LMFDB - Embedded newform 216.3.p.b.19.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(19,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("216.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.18
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75132 - 0.965848i) q^{2} +(2.13428 - 3.38303i) q^{4} +(-1.50948 + 0.871501i) q^{5} +(7.93804 + 4.58303i) q^{7} +(0.470322 - 7.98616i) q^{8} +O(q^{10})$	\(q+(1.75132 - 0.965848i) q^{2} +(2.13428 - 3.38303i) q^{4} +(-1.50948 + 0.871501i) q^{5} +(7.93804 + 4.58303i) q^{7} +(0.470322 - 7.98616i) q^{8} +(-1.80186 + 2.98421i) q^{10} +(4.09143 - 7.08657i) q^{11} +(19.9384 - 11.5114i) q^{13} +(18.3286 + 0.359434i) q^{14} +(-6.88973 - 14.4406i) q^{16} -18.4578 q^{17} -7.06353 q^{19} +(-0.273345 + 6.96665i) q^{20} +(0.320879 - 16.3626i) q^{22} +(-9.33623 + 5.39028i) q^{23} +(-10.9810 + 19.0196i) q^{25} +(23.8003 - 39.4177i) q^{26} +(32.4465 - 17.0732i) q^{28} +(14.3424 + 8.28059i) q^{29} +(-1.18604 + 0.684759i) q^{31} +(-26.0136 - 18.6358i) q^{32} +(-32.3255 + 17.8274i) q^{34} -15.9765 q^{35} +59.1369i q^{37} +(-12.3705 + 6.82229i) q^{38} +(6.25000 + 12.4649i) q^{40} +(19.6706 + 34.0705i) q^{41} +(8.49767 - 14.7184i) q^{43} +(-15.2418 - 28.9661i) q^{44} +(-11.1446 + 18.4575i) q^{46} +(-25.4446 - 14.6904i) q^{47} +(17.5083 + 30.3253i) q^{49} +(-0.861206 + 43.9154i) q^{50} +(3.61054 - 92.0207i) q^{52} +49.1072i q^{53} +14.2628i q^{55} +(40.3343 - 61.2390i) q^{56} +(33.1160 + 0.649423i) q^{58} +(-32.8202 - 56.8463i) q^{59} +(11.8863 + 6.86257i) q^{61} +(-1.41576 + 2.34477i) q^{62} +(-63.5576 - 7.51213i) q^{64} +(-20.0645 + 34.7527i) q^{65} +(-24.8578 - 43.0550i) q^{67} +(-39.3940 + 62.4431i) q^{68} +(-27.9800 + 15.4308i) q^{70} +136.669i q^{71} -120.569 q^{73} +(57.1173 + 103.568i) q^{74} +(-15.0755 + 23.8961i) q^{76} +(64.9559 - 37.5023i) q^{77} +(-82.5422 - 47.6557i) q^{79} +(22.9850 + 15.7935i) q^{80} +(67.3566 + 40.6697i) q^{82} +(39.2191 - 67.9294i) q^{83} +(27.8617 - 16.0860i) q^{85} +(0.666448 - 33.9841i) q^{86} +(-54.6702 - 36.0078i) q^{88} +72.9529 q^{89} +211.029 q^{91} +(-1.69065 + 43.0891i) q^{92} +(-58.7505 - 1.15213i) q^{94} +(10.6623 - 6.15587i) q^{95} +(-25.9069 + 44.8721i) q^{97} +(59.9524 + 36.1991i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.75132	−	0.965848i	0.875662	−	0.482924i
$2$	1.75132	−	0.965848i	0.875662	−	0.482924i
$3$		0			0
$3$		0			0
$4$	2.13428	−	3.38303i	0.533569	−	0.845757i
$5$	−1.50948	+	0.871501i	−0.301897	+	0.174300i	−0.643295	−	0.765619i	$-0.722433\pi$
$5$	−1.50948	+	0.871501i	−0.301897	+	0.174300i	0.341398	+	0.939919i	$0.389100\pi$
$6$		0			0
$7$	7.93804	+	4.58303i	1.13401	+	0.654719i	0.944939	−	0.327246i	$-0.106120\pi$
$7$	7.93804	+	4.58303i	1.13401	+	0.654719i	0.189067	+	0.981964i	$0.439454\pi$
$8$	0.470322	−	7.98616i	0.0587902	−	0.998270i
$9$		0			0
$10$	−1.80186	+	2.98421i	−0.180186	+	0.298421i
$11$	4.09143	−	7.08657i	0.371949	−	0.644234i	−0.617917	−	0.786244i	$-0.712023\pi$
$11$	4.09143	−	7.08657i	0.371949	−	0.644234i	0.989865	+	0.142010i	$0.0453565\pi$
$12$		0			0
$13$	19.9384	−	11.5114i	1.53372	−	0.885495i	0.534537	−	0.845145i	$-0.320486\pi$
$13$	19.9384	−	11.5114i	1.53372	−	0.885495i	0.999186	−	0.0403503i	$-0.0128474\pi$
$14$	18.3286	+	0.359434i	1.30919	+	0.0256738i
$15$		0			0
$16$	−6.88973	−	14.4406i	−0.430608	−	0.902539i
$17$	−18.4578			−1.08575			−0.542876	−	0.839813i	$-0.682664\pi$
$17$	−18.4578			−1.08575			−0.542876	+	0.839813i	$0.682664\pi$
$18$		0			0
$19$	−7.06353			−0.371765			−0.185882	−	0.982572i	$-0.559514\pi$
$19$	−7.06353			−0.371765			−0.185882	+	0.982572i	$0.559514\pi$
$20$	−0.273345	+	6.96665i	−0.0136672	+	0.348332i
$21$		0			0
$22$	0.320879	−	16.3626i	0.0145854	−	0.743754i
$23$	−9.33623	+	5.39028i	−0.405923	+	0.234360i	−0.689037	−	0.724727i	$-0.741966\pi$
$23$	−9.33623	+	5.39028i	−0.405923	+	0.234360i	0.283113	+	0.959086i	$0.408633\pi$
$24$		0			0
$25$	−10.9810	+	19.0196i	−0.439239	+	0.760784i
$26$	23.8003	−	39.4177i	0.915396	−	1.51607i
$27$		0			0
$28$	32.4465	−	17.0732i	1.15880	−	0.609755i
$29$	14.3424	+	8.28059i	0.494566	+	0.285538i	0.726467	−	0.687202i	$-0.241161\pi$
$29$	14.3424	+	8.28059i	0.494566	+	0.285538i	−0.231901	+	0.972739i	$0.574495\pi$
$30$		0			0
$31$	−1.18604	+	0.684759i	−0.0382593	+	0.0220890i	−0.519008	−	0.854770i	$-0.673698\pi$
$31$	−1.18604	+	0.684759i	−0.0382593	+	0.0220890i	0.480748	+	0.876859i	$0.340365\pi$
$32$	−26.0136	−	18.6358i	−0.812925	−	0.582368i
$33$		0			0
$34$	−32.3255	+	17.8274i	−0.950751	+	0.524335i
$35$	−15.9765			−0.456470
$36$		0			0
$37$			59.1369i			1.59829i	0.601135	+	0.799147i	$0.294715\pi$
$37$			59.1369i			1.59829i	−0.601135	+	0.799147i	$0.705285\pi$
$38$	−12.3705	+	6.82229i	−0.325540	+	0.179534i
$39$		0			0
$40$	6.25000	+	12.4649i	0.156250	+	0.311622i
$41$	19.6706	+	34.0705i	0.479771	+	0.830988i	0.999731	−	0.0232025i	$-0.00738625\pi$
$41$	19.6706	+	34.0705i	0.479771	+	0.830988i	−0.519959	+	0.854191i	$0.674053\pi$
$42$		0			0
$43$	8.49767	−	14.7184i	0.197620	−	0.342288i	−0.750136	−	0.661283i	$-0.770012\pi$
$43$	8.49767	−	14.7184i	0.197620	−	0.342288i	0.947756	+	0.318995i	$0.103345\pi$
$44$	−15.2418	−	28.9661i	−0.346405	−	0.658321i
$45$		0			0
$46$	−11.1446	+	18.4575i	−0.242274	+	0.401250i
$47$	−25.4446	−	14.6904i	−0.541375	−	0.312563i	0.204261	−	0.978916i	$-0.434521\pi$
$47$	−25.4446	−	14.6904i	−0.541375	−	0.312563i	−0.745636	+	0.666354i	$0.767854\pi$
$48$		0			0
$49$	17.5083	+	30.3253i	0.357313	+	0.618884i
$50$	−0.861206	+	43.9154i	−0.0172241	+	0.878309i
$51$		0			0
$52$	3.61054	−	92.0207i	0.0694335	−	1.76963i
$53$			49.1072i			0.926551i	0.886214	+	0.463275i	$0.153326\pi$
$53$			49.1072i			0.926551i	−0.886214	+	0.463275i	$0.846674\pi$
$54$		0			0
$55$			14.2628i			0.259323i
$56$	40.3343	−	61.2390i	0.720255	−	1.09355i
$57$		0			0
$58$	33.1160	+	0.649423i	0.570965	+	0.0111969i
$59$	−32.8202	−	56.8463i	−0.556275	−	0.963496i	−0.997803	−	0.0662488i	$-0.978897\pi$
$59$	−32.8202	−	56.8463i	−0.556275	−	0.963496i	0.441528	−	0.897247i	$-0.354436\pi$
$60$		0			0
$61$	11.8863	+	6.86257i	0.194858	+	0.112501i	0.594255	−	0.804277i	$-0.297447\pi$
$61$	11.8863	+	6.86257i	0.194858	+	0.112501i	−0.399397	+	0.916778i	$0.630780\pi$
$62$	−1.41576	+	2.34477i	−0.0228349	+	0.0378188i
$63$		0			0
$64$	−63.5576	−	7.51213i	−0.993087	−	0.117377i
$65$	−20.0645	+	34.7527i	−0.308684	+	0.534656i
$66$		0			0
$67$	−24.8578	−	43.0550i	−0.371012	−	0.642612i	0.618709	−	0.785620i	$-0.287656\pi$
$67$	−24.8578	−	43.0550i	−0.371012	−	0.642612i	−0.989722	+	0.143008i	$0.954323\pi$
$68$	−39.3940	+	62.4431i	−0.579323	+	0.918281i
$69$		0			0
$70$	−27.9800	+	15.4308i	−0.399714	+	0.220440i
$71$			136.669i			1.92492i	0.271421	+	0.962461i	$0.412507\pi$
$71$			136.669i			1.92492i	−0.271421	+	0.962461i	$0.587493\pi$
$72$		0			0
$73$	−120.569			−1.65163			−0.825813	−	0.563945i	$-0.809283\pi$
$73$	−120.569			−1.65163			−0.825813	+	0.563945i	$0.809283\pi$
$74$	57.1173	+	103.568i	0.771855	+	1.39957i
$75$		0			0
$76$	−15.0755	+	23.8961i	−0.198362	+	0.314422i
$77$	64.9559	−	37.5023i	0.843584	−	0.487043i
$78$		0			0
$79$	−82.5422	−	47.6557i	−1.04484	−	0.603237i	−0.123638	−	0.992327i	$-0.539456\pi$
$79$	−82.5422	−	47.6557i	−1.04484	−	0.603237i	−0.921200	+	0.389090i	$0.872789\pi$
$80$	22.9850	+	15.7935i	0.287312	+	0.197418i
$81$		0			0
$82$	67.3566	+	40.6697i	0.821422	+	0.495972i
$83$	39.2191	−	67.9294i	0.472519	−	0.818427i	−0.526986	−	0.849874i	$-0.676678\pi$
$83$	39.2191	−	67.9294i	0.472519	−	0.818427i	0.999505	+	0.0314467i	$0.0100114\pi$
$84$		0			0
$85$	27.8617	−	16.0860i	0.327785	−	0.189247i
$86$	0.666448	−	33.9841i	0.00774939	−	0.395164i
$87$		0			0
$88$	−54.6702	−	36.0078i	−0.621252	−	0.409180i
$89$	72.9529			0.819696			0.409848	−	0.912154i	$-0.365582\pi$
$89$	72.9529			0.819696			0.409848	+	0.912154i	$0.365582\pi$
$90$		0			0
$91$	211.029			2.31900
$92$	−1.69065	+	43.0891i	−0.0183766	+	0.468359i
$93$		0			0
$94$	−58.7505	−	1.15213i	−0.625005	−	0.0122567i
$95$	10.6623	−	6.15587i	0.112234	−	0.0647986i
$96$		0			0
$97$	−25.9069	+	44.8721i	−0.267082	+	0.462599i	−0.968107	−	0.250537i	$-0.919393\pi$
$97$	−25.9069	+	44.8721i	−0.267082	+	0.462599i	0.701025	+	0.713137i	$0.252726\pi$
$98$	59.9524	+	36.1991i	0.611759	+	0.369379i
$99$		0			0
$100$	40.9074	+	77.7420i	0.409074	+	0.777420i
$101$	−73.2484	−	42.2900i	−0.725231	−	0.418712i	0.0914438	−	0.995810i	$-0.470852\pi$
$101$	−73.2484	−	42.2900i	−0.725231	−	0.418712i	−0.816675	+	0.577098i	$0.804185\pi$
$102$		0			0
$103$	9.75070	−	5.62957i	0.0946670	−	0.0546560i	−0.451919	−	0.892059i	$-0.649260\pi$
$103$	9.75070	−	5.62957i	0.0946670	−	0.0546560i	0.546586	+	0.837403i	$0.315927\pi$
$104$	−82.5548	−	164.645i	−0.793796	−	1.58313i
$105$		0			0
$106$	47.4301	+	86.0026i	0.447454	+	0.811346i
$107$	−117.934			−1.10218			−0.551091	−	0.834445i	$-0.685788\pi$
$107$	−117.934			−1.10218			−0.551091	+	0.834445i	$0.685788\pi$
$108$		0			0
$109$			37.1180i			0.340532i	0.985398	+	0.170266i	$0.0544627\pi$
$109$			37.1180i			0.340532i	−0.985398	+	0.170266i	$0.945537\pi$
$110$	13.7756	+	24.9787i	0.125233	+	0.227079i
$111$		0			0
$112$	11.4908	−	146.206i	0.102597	−	1.30541i
$113$	69.7264	+	120.770i	0.617048	+	1.06876i	0.990021	+	0.140916i	$0.0450049\pi$
$113$	69.7264	+	120.770i	0.617048	+	1.06876i	−0.372974	+	0.927842i	$0.621662\pi$
$114$		0			0
$115$	9.39526	−	16.2731i	0.0816979	−	0.141505i
$116$	58.6241	−	30.8477i	0.505380	−	0.265928i
$117$		0			0
$118$	−112.384	−	67.8569i	−0.952404	−	0.575059i
$119$	−146.519	−	84.5925i	−1.23125	−	0.710861i
$120$		0			0
$121$	27.0203	+	46.8006i	0.223309	+	0.386782i
$122$	27.4450	+	0.538211i	0.224959	+	0.00441157i
$123$		0			0
$124$	−0.214773	+	5.47386i	−0.00173204	+	0.0441440i
$125$		−	81.8547i		−	0.654838i
$126$		0			0
$127$		−	158.147i		−	1.24525i	−0.782521	−	0.622624i	$-0.786066\pi$
$127$		−	158.147i		−	1.24525i	0.782521	−	0.622624i	$-0.213934\pi$
$128$	−118.566	+	48.2308i	−0.926293	+	0.376803i
$129$		0			0
$130$	−1.57360	+	80.2424i	−0.0121046	+	0.617249i
$131$	22.8574	+	39.5902i	0.174484	+	0.302215i	0.939983	−	0.341223i	$-0.110841\pi$
$131$	22.8574	+	39.5902i	0.174484	+	0.302215i	−0.765499	+	0.643437i	$0.777508\pi$
$132$		0			0
$133$	−56.0706	−	32.3724i	−0.421583	−	0.243401i
$134$	−85.1187	−	51.3944i	−0.635214	−	0.383541i
$135$		0			0
$136$	−8.68109	+	147.407i	−0.0638315	+	1.08387i
$137$	42.9421	−	74.3779i	0.313446	−	0.542904i	−0.665660	−	0.746255i	$-0.731850\pi$
$137$	42.9421	−	74.3779i	0.313446	−	0.542904i	0.979106	+	0.203351i	$0.0651832\pi$
$138$		0			0
$139$	−54.3910	−	94.2080i	−0.391302	−	0.677755i	0.601319	−	0.799009i	$-0.294642\pi$
$139$	−54.3910	−	94.2080i	−0.391302	−	0.677755i	−0.992622	+	0.121253i	$0.961309\pi$
$140$	−34.0982	+	54.0488i	−0.243558	+	0.386063i
$141$		0			0
$142$	132.002	+	239.353i	0.929591	+	1.68558i
$143$		−	188.393i		−	1.31743i
$144$		0			0
$145$	−28.8662			−0.199077
$146$	−211.155	+	116.451i	−1.44627	+	0.797609i
$147$		0			0
$148$	200.062	+	126.214i	1.35177	+	0.852801i
$149$	234.730	−	135.521i	1.57537	−	0.909540i	0.579877	−	0.814704i	$-0.303101\pi$
$149$	234.730	−	135.521i	1.57537	−	0.909540i	0.995493	−	0.0948359i	$-0.0302326\pi$
$150$		0			0
$151$	39.0877	+	22.5673i	0.258859	+	0.149452i	0.623814	−	0.781573i	$-0.285582\pi$
$151$	39.0877	+	22.5673i	0.258859	+	0.149452i	−0.364955	+	0.931025i	$0.618916\pi$
$152$	−3.32213	+	56.4105i	−0.0218561	+	0.371121i
$153$		0			0
$154$	77.5374	−	128.416i	0.503490	−	0.833872i
$155$	1.19354	−	2.06726i	0.00770023	−	0.0133372i
$156$		0			0
$157$	7.00484	−	4.04425i	0.0446168	−	0.0257595i	−0.477526	−	0.878618i	$-0.658466\pi$
$157$	7.00484	−	4.04425i	0.0446168	−	0.0257595i	0.522143	+	0.852858i	$0.325133\pi$
$158$	−190.586	−	3.73750i	−1.20624	−	0.0236551i
$159$		0			0
$160$	55.5082	+	5.45954i	0.346926	+	0.0341221i
$161$	−98.8152			−0.613759
$162$		0			0
$163$	−83.4116			−0.511727			−0.255864	−	0.966713i	$-0.582360\pi$
$163$	−83.4116			−0.511727			−0.255864	+	0.966713i	$0.582360\pi$
$164$	157.244	+	6.16966i	0.958805	+	0.0376199i
$165$		0			0
$166$	3.07584	−	156.846i	0.0185292	−	0.944857i
$167$	190.748	−	110.128i	1.14220	−	0.659451i	0.195227	−	0.980758i	$-0.437456\pi$
$167$	190.748	−	110.128i	1.14220	−	0.659451i	0.946975	+	0.321307i	$0.104122\pi$
$168$		0			0
$169$	180.526	−	312.681i	1.06820	−	1.85018i
$170$	33.2583	−	55.0819i	0.195637	−	0.324011i
$171$		0			0
$172$	−31.6563	−	60.1609i	−0.184048	−	0.349773i
$173$	−49.1884	−	28.3989i	−0.284326	−	0.164156i	0.351054	−	0.936355i	$-0.385823\pi$
$173$	−49.1884	−	28.3989i	−0.284326	−	0.164156i	−0.635380	+	0.772199i	$0.719157\pi$
$174$		0			0
$175$	−174.335	+	100.652i	−0.996199	+	0.575156i
$176$	−130.523	−	10.2583i	−0.741610	−	0.0582856i
$177$		0			0
$178$	127.764	−	70.4614i	0.717777	−	0.395851i
$179$	288.794			1.61338			0.806689	−	0.590977i	$-0.201258\pi$
$179$	288.794			1.61338			0.806689	+	0.590977i	$0.201258\pi$
$180$		0			0
$181$		−	170.713i		−	0.943165i	−0.881822	−	0.471583i	$-0.843683\pi$
$181$		−	170.713i		−	0.943165i	0.881822	−	0.471583i	$-0.156317\pi$
$182$	369.580	−	203.822i	2.03066	−	1.11990i
$183$		0			0
$184$	38.6566	+	77.0958i	0.210090	+	0.418999i
$185$	−51.5379	−	89.2662i	−0.278583	−	0.482520i
$186$		0			0
$187$	−75.5187	+	130.802i	−0.403843	+	0.699477i
$188$	−104.004	+	54.7263i	−0.553213	+	0.291097i
$189$		0			0
$190$	12.7275	−	21.0791i	0.0669867	−	0.110942i
$191$	145.804	+	84.1800i	0.763372	+	0.440733i	0.830505	−	0.557011i	$-0.188052\pi$
$191$	145.804	+	84.1800i	0.763372	+	0.440733i	−0.0671330	+	0.997744i	$0.521385\pi$
$192$		0			0
$193$	100.494	+	174.060i	0.520692	+	0.901866i	0.999711	+	0.0240607i	$0.00765948\pi$
$193$	100.494	+	174.060i	0.520692	+	0.901866i	−0.479018	+	0.877805i	$0.659007\pi$
$194$	−2.03181	+	103.608i	−0.0104732	+	0.534061i
$195$		0			0
$196$	139.959	+	5.49146i	0.714076	+	0.0280176i
$197$			189.611i			0.962493i	0.876585	+	0.481246i	$0.159816\pi$
$197$			189.611i			0.962493i	−0.876585	+	0.481246i	$0.840184\pi$
$198$		0			0
$199$		−	65.1922i		−	0.327599i	−0.986494	−	0.163799i	$-0.947625\pi$
$199$		−	65.1922i		−	0.327599i	0.986494	−	0.163799i	$-0.0523750\pi$
$200$	146.729	+	96.6412i	0.733645	+	0.483206i
$201$		0			0
$202$	−169.127	−	3.31668i	−0.837264	−	0.0164192i
$203$	75.9004	+	131.463i	0.373894	+	0.647603i
$204$		0			0
$205$	−59.3850	−	34.2859i	−0.289683	−	0.167248i
$206$	11.6393	−	19.2769i	0.0565016	−	0.0935772i
$207$		0			0
$208$	−303.603	−	208.612i	−1.45963	−	1.00294i
$209$	−28.8999	+	50.0562i	−0.138277	+	0.239503i
$210$		0			0
$211$	−63.8197	−	110.539i	−0.302463	−	0.523881i	0.674230	−	0.738521i	$-0.264476\pi$
$211$	−63.8197	−	110.539i	−0.302463	−	0.523881i	−0.976693	+	0.214640i	$0.931142\pi$
$212$	166.131	+	104.808i	0.783636	+	0.494379i
$213$		0			0
$214$	−206.540	+	113.906i	−0.965139	+	0.532270i
$215$			29.6229i			0.137781i
$216$		0			0
$217$	−12.5531			−0.0578483
$218$	35.8503	+	65.0056i	0.164451	+	0.298191i
$219$		0			0
$220$	48.2513	+	30.4406i	0.219324	+	0.138367i
$221$	−368.018	+	212.475i	−1.66524	+	0.961427i
$222$		0			0
$223$	372.713	+	215.186i	1.67136	+	0.964959i	0.966879	+	0.255235i	$0.0821529\pi$
$223$	372.713	+	215.186i	1.67136	+	0.964959i	0.704480	+	0.709724i	$0.251180\pi$
$224$	−121.089	−	267.153i	−0.540574	−	1.19265i
$225$		0			0
$226$	238.759	+	144.162i	1.05645	+	0.637884i
$227$	−2.36198	+	4.09106i	−0.0104052	+	0.0180223i	−0.871181	−	0.490962i	$-0.836645\pi$
$227$	−2.36198	+	4.09106i	−0.0104052	+	0.0180223i	0.860776	+	0.508984i	$0.169979\pi$
$228$		0			0
$229$	−45.5330	+	26.2885i	−0.198834	+	0.114797i	−0.596112	−	0.802902i	$-0.703288\pi$
$229$	−45.5330	+	26.2885i	−0.198834	+	0.114797i	0.397277	+	0.917699i	$0.369955\pi$
$230$	0.736843	−	37.5738i	0.00320367	−	0.163364i
$231$		0			0
$232$	72.8757	−	110.646i	0.314119	−	0.476923i
$233$	−101.858			−0.437157			−0.218579	−	0.975819i	$-0.570142\pi$
$233$	−101.858			−0.437157			−0.218579	+	0.975819i	$0.570142\pi$
$234$		0			0
$235$	51.2110			0.217919
$236$	−262.360	−	10.2940i	−1.11169	−	0.0436186i
$237$		0			0
$238$	−338.305	−	6.63435i	−1.42145	−	0.0278754i
$239$	−178.346	+	102.968i	−0.746216	+	0.430828i	−0.824325	−	0.566117i	$-0.808445\pi$
$239$	−178.346	+	102.968i	−0.746216	+	0.430828i	0.0781092	+	0.996945i	$0.475112\pi$
$240$		0			0
$241$	24.1484	−	41.8263i	0.100201	−	0.173553i	−0.811566	−	0.584260i	$-0.801385\pi$
$241$	24.1484	−	41.8263i	0.100201	−	0.173553i	0.911767	+	0.410707i	$0.134718\pi$
$242$	92.5237	+	55.8655i	0.382329	+	0.230849i
$243$		0			0
$244$	48.5849	−	25.5651i	0.199119	−	0.104775i
$245$	−52.8571	−	30.5171i	−0.215743	−	0.124559i
$246$		0			0
$247$	−140.835	+	81.3113i	−0.570184	+	0.329196i
$248$	4.91078	+	9.79394i	0.0198015	+	0.0394917i
$249$		0			0
$250$	−79.0592	−	143.354i	−0.316237	−	0.573417i
$251$	−316.851			−1.26235			−0.631177	−	0.775639i	$-0.717428\pi$
$251$	−316.851			−1.26235			−0.631177	+	0.775639i	$0.717428\pi$
$252$		0			0
$253$			88.2158i			0.348679i
$254$	−152.746	−	276.966i	−0.601360	−	1.09042i
$255$		0			0
$256$	−161.063	+	198.984i	−0.629153	+	0.777281i
$257$	−141.785	−	245.579i	−0.551692	−	0.955559i	−0.998153	−	0.0607553i	$-0.980649\pi$
$257$	−141.785	−	245.579i	−0.551692	−	0.955559i	0.446461	−	0.894803i	$-0.352684\pi$
$258$		0			0
$259$	−271.026	+	469.431i	−1.04643	+	1.81248i
$260$	74.7461	+	142.050i	0.287485	+	0.546347i
$261$		0			0
$262$	78.2688	+	47.2585i	0.298736	+	0.180376i
$263$	64.9560	+	37.5024i	0.246981	+	0.142595i	0.618381	−	0.785878i	$-0.287789\pi$
$263$	64.9560	+	37.5024i	0.246981	+	0.142595i	−0.371400	+	0.928473i	$0.621122\pi$
$264$		0			0
$265$	−42.7970	−	74.1265i	−0.161498	−	0.279723i
$266$	−129.465	−	2.53887i	−0.486709	−	0.00954463i
$267$		0			0
$268$	−198.710	−	7.79661i	−0.741454	−	0.0290918i
$269$			8.29392i			0.0308324i	0.999881	+	0.0154162i	$0.00490733\pi$
$269$			8.29392i			0.0308324i	−0.999881	+	0.0154162i	$0.995093\pi$
$270$		0			0
$271$			102.530i			0.378340i	0.981944	+	0.189170i	$0.0605797\pi$
$271$			102.530i			0.378340i	−0.981944	+	0.189170i	$0.939420\pi$
$272$	127.169	+	266.542i	0.467533	+	0.979933i
$273$		0			0
$274$	3.36783	−	171.735i	0.0122913	−	0.626772i
$275$	89.8558	+	155.635i	0.326749	+	0.565945i
$276$		0			0
$277$	−93.0941	−	53.7479i	−0.336080	−	0.194036i	0.322457	−	0.946584i	$-0.395491\pi$
$277$	−93.0941	−	53.7479i	−0.336080	−	0.194036i	−0.658537	+	0.752548i	$0.728824\pi$
$278$	−186.247	−	112.455i	−0.669953	−	0.404516i
$279$		0			0
$280$	−7.51407	+	127.591i	−0.0268360	+	0.455681i
$281$	146.557	−	253.843i	0.521554	−	0.903357i	−0.478132	−	0.878288i	$-0.658686\pi$
$281$	146.557	−	253.843i	0.521554	−	0.903357i	0.999686	−	0.0250694i	$-0.00798068\pi$
$282$		0			0
$283$	90.8248	+	157.313i	0.320936	+	0.555877i	0.980681	−	0.195612i	$-0.0626693\pi$
$283$	90.8248	+	157.313i	0.320936	+	0.555877i	−0.659746	+	0.751489i	$0.729336\pi$
$284$	462.356	+	291.690i	1.62802	+	1.02708i
$285$		0			0
$286$	−181.959	−	329.938i	−0.636221	−	1.15363i
$287$			360.604i			1.25646i
$288$		0			0
$289$	51.6892			0.178855
$290$	−50.5540	+	27.8803i	−0.174324	+	0.0961390i
$291$		0			0
$292$	−257.327	+	407.887i	−0.881256	+	1.39687i
$293$	−283.009	+	163.395i	−0.965900	+	0.557663i	−0.897984	−	0.440028i	$-0.854968\pi$
$293$	−283.009	+	163.395i	−0.965900	+	0.557663i	−0.0679163	+	0.997691i	$0.521635\pi$
$294$		0			0
$295$	99.0831	+	57.2057i	0.335875	+	0.193918i
$296$	472.277	+	27.8134i	1.59553	+	0.0939641i
$297$		0			0
$298$	280.195	−	464.056i	0.940253	−	1.55723i
$299$	−124.100	+	214.947i	−0.415049	+	0.718886i
$300$		0			0
$301$	134.910	−	77.8901i	0.448205	−	0.258771i
$302$	90.2519	+	1.76989i	0.298847	+	0.00586056i
$303$		0			0
$304$	48.6658	+	102.002i	0.160085	+	0.335532i
$305$	−23.9229			−0.0784358
$306$		0			0
$307$	−68.1862			−0.222105			−0.111052	−	0.993815i	$-0.535422\pi$
$307$	−68.1862			−0.222105			−0.111052	+	0.993815i	$0.535422\pi$
$308$	11.7625	−	299.788i	0.0381901	−	0.973338i
$309$		0			0
$310$	0.0936056	−	4.77323i	0.000301954	−	0.0153975i
$311$	−43.3779	+	25.0442i	−0.139479	+	0.0805280i	−0.568116	−	0.822949i	$-0.692327\pi$
$311$	−43.3779	+	25.0442i	−0.139479	+	0.0805280i	0.428637	+	0.903477i	$0.358994\pi$
$312$		0			0
$313$	123.756	−	214.351i	0.395385	−	0.684827i	−0.597765	−	0.801671i	$-0.703945\pi$
$313$	123.756	−	214.351i	0.395385	−	0.684827i	0.993150	+	0.116844i	$0.0372778\pi$
$314$	8.36163	−	13.8484i	0.0266294	−	0.0441032i
$315$		0			0
$316$	−337.388	+	177.532i	−1.06768	+	0.561809i
$317$	394.522	+	227.777i	1.24455	+	0.718541i	0.970017	−	0.243037i	$-0.0781436\pi$
$317$	394.522	+	227.777i	1.24455	+	0.718541i	0.274532	+	0.961578i	$0.411477\pi$
$318$		0			0
$319$	117.362	−	67.7590i	0.367906	−	0.212411i
$320$	102.486	−	44.0511i	0.320269	−	0.137660i
$321$		0			0
$322$	−173.058	+	95.4405i	−0.537446	+	0.296399i
$323$	130.377			0.403644
$324$		0			0
$325$			505.627i			1.55578i
$326$	−146.081	+	80.5629i	−0.448100	+	0.247125i
$327$		0			0
$328$	281.344	−	141.069i	0.857757	−	0.430088i
$329$	−134.654	−	233.227i	−0.409281	−	0.708896i
$330$		0			0
$331$	−4.25754	+	7.37428i	−0.0128627	+	0.0222788i	−0.872385	−	0.488819i	$-0.837428\pi$
$331$	−4.25754	+	7.37428i	−0.0128627	+	0.0222788i	0.859522	+	0.511098i	$0.170761\pi$
$332$	−146.103	−	277.659i	−0.440069	−	0.836323i
$333$		0			0
$334$	227.694	−	377.104i	0.681719	−	1.12905i
$335$	75.0450	+	43.3272i	0.224015	+	0.129335i
$336$		0			0
$337$	67.6449	+	117.164i	0.200727	+	0.347669i	0.948763	−	0.315989i	$-0.102336\pi$
$337$	67.6449	+	117.164i	0.200727	+	0.347669i	−0.748036	+	0.663658i	$0.769003\pi$
$338$	14.1582	−	721.967i	0.0418881	−	2.13600i
$339$		0			0
$340$	5.04533	−	128.589i	0.0148392	−	0.378202i
$341$			11.2066i			0.0328639i
$342$		0			0
$343$		−	128.172i		−	0.373679i
$344$	−113.547	−	74.7861i	−0.330078	−	0.217402i
$345$		0			0
$346$	−113.574	−	2.22725i	−0.328248	−	0.00643713i
$347$	−53.8430	−	93.2589i	−0.155167	−	0.268758i	0.777953	−	0.628323i	$-0.216258\pi$
$347$	−53.8430	−	93.2589i	−0.155167	−	0.268758i	−0.933120	+	0.359565i	$0.882925\pi$
$348$		0			0
$349$	−142.049	−	82.0118i	−0.407016	−	0.234991i	0.282491	−	0.959270i	$-0.408839\pi$
$349$	−142.049	−	82.0118i	−0.407016	−	0.234991i	−0.689507	+	0.724279i	$0.742173\pi$
$350$	−208.102	+	344.656i	−0.594577	+	0.984731i
$351$		0			0
$352$	−238.497	+	108.100i	−0.677548	+	0.307103i
$353$	−124.042	+	214.848i	−0.351395	+	0.608633i	−0.986494	−	0.163797i	$-0.947626\pi$
$353$	−124.042	+	214.848i	−0.351395	+	0.608633i	0.635099	+	0.772430i	$0.280959\pi$
$354$		0			0
$355$	−119.108	−	206.300i	−0.335514	−	0.581128i
$356$	155.702	−	246.802i	0.437364	−	0.693263i
$357$		0			0
$358$	505.773	−	278.932i	1.41277	−	0.779138i
$359$		−	496.430i		−	1.38281i	−0.722466	−	0.691407i	$-0.756991\pi$
$359$		−	496.430i		−	1.38281i	0.722466	−	0.691407i	$-0.243009\pi$
$360$		0			0
$361$	−311.107			−0.861791
$362$	−164.883	−	298.974i	−0.455477	−	0.825894i
$363$		0			0
$364$	450.394	−	713.917i	1.23735	−	1.96131i
$365$	181.996	−	105.076i	0.498620	−	0.287879i
$366$		0			0
$367$	336.190	+	194.099i	0.916048	+	0.528881i	0.882372	−	0.470552i	$-0.155945\pi$
$367$	336.190	+	194.099i	0.916048	+	0.528881i	0.0336760	+	0.999433i	$0.489279\pi$
$368$	142.163	+	97.6835i	0.386313	+	0.265444i
$369$		0			0
$370$	−176.477	−	106.556i	−0.476965	−	0.287990i
$371$	−225.060	+	389.815i	−0.606630	+	1.05071i
$372$		0			0
$373$	226.063	−	130.518i	0.606067	−	0.349913i	−0.165357	−	0.986234i	$-0.552878\pi$
$373$	226.063	−	130.518i	0.606067	−	0.349913i	0.771425	+	0.636321i	$0.219544\pi$
$374$	−5.92272	+	302.017i	−0.0158361	+	0.807532i
$375$		0			0
$376$	−129.287	+	196.296i	−0.343850	+	0.522063i
$377$	381.286			1.01137
$378$		0			0
$379$	140.019			0.369444			0.184722	−	0.982791i	$-0.440862\pi$
$379$	140.019			0.369444			0.184722	+	0.982791i	$0.440862\pi$
$380$	1.93078	−	49.2091i	0.00508099	−	0.129498i
$381$		0			0
$382$	336.655	+	6.60200i	0.881297	+	0.0172827i
$383$	205.356	−	118.562i	0.536178	−	0.309562i	−0.207351	−	0.978267i	$-0.566484\pi$
$383$	205.356	−	118.562i	0.536178	−	0.309562i	0.743528	+	0.668704i	$0.233151\pi$
$384$		0			0
$385$	−65.3666	+	113.218i	−0.169783	+	0.294074i
$386$	344.113	+	207.774i	0.891483	+	0.538275i
$387$		0			0
$388$	96.5110	+	183.413i	0.248740	+	0.472715i
$389$	−400.152	−	231.028i	−1.02867	−	0.593902i	−0.112066	−	0.993701i	$-0.535747\pi$
$389$	−400.152	−	231.028i	−1.02867	−	0.593902i	−0.916603	+	0.399798i	$0.869080\pi$
$390$		0			0
$391$	172.326	−	99.4925i	0.440732	−	0.254456i
$392$	250.418	−	125.562i	0.638820	−	0.320311i
$393$		0			0
$394$	183.135	+	332.071i	0.464811	+	0.842819i
$395$	166.128			0.420577
$396$		0			0
$397$		−	237.639i		−	0.598586i	−0.954161	−	0.299293i	$-0.903249\pi$
$397$		−	237.639i		−	0.598586i	0.954161	−	0.299293i	$-0.0967508\pi$
$398$	−62.9657	−	114.173i	−0.158205	−	0.286866i
$399$		0			0
$400$	350.311	+	27.5321i	0.875777	+	0.0688303i
$401$	177.482	+	307.408i	0.442599	+	0.766604i	0.997882	−	0.0650577i	$-0.0207231\pi$
$401$	177.482	+	307.408i	0.442599	+	0.766604i	−0.555282	+	0.831662i	$0.687390\pi$
$402$		0			0
$403$	−15.7651	+	27.3060i	−0.0391194	+	0.0677568i
$404$	−299.400	+	157.543i	−0.741090	+	0.389957i
$405$		0			0
$406$	259.900	+	156.927i	0.640147	+	0.386519i
$407$	419.078	+	241.955i	1.02968	+	0.594483i
$408$		0			0
$409$	−241.822	−	418.847i	−0.591251	−	1.02408i	−0.994064	−	0.108795i	$-0.965301\pi$
$409$	−241.822	−	418.847i	−0.591251	−	1.02408i	0.402813	−	0.915282i	$-0.368032\pi$
$410$	−137.117	−	2.68895i	−0.334433	−	0.00655841i
$411$		0			0
$412$	1.76571	−	45.0020i	0.00428569	−	0.109228i
$413$		−	601.664i		−	1.45681i
$414$		0			0
$415$			136.718i			0.329441i
$416$	−733.194	−	72.1137i	−1.76249	−	0.173350i
$417$		0			0
$418$	−2.26654	+	115.578i	−0.00542234	+	0.276501i
$419$	−235.133	−	407.263i	−0.561177	−	0.971987i	−0.997394	−	0.0721456i	$-0.977015\pi$
$419$	−235.133	−	407.263i	−0.561177	−	0.971987i	0.436217	−	0.899841i	$-0.356318\pi$
$420$		0			0
$421$	188.753	+	108.976i	0.448343	+	0.258851i	0.707130	−	0.707083i	$-0.249989\pi$
$421$	188.753	+	108.976i	0.448343	+	0.258851i	−0.258787	+	0.965934i	$0.583323\pi$
$422$	−218.533	−	131.950i	−0.517850	−	0.312677i
$423$		0			0
$424$	392.178	+	23.0962i	0.924948	+	0.0544721i
$425$	202.684	−	351.059i	0.476904	−	0.826022i
$426$		0			0
$427$	62.9027	+	108.951i	0.147313	+	0.255154i
$428$	−251.703	+	398.972i	−0.588090	+	0.932178i
$429$		0			0
$430$	28.6112	+	51.8793i	0.0665377	+	0.120650i
$431$			53.9654i			0.125210i	0.998038	+	0.0626049i	$0.0199408\pi$
$431$			53.9654i			0.125210i	−0.998038	+	0.0626049i	$0.980059\pi$
$432$		0			0
$433$	−37.1826			−0.0858720			−0.0429360	−	0.999078i	$-0.513671\pi$
$433$	−37.1826			−0.0858720			−0.0429360	+	0.999078i	$0.513671\pi$
$434$	−21.9845	+	12.1244i	−0.0506556	+	0.0279363i
$435$		0			0
$436$	125.571	+	79.2200i	0.288007	+	0.181697i
$437$	65.9467	−	38.0744i	0.150908	−	0.0871267i
$438$		0			0
$439$	−659.014	−	380.482i	−1.50117	−	0.866701i	−0.999999	−	0.00135257i	$-0.999569\pi$
$439$	−659.014	−	380.482i	−1.50117	−	0.866701i	−0.501171	−	0.865348i	$-0.667097\pi$
$440$	113.905	+	6.70808i	0.258874	+	0.0152456i
$441$		0			0
$442$	−439.301	+	727.563i	−0.993893	+	1.64607i
$443$	198.202	−	343.296i	0.447409	−	0.774935i	−0.550808	−	0.834632i	$-0.685680\pi$
$443$	198.202	−	343.296i	0.447409	−	0.774935i	0.998217	+	0.0596974i	$0.0190136\pi$
$444$		0			0
$445$	−110.121	+	63.5785i	−0.247464	+	0.142873i
$446$	860.578	+	16.8764i	1.92955	+	0.0378395i
$447$		0			0
$448$	−470.095	−	350.918i	−1.04932	−	0.783299i
$449$	−442.341			−0.985170			−0.492585	−	0.870264i	$-0.663948\pi$
$449$	−442.341			−0.985170			−0.492585	+	0.870264i	$0.663948\pi$
$450$		0			0
$451$	321.924			0.713801
$452$	557.382	+	21.8696i	1.23315	+	0.0483840i
$453$		0			0
$454$	−0.185243	+	9.44609i	−0.000408024	+	0.0208064i
$455$	−318.545	+	183.912i	−0.700099	+	0.404202i
$456$		0			0
$457$	227.696	−	394.382i	0.498241	−	0.862979i	−0.501757	−	0.865009i	$-0.667313\pi$
$457$	227.696	−	394.382i	0.498241	−	0.862979i	0.999998	+	0.00202958i	$0.000646036\pi$
$458$	−54.3524	+	90.0177i	−0.118673	+	0.196545i
$459$		0			0
$460$	−35.0001	−	66.5156i	−0.0760873	−	0.144599i
$461$	108.614	+	62.7084i	0.235606	+	0.136027i	0.613155	−	0.789962i	$-0.289900\pi$
$461$	108.614	+	62.7084i	0.235606	+	0.136027i	−0.377550	+	0.925989i	$0.623233\pi$
$462$		0			0
$463$	107.647	−	62.1501i	0.232499	−	0.134233i	−0.379225	−	0.925304i	$-0.623809\pi$
$463$	107.647	−	62.1501i	0.232499	−	0.134233i	0.611724	+	0.791071i	$0.290476\pi$
$464$	20.7616	−	264.164i	0.0447447	−	0.569320i
$465$		0			0
$466$	−178.386	+	98.3790i	−0.382802	+	0.211114i
$467$	273.921			0.586554			0.293277	−	0.956027i	$-0.405254\pi$
$467$	273.921			0.586554			0.293277	+	0.956027i	$0.405254\pi$
$468$		0			0
$469$		−	455.697i		−	0.971635i
$470$	89.6870	−	49.4620i	0.190823	−	0.105238i
$471$		0			0
$472$	−469.420	+	235.372i	−0.994533	+	0.498668i
$473$	−69.5353	−	120.439i	−0.147009	−	0.254627i
$474$		0			0
$475$	77.5644	−	134.345i	0.163293	−	0.282833i
$476$	−598.890	+	315.132i	−1.25817	+	0.662043i
$477$		0			0
$478$	−212.890	+	352.585i	−0.445376	+	0.737625i
$479$	−553.334	−	319.468i	−1.15519	−	0.666947i	−0.205041	−	0.978753i	$-0.565733\pi$
$479$	−553.334	−	319.468i	−1.15519	−	0.666947i	−0.950146	+	0.311806i	$0.899066\pi$
$480$		0			0
$481$	680.751	+	1179.10i	1.41528	+	2.45134i
$482$	1.89389	−	96.5752i	0.00392924	−	0.200363i
$483$		0			0
$484$	215.997	+	8.47488i	0.446274	+	0.0175101i
$485$		−	90.3117i		−	0.186210i
$486$		0			0
$487$			418.623i			0.859596i	0.902925	+	0.429798i	$0.141415\pi$
$487$			418.623i			0.859596i	−0.902925	+	0.429798i	$0.858585\pi$
$488$	60.3960	−	91.6984i	0.123762	−	0.187907i
$489$		0			0
$490$	−122.045	−	2.39336i	−0.249071	−	0.00488442i
$491$	100.929	+	174.814i	0.205558	+	0.356038i	0.950311	−	0.311304i	$-0.100766\pi$
$491$	100.929	+	174.814i	0.205558	+	0.356038i	−0.744752	+	0.667341i	$0.767432\pi$
$492$		0			0
$493$	−264.729	−	152.841i	−0.536975	−	0.310023i
$494$	−168.114	+	278.428i	−0.340312	+	0.563620i
$495$		0			0
$496$	18.0598	+	12.4093i	0.0364109	+	0.0250188i
$497$	−626.360	+	1084.89i	−1.26028	+	2.18287i
$498$		0			0
$499$	−150.812	−	261.215i	−0.302229	−	0.523477i	0.674411	−	0.738356i	$-0.264398\pi$
$499$	−150.812	−	261.215i	−0.302229	−	0.523477i	−0.976641	+	0.214879i	$0.931064\pi$
$500$	−276.917	−	174.701i	−0.553834	−	0.349401i
$501$		0			0
$502$	−554.909	+	306.030i	−1.10540	+	0.609621i
$503$		−	566.759i		−	1.12676i	−0.826199	−	0.563378i	$-0.809501\pi$
$503$		−	566.759i		−	1.12676i	0.826199	−	0.563378i	$-0.190499\pi$
$504$		0			0
$505$	147.423			0.291927
$506$	85.2031	+	154.495i	0.168386	+	0.305325i
$507$		0			0
$508$	−535.014	−	337.529i	−1.05318	−	0.664426i
$509$	−477.760	+	275.835i	−0.938625	+	0.541915i	−0.889529	−	0.456879i	$-0.848967\pi$
$509$	−477.760	+	275.835i	−0.938625	+	0.541915i	−0.0490958	+	0.998794i	$0.515634\pi$
$510$		0			0
$511$	−957.079	−	552.570i	−1.87295	−	1.08135i
$512$	−89.8856	+	504.048i	−0.175558	+	0.984469i
$513$		0			0
$514$	−485.503	−	293.145i	−0.944558	−	0.570321i
$515$	−9.81235	+	16.9955i	−0.0190531	+	0.0330010i
$516$		0			0
$517$	−208.210	+	120.210i	−0.402727	+	0.232515i
$518$	−21.2558	+	1083.90i	−0.0410344	+	2.09246i
$519$		0			0
$520$	268.104	+	176.583i	0.515584	+	0.339583i
$521$	845.976			1.62375			0.811877	−	0.583828i	$-0.198446\pi$
$521$	845.976			1.62375			0.811877	+	0.583828i	$0.198446\pi$
$522$		0			0
$523$	−309.009			−0.590839			−0.295419	−	0.955368i	$-0.595459\pi$
$523$	−309.009			−0.590839			−0.295419	+	0.955368i	$0.595459\pi$
$524$	182.718	+	7.16918i	0.348699	+	0.0136816i
$525$		0			0
$526$	149.981	+	2.94120i	0.285134	+	0.00559164i
$527$	21.8916	−	12.6391i	0.0415400	−	0.0239832i
$528$		0			0
$529$	−206.390	+	357.478i	−0.390151	+	0.675761i
$530$	−146.546	−	88.4842i	−0.276502	−	0.166951i
$531$		0			0
$532$	−229.187	+	120.597i	−0.430802	+	0.226685i
$533$	784.402	+	452.874i	1.47167	+	0.849671i
$534$		0			0
$535$	178.019	−	102.779i	0.332745	−	0.192111i
$536$	−355.536	+	178.269i	−0.663313	+	0.332591i
$537$		0			0
$538$	8.01067	+	14.5254i	0.0148897	+	0.0269988i
$539$	286.537			0.531608
$540$		0			0
$541$			451.827i			0.835170i	0.908638	+	0.417585i	$0.137123\pi$
$541$			451.827i			0.835170i	−0.908638	+	0.417585i	$0.862877\pi$
$542$	99.0284	+	179.563i	0.182709	+	0.331298i
$543$		0			0
$544$	480.153	+	343.975i	0.882634	+	0.632307i
$545$	−32.3483	−	56.0290i	−0.0593548	−	0.102805i
$546$		0			0
$547$	247.151	−	428.078i	0.451830	−	0.782593i	−0.546670	−	0.837348i	$-0.684105\pi$
$547$	247.151	−	428.078i	0.451830	−	0.782593i	0.998500	+	0.0547557i	$0.0174380\pi$
$548$	−159.972	−	304.017i	−0.291920	−	0.554776i
$549$		0			0
$550$	307.686	+	185.780i	0.559430	+	0.337782i
$551$	−101.308	−	58.4902i	−0.183862	−	0.106153i
$552$		0			0
$553$	−436.815	−	756.586i	−0.789901	−	1.36815i
$554$	−214.950	−	4.21530i	−0.387997	−	0.00760884i
$555$		0			0
$556$	−434.794	−	17.0596i	−0.782003	−	0.0306828i
$557$			509.910i			0.915457i	0.889092	+	0.457729i	$0.151337\pi$
$557$			509.910i			0.915457i	−0.889092	+	0.457729i	$0.848663\pi$
$558$		0			0
$559$		−	391.282i		−	0.699967i
$560$	110.074	+	230.710i	0.196560	+	0.411982i
$561$		0			0
$562$	11.4940	−	586.114i	0.0204520	−	1.04291i
$563$	−140.784	−	243.844i	−0.250060	−	0.433116i	0.713482	−	0.700673i	$-0.247117\pi$
$563$	−140.784	−	243.844i	−0.250060	−	0.433116i	−0.963542	+	0.267557i	$0.913784\pi$
$564$		0			0
$565$	−210.502	−	121.533i	−0.372570	−	0.215103i
$566$	311.004	+	187.784i	0.549478	+	0.331773i
$567$		0			0
$568$	1091.46	+	64.2786i	1.92159	+	0.113167i
$569$	278.526	−	482.421i	0.489501	−	0.847841i	−0.510426	−	0.859922i	$-0.670512\pi$
$569$	278.526	−	482.421i	0.489501	−	0.847841i	0.999927	+	0.0120809i	$0.00384556\pi$
$570$		0			0
$571$	−268.120	−	464.397i	−0.469561	−	0.813304i	0.529833	−	0.848102i	$-0.322255\pi$
$571$	−268.120	−	464.397i	−0.469561	−	0.813304i	−0.999394	+	0.0347977i	$0.988921\pi$
$572$	−637.339	−	402.083i	−1.11423	−	0.702942i
$573$		0			0
$574$	348.289	+	631.535i	0.606775	+	1.10024i
$575$		−	236.762i		−	0.411760i
$576$		0			0
$577$	443.679			0.768941			0.384471	−	0.923137i	$-0.374384\pi$
$577$	443.679			0.768941			0.384471	+	0.923137i	$0.374384\pi$
$578$	90.5245	−	49.9239i	0.156617	−	0.0863735i
$579$		0			0
$580$	−61.6084	+	97.6550i	−0.106221	+	0.168371i
$581$	622.645	−	359.485i	1.07168	−	0.618734i
$582$		0			0
$583$	348.002	+	200.919i	0.596915	+	0.344629i
$584$	−56.7060	+	962.881i	−0.0970994	+	1.64877i
$585$		0			0
$586$	−337.825	+	559.501i	−0.576494	+	0.954781i
$587$	391.488	−	678.077i	0.666930	−	1.15516i	−0.311828	−	0.950139i	$-0.600941\pi$
$587$	391.488	−	678.077i	0.666930	−	1.15516i	0.978758	−	0.205018i	$-0.0657253\pi$
$588$		0			0
$589$	8.37760	−	4.83681i	0.0142234	−	0.00821191i
$590$	228.779	+	4.48648i	0.387761	+	0.00760420i
$591$		0			0
$592$	853.974	−	407.437i	1.44252	−	0.688239i
$593$	−335.436			−0.565660			−0.282830	−	0.959170i	$-0.591273\pi$
$593$	−335.436			−0.565660			−0.282830	+	0.959170i	$0.591273\pi$
$594$		0			0
$595$	294.890			0.495613
$596$	42.5061	−	1083.34i	0.0713189	−	1.81768i
$597$		0			0
$598$	−9.73278	+	496.303i	−0.0162756	+	0.829939i
$599$	−707.383	+	408.408i	−1.18094	+	0.681816i	−0.956232	−	0.292611i	$-0.905476\pi$
$599$	−707.383	+	408.408i	−1.18094	+	0.681816i	−0.224708	+	0.974426i	$0.572143\pi$
$600$		0			0
$601$	−386.367	+	669.207i	−0.642873	+	1.11349i	0.341916	+	0.939731i	$0.388924\pi$
$601$	−386.367	+	669.207i	−0.642873	+	1.11349i	−0.984788	+	0.173758i	$0.944409\pi$
$602$	161.041	−	266.713i	0.267509	−	0.443045i
$603$		0			0
$604$	159.770	−	84.0699i	0.264520	−	0.139189i
$605$	−81.5735	−	47.0965i	−0.134832	−	0.0778455i
$606$		0			0
$607$	−714.145	+	412.312i	−1.17652	+	0.679262i	−0.955206	−	0.295942i	$-0.904367\pi$
$607$	−714.145	+	412.312i	−1.17652	+	0.679262i	−0.221310	+	0.975204i	$0.571033\pi$
$608$	183.748	+	131.634i	0.302217	+	0.216504i
$609$		0			0
$610$	−41.8968	+	23.1059i	−0.0686833	+	0.0378785i
$611$	−676.433			−1.10709
$612$		0			0
$613$		−	105.013i		−	0.171310i	−0.996325	−	0.0856551i	$-0.972702\pi$
$613$		−	105.013i		−	0.171310i	0.996325	−	0.0856551i	$-0.0272983\pi$
$614$	−119.416	+	65.8575i	−0.194489	+	0.107260i
$615$		0			0
$616$	−268.950	−	536.387i	−0.436606	−	0.870758i
$617$	400.803	+	694.210i	0.649599	+	1.12514i	0.983219	+	0.182431i	$0.0583965\pi$
$617$	400.803	+	694.210i	0.649599	+	1.12514i	−0.333620	+	0.942708i	$0.608270\pi$
$618$		0			0
$619$	243.980	−	422.586i	0.394152	−	0.682692i	−0.598840	−	0.800869i	$-0.704372\pi$
$619$	243.980	−	422.586i	0.394152	−	0.682692i	0.992993	+	0.118177i	$0.0377049\pi$
$620$	−4.44628	−	8.44988i	−0.00717141	−	0.0136288i
$621$		0			0
$622$	−51.7798	+	85.7570i	−0.0832473	+	0.137873i
$623$	579.103	+	334.346i	0.929540	+	0.536670i
$624$		0			0
$625$	−203.188	−	351.932i	−0.325101	−	0.563091i
$626$	9.70579	−	494.927i	0.0155045	−	0.790618i
$627$		0			0
$628$	1.26847	−	32.3291i	0.00201986	−	0.0514795i
$629$		−	1091.54i		−	1.73535i
$630$		0			0
$631$		−	213.869i		−	0.338937i	−0.985536	−	0.169469i	$-0.945795\pi$
$631$		−	213.869i		−	0.338937i	0.985536	−	0.169469i	$-0.0542051\pi$
$632$	−419.408	+	636.782i	−0.663620	+	1.00757i
$633$		0			0
$634$	910.935	+	17.8639i	1.43681	+	0.0281766i
$635$	137.825	+	238.720i	0.217047	+	0.375937i
$636$		0			0
$637$	698.176	+	403.092i	1.09604	+	0.632798i
$638$	140.094	−	232.022i	0.219583	−	0.363670i
$639$		0			0
$640$	136.940	−	176.134i	0.213968	−	0.275209i
$641$	−105.403	+	182.563i	−0.164435	+	0.284810i	−0.936455	−	0.350789i	$-0.885914\pi$
$641$	−105.403	+	182.563i	−0.164435	+	0.284810i	0.772019	+	0.635599i	$0.219247\pi$
$642$		0			0
$643$	588.940	+	1020.07i	0.915926	+	1.58643i	0.805540	+	0.592541i	$0.201875\pi$
$643$	588.940	+	1020.07i	0.915926	+	1.58643i	0.110386	+	0.993889i	$0.464791\pi$
$644$	−210.899	+	334.294i	−0.327483	+	0.519091i
$645$		0			0
$646$	228.332	−	125.924i	0.353456	−	0.194929i
$647$			798.714i			1.23449i	0.786772	+	0.617244i	$0.211751\pi$
$647$			798.714i			1.23449i	−0.786772	+	0.617244i	$0.788249\pi$
$648$		0			0
$649$	−537.127			−0.827622
$650$	488.359	+	885.517i	0.751321	+	1.36233i
$651$		0			0
$652$	−178.023	+	282.184i	−0.273042	+	0.432797i
$653$	336.680	−	194.382i	0.515589	−	0.297676i	−0.219539	−	0.975604i	$-0.570455\pi$
$653$	336.680	−	194.382i	0.515589	−	0.297676i	0.735128	+	0.677928i	$0.237122\pi$
$654$		0			0
$655$	−69.0057	−	39.8405i	−0.105352	−	0.0608251i
$656$	356.474	−	518.793i	0.543406	−	0.790843i
$657$		0			0
$658$	−461.084	−	278.401i	−0.700735	−	0.423102i
$659$	121.124	−	209.793i	0.183800	−	0.318350i	−0.759372	−	0.650657i	$-0.774494\pi$
$659$	121.124	−	209.793i	0.183800	−	0.318350i	0.943171	+	0.332307i	$0.107827\pi$
$660$		0			0
$661$	349.926	−	202.030i	0.529389	−	0.305643i	−0.211379	−	0.977404i	$-0.567795\pi$
$661$	349.926	−	202.030i	0.529389	−	0.305643i	0.740768	+	0.671761i	$0.234462\pi$
$662$	−0.333907	+	17.0269i	−0.000504391	+	0.0257204i
$663$		0			0
$664$	−524.050	−	345.159i	−0.789232	−	0.519817i
$665$	112.850			0.169699
$666$		0			0
$667$	−178.539			−0.267674
$668$	34.5415	−	880.349i	0.0517089	−	1.31789i
$669$		0			0
$670$	173.276	+	3.39803i	0.258620	+	0.00507169i
$671$	97.2641	−	56.1555i	0.144954	−	0.0836892i
$672$		0			0
$673$	−465.340	+	805.993i	−0.691441	+	1.19761i	0.279924	+	0.960022i	$0.409691\pi$
$673$	−465.340	+	805.993i	−0.691441	+	1.19761i	−0.971366	+	0.237589i	$0.923643\pi$
$674$	231.631	+	139.858i	0.343667	+	0.207505i
$675$		0			0
$676$	−672.515	−	1278.07i	−0.994844	−	1.89064i
$677$	−24.2768	−	14.0162i	−0.0358593	−	0.0207034i	0.481963	−	0.876191i	$-0.339924\pi$
$677$	−24.2768	−	14.0162i	−0.0358593	−	0.0207034i	−0.517822	+	0.855488i	$0.673257\pi$
$678$		0			0
$679$	−411.301	+	237.465i	−0.605745	+	0.349727i
$680$	−115.361	−	230.074i	−0.169649	−	0.338344i
$681$		0			0
$682$	10.8239	+	19.6264i	0.0158708	+	0.0287777i
$683$	−715.530			−1.04763			−0.523814	−	0.851833i	$-0.675491\pi$
$683$	−715.530			−1.04763			−0.523814	+	0.851833i	$0.675491\pi$
$684$		0			0
$685$			149.696i			0.218535i
$686$	−123.795	−	224.471i	−0.180459	−	0.327217i
$687$		0			0
$688$	−271.089	−	21.3058i	−0.394025	−	0.0309678i
$689$	565.294	+	979.119i	0.820456	+	1.42107i
$690$		0			0
$691$	639.653	−	1107.91i	0.925692	−	1.60335i	0.135249	−	0.990812i	$-0.456817\pi$
$691$	639.653	−	1107.91i	0.925692	−	1.60335i	0.790444	−	0.612535i	$-0.209850\pi$
$692$	−201.056	+	105.794i	−0.290543	+	0.152882i
$693$		0			0
$694$	−184.371	−	111.322i	−0.265664	−	0.160407i
$695$	164.205	+	94.8036i	0.236266	+	0.136408i
$696$		0			0
$697$	−363.076	−	628.866i	−0.520912	−	0.902247i
$698$	−327.984	−	6.43195i	−0.469891	−	0.00921483i
$699$		0			0
$700$	−31.5694	+	804.599i	−0.0450991	+	1.14943i
$701$			228.638i			0.326160i	0.986613	+	0.163080i	$0.0521429\pi$
$701$			228.638i			0.326160i	−0.986613	+	0.163080i	$0.947857\pi$
$702$		0			0
$703$		−	417.715i		−	0.594189i
$704$	−313.277	+	419.670i	−0.444996	+	0.596122i
$705$		0			0
$706$	−9.72828	+	496.074i	−0.0137794	+	0.702654i
$707$	−387.632	−	671.399i	−0.548278	−	0.949645i
$708$		0			0
$709$	177.925	+	102.725i	0.250952	+	0.144887i	0.620200	−	0.784444i	$-0.287051\pi$
$709$	177.925	+	102.725i	0.250952	+	0.144887i	−0.369248	+	0.929331i	$0.620385\pi$
$710$	−407.851	−	246.259i	−0.574438	−	0.346844i
$711$		0			0
$712$	34.3113	−	582.614i	0.0481901	−	0.818278i
$713$	7.38208	−	12.7861i	0.0103535	−	0.0179329i
$714$		0			0
$715$	164.185	+	284.376i	0.229629	+	0.397729i
$716$	616.367	−	976.999i	0.860848	−	1.36452i
$717$		0			0
$718$	−479.476	−	869.410i	−0.667794	−	1.21088i
$719$		−	342.212i		−	0.475955i	−0.971271	−	0.237978i	$-0.923515\pi$
$719$		−	342.212i		−	0.475955i	0.971271	−	0.237978i	$-0.0764845\pi$
$720$		0			0
$721$	103.202			0.143137
$722$	−544.849	+	300.482i	−0.754638	+	0.416180i
$723$		0			0
$724$	−577.526	−	364.348i	−0.797688	−	0.503244i
$725$	−314.987	+	181.858i	−0.434465	+	0.250838i
$726$		0			0
$727$	867.595	+	500.906i	1.19339	+	0.689005i	0.959074	−	0.283156i	$-0.0913813\pi$
$727$	867.595	+	500.906i	1.19339	+	0.689005i	0.234317	+	0.972160i	$0.424715\pi$
$728$	99.2515	−	1685.31i	0.136335	−	2.31499i
$729$		0			0
$730$	217.248	−	359.802i	0.297600	−	0.492880i
$731$	−156.848	+	271.669i	−0.214566	+	0.371640i
$732$		0			0
$733$	−435.819	+	251.620i	−0.594568	+	0.343274i	−0.766902	−	0.641765i	$-0.778203\pi$
$733$	−435.819	+	251.620i	−0.594568	+	0.343274i	0.172334	+	0.985039i	$0.444869\pi$
$734$	776.248	+	15.2226i	1.05756	+	0.0207393i
$735$		0			0
$736$	343.321	+	33.7675i	0.466469	+	0.0458798i
$737$	−406.817			−0.551990
$738$		0			0
$739$	−169.283			−0.229070			−0.114535	−	0.993419i	$-0.536538\pi$
$739$	−169.283			−0.229070			−0.114535	+	0.993419i	$0.536538\pi$
$740$	−411.986	−	16.1648i	−0.556738	−	0.0218443i
$741$		0			0
$742$	−17.6508	+	900.066i	−0.0237881	+	1.21303i
$743$	379.353	−	219.019i	0.510569	−	0.294777i	−0.222499	−	0.974933i	$-0.571421\pi$
$743$	379.353	−	219.019i	0.510569	−	0.294777i	0.733067	+	0.680156i	$0.238088\pi$
$744$		0			0
$745$	−236.214	+	409.135i	−0.317066	+	0.549174i
$746$	269.850	−	446.921i	0.361729	−	0.599090i
$747$		0			0
$748$	281.330	+	534.650i	0.376109	+	0.714773i
$749$	−936.161	−	540.493i	−1.24988	−	0.721619i
$750$		0			0
$751$	989.948	−	571.547i	1.31817	−	0.761048i	0.334739	−	0.942311i	$-0.391352\pi$
$751$	989.948	−	571.547i	1.31817	−	0.761048i	0.983435	+	0.181263i	$0.0580186\pi$
$752$	−36.8327	+	468.649i	−0.0489797	+	0.623204i
$753$		0			0
$754$	667.756	−	368.264i	0.885618	−	0.488414i
$755$	−78.6697			−0.104198
$756$		0			0
$757$			455.422i			0.601615i	0.953685	+	0.300807i	$0.0972561\pi$
$757$			455.422i			0.601615i	−0.953685	+	0.300807i	$0.902744\pi$
$758$	245.219	−	135.237i	0.323508	−	0.178413i
$759$		0			0
$760$	−44.1471	−	88.0459i	−0.0580882	−	0.115850i
$761$	−615.831	−	1066.65i	−0.809240	−	1.40164i	−0.913391	−	0.407083i	$-0.866546\pi$
$761$	−615.831	−	1066.65i	−0.809240	−	1.40164i	0.104152	−	0.994561i	$-0.466787\pi$
$762$		0			0
$763$	−170.113	+	294.644i	−0.222953	+	0.386165i
$764$	595.969	−	313.596i	0.780065	−	0.410465i
$765$		0			0
$766$	245.132	−	405.984i	0.320016	−	0.530005i
$767$	−1308.76	−	755.616i	−1.70634	−	0.985157i
$768$		0			0
$769$	424.464	+	735.194i	0.551969	+	0.956039i	0.998132	+	0.0610873i	$0.0194568\pi$
$769$	424.464	+	735.194i	0.551969	+	0.956039i	−0.446163	+	0.894952i	$0.647210\pi$
$770$	−5.12652	+	261.416i	−0.00665781	+	0.339502i
$771$		0			0
$772$	803.331	+	31.5196i	1.04058	+	0.0408286i
$773$			1340.04i			1.73356i	0.498692	+	0.866779i	$0.333814\pi$
$773$			1340.04i			1.73356i	−0.498692	+	0.866779i	$0.666186\pi$
$774$		0			0
$775$		−	30.0773i		−	0.0388094i
$776$	346.172	+	228.001i	0.446097	+	0.293816i
$777$		0			0
$778$	−923.934	−	18.1189i	−1.18758	−	0.0232890i
$779$	−138.944	−	240.658i	−0.178362	−	0.308932i
$780$		0			0
$781$	968.518	+	559.174i	1.24010	+	0.715972i
$782$	205.704	−	340.684i	0.263049	−	0.435658i
$783$		0			0
$784$	317.289	−	461.765i	0.404705	−	0.588986i
$785$	−7.04913	+	12.2095i	−0.00897978	+	0.0155534i
$786$		0			0
$787$	456.332	+	790.391i	0.579838	+	1.00431i	0.995497	+	0.0947881i	$0.0302174\pi$
$787$	456.332	+	790.391i	0.579838	+	1.00431i	−0.415660	+	0.909520i	$0.636449\pi$
$788$	641.459	+	404.682i	0.814034	+	0.513556i
$789$		0			0
$790$	290.944	−	160.454i	0.368284	−	0.203107i
$791$			1278.23i			1.61597i
$792$		0			0
$793$	315.992			0.398477
$794$	−229.523	−	416.183i	−0.289072	−	0.524159i
$795$		0			0
$796$	−220.547	−	139.138i	−0.277069	−	0.174797i
$797$	678.002	−	391.445i	0.850693	−	0.491148i	−0.0101916	−	0.999948i	$-0.503244\pi$
$797$	678.002	−	391.445i	0.850693	−	0.491148i	0.860885	+	0.508800i	$0.169911\pi$
$798$		0			0
$799$	469.651	+	271.153i	0.587798	+	0.339365i
$800$	640.100	−	290.129i	0.800125	−	0.362662i
$801$		0			0
$802$	607.739	+	366.951i	0.757779	+	0.457545i
$803$	−493.299	+	854.418i	−0.614320	+	1.06403i
$804$		0			0
$805$	149.160	−	86.1175i	0.185292	−	0.106978i
$806$	−1.23641	+	63.0484i	−0.00153401	+	0.0782238i
$807$		0			0
$808$	−372.185	+	565.083i	−0.460625	+	0.699361i
$809$	436.104			0.539065			0.269533	−	0.962991i	$-0.413131\pi$
$809$	436.104			0.539065			0.269533	+	0.962991i	$0.413131\pi$
$810$		0			0
$811$	−1379.18			−1.70060			−0.850299	−	0.526300i	$-0.823579\pi$
$811$	−1379.18			−1.70060			−0.850299	+	0.526300i	$0.823579\pi$
$812$	606.736	+	23.8060i	0.747212	+	0.0293178i
$813$		0			0
$814$	967.633	+	18.9758i	1.18874	+	0.0233118i
$815$	125.908	−	72.6932i	0.154489	−	0.0891942i
$816$		0			0
$817$	−60.0235	+	103.964i	−0.0734682	+	0.127251i
$818$	−828.051	−	499.975i	−1.01229	−	0.611216i
$819$		0			0
$820$	−242.734	+	127.725i	−0.296017	+	0.155763i
$821$	−60.6308	−	35.0052i	−0.0738499	−	0.0426373i	0.462620	−	0.886556i	$-0.346909\pi$
$821$	−60.6308	−	35.0052i	−0.0738499	−	0.0426373i	−0.536470	+	0.843919i	$0.680243\pi$
$822$		0			0
$823$	780.819	−	450.806i	0.948748	−	0.547760i	0.0560561	−	0.998428i	$-0.482147\pi$
$823$	780.819	−	450.806i	0.948748	−	0.547760i	0.892692	+	0.450668i	$0.148814\pi$
$824$	−40.3727	−	80.5184i	−0.0489960	−	0.0977165i
$825$		0			0
$826$	−581.116	−	1053.71i	−0.703530	−	1.27568i
$827$	616.338			0.745270			0.372635	−	0.927978i	$-0.378454\pi$
$827$	616.338			0.745270			0.372635	+	0.927978i	$0.378454\pi$
$828$		0			0
$829$		−	1040.27i		−	1.25485i	−0.778676	−	0.627426i	$-0.784108\pi$
$829$		−	1040.27i		−	1.25485i	0.778676	−	0.627426i	$-0.215892\pi$
$830$	132.049	+	239.437i	0.159095	+	0.288479i
$831$		0			0
$832$	−1353.71	+	581.860i	−1.62706	+	0.699350i
$833$	−323.165	−	559.738i	−0.387953	−	0.671954i
$834$		0			0
$835$	−191.954	+	332.474i	−0.229885	+	0.398172i
$836$	107.661	+	204.603i	0.128781	+	0.244740i
$837$		0			0
$838$	−805.148	−	486.146i	−0.960797	−	0.580127i
$839$	−308.850	−	178.314i	−0.368116	−	0.212532i	0.304519	−	0.952506i	$-0.401504\pi$
$839$	−308.850	−	178.314i	−0.368116	−	0.212532i	−0.672635	+	0.739974i	$0.734838\pi$
$840$		0			0
$841$	−283.364	−	490.800i	−0.336937	−	0.583591i
$842$	435.822	+	8.54670i	0.517603	+	0.0101505i
$843$		0			0
$844$	−510.165	−	20.0169i	−0.604461	−	0.0237168i
$845$			629.316i			0.744752i
$846$		0			0
$847$			495.340i			0.584817i
$848$	709.138	−	338.335i	0.836248	−	0.398980i
$849$		0			0
$850$	15.8959	−	810.581i	0.0187011	−	0.953625i
$851$	−318.764	−	552.116i	−0.374576	−	0.648785i
$852$		0			0
$853$	1275.01	+	736.130i	1.49474	+	0.862990i	0.999982	−	0.00604005i	$-0.00192262\pi$
$853$	1275.01	+	736.130i	1.49474	+	0.862990i	0.494760	+	0.869030i	$0.335256\pi$
$854$	215.393	+	130.054i	0.252216	+	0.152288i
$855$		0			0
$856$	−55.4667	+	941.836i	−0.0647975	+	1.10028i
$857$	167.329	−	289.823i	0.195250	−	0.338183i	−0.751732	−	0.659468i	$-0.770781\pi$
$857$	167.329	−	289.823i	0.195250	−	0.338183i	0.946982	+	0.321285i	$0.104115\pi$
$858$		0			0
$859$	−373.586	−	647.070i	−0.434908	−	0.753283i	0.562380	−	0.826879i	$-0.309886\pi$
$859$	−373.586	−	647.070i	−0.434908	−	0.753283i	−0.997288	+	0.0735962i	$0.976552\pi$
$860$	100.215	+	63.2234i	0.116529	+	0.0735156i
$861$		0			0
$862$	52.1224	+	94.5110i	0.0604668	+	0.109642i
$863$			849.293i			0.984117i	0.870562	+	0.492059i	$0.163755\pi$
$863$			849.293i			0.984117i	−0.870562	+	0.492059i	$0.836245\pi$
$864$		0			0
$865$	98.9987			0.114449
$866$	−65.1188	+	35.9127i	−0.0751949	+	0.0414697i
$867$		0			0
$868$	−26.7917	+	42.4674i	−0.0308661	+	0.0489256i
$869$	−675.432	+	389.961i	−0.777251	+	0.448746i
$870$		0			0
$871$	−991.250	−	572.299i	−1.13806	−	0.657059i
$872$	296.430	+	17.4574i	0.339943	+	0.0200199i
$873$		0			0
$874$	78.7201	−	130.375i	0.0900687	−	0.149171i
$875$	375.143	−	649.766i	0.428735	−	0.742590i
$876$		0			0
$877$	−643.077	+	371.280i	−0.733269	+	0.423353i	−0.819617	−	0.572912i	$-0.805814\pi$
$877$	−643.077	+	371.280i	−0.733269	+	0.423353i	0.0863482	+	0.996265i	$0.472480\pi$
$878$	−1521.63	−	29.8401i	−1.73307	−	0.0339864i
$879$		0			0
$880$	205.963	−	98.2665i	0.234049	−	0.111667i
$881$	−202.649			−0.230022			−0.115011	−	0.993364i	$-0.536690\pi$
$881$	−202.649			−0.230022			−0.115011	+	0.993364i	$0.536690\pi$
$882$		0			0
$883$	646.330			0.731970			0.365985	−	0.930621i	$-0.380732\pi$
$883$	646.330			0.731970			0.365985	+	0.930621i	$0.380732\pi$
$884$	−66.6425	+	1698.50i	−0.0753875	+	1.92138i
$885$		0			0
$886$	15.5444	−	792.656i	0.0175445	−	0.894646i
$887$	307.226	−	177.377i	0.346366	−	0.199974i	−0.316718	−	0.948520i	$-0.602581\pi$
$887$	307.226	−	177.377i	0.346366	−	0.199974i	0.663083	+	0.748545i	$0.269247\pi$
$888$		0			0
$889$	724.791	−	1255.37i	0.815288	−	1.41212i
$890$	−131.451	+	217.707i	−0.147698	+	0.244615i
$891$		0			0
$892$	1523.45	−	801.632i	1.70791	−	0.898690i
$893$	179.729	+	103.766i	0.201264	+	0.116200i
$894$		0			0
$895$	−435.931	+	251.685i	−0.487073	+	0.281212i
$896$	−1162.22	−	160.532i	−1.29712	−	0.179165i
$897$		0			0
$898$	−774.683	+	427.234i	−0.862676	+	0.475762i
$899$	−22.6808			−0.0252290
$900$		0			0
$901$		−	906.409i		−	1.00600i
$902$	563.794	−	310.930i	0.625049	−	0.344712i
$903$		0			0
$904$	997.280	−	500.046i	1.10319	−	0.553148i
$905$	148.776	+	257.688i	0.164394	+	0.284738i
$906$		0			0
$907$	−592.814	+	1026.78i	−0.653598	+	1.13207i	0.328645	+	0.944454i	$0.393408\pi$
$907$	−592.814	+	1026.78i	−0.653598	+	1.13207i	−0.982243	+	0.187612i	$0.939925\pi$
$908$	8.79906	+	16.7221i	0.00969060	+	0.0184164i
$909$		0			0
$910$	−380.245	+	629.756i	−0.417851	+	0.692039i
$911$	1028.04	+	593.538i	1.12847	+	0.651524i	0.943550	−	0.331229i	$-0.107463\pi$
$911$	1028.04	+	593.538i	1.12847	+	0.651524i	0.184922	+	0.982753i	$0.440797\pi$
$912$		0			0
$913$	−320.925	−	555.858i	−0.351506	−	0.608825i
$914$	17.8576	−	910.610i	0.0195378	−	0.996291i
$915$		0			0
$916$	−8.24535	+	210.146i	−0.00900147	+	0.229418i
$917$			419.024i			0.456951i
$918$		0			0
$919$			1666.98i			1.81391i	0.421229	+	0.906954i	$0.361599\pi$
$919$			1666.98i			1.81391i	−0.421229	+	0.906954i	$0.638401\pi$
$920$	−125.541	−	82.6857i	−0.136457	−	0.0898757i
$921$		0			0
$922$	250.785	+	4.91804i	0.272002	+	0.00533410i
$923$	1573.26	+	2724.97i	1.70451	+	2.95230i
$924$		0			0
$925$	−1124.76	−	649.381i	−1.21596	−	0.702033i
$926$	128.497	−	212.816i	0.138766	−	0.229823i
$927$		0			0
$928$	−218.782	−	482.690i	−0.235757	−	0.520140i
$929$	91.1726	−	157.916i	0.0981406	−	0.169985i	−0.812774	−	0.582579i	$-0.802044\pi$
$929$	91.1726	−	157.916i	0.0981406	−	0.169985i	0.910915	+	0.412594i	$0.135377\pi$
$930$		0			0
$931$	−123.671	−	214.204i	−0.132836	−	0.230079i
$932$	−217.392	+	344.587i	−0.233254	+	0.369729i
$933$		0			0
$934$	479.724	−	264.566i	0.513624	−	0.283261i
$935$		−	263.259i		−	0.281560i
$936$		0			0
$937$	1397.34			1.49129			0.745646	−	0.666342i	$-0.232141\pi$
$937$	1397.34			1.49129			0.745646	+	0.666342i	$0.232141\pi$
$938$	−440.134	−	798.073i	−0.469226	−	0.850824i
$939$		0			0
$940$	109.298	−	173.248i	0.116275	−	0.184306i
$941$	869.488	−	501.999i	0.924005	−	0.533474i	0.0390942	−	0.999236i	$-0.487553\pi$
$941$	869.488	−	501.999i	0.924005	−	0.533474i	0.884910	+	0.465761i	$0.154219\pi$
$942$		0			0
$943$	−367.299	−	212.060i	−0.389501	−	0.224878i
$944$	−594.773	+	865.600i	−0.630056	+	0.916949i
$945$		0			0
$946$	−238.104	−	143.767i	−0.251696	−	0.151973i
$947$	−424.461	+	735.187i	−0.448216	+	0.776333i	−0.998270	−	0.0587961i	$-0.981274\pi$
$947$	−424.461	+	735.187i	−0.448216	+	0.776333i	0.550054	+	0.835129i	$0.314607\pi$
$948$		0			0
$949$	−2403.95	+	1387.92i	−2.53314	+	1.46251i
$950$	6.08315	−	310.198i	0.00640332	−	0.326524i
$951$		0			0
$952$	−744.480	+	1130.34i	−0.782017	+	1.18733i
$953$	−1069.97			−1.12274			−0.561371	−	0.827564i	$-0.689726\pi$
$953$	−1069.97			−1.12274			−0.561371	+	0.827564i	$0.689726\pi$
$954$		0			0
$955$	−293.452			−0.307279
$956$	−32.2957	+	823.110i	−0.0337821	+	0.860993i
$957$		0			0
$958$	−1277.63	−	25.0549i	−1.33364	−	0.0261534i
$959$	681.752	−	393.610i	0.710899	−	0.410438i
$960$		0			0
$961$	−479.562	+	830.626i	−0.499024	+	0.864335i
$962$	2331.04	+	1407.48i	2.42312	+	1.46307i
$963$		0			0
$964$	−89.9601	−	170.964i	−0.0933196	−	0.177348i
$965$	−303.387	−	175.161i	−0.314391	−	0.181514i
$966$		0			0
$967$	141.089	−	81.4579i	0.145904	−	0.0842377i	−0.425271	−	0.905066i	$-0.639821\pi$
$967$	141.089	−	81.4579i	0.145904	−	0.0842377i	0.571175	+	0.820828i	$0.306488\pi$
$968$	386.466	−	193.778i	0.399241	−	0.200183i
$969$		0			0
$970$	−87.2273	−	158.165i	−0.0899251	−	0.163057i
$971$	−777.286			−0.800500			−0.400250	−	0.916406i	$-0.631077\pi$
$971$	−777.286			−0.800500			−0.400250	+	0.916406i	$0.631077\pi$
$972$		0			0
$973$		−	997.103i		−	1.02477i
$974$	404.326	+	733.145i	0.415120	+	0.752716i
$975$		0			0
$976$	17.2062	−	218.927i	0.0176293	−	0.224310i
$977$	−10.4287	−	18.0630i	−0.0106742	−	0.0184882i	0.860639	−	0.509216i	$-0.170064\pi$
$977$	−10.4287	−	18.0630i	−0.0106742	−	0.0184882i	−0.871313	+	0.490727i	$0.836731\pi$
$978$		0			0
$979$	298.482	−	516.986i	0.304885	−	0.528076i
$980$	−216.052	+	113.685i	−0.220461	+	0.116005i
$981$		0			0
$982$	345.604	+	208.675i	0.351939	+	0.212500i
$983$	−570.070	−	329.130i	−0.579929	−	0.334822i	0.181176	−	0.983451i	$-0.442009\pi$
$983$	−570.070	−	329.130i	−0.579929	−	0.334822i	−0.761105	+	0.648629i	$0.775343\pi$
$984$		0			0
$985$	−165.246	−	286.215i	−0.167763	−	0.290573i
$986$	−611.247	−	11.9869i	−0.619926	−	0.0121571i
$987$		0			0
$988$	−25.5032	+	649.991i	−0.0258129	+	0.657885i
$989$			183.219i			0.185257i
$990$		0			0
$991$			1111.84i			1.12193i	0.827838	+	0.560967i	$0.189571\pi$
$991$			1111.84i			1.12193i	−0.827838	+	0.560967i	$0.810429\pi$
$992$	43.6141	+	4.28969i	0.0439658	+	0.00432428i
$993$		0			0
$994$	−49.1236	+	2504.96i	−0.0494201	+	2.52008i
$995$	56.8150	+	98.4065i	0.0571005	+	0.0989010i
$996$		0			0
$997$	−1323.93	−	764.369i	−1.32791	−	0.766669i	−0.342934	−	0.939359i	$-0.611421\pi$
$997$	−1323.93	−	764.369i	−1.32791	−	0.766669i	−0.984976	+	0.172690i	$0.944754\pi$
$998$	−516.415	−	311.810i	−0.517450	−	0.312435i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.p.b.19.18		40
3.2	odd	2		72.3.p.b.43.3	✓	40
4.3	odd	2		864.3.t.b.559.9		40
8.3	odd	2	inner	216.3.p.b.19.9		40
8.5	even	2		864.3.t.b.559.12		40
9.2	odd	6		648.3.b.f.163.16		20
9.4	even	3	inner	216.3.p.b.91.9		40
9.5	odd	6		72.3.p.b.67.12	yes	40
9.7	even	3		648.3.b.e.163.5		20
12.11	even	2		288.3.t.b.79.20		40
24.5	odd	2		288.3.t.b.79.19		40
24.11	even	2		72.3.p.b.43.12	yes	40
36.7	odd	6		2592.3.b.f.1135.9		20
36.11	even	6		2592.3.b.e.1135.12		20
36.23	even	6		288.3.t.b.175.19		40
36.31	odd	6		864.3.t.b.847.12		40
72.5	odd	6		288.3.t.b.175.20		40
72.11	even	6		648.3.b.f.163.15		20
72.13	even	6		864.3.t.b.847.9		40
72.29	odd	6		2592.3.b.e.1135.9		20
72.43	odd	6		648.3.b.e.163.6		20
72.59	even	6		72.3.p.b.67.3	yes	40
72.61	even	6		2592.3.b.f.1135.12		20
72.67	odd	6	inner	216.3.p.b.91.18		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.3	✓	40	3.2	odd	2
72.3.p.b.43.12	yes	40	24.11	even	2
72.3.p.b.67.3	yes	40	72.59	even	6
72.3.p.b.67.12	yes	40	9.5	odd	6
216.3.p.b.19.9		40	8.3	odd	2	inner
216.3.p.b.19.18		40	1.1	even	1	trivial
216.3.p.b.91.9		40	9.4	even	3	inner
216.3.p.b.91.18		40	72.67	odd	6	inner
288.3.t.b.79.19		40	24.5	odd	2
288.3.t.b.79.20		40	12.11	even	2
288.3.t.b.175.19		40	36.23	even	6
288.3.t.b.175.20		40	72.5	odd	6
648.3.b.e.163.5		20	9.7	even	3
648.3.b.e.163.6		20	72.43	odd	6
648.3.b.f.163.15		20	72.11	even	6
648.3.b.f.163.16		20	9.2	odd	6
864.3.t.b.559.9		40	4.3	odd	2
864.3.t.b.559.12		40	8.5	even	2
864.3.t.b.847.9		40	72.13	even	6
864.3.t.b.847.12		40	36.31	odd	6
2592.3.b.e.1135.9		20	72.29	odd	6
2592.3.b.e.1135.12		20	36.11	even	6
2592.3.b.f.1135.9		20	36.7	odd	6
2592.3.b.f.1135.12		20	72.61	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.75132 - 0.965848i) q^{2} +(2.13428 - 3.38303i) q^{4} +(-1.50948 + 0.871501i) q^{5} +(7.93804 + 4.58303i) q^{7} +(0.470322 - 7.98616i) q^{8} +O(q^{10})\)	\(q+(1.75132 - 0.965848i) q^{2} +(2.13428 - 3.38303i) q^{4} +(-1.50948 + 0.871501i) q^{5} +(7.93804 + 4.58303i) q^{7} +(0.470322 - 7.98616i) q^{8} +(-1.80186 + 2.98421i) q^{10} +(4.09143 - 7.08657i) q^{11} +(19.9384 - 11.5114i) q^{13} +(18.3286 + 0.359434i) q^{14} +(-6.88973 - 14.4406i) q^{16} -18.4578 q^{17} -7.06353 q^{19} +(-0.273345 + 6.96665i) q^{20} +(0.320879 - 16.3626i) q^{22} +(-9.33623 + 5.39028i) q^{23} +(-10.9810 + 19.0196i) q^{25} +(23.8003 - 39.4177i) q^{26} +(32.4465 - 17.0732i) q^{28} +(14.3424 + 8.28059i) q^{29} +(-1.18604 + 0.684759i) q^{31} +(-26.0136 - 18.6358i) q^{32} +(-32.3255 + 17.8274i) q^{34} -15.9765 q^{35} +59.1369i q^{37} +(-12.3705 + 6.82229i) q^{38} +(6.25000 + 12.4649i) q^{40} +(19.6706 + 34.0705i) q^{41} +(8.49767 - 14.7184i) q^{43} +(-15.2418 - 28.9661i) q^{44} +(-11.1446 + 18.4575i) q^{46} +(-25.4446 - 14.6904i) q^{47} +(17.5083 + 30.3253i) q^{49} +(-0.861206 + 43.9154i) q^{50} +(3.61054 - 92.0207i) q^{52} +49.1072i q^{53} +14.2628i q^{55} +(40.3343 - 61.2390i) q^{56} +(33.1160 + 0.649423i) q^{58} +(-32.8202 - 56.8463i) q^{59} +(11.8863 + 6.86257i) q^{61} +(-1.41576 + 2.34477i) q^{62} +(-63.5576 - 7.51213i) q^{64} +(-20.0645 + 34.7527i) q^{65} +(-24.8578 - 43.0550i) q^{67} +(-39.3940 + 62.4431i) q^{68} +(-27.9800 + 15.4308i) q^{70} +136.669i q^{71} -120.569 q^{73} +(57.1173 + 103.568i) q^{74} +(-15.0755 + 23.8961i) q^{76} +(64.9559 - 37.5023i) q^{77} +(-82.5422 - 47.6557i) q^{79} +(22.9850 + 15.7935i) q^{80} +(67.3566 + 40.6697i) q^{82} +(39.2191 - 67.9294i) q^{83} +(27.8617 - 16.0860i) q^{85} +(0.666448 - 33.9841i) q^{86} +(-54.6702 - 36.0078i) q^{88} +72.9529 q^{89} +211.029 q^{91} +(-1.69065 + 43.0891i) q^{92} +(-58.7505 - 1.15213i) q^{94} +(10.6623 - 6.15587i) q^{95} +(-25.9069 + 44.8721i) q^{97} +(59.9524 + 36.1991i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

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