi$
$263$			212.968i			0.809765i	−0.914369	+	0.404883i	$0.867312\pi$
$264$		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	$-0.825205\pi$
$269$	−126.349	−	388.861i	−0.469698	−	1.44558i	0.383279	−	0.923632i	$-0.374795\pi$
$270$		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	−0.724265	−	0.689521i	$-0.757821\pi$
$281$	−254.282	+	82.6212i	−0.904918	+	0.294026i	−0.180652	+	0.983547i	$0.557821\pi$
$282$		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	−0.447965	−	0.894051i	$-0.647851\pi$
$293$	158.442	−	218.076i	0.540757	−	0.744288i	0.988722	+	0.149763i	$0.0478511\pi$
$294$		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	−0.107423	−	0.994213i	$-0.534260\pi$
$311$	250.335	−	181.879i	0.804935	−	0.584819i	0.912358	+	0.409394i	$0.134260\pi$
$312$		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	$-0.702265\pi$
$317$	114.026	−	350.937i	0.359705	−	1.10706i	0.953231	−	0.302243i	$-0.0977354\pi$
$318$		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	−0.806371	−	0.591410i	$-0.798572\pi$
$347$	−385.558	+	125.275i	−1.11112	+	0.361024i	−0.304746	+	0.952434i	$0.598572\pi$
$348$		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	$-0.701548\pi$
$353$	−417.749			−1.18343			−0.591713	+	0.806149i	$0.701548\pi$
$354$		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	−0.452728	−	0.891649i	$-0.649549\pi$
$359$	192.130	−	264.444i	0.535181	−	0.736613i	0.987909	+	0.155036i	$0.0495492\pi$
$360$		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	−0.845354	−	0.534206i	$-0.820611\pi$
$383$	58.4266	−	179.819i	0.152550	−	0.469500i	0.997904	+	0.0647053i	$0.0206107\pi$
$384$		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	0.983357	−	0.181683i	$-0.0581543\pi$
$389$	433.518	+	314.969i	1.11444	+	0.809689i	0.131084	+	0.991371i	$0.458154\pi$
$390$		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	$0.181654\pi$
$401$	191.776	+	590.226i	0.478245	+	1.47189i	−0.363287	+	0.931677i	$0.618346\pi$
$402$		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	$-0.0673579\pi$
$419$	819.307			1.95539			0.977694	+	0.210035i	$0.0673579\pi$
$420$		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	0.213689	−	0.976902i	$-0.431452\pi$
$431$	−80.8735	−	26.2774i	−0.187642	−	0.0609684i	−0.401330	+	0.915933i	$0.631452\pi$
$432$		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	−0.422729	−	0.906256i	$-0.638928\pi$
$443$	136.683	−	99.3063i	0.308541	−	0.224168i	0.731270	+	0.682088i	$0.238928\pi$
$444$		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	$0.372034\pi$
$449$	−209.322	+	644.227i	−0.466196	+	1.43480i	−0.857472	+	0.514530i	$0.827966\pi$
$450$		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	$0.117677\pi$
$461$			333.147i			0.722661i	−0.932438	+	0.361330i	$0.882323\pi$
$462$		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	0.949291	−	0.314399i	$-0.101803\pi$
$467$	−1.63484	−	5.03152i	−0.00350073	−	0.0107741i	−0.952792	+	0.303625i	$0.901803\pi$
$468$		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	−0.182605	−	0.983186i	$-0.558453\pi$
$479$	118.584	−	38.5304i	0.247566	−	0.0804392i	0.430172	+	0.902747i	$0.358453\pi$
$480$		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	−0.947945	−	0.318435i	$-0.896843\pi$
$491$	−172.912	+	237.993i	−0.352164	+	0.484712i	0.595781	+	0.803147i	$0.296843\pi$
$492$		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	0.918217	−	0.396077i	$-0.129629\pi$
$503$	129.664	+	178.467i	0.257780	+	0.354804i	−0.660437	+	0.750882i	$0.729629\pi$
$504$		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	0.108115	−	0.994138i	$-0.465518\pi$
$509$	553.286	−	401.986i	1.08701	−	0.789756i	0.978891	+	0.204382i	$0.0655185\pi$
$510$		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	0.337947	−	0.941165i	$-0.390268\pi$
$521$	−235.869	−	171.369i	−0.452724	−	0.328923i	−0.790670	+	0.612242i	$0.790268\pi$
$522$		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	−0.819963	−	0.572417i	$-0.806006\pi$
$557$	−12.3540	+	17.0038i	−0.0221795	+	0.0305274i	0.797783	+	0.602944i	$0.206006\pi$
$558$		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	0.306656	−	0.951820i	$-0.400790\pi$
$563$	−2.65747	−	0.863465i	−0.00472020	−	0.00153368i	−0.311376	+	0.950287i	$0.600790\pi$
$564$		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	0.940958	−	0.338524i	$-0.109927\pi$
$569$	186.763	+	257.058i	0.328231	+	0.451771i	−0.612727	+	0.790295i	$0.709927\pi$
$570$		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	$-0.962687\pi$
$587$	−828.411	−	601.876i	−1.41126	−	1.02534i	−0.418125	−	0.908389i	$-0.637313\pi$
$588$		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	$-0.954673\pi$
$593$		−	168.317i		−	0.283839i	0.989878	−	0.141920i	$-0.0453275\pi$
$594$		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	0.968031	−	0.250830i	$-0.0807036\pi$
$599$	22.4285	+	69.0277i	0.0374432	+	0.115238i	−0.930588	+	0.366068i	$0.880704\pi$
$600$		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	$-0.550888\pi$
$617$	−196.438			−0.318376			−0.159188	+	0.987248i	$0.550888\pi$
$618$		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	−0.373438	−	0.927655i	$-0.621821\pi$
$641$	252.179	−	183.219i	0.393415	−	0.285833i	0.766854	+	0.641822i	$0.221821\pi$
$642$		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	−0.832987	−	0.553293i	$-0.813371\pi$
$647$	107.487	−	330.811i	0.166131	−	0.511299i	0.999118	+	0.0419938i	$0.0133710\pi$
$648$		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	0.251130	−	0.967953i	$-0.419198\pi$
$653$	−386.475	−	280.791i	−0.591846	−	0.430001i	−0.842975	+	0.537952i	$0.819198\pi$
$654$		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	$-0.788278\pi$
$659$		−	813.433i		−	1.23434i	0.786828	−	0.617172i	$-0.211722\pi$
$660$		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	0.330821	−	0.943694i	$-0.392674\pi$
$677$	780.683	−	253.659i	1.15315	−	0.374681i	0.822329	+	0.569012i	$0.192674\pi$
$678$		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	$-0.702315\pi$
$683$	−810.930			−1.18731			−0.593653	+	0.804721i	$0.702315\pi$
$684$		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	0.751514	−	0.659718i	$-0.229324\pi$
$701$	−75.8101	−	104.344i	−0.108146	−	0.148850i	−0.859659	+	0.510868i	$0.829324\pi$
$702$		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	0.850750	−	0.525571i	$-0.176148\pi$
$719$	441.321	+	320.639i	0.613799	+	0.445951i	−0.236951	+	0.971522i	$0.576148\pi$
$720$		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	−0.0888156	−	0.996048i	$-0.528308\pi$
$743$	315.622	−	102.552i	0.424793	−	0.138024i	0.513609	+	0.858024i	$0.328308\pi$
$744$		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	−0.189594	−	0.981863i	$-0.560717\pi$
$761$	−700.198	−	227.508i	−0.920103	−	0.298959i	−0.730509	+	0.682903i	$0.760717\pi$
$762$		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	−0.234267	−	0.972172i	$-0.575269\pi$
$773$	477.661	−	347.041i	0.617932	−	0.448954i	0.852198	+	0.523219i	$0.175269\pi$
$774$		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	0.925812	−	0.377985i	$-0.123383\pi$
$797$	−36.1517	−	111.264i	−0.0453598	−	0.139603i	−0.971171	+	0.238382i	$0.923383\pi$
$798$		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	−0.724054	−	0.689744i	$-0.757723\pi$
$809$	−731.663	+	237.732i	−0.904404	+	0.293859i	−0.180351	+	0.983602i	$0.557723\pi$
$810$		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	−0.450819	−	0.892615i	$-0.648868\pi$
$821$	441.221	−	607.288i	0.537419	−	0.739694i	0.988238	+	0.152922i	$0.0488682\pi$
$822$		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	−0.0564717	−	0.998404i	$-0.517985\pi$
$827$	−569.808	−	185.142i	−0.689005	−	0.223871i	−0.632534	+	0.774533i	$0.717985\pi$
$828$		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	−0.765176	−	0.643821i	$-0.777348\pi$
$839$	−326.638	+	237.316i	−0.389318	+	0.282856i	0.375858	+	0.926677i	$0.377348\pi$
$840$		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	$0.198225\pi$
$857$			999.714i			1.16653i	−0.812283	+	0.583264i	$0.801775\pi$
$858$		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	$0.222406\pi$
$863$	452.481	+	1392.59i	0.524311	+	1.61366i	−0.241362	+	0.970435i	$0.577594\pi$
$864$		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	$-0.696849\pi$
$881$	−1021.52			−1.15950			−0.579748	+	0.814796i	$0.696849\pi$
$882$		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	−0.851820	−	0.523834i	$-0.824501\pi$
$887$	−80.1825	+	110.362i	−0.0903974	+	0.124421i	0.761423	+	0.648256i	$0.224501\pi$
$888$		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	−0.978318	−	0.207108i	$-0.933595\pi$
$911$	−59.3128	+	182.546i	−0.0651074	+	0.200380i	0.913211	+	0.407487i	$0.133595\pi$
$912$		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	$0.0143639\pi$
$929$	201.875	+	621.308i	0.217304	+	0.668792i	−0.781678	+	0.623682i	$0.785636\pi$
$930$		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	−0.145174	−	0.989406i	$-0.546374\pi$
$941$	300.119	−	97.5145i	0.318936	−	0.103629i	0.464110	+	0.885778i	$0.346374\pi$
$942$		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	$-0.593553\pi$
$947$	−548.676			−0.579383			−0.289691	+	0.957120i	$0.593553\pi$
$948$		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	$-0.459550\pi$
$953$	982.505	−	1352.30i	1.03096	−	1.41900i	0.904224	−	0.427059i	$-0.140450\pi$
$954$		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	−0.795251	−	0.606280i	$-0.792661\pi$
$971$	−450.923	+	327.615i	−0.464390	+	0.337399i	0.330861	+	0.943680i	$0.392661\pi$
$972$		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	−0.995709	−	0.0925396i	$-0.970502\pi$
$977$	−132.647	+	408.247i	−0.135770	+	0.417857i	0.859939	+	0.510397i	$0.170502\pi$
$978$		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	0.977440	−	0.211212i	$-0.0677412\pi$
$983$	1060.27	+	770.334i	1.07861	+	0.783657i	0.101171	+	0.994869i	$0.467741\pi$
$984$		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.46.1	yes	16
3.2	odd	2	inner	99.3.k.b.46.4	yes	16
11.4	even	5		1089.3.c.l.604.3		16
11.6	odd	10	inner	99.3.k.b.28.1	✓	16
11.7	odd	10		1089.3.c.l.604.13		16
33.17	even	10	inner	99.3.k.b.28.4	yes	16
33.26	odd	10		1089.3.c.l.604.14		16
33.29	even	10		1089.3.c.l.604.4		16

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

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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