LMFDB - Embedded newform 400.3.bg.f.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	400.17
Dual form			400.3.bg.f.353.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.298963 - 1.88758i) q^{3} +(4.96497 + 0.590862i) q^{5} +(0.603173 + 0.603173i) q^{7} +(5.08593 + 1.65252i) q^{9} +O(q^{10})$	\(q+(0.298963 - 1.88758i) q^{3} +(4.96497 + 0.590862i) q^{5} +(0.603173 + 0.603173i) q^{7} +(5.08593 + 1.65252i) q^{9} +(1.32991 + 4.09306i) q^{11} +(5.11090 + 10.0307i) q^{13} +(2.59964 - 9.19513i) q^{15} +(1.48017 + 9.34543i) q^{17} +(4.55381 - 6.26779i) q^{19} +(1.31886 - 0.958211i) q^{21} +(-11.6689 - 5.94559i) q^{23} +(24.3018 + 5.86721i) q^{25} +(12.4484 - 24.4314i) q^{27} +(5.20126 + 7.15892i) q^{29} +(0.874688 + 0.635498i) q^{31} +(8.12357 - 1.28665i) q^{33} +(2.63834 + 3.35112i) q^{35} +(-12.9660 + 6.60651i) q^{37} +(20.4618 - 6.64843i) q^{39} +(19.9807 - 61.4943i) q^{41} +(-23.5787 + 23.5787i) q^{43} +(24.2750 + 11.2098i) q^{45} +(62.0961 + 9.83505i) q^{47} -48.2724i q^{49} +18.0828 q^{51} +(-0.0161839 + 0.102181i) q^{53} +(4.18455 + 21.1077i) q^{55} +(-10.4695 - 10.4695i) q^{57} +(47.1252 + 15.3119i) q^{59} +(-26.7093 - 82.2027i) q^{61} +(2.07094 + 4.06445i) q^{63} +(19.4487 + 52.8220i) q^{65} +(-6.94118 - 43.8249i) q^{67} +(-14.7114 + 20.2484i) q^{69} +(-18.7104 + 13.5939i) q^{71} +(-2.93919 - 1.49759i) q^{73} +(18.3402 - 44.1175i) q^{75} +(-1.66665 + 3.27099i) q^{77} +(83.1987 + 114.513i) q^{79} +(-3.45743 - 2.51197i) q^{81} +(-127.531 + 20.1989i) q^{83} +(1.82714 + 47.2743i) q^{85} +(15.0680 - 7.67755i) q^{87} +(-71.6570 + 23.2828i) q^{89} +(-2.96750 + 9.13301i) q^{91} +(1.46105 - 1.46105i) q^{93} +(26.3129 - 28.4287i) q^{95} +(-90.2730 - 14.2978i) q^{97} +23.0147i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.298963	−	1.88758i	0.0996545	−	0.629194i	−0.886419	−	0.462884i	$-0.846815\pi$
$3$	0.298963	−	1.88758i	0.0996545	−	0.629194i	0.986074	−	0.166310i	$-0.0531852\pi$
$4$		0			0
$5$	4.96497	+	0.590862i	0.992993	+	0.118172i
$5$	4.96497	+	0.590862i	0.992993	+	0.118172i
$6$		0			0
$7$	0.603173	+	0.603173i	0.0861675	+	0.0861675i	0.748877	−	0.662709i	$-0.230593\pi$
$7$	0.603173	+	0.603173i	0.0861675	+	0.0861675i	−0.662709	+	0.748877i	$0.730593\pi$
$8$		0			0
$9$	5.08593	+	1.65252i	0.565103	+	0.183613i
$10$		0			0
$11$	1.32991	+	4.09306i	0.120901	+	0.372096i	0.993132	−	0.116999i	$-0.0373273\pi$
$11$	1.32991	+	4.09306i	0.120901	+	0.372096i	−0.872231	+	0.489095i	$0.837327\pi$
$12$		0			0
$13$	5.11090	+	10.0307i	0.393146	+	0.771593i	0.999725	−	0.0234299i	$-0.00745864\pi$
$13$	5.11090	+	10.0307i	0.393146	+	0.771593i	−0.606579	+	0.795023i	$0.707459\pi$
$14$		0			0
$15$	2.59964	−	9.19513i	0.173309	−	0.613009i
$16$		0			0
$17$	1.48017	+	9.34543i	0.0870689	+	0.549731i	0.992206	+	0.124611i	$0.0397682\pi$
$17$	1.48017	+	9.34543i	0.0870689	+	0.549731i	−0.905137	+	0.425120i	$0.860232\pi$
$18$		0			0
$19$	4.55381	−	6.26779i	0.239674	−	0.329883i	−0.672187	−	0.740381i	$-0.734645\pi$
$19$	4.55381	−	6.26779i	0.239674	−	0.329883i	0.911862	+	0.410498i	$0.134645\pi$
$20$		0			0
$21$	1.31886	−	0.958211i	0.0628031	−	0.0456291i
$22$		0			0
$23$	−11.6689	−	5.94559i	−0.507342	−	0.258504i	0.181531	−	0.983385i	$-0.441895\pi$
$23$	−11.6689	−	5.94559i	−0.507342	−	0.258504i	−0.688874	+	0.724881i	$0.741895\pi$
$24$		0			0
$25$	24.3018	+	5.86721i	0.972071	+	0.234689i
$26$		0			0
$27$	12.4484	−	24.4314i	0.461052	−	0.904865i
$28$		0			0
$29$	5.20126	+	7.15892i	0.179354	+	0.246859i	0.889223	−	0.457474i	$-0.151246\pi$
$29$	5.20126	+	7.15892i	0.179354	+	0.246859i	−0.709869	+	0.704334i	$0.751246\pi$
$30$		0			0
$31$	0.874688	+	0.635498i	0.0282158	+	0.0204999i	0.601804	−	0.798644i	$-0.294449\pi$
$31$	0.874688	+	0.635498i	0.0282158	+	0.0204999i	−0.573588	+	0.819144i	$0.694449\pi$
$32$		0			0
$33$	8.12357	−	1.28665i	0.246169	−	0.0389893i
$34$		0			0
$35$	2.63834	+	3.35112i	0.0753812	+	0.0957464i
$36$		0			0
$37$	−12.9660	+	6.60651i	−0.350433	+	0.178554i	−0.620342	−	0.784331i	$-0.713006\pi$
$37$	−12.9660	+	6.60651i	−0.350433	+	0.178554i	0.269909	+	0.962886i	$0.413006\pi$
$38$		0			0
$39$	20.4618	−	6.64843i	0.524660	−	0.170473i
$40$		0			0
$41$	19.9807	−	61.4943i	0.487334	−	1.49986i	−0.341237	−	0.939977i	$-0.610846\pi$
$41$	19.9807	−	61.4943i	0.487334	−	1.49986i	0.828571	−	0.559883i	$-0.189154\pi$
$42$		0			0
$43$	−23.5787	+	23.5787i	−0.548341	+	0.548341i	−0.925961	−	0.377620i	$-0.876743\pi$
$43$	−23.5787	+	23.5787i	−0.548341	+	0.548341i	0.377620	+	0.925961i	$0.376743\pi$
$44$		0			0
$45$	24.2750	+	11.2098i	0.539445	+	0.249106i
$46$		0			0
$47$	62.0961	+	9.83505i	1.32119	+	0.209256i	0.776892	−	0.629634i	$-0.216795\pi$
$47$	62.0961	+	9.83505i	1.32119	+	0.209256i	0.544301	+	0.838890i	$0.316795\pi$
$48$		0			0
$49$		−	48.2724i		−	0.985150i
$50$		0			0
$51$	18.0828			0.354564
$52$		0			0
$53$	−0.0161839	+	0.102181i	−0.000305357	+	0.00192795i	−0.987841	−	0.155470i	$-0.950311\pi$
$53$	−0.0161839	+	0.102181i	−0.000305357	+	0.00192795i	0.987535	+	0.157398i	$0.0503107\pi$
$54$		0			0
$55$	4.18455	+	21.1077i	0.0760827	+	0.383776i
$56$		0			0
$57$	−10.4695	−	10.4695i	−0.183676	−	0.183676i
$58$		0			0
$59$	47.1252	+	15.3119i	0.798732	+	0.259524i	0.679818	−	0.733381i	$-0.262059\pi$
$59$	47.1252	+	15.3119i	0.798732	+	0.259524i	0.118914	+	0.992905i	$0.462059\pi$
$60$		0			0
$61$	−26.7093	−	82.2027i	−0.437857	−	1.34758i	−0.890131	−	0.455705i	$-0.849387\pi$
$61$	−26.7093	−	82.2027i	−0.437857	−	1.34758i	0.452274	−	0.891879i	$-0.350613\pi$
$62$		0			0
$63$	2.07094	+	4.06445i	0.0328720	+	0.0645150i
$64$		0			0
$65$	19.4487	+	52.8220i	0.299211	+	0.812646i
$66$		0			0
$67$	−6.94118	−	43.8249i	−0.103600	−	0.654103i	−0.983769	−	0.179442i	$-0.942571\pi$
$67$	−6.94118	−	43.8249i	−0.103600	−	0.654103i	0.880169	−	0.474661i	$-0.157429\pi$
$68$		0			0
$69$	−14.7114	+	20.2484i	−0.213208	+	0.293456i
$70$		0			0
$71$	−18.7104	+	13.5939i	−0.263527	+	0.191463i	−0.711700	−	0.702483i	$-0.752075\pi$
$71$	−18.7104	+	13.5939i	−0.263527	+	0.191463i	0.448174	+	0.893946i	$0.352075\pi$
$72$		0			0
$73$	−2.93919	−	1.49759i	−0.0402629	−	0.0205150i	0.433743	−	0.901037i	$-0.357193\pi$
$73$	−2.93919	−	1.49759i	−0.0402629	−	0.0205150i	−0.474006	+	0.880522i	$0.657193\pi$
$74$		0			0
$75$	18.3402	−	44.1175i	0.244536	−	0.588233i
$76$		0			0
$77$	−1.66665	+	3.27099i	−0.0216448	+	0.0424804i
$78$		0			0
$79$	83.1987	+	114.513i	1.05315	+	1.44953i	0.886047	+	0.463595i	$0.153441\pi$
$79$	83.1987	+	114.513i	1.05315	+	1.44953i	0.167101	+	0.985940i	$0.446559\pi$
$80$		0			0
$81$	−3.45743	−	2.51197i	−0.0426843	−	0.0310119i
$82$		0			0
$83$	−127.531	+	20.1989i	−1.53651	+	0.243360i	−0.866572	−	0.499052i	$-0.833682\pi$
$83$	−127.531	+	20.1989i	−1.53651	+	0.243360i	−0.669943	+	0.742412i	$0.733682\pi$
$84$		0			0
$85$	1.82714	+	47.2743i	0.0214958	+	0.556168i
$86$		0			0
$87$	15.0680	−	7.67755i	0.173196	−	0.0882477i
$88$		0			0
$89$	−71.6570	+	23.2828i	−0.805135	+	0.261604i	−0.682536	−	0.730852i	$-0.739123\pi$
$89$	−71.6570	+	23.2828i	−0.805135	+	0.261604i	−0.122599	+	0.992456i	$0.539123\pi$
$90$		0			0
$91$	−2.96750	+	9.13301i	−0.0326098	+	0.100363i
$92$		0			0
$93$	1.46105	−	1.46105i	0.0157103	−	0.0157103i
$94$		0			0
$95$	26.3129	−	28.4287i	0.276978	−	0.299249i
$96$		0			0
$97$	−90.2730	−	14.2978i	−0.930649	−	0.147400i	−0.327339	−	0.944907i	$-0.606152\pi$
$97$	−90.2730	−	14.2978i	−0.930649	−	0.147400i	−0.603310	+	0.797507i	$0.706152\pi$
$98$		0			0
$99$			23.0147i			0.232472i
$100$		0			0
$101$	−37.8631			−0.374882			−0.187441	−	0.982276i	$-0.560019\pi$
$101$	−37.8631			−0.374882			−0.187441	+	0.982276i	$0.560019\pi$
$102$		0			0
$103$	−28.0145	+	176.877i	−0.271986	+	1.71725i	0.352157	+	0.935941i	$0.385448\pi$
$103$	−28.0145	+	176.877i	−0.271986	+	1.71725i	−0.624143	+	0.781310i	$0.714552\pi$
$104$		0			0
$105$	7.11429	−	3.97822i	0.0677551	−	0.0378878i
$106$		0			0
$107$	−136.408	−	136.408i	−1.27484	−	1.27484i	−0.943517	−	0.331325i	$-0.892504\pi$
$107$	−136.408	−	136.408i	−1.27484	−	1.27484i	−0.331325	−	0.943517i	$-0.607496\pi$
$108$		0			0
$109$	−85.4347	−	27.7594i	−0.783804	−	0.254673i	−0.110341	−	0.993894i	$-0.535194\pi$
$109$	−85.4347	−	27.7594i	−0.783804	−	0.254673i	−0.673464	+	0.739220i	$0.735194\pi$
$110$		0			0
$111$	8.59397	+	26.4495i	0.0774231	+	0.238284i
$112$		0			0
$113$	31.6343	+	62.0857i	0.279949	+	0.549431i	0.987574	−	0.157158i	$-0.0502331\pi$
$113$	31.6343	+	62.0857i	0.279949	+	0.549431i	−0.707624	+	0.706589i	$0.750233\pi$
$114$		0			0
$115$	−54.4226	−	36.4143i	−0.473240	−	0.316646i
$116$		0			0
$117$	9.41775	+	59.4613i	0.0804936	+	0.508216i
$118$		0			0
$119$	−4.74411	+	6.52971i	−0.0398665	+	0.0548715i
$120$		0			0
$121$	82.9066	−	60.2352i	0.685179	−	0.497811i
$122$		0			0
$123$	−110.102	−	56.0997i	−0.895138	−	0.456095i
$124$		0			0
$125$	117.191	+	43.4895i	0.937526	+	0.347916i
$126$		0			0
$127$	−20.8031	+	40.8285i	−0.163804	+	0.321484i	−0.958289	−	0.285800i	$-0.907741\pi$
$127$	−20.8031	+	40.8285i	−0.163804	+	0.321484i	0.794485	+	0.607284i	$0.207741\pi$
$128$		0			0
$129$	37.4575	+	51.5558i	0.290368	+	0.399657i
$130$		0			0
$131$	−195.455	−	142.006i	−1.49202	−	1.08402i	−0.973427	−	0.228996i	$-0.926456\pi$
$131$	−195.455	−	142.006i	−1.49202	−	1.08402i	−0.518594	−	0.855021i	$-0.673544\pi$
$132$		0			0
$133$	6.52729	−	1.03382i	0.0490774	−	0.00777310i
$134$		0			0
$135$	76.2414	−	113.946i	0.564751	−	0.844041i
$136$		0			0
$137$	−164.634	+	83.8854i	−1.20171	+	0.612303i	−0.936085	−	0.351774i	$-0.885579\pi$
$137$	−164.634	+	83.8854i	−1.20171	+	0.612303i	−0.265626	+	0.964076i	$0.585579\pi$
$138$		0			0
$139$	−4.78437	+	1.55453i	−0.0344199	+	0.0111837i	−0.326176	−	0.945309i	$-0.605760\pi$
$139$	−4.78437	+	1.55453i	−0.0344199	+	0.0111837i	0.291756	+	0.956493i	$0.405760\pi$
$140$		0			0
$141$	37.1289	−	114.271i	0.263326	−	0.810433i
$142$		0			0
$143$	−34.2592	+	34.2592i	−0.239575	+	0.239575i
$144$		0			0
$145$	21.5942	+	38.6170i	0.148925	+	0.266324i
$146$		0			0
$147$	−91.1180	−	14.4317i	−0.619850	−	0.0981746i
$148$		0			0
$149$			155.703i			1.04498i	0.852644	+	0.522492i	$0.174997\pi$
$149$			155.703i			1.04498i	−0.852644	+	0.522492i	$0.825003\pi$
$150$		0			0
$151$	160.886			1.06547			0.532736	−	0.846282i	$-0.321164\pi$
$151$	160.886			1.06547			0.532736	+	0.846282i	$0.321164\pi$
$152$		0			0
$153$	−7.91545	+	49.9762i	−0.0517350	+	0.326642i
$154$		0			0
$155$	3.96731	+	3.67205i	0.0255955	+	0.0236906i
$156$		0			0
$157$	−63.4163	−	63.4163i	−0.403925	−	0.403925i	0.475688	−	0.879614i	$-0.342199\pi$
$157$	−63.4163	−	63.4163i	−0.403925	−	0.403925i	−0.879614	+	0.475688i	$0.842199\pi$
$158$		0			0
$159$	0.188037	+	0.0610969i	0.00118262	+	0.000384257i
$160$		0			0
$161$	−3.45213	−	10.6246i	−0.0214418	−	0.0659911i
$162$		0			0
$163$	−50.9048	−	99.9062i	−0.312299	−	0.612922i	0.680495	−	0.732753i	$-0.261765\pi$
$163$	−50.9048	−	99.9062i	−0.312299	−	0.612922i	−0.992794	+	0.119831i	$0.961765\pi$
$164$		0			0
$165$	41.0935	−	1.58825i	0.249051	−	0.00962578i
$166$		0			0
$167$	−14.3867	−	90.8343i	−0.0861482	−	0.543918i	−0.992583	−	0.121572i	$-0.961207\pi$
$167$	−14.3867	−	90.8343i	−0.0861482	−	0.543918i	0.906434	−	0.422346i	$-0.138793\pi$
$168$		0			0
$169$	24.8418	−	34.1919i	0.146993	−	0.202319i
$170$		0			0
$171$	33.5180	−	24.3522i	0.196012	−	0.142411i
$172$		0			0
$173$	−162.020	−	82.5533i	−0.936531	−	0.477187i	−0.0820267	−	0.996630i	$-0.526139\pi$
$173$	−162.020	−	82.5533i	−0.936531	−	0.477187i	−0.854505	+	0.519444i	$0.826139\pi$
$174$		0			0
$175$	11.1192	+	18.1971i	0.0635384	+	0.103983i
$176$		0			0
$177$	42.9912	−	84.3749i	0.242888	−	0.476695i
$178$		0			0
$179$	52.7840	+	72.6509i	0.294883	+	0.405871i	0.930592	−	0.366057i	$-0.119293\pi$
$179$	52.7840	+	72.6509i	0.294883	+	0.405871i	−0.635710	+	0.771928i	$0.719293\pi$
$180$		0			0
$181$	45.3884	+	32.9766i	0.250764	+	0.182191i	0.706066	−	0.708146i	$-0.250468\pi$
$181$	45.3884	+	32.9766i	0.250764	+	0.182191i	−0.455301	+	0.890338i	$0.650468\pi$
$182$		0			0
$183$	−163.149	+	25.8403i	−0.891526	+	0.141204i
$184$		0			0
$185$	−68.2793	+	25.1400i	−0.369078	+	0.135892i
$186$		0			0
$187$	−36.2829	+	18.4870i	−0.194026	+	0.0988612i
$188$		0			0
$189$	22.2449	−	7.22780i	0.117698	−	0.0382423i
$190$		0			0
$191$	26.3975	−	81.2433i	0.138207	−	0.425358i	−0.857868	−	0.513870i	$-0.828211\pi$
$191$	26.3975	−	81.2433i	0.138207	−	0.425358i	0.996075	+	0.0885125i	$0.0282113\pi$
$192$		0			0
$193$	−131.997	+	131.997i	−0.683922	+	0.683922i	−0.960882	−	0.276959i	$-0.910673\pi$
$193$	−131.997	+	131.997i	−0.683922	+	0.683922i	0.276959	+	0.960882i	$0.410673\pi$
$194$		0			0
$195$	105.520	−	20.9191i	0.541129	−	0.107278i
$196$		0			0
$197$	−179.500	−	28.4300i	−0.911166	−	0.144315i	−0.316784	−	0.948498i	$-0.602603\pi$
$197$	−179.500	−	28.4300i	−0.911166	−	0.144315i	−0.594382	+	0.804183i	$0.702603\pi$
$198$		0			0
$199$			231.226i			1.16194i	0.813925	+	0.580970i	$0.197327\pi$
$199$			231.226i			1.16194i	−0.813925	+	0.580970i	$0.802673\pi$
$200$		0			0
$201$	−84.7982			−0.421882
$202$		0			0
$203$	−1.18081	+	7.45533i	−0.00581679	+	0.0367258i
$204$		0			0
$205$	135.538	−	293.511i	0.661162	−	1.43176i
$206$		0			0
$207$	−49.5219	−	49.5219i	−0.239236	−	0.239236i
$208$		0			0
$209$	31.7106	+	10.3034i	0.151725	+	0.0492985i
$210$		0			0
$211$	32.6136	+	100.374i	0.154567	+	0.475708i	0.998117	−	0.0613431i	$-0.0195384\pi$
$211$	32.6136	+	100.374i	0.154567	+	0.475708i	−0.843550	+	0.537051i	$0.819538\pi$
$212$		0			0
$213$	20.0659	+	39.3815i	0.0942059	+	0.184889i
$214$		0			0
$215$	−130.999	+	103.135i	−0.609297	+	0.479700i
$216$		0			0
$217$	0.144273	+	0.910904i	0.000664852	+	0.00419771i
$218$		0			0
$219$	−3.70554	+	5.10024i	−0.0169203	+	0.0232887i
$220$		0			0
$221$	−86.1763	+	62.6108i	−0.389938	+	0.283307i
$222$		0			0
$223$	321.357	+	163.740i	1.44106	+	0.734259i	0.987596	−	0.157014i	$-0.0501867\pi$
$223$	321.357	+	163.740i	1.44106	+	0.734259i	0.453468	+	0.891273i	$0.350187\pi$
$224$		0			0
$225$	113.901	+	69.9993i	0.506228	+	0.311108i
$226$		0			0
$227$	−57.0483	+	111.963i	−0.251314	+	0.493231i	−0.981854	−	0.189639i	$-0.939268\pi$
$227$	−57.0483	+	111.963i	−0.251314	+	0.493231i	0.730540	+	0.682870i	$0.239268\pi$
$228$		0			0
$229$	171.912	+	236.616i	0.750706	+	1.03326i	0.997931	+	0.0643000i	$0.0204815\pi$
$229$	171.912	+	236.616i	0.750706	+	1.03326i	−0.247225	+	0.968958i	$0.579519\pi$
$230$		0			0
$231$	5.67599	+	4.12385i	0.0245714	+	0.0178522i
$232$		0			0
$233$	30.3537	−	4.80755i	0.130273	−	0.0206333i	−0.0909573	−	0.995855i	$-0.528993\pi$
$233$	30.3537	−	4.80755i	0.130273	−	0.0206333i	0.221231	+	0.975222i	$0.428993\pi$
$234$		0			0
$235$	302.494	+	85.5209i	1.28721	+	0.363919i
$236$		0			0
$237$	241.026	−	122.809i	1.01699	−	0.518182i
$238$		0			0
$239$	−161.833	+	52.5828i	−0.677127	+	0.220012i	−0.627337	−	0.778748i	$-0.715855\pi$
$239$	−161.833	+	52.5828i	−0.677127	+	0.220012i	−0.0497897	+	0.998760i	$0.515855\pi$
$240$		0			0
$241$	129.395	−	398.236i	0.536907	−	1.65243i	−0.202584	−	0.979265i	$-0.564934\pi$
$241$	129.395	−	398.236i	0.536907	−	1.65243i	0.739491	−	0.673166i	$-0.235066\pi$
$242$		0			0
$243$	168.724	−	168.724i	0.694339	−	0.694339i
$244$		0			0
$245$	28.5223	−	239.671i	0.116417	−	0.978247i
$246$		0			0
$247$	86.1445	+	13.6439i	0.348763	+	0.0552386i
$248$		0			0
$249$			246.763i			0.991017i
$250$		0			0
$251$	178.268			0.710230			0.355115	−	0.934823i	$-0.384442\pi$
$251$	178.268			0.710230			0.355115	+	0.934823i	$0.384442\pi$
$252$		0			0
$253$	8.81702	−	55.6685i	0.0348499	−	0.220034i
$254$		0			0
$255$	89.7803	+	10.6844i	0.352080	+	0.0418997i
$256$		0			0
$257$	−318.413	−	318.413i	−1.23896	−	1.23896i	−0.960426	−	0.278535i	$-0.910151\pi$
$257$	−318.413	−	318.413i	−1.23896	−	1.23896i	−0.278535	−	0.960426i	$-0.589849\pi$
$258$		0			0
$259$	−11.8056	−	3.83588i	−0.0455815	−	0.0148103i
$260$		0			0
$261$	14.6230	+	45.0049i	0.0560268	+	0.172433i
$262$		0			0
$263$	20.9468	+	41.1104i	0.0796455	+	0.156313i	0.927395	−	0.374084i	$-0.122043\pi$
$263$	20.9468	+	41.1104i	0.0796455	+	0.156313i	−0.847749	+	0.530397i	$0.822043\pi$
$264$		0			0
$265$	−0.140728	+	0.497764i	−0.000531048	+	0.00187836i
$266$		0			0
$267$	22.5253	+	142.219i	0.0843644	+	0.532656i
$268$		0			0
$269$	−9.33991	+	12.8553i	−0.0347208	+	0.0477891i	−0.826024	−	0.563634i	$-0.809403\pi$
$269$	−9.33991	+	12.8553i	−0.0347208	+	0.0477891i	0.791304	+	0.611423i	$0.209403\pi$
$270$		0			0
$271$	356.162	−	258.767i	1.31425	−	0.954860i	0.314267	−	0.949335i	$-0.398241\pi$
$271$	356.162	−	258.767i	1.31425	−	0.954860i	0.999985	−	0.00552502i	$-0.00175868\pi$
$272$		0			0
$273$	16.3521	+	8.33182i	0.0598979	+	0.0305195i
$274$		0			0
$275$	8.30443	+	107.271i	0.0301979	+	0.390078i
$276$		0			0
$277$	11.1459	−	21.8751i	0.0402379	−	0.0789714i	−0.870012	−	0.493030i	$-0.835889\pi$
$277$	11.1459	−	21.8751i	0.0402379	−	0.0789714i	0.910250	+	0.414059i	$0.135889\pi$
$278$		0			0
$279$	3.39843	+	4.67753i	0.0121807	+	0.0167654i
$280$		0			0
$281$	377.771	+	274.466i	1.34438	+	0.976749i	0.999271	+	0.0381864i	$0.0121581\pi$
$281$	377.771	+	274.466i	1.34438	+	0.976749i	0.345109	+	0.938563i	$0.387842\pi$
$282$		0			0
$283$	251.644	−	39.8565i	0.889201	−	0.140836i	0.304911	−	0.952381i	$-0.401373\pi$
$283$	251.644	−	39.8565i	0.889201	−	0.140836i	0.584290	+	0.811545i	$0.301373\pi$
$284$		0			0
$285$	−45.7948	−	58.1669i	−0.160684	−	0.204094i
$286$		0			0
$287$	49.1435	−	25.0399i	0.171232	−	0.0872469i
$288$		0			0
$289$	189.709	−	61.6403i	0.656433	−	0.213288i
$290$		0			0
$291$	−53.9766	+	166.123i	−0.185487	+	0.570869i
$292$		0			0
$293$	−186.595	+	186.595i	−0.636844	+	0.636844i	−0.949776	−	0.312931i	$-0.898689\pi$
$293$	−186.595	+	186.595i	−0.636844	+	0.636844i	0.312931	+	0.949776i	$0.398689\pi$
$294$		0			0
$295$	224.928	+	103.868i	0.762467	+	0.352093i
$296$		0			0
$297$	116.554	+	18.4604i	0.392438	+	0.0621562i
$298$		0			0
$299$		−	147.434i		−	0.493092i
$300$		0			0
$301$	−28.4440			−0.0944984
$302$		0			0
$303$	−11.3197	+	71.4696i	−0.0373587	+	0.235873i
$304$		0			0
$305$	−84.0402	−	423.915i	−0.275542	−	1.38988i
$306$		0			0
$307$	−282.940	−	282.940i	−0.921628	−	0.921628i	0.0755167	−	0.997145i	$-0.475939\pi$
$307$	−282.940	−	282.940i	−0.921628	−	0.921628i	−0.997145	+	0.0755167i	$0.975939\pi$
$308$		0			0
$309$	325.494	+	105.759i	1.05338	+	0.342264i
$310$		0			0
$311$	−151.808	−	467.218i	−0.488130	−	1.50231i	−0.827397	−	0.561618i	$-0.810179\pi$
$311$	−151.808	−	467.218i	−0.488130	−	1.50231i	0.339267	−	0.940690i	$-0.389821\pi$
$312$		0			0
$313$	73.1875	+	143.639i	0.233826	+	0.458909i	0.977868	−	0.209224i	$-0.0670937\pi$
$313$	73.1875	+	143.639i	0.233826	+	0.458909i	−0.744042	+	0.668133i	$0.767094\pi$
$314$		0			0
$315$	7.88061	+	21.4035i	0.0250178	+	0.0679475i
$316$		0			0
$317$	11.5796	+	73.1107i	0.0365287	+	0.230633i	0.999198	−	0.0400480i	$-0.0127511\pi$
$317$	11.5796	+	73.1107i	0.0365287	+	0.230633i	−0.962669	+	0.270681i	$0.912751\pi$
$318$		0			0
$319$	−22.3846	+	30.8098i	−0.0701713	+	0.0965825i
$320$		0			0
$321$	−298.262	+	216.700i	−0.929166	+	0.675079i
$322$		0			0
$323$	65.3156	+	33.2799i	0.202215	+	0.103034i
$324$		0			0
$325$	65.3516	+	273.751i	0.201082	+	0.842310i
$326$		0			0
$327$	−77.9400	+	152.966i	−0.238349	+	0.467785i
$328$		0			0
$329$	31.5224	+	43.3869i	0.0958129	+	0.131875i
$330$		0			0
$331$	−494.917	−	359.578i	−1.49522	−	1.08634i	−0.972238	−	0.233993i	$-0.924821\pi$
$331$	−494.917	−	359.578i	−1.49522	−	1.08634i	−0.522979	−	0.852346i	$-0.675179\pi$
$332$		0			0
$333$	−76.8616	+	12.1737i	−0.230816	+	0.0365576i
$334$		0			0
$335$	−8.56828	−	221.690i	−0.0255770	−	0.661762i
$336$		0			0
$337$	411.395	−	209.616i	1.22076	−	0.622007i	0.279646	−	0.960103i	$-0.409783\pi$
$337$	411.395	−	209.616i	1.22076	−	0.622007i	0.941112	+	0.338096i	$0.109783\pi$
$338$		0			0
$339$	126.649	−	41.1509i	0.373597	−	0.121389i
$340$		0			0
$341$	−1.43787	+	4.42531i	−0.00421663	+	0.0129774i
$342$		0			0
$343$	58.6720	−	58.6720i	0.171056	−	0.171056i
$344$		0			0
$345$	−85.0054	+	91.8404i	−0.246392	+	0.266204i
$346$		0			0
$347$	−293.541	−	46.4923i	−0.845939	−	0.133984i	−0.281605	−	0.959530i	$-0.590867\pi$
$347$	−293.541	−	46.4923i	−0.845939	−	0.133984i	−0.564334	+	0.825547i	$0.690867\pi$
$348$		0			0
$349$		−	71.5411i		−	0.204989i	−0.994734	−	0.102494i	$-0.967318\pi$
$349$		−	71.5411i		−	0.204989i	0.994734	−	0.102494i	$-0.0326824\pi$
$350$		0			0
$351$	308.686			0.879449
$352$		0			0
$353$	39.3926	−	248.715i	0.111594	−	0.704575i	−0.866928	−	0.498433i	$-0.833909\pi$
$353$	39.3926	−	248.715i	0.111594	−	0.704575i	0.978522	−	0.206142i	$-0.0660909\pi$
$354$		0			0
$355$	−100.929	+	56.4380i	−0.284306	+	0.158980i
$356$		0			0
$357$	10.9070	+	10.9070i	0.0305519	+	0.0305519i
$358$		0			0
$359$	−470.695	−	152.938i	−1.31113	−	0.426011i	−0.431689	−	0.902023i	$-0.642082\pi$
$359$	−470.695	−	152.938i	−1.31113	−	0.426011i	−0.879439	+	0.476011i	$0.842082\pi$
$360$		0			0
$361$	93.0072	+	286.247i	0.257638	+	0.792927i
$362$		0			0
$363$	−88.9127	−	174.501i	−0.244939	−	0.480719i
$364$		0			0
$365$	−13.7081	−	9.17215i	−0.0375565	−	0.0251292i
$366$		0			0
$367$	61.7236	+	389.708i	0.168184	+	1.06187i	0.916939	+	0.399027i	$0.130652\pi$
$367$	61.7236	+	389.708i	0.168184	+	1.06187i	−0.748755	+	0.662847i	$0.769348\pi$
$368$		0			0
$369$	203.241	−	279.737i	0.550788	−	0.758095i
$370$		0			0
$371$	−0.0713947	+	0.0518713i	−0.000192438	+	0.000139815i
$372$		0			0
$373$	−305.107	−	155.460i	−0.817981	−	0.416782i	−0.00565378	−	0.999984i	$-0.501800\pi$
$373$	−305.107	−	155.460i	−0.817981	−	0.416782i	−0.812327	+	0.583202i	$0.801800\pi$
$374$		0			0
$375$	117.126	−	208.205i	0.312335	−	0.555214i
$376$		0			0
$377$	−45.2260	+	88.7609i	−0.119963	+	0.235440i
$378$		0			0
$379$	−13.2850	−	18.2853i	−0.0350528	−	0.0482461i	0.791131	−	0.611647i	$-0.209493\pi$
$379$	−13.2850	−	18.2853i	−0.0350528	−	0.0482461i	−0.826184	+	0.563401i	$0.809493\pi$
$380$		0			0
$381$	70.8477	+	51.4738i	0.185952	+	0.135102i
$382$		0			0
$383$	−388.248	+	61.4924i	−1.01370	+	0.160555i	−0.641117	−	0.767443i	$-0.721529\pi$
$383$	−388.248	+	61.4924i	−1.01370	+	0.160555i	−0.372585	+	0.927998i	$0.621529\pi$
$384$		0			0
$385$	−10.2076	+	15.2556i	−0.0265132	+	0.0396249i
$386$		0			0
$387$	−158.883	+	80.9551i	−0.410551	+	0.209186i
$388$		0			0
$389$	−238.105	+	77.3649i	−0.612094	+	0.198881i	−0.598627	−	0.801028i	$-0.704287\pi$
$389$	−238.105	+	77.3649i	−0.612094	+	0.198881i	−0.0134671	+	0.999909i	$0.504287\pi$
$390$		0			0
$391$	38.2922	−	117.851i	0.0979339	−	0.301410i
$392$		0			0
$393$	−326.482	+	326.482i	−0.830743	+	0.830743i
$394$		0			0
$395$	345.417	+	617.713i	0.874474	+	1.56383i
$396$		0			0
$397$	500.801	+	79.3191i	1.26146	+	0.199796i	0.751115	−	0.660171i	$-0.229516\pi$
$397$	500.801	+	79.3191i	1.26146	+	0.199796i	0.510349	+	0.859967i	$0.329516\pi$
$398$		0			0
$399$		−	12.6299i		−	0.0316538i
$400$		0			0
$401$	2.14623			0.00535220			0.00267610	−	0.999996i	$-0.499148\pi$
$401$	2.14623			0.00535220			0.00267610	+	0.999996i	$0.499148\pi$
$402$		0			0
$403$	−1.90405	+	12.0217i	−0.00472470	+	0.0298306i
$404$		0			0
$405$	−15.6818	−	14.5147i	−0.0387204	−	0.0358387i
$406$		0			0
$407$	−44.2845	−	44.2845i	−0.108807	−	0.108807i
$408$		0			0
$409$	−98.8503	−	32.1184i	−0.241688	−	0.0785291i	0.185668	−	0.982612i	$-0.440555\pi$
$409$	−98.8503	−	32.1184i	−0.241688	−	0.0785291i	−0.427356	+	0.904083i	$0.640555\pi$
$410$		0			0
$411$	109.121	+	335.840i	0.265501	+	0.817128i
$412$		0			0
$413$	19.1889	+	37.6604i	0.0464623	+	0.0911873i
$414$		0			0
$415$	−645.120	+	24.9338i	−1.55451	+	0.0600813i
$416$		0			0
$417$	1.50396	+	9.49563i	0.00360662	+	0.0227713i
$418$		0			0
$419$	377.500	−	519.584i	0.900955	−	1.24006i	−0.0692080	−	0.997602i	$-0.522047\pi$
$419$	377.500	−	519.584i	0.900955	−	1.24006i	0.970163	−	0.242455i	$-0.0779528\pi$
$420$		0			0
$421$	−433.225	+	314.757i	−1.02904	+	0.747640i	−0.968116	−	0.250502i	$-0.919404\pi$
$421$	−433.225	+	314.757i	−1.02904	+	0.747640i	−0.0609224	+	0.998143i	$0.519404\pi$
$422$		0			0
$423$	299.563	+	152.635i	0.708188	+	0.360840i
$424$		0			0
$425$	−18.8609	+	235.795i	−0.0443785	+	0.554812i
$426$		0			0
$427$	33.4721	−	65.6927i	0.0783890	−	0.153847i
$428$		0			0
$429$	54.4248	+	74.9093i	0.126864	+	0.174614i
$430$		0			0
$431$	−628.924	−	456.940i	−1.45922	−	1.06019i	−0.983565	−	0.180555i	$-0.942211\pi$
$431$	−628.924	−	456.940i	−1.45922	−	1.06019i	−0.475657	−	0.879631i	$-0.657789\pi$
$432$		0			0
$433$	42.6465	−	6.75453i	0.0984907	−	0.0155994i	−0.106995	−	0.994260i	$-0.534123\pi$
$433$	42.6465	−	6.75453i	0.0984907	−	0.0155994i	0.205485	+	0.978660i	$0.434123\pi$
$434$		0			0
$435$	79.3486	−	29.2156i	0.182411	−	0.0671624i
$436$		0			0
$437$	−90.4036	+	46.0629i	−0.206873	+	0.105407i
$438$		0			0
$439$	−455.453	+	147.986i	−1.03748	+	0.337097i	−0.777743	−	0.628583i	$-0.783635\pi$
$439$	−455.453	+	147.986i	−1.03748	+	0.337097i	−0.259736	+	0.965680i	$0.583635\pi$
$440$		0			0
$441$	79.7709	−	245.510i	0.180886	−	0.556711i
$442$		0			0
$443$	12.9006	−	12.9006i	0.0291210	−	0.0291210i	−0.692396	−	0.721517i	$-0.743445\pi$
$443$	12.9006	−	12.9006i	0.0291210	−	0.0291210i	0.721517	+	0.692396i	$0.243445\pi$
$444$		0			0
$445$	−369.532	+	73.2588i	−0.830408	+	0.164627i
$446$		0			0
$447$	293.901	+	46.5494i	0.657497	+	0.104137i
$448$		0			0
$449$		−	314.015i		−	0.699365i	−0.936868	−	0.349683i	$-0.886289\pi$
$449$		−	314.015i		−	0.699365i	0.936868	−	0.349683i	$-0.113711\pi$
$450$		0			0
$451$	278.272			0.617012
$452$		0			0
$453$	48.0991	−	303.686i	0.106179	−	0.670388i
$454$		0			0
$455$	−20.1299	+	43.5917i	−0.0442414	+	0.0958060i
$456$		0			0
$457$	23.7311	+	23.7311i	0.0519280	+	0.0519280i	0.732594	−	0.680666i	$-0.238309\pi$
$457$	23.7311	+	23.7311i	0.0519280	+	0.0519280i	−0.680666	+	0.732594i	$0.738309\pi$
$458$		0			0
$459$	246.747	+	80.1731i	0.537576	+	0.174669i
$460$		0			0
$461$	80.2723	+	247.053i	0.174126	+	0.535906i	0.999592	−	0.0285458i	$-0.00908765\pi$
$461$	80.2723	+	247.053i	0.174126	+	0.535906i	−0.825466	+	0.564452i	$0.809088\pi$
$462$		0			0
$463$	−91.5411	−	179.659i	−0.197713	−	0.388033i	0.770770	−	0.637114i	$-0.219872\pi$
$463$	−91.5411	−	179.659i	−0.197713	−	0.388033i	−0.968483	+	0.249080i	$0.919872\pi$
$464$		0			0
$465$	8.11736	−	6.39080i	0.0174567	−	0.0137437i
$466$		0			0
$467$	99.3749	+	627.428i	0.212794	+	1.34353i	0.830455	+	0.557085i	$0.188080\pi$
$467$	99.3749	+	627.428i	0.212794	+	1.34353i	−0.617661	+	0.786444i	$0.711920\pi$
$468$		0			0
$469$	22.2473	−	30.6207i	0.0474355	−	0.0652894i
$470$		0			0
$471$	−138.663	+	100.744i	−0.294400	+	0.213894i
$472$		0			0
$473$	−127.866	−	65.1512i	−0.270331	−	0.137740i
$474$		0			0
$475$	147.440	−	125.600i	0.310400	−	0.264421i
$476$		0			0
$477$	−0.251167	+	0.492942i	−0.000526555	+	0.00103342i
$478$		0			0
$479$	−183.182	−	252.129i	−0.382426	−	0.526365i	0.573799	−	0.818996i	$-0.305469\pi$
$479$	−183.182	−	252.129i	−0.382426	−	0.526365i	−0.956225	+	0.292632i	$0.905469\pi$
$480$		0			0
$481$	−132.536	−	96.2931i	−0.275543	−	0.200194i
$482$		0			0
$483$	−21.0868	+	3.33982i	−0.0436580	+	0.00691474i
$484$		0			0
$485$	−439.754	−	124.327i	−0.906709	−	0.256344i
$486$		0			0
$487$	517.298	−	263.577i	1.06221	−	0.541225i	0.166585	−	0.986027i	$-0.446726\pi$
$487$	517.298	−	263.577i	1.06221	−	0.541225i	0.895629	+	0.444802i	$0.146726\pi$
$488$		0			0
$489$	−203.800	+	66.2185i	−0.416768	+	0.135416i
$490$		0			0
$491$	−283.716	+	873.187i	−0.577832	+	1.77838i	0.0484944	+	0.998823i	$0.484558\pi$
$491$	−283.716	+	873.187i	−0.577832	+	1.77838i	−0.626327	+	0.779561i	$0.715442\pi$
$492$		0			0
$493$	−59.2045	+	59.2045i	−0.120090	+	0.120090i
$494$		0			0
$495$	−13.5985	+	114.267i	−0.0274717	+	0.230843i
$496$		0			0
$497$	−19.4851	−	3.08613i	−0.0392054	−	0.00620952i
$498$		0			0
$499$			133.233i			0.267000i	0.991049	+	0.133500i	$0.0426216\pi$
$499$			133.233i			0.267000i	−0.991049	+	0.133500i	$0.957378\pi$
$500$		0			0
$501$	−175.758			−0.350815
$502$		0			0
$503$	−61.9059	+	390.859i	−0.123073	+	0.777055i	0.846524	+	0.532350i	$0.178691\pi$
$503$	−61.9059	+	390.859i	−0.123073	+	0.777055i	−0.969598	+	0.244705i	$0.921309\pi$
$504$		0			0
$505$	−187.989	−	22.3718i	−0.372255	−	0.0443007i
$506$		0			0
$507$	−57.1131	−	57.1131i	−0.112649	−	0.112649i
$508$		0			0
$509$	−502.891	−	163.399i	−0.987998	−	0.321020i	−0.229938	−	0.973205i	$-0.573852\pi$
$509$	−502.891	−	163.399i	−0.987998	−	0.321020i	−0.758060	+	0.652185i	$0.773852\pi$
$510$		0			0
$511$	−0.869533	−	2.67615i	−0.00170163	−	0.00523708i
$512$		0			0
$513$	−96.4428	−	189.280i	−0.187998	−	0.368966i
$514$		0			0
$515$	−243.601	+	861.635i	−0.473012	+	1.67308i
$516$		0			0
$517$	42.3271	+	267.243i	0.0818705	+	0.516910i
$518$		0			0
$519$	−204.264	+	281.145i	−0.393572	+	0.541706i
$520$		0			0
$521$	−427.027	+	310.253i	−0.819630	+	0.595496i	−0.916607	−	0.399791i	$-0.869083\pi$
$521$	−427.027	+	310.253i	−0.819630	+	0.595496i	0.0969764	+	0.995287i	$0.469083\pi$
$522$		0			0
$523$	187.207	+	95.3867i	0.357948	+	0.182384i	0.623712	−	0.781655i	$-0.285624\pi$
$523$	187.207	+	95.3867i	0.357948	+	0.182384i	−0.265763	+	0.964038i	$0.585624\pi$
$524$		0			0
$525$	37.6728	−	15.5482i	0.0717576	−	0.0296155i
$526$		0			0
$527$	−4.64432	+	9.11498i	−0.00881274	+	0.0172960i
$528$		0			0
$529$	−210.126	−	289.213i	−0.397213	−	0.546717i
$530$		0			0
$531$	214.372	+	155.750i	0.403714	+	0.293315i
$532$		0			0
$533$	718.951	−	113.871i	1.34888	−	0.213641i
$534$		0			0
$535$	−596.663	−	757.860i	−1.11526	−	1.41656i
$536$		0			0
$537$	152.915	−	77.9141i	0.284758	−	0.145091i
$538$		0			0
$539$	197.582	−	64.1981i	0.366571	−	0.119106i
$540$		0			0
$541$	239.753	−	737.883i	0.443166	−	1.36392i	−0.441317	−	0.897351i	$-0.645489\pi$
$541$	239.753	−	737.883i	0.443166	−	1.36392i	0.884483	−	0.466572i	$-0.154511\pi$
$542$		0			0
$543$	75.8154	−	75.8154i	0.139623	−	0.139623i
$544$		0			0
$545$	−407.778	−	188.305i	−0.748217	−	0.345513i
$546$		0			0
$547$	−100.225	−	15.8741i	−0.183227	−	0.0290203i	0.0641464	−	0.997940i	$-0.479568\pi$
$547$	−100.225	−	15.8741i	−0.183227	−	0.0290203i	−0.247374	+	0.968920i	$0.579568\pi$
$548$		0			0
$549$		−	462.214i		−	0.841920i
$550$		0			0
$551$	68.5562			0.124421
$552$		0			0
$553$	−18.8881	+	119.254i	−0.0341556	+	0.215650i
$554$		0			0
$555$	27.0407	+	136.399i	0.0487221	+	0.245763i
$556$		0			0
$557$	−622.801	−	622.801i	−1.11814	−	1.11814i	−0.992015	−	0.126120i	$-0.959747\pi$
$557$	−622.801	−	622.801i	−1.11814	−	1.11814i	−0.126120	−	0.992015i	$-0.540253\pi$
$558$		0			0
$559$	−357.019	−	116.002i	−0.638674	−	0.207518i
$560$		0			0
$561$	24.0485	+	74.0138i	0.0428673	+	0.131932i
$562$		0			0
$563$	−256.920	−	504.233i	−0.456340	−	0.895619i	−0.998469	−	0.0553227i	$-0.982381\pi$
$563$	−256.920	−	504.233i	−0.456340	−	0.895619i	0.542128	−	0.840296i	$-0.317619\pi$
$564$		0			0
$565$	120.379	+	326.945i	0.213060	+	0.578664i
$566$		0			0
$567$	−0.570275	−	3.60057i	−0.00100578	−	0.00635022i
$568$		0			0
$569$	−66.4984	+	91.5272i	−0.116869	+	0.160856i	−0.863444	−	0.504445i	$-0.831697\pi$
$569$	−66.4984	+	91.5272i	−0.116869	+	0.160856i	0.746575	+	0.665302i	$0.231697\pi$
$570$		0			0
$571$	−403.405	+	293.091i	−0.706488	+	0.513294i	−0.882039	−	0.471177i	$-0.843829\pi$
$571$	−403.405	+	293.091i	−0.706488	+	0.513294i	0.175551	+	0.984470i	$0.443829\pi$
$572$		0			0
$573$	−145.461	−	74.1163i	−0.253859	−	0.129348i
$574$		0			0
$575$	−248.690	−	212.952i	−0.432505	−	0.370352i
$576$		0			0
$577$	−344.419	+	675.960i	−0.596913	+	1.17151i	0.372949	+	0.927852i	$0.378347\pi$
$577$	−344.419	+	675.960i	−0.596913	+	1.17151i	−0.969862	+	0.243656i	$0.921653\pi$
$578$		0			0
$579$	209.693	+	288.617i	0.362164	+	0.498475i
$580$		0			0
$581$	−89.1065	−	64.7397i	−0.153367	−	0.111428i
$582$		0			0
$583$	−0.439757	+	0.0696507i	−0.000754300	+	0.000119469i
$584$		0			0
$585$	11.6254	+	300.788i	0.0198725	+	0.514168i
$586$		0			0
$587$	745.664	−	379.935i	1.27030	−	0.647248i	0.316754	−	0.948508i	$-0.397407\pi$
$587$	745.664	−	379.935i	1.27030	−	0.647248i	0.953542	+	0.301259i	$0.0974070\pi$
$588$		0			0
$589$	7.96633	−	2.58842i	0.0135252	−	0.00439460i
$590$		0			0
$591$	−107.328	+	330.321i	−0.181604	+	0.558918i
$592$		0			0
$593$	584.072	−	584.072i	0.984944	−	0.984944i	−0.0149445	−	0.999888i	$-0.504757\pi$
$593$	584.072	−	584.072i	0.984944	−	0.984944i	0.999888	+	0.0149445i	$0.00475715\pi$
$594$		0			0
$595$	−27.4125	+	29.6167i	−0.0460714	+	0.0497759i
$596$		0			0
$597$	436.458	+	69.1282i	0.731086	+	0.115793i
$598$		0			0
$599$		−	988.360i		−	1.65002i	−0.565121	−	0.825008i	$-0.691170\pi$
$599$		−	988.360i		−	1.65002i	0.565121	−	0.825008i	$-0.308830\pi$
$600$		0			0
$601$	−333.263			−0.554514			−0.277257	−	0.960796i	$-0.589425\pi$
$601$	−333.263			−0.554514			−0.277257	+	0.960796i	$0.589425\pi$
$602$		0			0
$603$	37.1191	−	234.361i	0.0615573	−	0.388658i
$604$		0			0
$605$	447.219	−	250.079i	0.739205	−	0.413354i
$606$		0			0
$607$	65.4271	+	65.4271i	0.107788	+	0.107788i	0.758944	−	0.651156i	$-0.225716\pi$
$607$	65.4271	+	65.4271i	0.107788	+	0.107788i	−0.651156	+	0.758944i	$0.725716\pi$
$608$		0			0
$609$	13.7195	+	4.45774i	0.0225279	+	0.00731977i
$610$		0			0
$611$	218.714	+	673.134i	0.357962	+	1.10169i
$612$		0			0
$613$	522.114	+	1024.71i	0.851736	+	1.67163i	0.734589	+	0.678512i	$0.237375\pi$
$613$	522.114	+	1024.71i	0.851736	+	1.67163i	0.117148	+	0.993115i	$0.462625\pi$
$614$		0			0
$615$	−513.505	−	343.588i	−0.834968	−	0.558680i
$616$		0			0
$617$	110.881	+	700.076i	0.179710	+	1.13465i	0.898356	+	0.439269i	$0.144762\pi$
$617$	110.881	+	700.076i	0.179710	+	1.13465i	−0.718646	+	0.695377i	$0.755238\pi$
$618$		0			0
$619$	245.253	−	337.562i	0.396209	−	0.545335i	−0.563579	−	0.826062i	$-0.690576\pi$
$619$	245.253	−	337.562i	0.396209	−	0.545335i	0.959787	+	0.280728i	$0.0905758\pi$
$620$		0			0
$621$	−290.518	+	211.073i	−0.467822	+	0.339893i
$622$		0			0
$623$	−57.2651	−	29.1780i	−0.0919183	−	0.0468347i
$624$		0			0
$625$	556.152	+	285.167i	0.889843	+	0.456268i
$626$		0			0
$627$	28.9288	−	56.7760i	0.0461384	−	0.0905518i
$628$		0			0
$629$	−80.9326	−	111.394i	−0.128669	−	0.177097i
$630$		0			0
$631$	−80.9290	−	58.7983i	−0.128255	−	0.0931828i	0.521808	−	0.853063i	$-0.325258\pi$
$631$	−80.9290	−	58.7983i	−0.128255	−	0.0931828i	−0.650063	+	0.759880i	$0.725258\pi$
$632$		0			0
$633$	199.215	−	31.5525i	0.314715	−	0.0498460i
$634$		0			0
$635$	−127.411	+	190.420i	−0.200647	+	0.299874i
$636$		0			0
$637$	484.206	−	246.715i	0.760135	−	0.387308i
$638$		0			0
$639$	−117.624	+	38.2183i	−0.184075	+	0.0598095i
$640$		0			0
$641$	206.921	−	636.836i	0.322809	−	0.993504i	−0.649611	−	0.760267i	$-0.725068\pi$
$641$	206.921	−	636.836i	0.322809	−	0.993504i	0.972420	−	0.233237i	$-0.0749319\pi$
$642$		0			0
$643$	808.516	−	808.516i	1.25741	−	1.25741i	0.305088	−	0.952324i	$-0.401314\pi$
$643$	808.516	−	808.516i	1.25741	−	1.25741i	0.952324	−	0.305088i	$-0.0986858\pi$
$644$		0			0
$645$	155.513	+	278.105i	0.241105	+	0.431170i
$646$		0			0
$647$	1006.44	+	159.404i	1.55554	+	0.246374i	0.874191	−	0.485583i	$-0.161392\pi$
$647$	1006.44	+	159.404i	1.55554	+	0.246374i	0.681352	+	0.731956i	$0.261392\pi$
$648$		0			0
$649$			213.250i			0.328582i
$650$		0			0
$651$	1.76254			0.00270743
$652$		0			0
$653$	138.349	−	873.504i	0.211868	−	1.33768i	−0.620828	−	0.783947i	$-0.713203\pi$
$653$	138.349	−	873.504i	0.211868	−	1.33768i	0.832695	−	0.553732i	$-0.186797\pi$
$654$		0			0
$655$	−886.520	−	820.543i	−1.35347	−	1.25274i
$656$		0			0
$657$	−12.4737	−	12.4737i	−0.0189859	−	0.0189859i
$658$		0			0
$659$	901.530	+	292.925i	1.36803	+	0.444499i	0.898715	−	0.438533i	$-0.144502\pi$
$659$	901.530	+	292.925i	1.36803	+	0.444499i	0.469312	+	0.883032i	$0.344502\pi$
$660$		0			0
$661$	70.3569	+	216.536i	0.106440	+	0.327589i	0.990066	−	0.140605i	$-0.0449048\pi$
$661$	70.3569	+	216.536i	0.106440	+	0.327589i	−0.883626	+	0.468194i	$0.844905\pi$
$662$		0			0
$663$	92.4193	+	181.383i	0.139396	+	0.273579i
$664$		0			0
$665$	33.0186	−	1.27616i	0.0496521	−	0.00191904i
$666$		0			0
$667$	−18.1289	−	114.461i	−0.0271797	−	0.171606i
$668$		0			0
$669$	405.146	−	557.636i	0.605600	−	0.833536i
$670$		0			0
$671$	300.939	−	218.645i	0.448493	−	0.325850i
$672$		0			0
$673$	480.264	+	244.707i	0.713616	+	0.363606i	0.772807	−	0.634641i	$-0.218852\pi$
$673$	480.264	+	244.707i	0.713616	+	0.363606i	−0.0591908	+	0.998247i	$0.518852\pi$
$674$		0			0
$675$	445.862	−	520.688i	0.660536	−	0.771389i
$676$		0			0
$677$	−535.059	+	1050.11i	−0.790338	+	1.55113i	0.0434596	+	0.999055i	$0.486162\pi$
$677$	−535.059	+	1050.11i	−0.790338	+	1.55113i	−0.833798	+	0.552070i	$0.813838\pi$
$678$		0			0
$679$	−45.8261	−	63.0743i	−0.0674906	−	0.0928929i
$680$		0			0
$681$	194.285	+	141.156i	0.285293	+	0.207278i
$682$		0			0
$683$	−333.706	+	52.8539i	−0.488589	+	0.0773849i	−0.395868	−	0.918307i	$-0.629556\pi$
$683$	−333.706	+	52.8539i	−0.488589	+	0.0773849i	−0.0927206	+	0.995692i	$0.529556\pi$
$684$		0			0
$685$	−866.969	+	319.212i	−1.26565	+	0.466003i
$686$		0			0
$687$	498.027	−	253.758i	0.724931	−	0.369371i
$688$		0			0
$689$	−1.10767	+	0.359902i	−0.00160764	+	0.000522355i
$690$		0			0
$691$	−155.073	+	477.266i	−0.224418	+	0.690689i	0.773932	+	0.633269i	$0.218287\pi$
$691$	−155.073	+	477.266i	−0.224418	+	0.690689i	−0.998350	+	0.0574198i	$0.981713\pi$
$692$		0			0
$693$	−13.8818	+	13.8818i	−0.0200315	+	0.0200315i
$694$		0			0
$695$	−24.6727	+	4.89131i	−0.0355003	+	0.00703786i
$696$		0			0
$697$	604.265	+	95.7062i	0.866952	+	0.137312i
$698$		0			0
$699$		−	58.7323i		−	0.0840233i
$700$		0			0
$701$	1315.64			1.87681			0.938403	−	0.345544i	$-0.112306\pi$
$701$	1315.64			1.87681			0.938403	+	0.345544i	$0.112306\pi$
$702$		0			0
$703$	−17.6366	+	111.353i	−0.0250876	+	0.158397i
$704$		0			0
$705$	251.862	−	545.414i	0.357251	−	0.773637i
$706$		0			0
$707$	−22.8380	−	22.8380i	−0.0323026	−	0.0323026i
$708$		0			0
$709$	−221.223	−	71.8796i	−0.312020	−	0.101382i	0.148821	−	0.988864i	$-0.452452\pi$
$709$	−221.223	−	71.8796i	−0.312020	−	0.101382i	−0.460841	+	0.887483i	$0.652452\pi$
$710$		0			0
$711$	233.907	+	719.893i	0.328984	+	1.01251i
$712$		0			0
$713$	−6.42822	−	12.6161i	−0.00901573	−	0.0176944i
$714$		0			0
$715$	−190.338	+	149.853i	−0.266207	+	0.209585i
$716$		0			0
$717$	50.8721	+	321.194i	0.0709513	+	0.447969i
$718$		0			0
$719$	−115.268	+	158.652i	−0.160317	+	0.220657i	−0.881617	−	0.471965i	$-0.843545\pi$
$719$	−115.268	+	158.652i	−0.160317	+	0.220657i	0.721300	+	0.692622i	$0.243545\pi$
$720$		0			0
$721$	−123.585	+	89.7897i	−0.171408	+	0.124535i
$722$		0			0
$723$	−713.018	−	363.301i	−0.986194	−	0.502491i
$724$		0			0
$725$	84.3969	+	204.491i	0.116410	+	0.282057i
$726$		0			0
$727$	193.526	−	379.816i	0.266198	−	0.522443i	−0.718755	−	0.695263i	$-0.755288\pi$
$727$	193.526	−	379.816i	0.266198	−	0.522443i	0.984953	+	0.172820i	$0.0552879\pi$
$728$		0			0
$729$	−290.646	−	400.040i	−0.398692	−	0.548752i
$730$		0			0
$731$	−255.253	−	185.452i	−0.349183	−	0.253697i
$732$		0			0
$733$	1120.54	−	177.477i	1.52871	−	0.242124i	0.665280	−	0.746594i	$-0.268312\pi$
$733$	1120.54	−	177.477i	1.52871	−	0.242124i	0.863429	+	0.504470i	$0.168312\pi$
$734$		0			0
$735$	−443.871	−	125.491i	−0.603906	−	0.170736i
$736$		0			0
$737$	170.147	−	86.6940i	0.230864	−	0.117631i
$738$		0			0
$739$	423.395	−	137.569i	0.572929	−	0.186156i	−0.00820139	−	0.999966i	$-0.502611\pi$
$739$	423.395	−	137.569i	0.572929	−	0.186156i	0.581130	+	0.813810i	$0.302611\pi$
$740$		0			0
$741$	51.5081	−	158.526i	0.0695116	−	0.213935i
$742$		0			0
$743$	−368.179	+	368.179i	−0.495531	+	0.495531i	−0.910044	−	0.414513i	$-0.863952\pi$
$743$	−368.179	+	368.179i	−0.495531	+	0.495531i	0.414513	+	0.910044i	$0.363952\pi$
$744$		0			0
$745$	−91.9987	+	773.058i	−0.123488	+	1.03766i
$746$		0			0
$747$	−681.991	−	108.017i	−0.912973	−	0.144601i
$748$		0			0
$749$		−	164.555i		−	0.219700i
$750$		0			0
$751$	847.804			1.12890			0.564450	−	0.825467i	$-0.309088\pi$
$751$	847.804			1.12890			0.564450	+	0.825467i	$0.309088\pi$
$752$		0			0
$753$	53.2955	−	336.495i	0.0707776	−	0.446872i
$754$		0			0
$755$	798.795	+	95.0615i	1.05801	+	0.125909i
$756$		0			0
$757$	105.651	+	105.651i	0.139566	+	0.139566i	0.773438	−	0.633872i	$-0.218535\pi$
$757$	105.651	+	105.651i	0.139566	+	0.139566i	−0.633872	+	0.773438i	$0.718535\pi$
$758$		0			0
$759$	−102.443	−	33.2857i	−0.134971	−	0.0438547i
$760$		0			0
$761$	397.446	+	1223.21i	0.522268	+	1.60738i	0.769655	+	0.638460i	$0.220428\pi$
$761$	397.446	+	1223.21i	0.522268	+	1.60738i	−0.247387	+	0.968917i	$0.579572\pi$
$762$		0			0
$763$	−34.7882	−	68.2756i	−0.0455939	−	0.0894831i
$764$		0			0
$765$	−68.8289	+	243.453i	−0.0899724	+	0.318239i
$766$		0			0
$767$	87.2630	+	550.957i	0.113772	+	0.718327i
$768$		0			0
$769$	−455.111	+	626.407i	−0.591822	+	0.814574i	−0.994929	−	0.100579i	$-0.967930\pi$
$769$	−455.111	+	626.407i	−0.591822	+	0.814574i	0.403107	+	0.915153i	$0.367930\pi$
$770$		0			0
$771$	−696.224	+	505.836i	−0.903014	+	0.656078i
$772$		0			0
$773$	297.437	+	151.552i	0.384782	+	0.196056i	0.635672	−	0.771959i	$-0.280723\pi$
$773$	297.437	+	151.552i	0.384782	+	0.196056i	−0.250890	+	0.968016i	$0.580723\pi$
$774$		0			0
$775$	17.5279	+	20.5757i	0.0226166	+	0.0265493i
$776$		0			0
$777$	−10.7700	+	21.1373i	−0.0138610	+	0.0272037i
$778$		0			0
$779$	−294.445	−	405.268i	−0.377978	−	0.520242i
$780$		0			0
$781$	−80.5238	−	58.5040i	−0.103103	−	0.0749090i
$782$		0			0
$783$	239.650	−	37.9568i	0.306066	−	0.0484761i
$784$		0			0
$785$	−277.389	−	352.330i	−0.353362	−	0.448828i
$786$		0			0
$787$	229.238	−	116.803i	0.291281	−	0.148415i	−0.302244	−	0.953231i	$-0.597736\pi$
$787$	229.238	−	116.803i	0.291281	−	0.148415i	0.593525	+	0.804816i	$0.297736\pi$
$788$		0			0
$789$	83.8615	−	27.2482i	0.106288	−	0.0345352i
$790$		0			0
$791$	−18.3675	+	56.5294i	−0.0232206	+	0.0714657i
$792$		0			0
$793$	688.043	−	688.043i	0.867645	−	0.867645i
$794$		0			0
$795$	0.897498	+	0.414448i	0.00112893	+	0.000521318i
$796$		0			0
$797$	−688.874	−	109.107i	−0.864334	−	0.136897i	−0.291502	−	0.956570i	$-0.594155\pi$
$797$	−688.874	−	109.107i	−0.864334	−	0.136897i	−0.572832	+	0.819673i	$0.694155\pi$
$798$		0			0
$799$			594.872i			0.744521i
$800$		0			0
$801$	−402.918			−0.503018
$802$		0			0
$803$	2.22086	−	14.0219i	0.00276570	−	0.0174619i
$804$		0			0
$805$	−10.8621	−	54.7903i	−0.0134932	−	0.0680625i
$806$		0			0
$807$	21.4731	+	21.4731i	0.0266085	+	0.0266085i
$808$		0			0
$809$	−589.196	−	191.441i	−0.728301	−	0.236639i	−0.0786826	−	0.996900i	$-0.525071\pi$
$809$	−589.196	−	191.441i	−0.728301	−	0.236639i	−0.649619	+	0.760260i	$0.725071\pi$
$810$		0			0
$811$	292.300	+	899.606i	0.360419	+	1.10925i	0.952800	+	0.303597i	$0.0981878\pi$
$811$	292.300	+	899.606i	0.360419	+	1.10925i	−0.592382	+	0.805658i	$0.701812\pi$
$812$		0			0
$813$	−381.964	−	749.647i	−0.469821	−	0.922075i
$814$		0			0
$815$	−193.710	−	526.109i	−0.237681	−	0.645532i
$816$		0			0
$817$	40.4132	+	255.159i	0.0494653	+	0.312312i
$818$		0			0
$819$	−30.1849	+	41.5460i	−0.0368558	+	0.0507277i
$820$		0			0
$821$	−81.8277	+	59.4513i	−0.0996683	+	0.0724133i	−0.636503	−	0.771274i	$-0.719620\pi$
$821$	−81.8277	+	59.4513i	−0.0996683	+	0.0724133i	0.536835	+	0.843687i	$0.319620\pi$
$822$		0			0
$823$	931.854	+	474.803i	1.13226	+	0.576918i	0.916702	−	0.399572i	$-0.130841\pi$
$823$	931.854	+	474.803i	1.13226	+	0.576918i	0.215563	+	0.976490i	$0.430841\pi$
$824$		0			0
$825$	204.966	+	16.3949i	0.248444	+	0.0198726i
$826$		0			0
$827$	−380.730	+	747.224i	−0.460375	+	0.903536i	0.537796	+	0.843075i	$0.319257\pi$
$827$	−380.730	+	747.224i	−0.460375	+	0.903536i	−0.998171	+	0.0604611i	$0.980743\pi$
$828$		0			0
$829$	−705.081	−	970.460i	−0.850520	−	1.17064i	−0.983748	−	0.179554i	$-0.942534\pi$
$829$	−705.081	−	970.460i	−0.850520	−	1.17064i	0.133228	−	0.991085i	$-0.457466\pi$
$830$		0			0
$831$	−37.9587	−	27.5786i	−0.0456784	−	0.0331873i
$832$		0			0
$833$	451.126	−	71.4513i	0.541568	−	0.0857759i
$834$		0			0
$835$	−17.7592	−	459.490i	−0.0212685	−	0.550287i
$836$		0			0
$837$	26.4146	−	13.4589i	0.0315586	−	0.0160799i
$838$		0			0
$839$	847.426	−	275.346i	1.01004	−	0.328183i	0.243172	−	0.969983i	$-0.421812\pi$
$839$	847.426	−	275.346i	1.01004	−	0.328183i	0.766872	+	0.641800i	$0.221812\pi$
$840$		0			0
$841$	235.686	−	725.368i	0.280245	−	0.862506i
$842$		0			0
$843$	631.017	−	631.017i	0.748538	−	0.748538i
$844$		0			0
$845$	143.542	−	155.083i	0.169872	−	0.183531i
$846$		0			0
$847$	86.3392	+	13.6748i	0.101935	+	0.0161450i
$848$		0			0
$849$		−	486.914i		−	0.573515i
$850$		0			0
$851$	190.578			0.223946
$852$		0			0
$853$	−127.510	+	805.066i	−0.149484	+	0.943806i	0.792919	+	0.609327i	$0.208560\pi$
$853$	−127.510	+	805.066i	−0.149484	+	0.943806i	−0.942403	+	0.334479i	$0.891440\pi$
$854$		0			0
$855$	180.804	−	101.104i	0.211467	−	0.118250i
$856$		0			0
$857$	−427.423	−	427.423i	−0.498743	−	0.498743i	0.412303	−	0.911047i	$-0.364724\pi$
$857$	−427.423	−	427.423i	−0.498743	−	0.498743i	−0.911047	+	0.412303i	$0.864724\pi$
$858$		0			0
$859$	−284.058	−	92.2962i	−0.330685	−	0.107446i	0.138969	−	0.990297i	$-0.455621\pi$
$859$	−284.058	−	92.2962i	−0.330685	−	0.107446i	−0.469654	+	0.882851i	$0.655621\pi$
$860$		0			0
$861$	−32.5727	−	100.248i	−0.0378312	−	0.116432i
$862$		0			0
$863$	225.729	+	443.018i	0.261563	+	0.513347i	0.984017	−	0.178072i	$-0.0569860\pi$
$863$	225.729	+	443.018i	0.261563	+	0.513347i	−0.722454	+	0.691419i	$0.756986\pi$
$864$		0			0
$865$	−755.646	−	505.606i	−0.873579	−	0.584515i
$866$		0			0
$867$	−59.6348	−	376.520i	−0.0687830	−	0.434279i
$868$		0			0
$869$	−358.062	+	492.830i	−0.412039	+	0.567123i
$870$		0			0
$871$	404.119	−	293.610i	0.463972	−	0.337095i
$872$		0			0
$873$	−435.494	−	221.895i	−0.498848	−	0.254176i
$874$		0			0
$875$	44.4546	+	96.9179i	0.0508052	+	0.110763i
$876$		0			0
$877$	118.321	−	232.218i	0.134916	−	0.264787i	−0.813658	−	0.581344i	$-0.802527\pi$
$877$	118.321	−	232.218i	0.134916	−	0.264787i	0.948573	+	0.316558i	$0.102527\pi$
$878$		0			0
$879$	296.429	+	407.999i	0.337234	+	0.464163i
$880$		0			0
$881$	111.415	+	80.9479i	0.126464	+	0.0918818i	0.649219	−	0.760601i	$-0.275096\pi$
$881$	111.415	+	80.9479i	0.126464	+	0.0918818i	−0.522755	+	0.852483i	$0.675096\pi$
$882$		0			0
$883$	386.249	−	61.1758i	0.437428	−	0.0692818i	0.0661631	−	0.997809i	$-0.478924\pi$
$883$	386.249	−	61.1758i	0.437428	−	0.0692818i	0.371265	+	0.928527i	$0.378924\pi$
$884$		0			0
$885$	263.304	−	393.517i	0.297518	−	0.444652i
$886$		0			0
$887$	891.156	−	454.067i	1.00469	−	0.511913i	0.127384	−	0.991853i	$-0.459342\pi$
$887$	891.156	−	454.067i	1.00469	−	0.511913i	0.877301	+	0.479941i	$0.159342\pi$
$888$		0			0
$889$	−37.1745	+	12.0787i	−0.0418161	+	0.0135869i
$890$		0			0
$891$	5.68354	−	17.4921i	0.00637883	−	0.0196320i
$892$		0			0
$893$	344.418	−	344.418i	0.385686	−	0.385686i
$894$		0			0
$895$	219.144	+	391.897i	0.244854	+	0.437874i
$896$		0			0
$897$	−278.295	−	44.0775i	−0.310250	−	0.0491388i
$898$		0			0
$899$			9.56722i			0.0106421i
$900$		0			0
$901$	−0.978883			−0.00108644
$902$		0			0
$903$	−8.50372	+	53.6904i	−0.00941719	+	0.0594578i
$904$		0			0
$905$	205.867	+	190.546i	0.227477	+	0.210548i
$906$		0			0
$907$	−982.239	−	982.239i	−1.08295	−	1.08295i	−0.996233	−	0.0867208i	$-0.972361\pi$
$907$	−982.239	−	982.239i	−1.08295	−	1.08295i	−0.0867208	−	0.996233i	$-0.527639\pi$
$908$		0			0
$909$	−192.569	−	62.5694i	−0.211847	−	0.0688332i
$910$		0			0
$911$	1.27279	+	3.91723i	0.00139713	+	0.00429992i	0.951753	−	0.306866i	$-0.0992804\pi$
$911$	1.27279	+	3.91723i	0.00139713	+	0.00429992i	−0.950356	+	0.311166i	$0.899280\pi$
$912$		0			0
$913$	−252.280	−	495.128i	−0.276320	−	0.542309i
$914$		0			0
$915$	−825.299	+	31.8976i	−0.901966	+	0.0348608i
$916$		0			0
$917$	−32.2387	−	203.547i	−0.0351567	−	0.221971i
$918$		0			0
$919$	−851.191	+	1171.56i	−0.926214	+	1.27482i	0.0351036	+	0.999384i	$0.488824\pi$
$919$	−851.191	+	1171.56i	−0.926214	+	1.27482i	−0.961318	+	0.275441i	$0.911176\pi$
$920$		0			0
$921$	−618.660	+	449.483i	−0.671727	+	0.488038i
$922$		0			0
$923$	−231.983	−	118.201i	−0.251336	−	0.128062i
$924$		0			0
$925$	−353.859	+	84.4756i	−0.382550	+	0.0913249i
$926$		0			0
$927$	−434.772	+	853.288i	−0.469010	+	0.920484i
$928$		0			0
$929$	543.202	+	747.654i	0.584717	+	0.804794i	0.994203	−	0.107522i	$-0.0342917\pi$
$929$	543.202	+	747.654i	0.584717	+	0.804794i	−0.409485	+	0.912317i	$0.634292\pi$
$930$		0			0
$931$	−302.561	−	219.823i	−0.324985	−	0.236115i
$932$		0			0
$933$	−927.297	+	146.869i	−0.993887	+	0.157416i
$934$		0			0
$935$	−191.066	+	70.3494i	−0.204349	+	0.0752400i
$936$		0			0
$937$	1426.21	−	726.689i	1.52210	−	0.775548i	0.524960	−	0.851127i	$-0.324080\pi$
$937$	1426.21	−	726.689i	1.52210	−	0.775548i	0.997140	+	0.0755786i	$0.0240804\pi$
$938$		0			0
$939$	293.010	−	95.2046i	0.312044	−	0.101389i
$940$		0			0
$941$	−386.822	+	1190.52i	−0.411075	+	1.26516i	0.504639	+	0.863330i	$0.331626\pi$
$941$	−386.822	+	1190.52i	−0.411075	+	1.26516i	−0.915715	+	0.401829i	$0.868374\pi$
$942$		0			0
$943$	−598.772	+	598.772i	−0.634965	+	0.634965i
$944$		0			0
$945$	114.716	−	22.7421i	0.121392	−	0.0240657i
$946$		0			0
$947$	−106.051	−	16.7968i	−0.111986	−	0.0177368i	0.100190	−	0.994968i	$-0.468055\pi$
$947$	−106.051	−	16.7968i	−0.111986	−	0.0177368i	−0.212176	+	0.977232i	$0.568055\pi$
$948$		0			0
$949$		−	37.1362i		−	0.0391320i
$950$		0			0
$951$	141.464			0.148753
$952$		0			0
$953$	63.7764	−	402.669i	0.0669218	−	0.422527i	−0.931369	−	0.364078i	$-0.881384\pi$
$953$	63.7764	−	402.669i	0.0669218	−	0.422527i	0.998290	−	0.0584497i	$-0.0186157\pi$
$954$		0			0
$955$	179.066	−	387.773i	0.187504	−	0.406045i
$956$		0			0
$957$	51.4638	+	51.4638i	0.0537762	+	0.0537762i
$958$		0			0
$959$	−149.900	−	48.7056i	−0.156309	−	0.0507879i
$960$		0			0
$961$	−296.604	−	912.854i	−0.308641	−	0.949900i
$962$		0			0
$963$	−468.345	−	919.178i	−0.486339	−	0.954494i
$964$		0			0
$965$	−733.352	+	577.368i	−0.759951	+	0.598309i
$966$		0			0
$967$	119.989	+	757.581i	0.124084	+	0.783434i	0.968732	+	0.248111i	$0.0798099\pi$
$967$	119.989	+	757.581i	0.124084	+	0.783434i	−0.844648	+	0.535322i	$0.820190\pi$
$968$		0			0
$969$	82.3456	−	113.339i	0.0849799	−	0.116965i
$970$		0			0
$971$	−1183.95	+	860.190i	−1.21931	+	0.885880i	−0.996043	−	0.0888772i	$-0.971672\pi$
$971$	−1183.95	+	860.190i	−1.21931	+	0.885880i	−0.223267	+	0.974757i	$0.571672\pi$
$972$		0			0
$973$	−3.82345	−	1.94815i	−0.00392955	−	0.00200221i
$974$		0			0
$975$	536.265	−	41.5150i	0.550015	−	0.0425795i
$976$		0			0
$977$	−170.227	+	334.090i	−0.174235	+	0.341955i	−0.961565	−	0.274576i	$-0.911462\pi$
$977$	−170.227	+	334.090i	−0.174235	+	0.341955i	0.787331	+	0.616531i	$0.211462\pi$
$978$		0			0
$979$	−190.596	−	262.332i	−0.194684	−	0.267959i
$980$		0			0
$981$	−388.641	−	282.365i	−0.396169	−	0.287833i
$982$		0			0
$983$	−638.687	+	101.158i	−0.649732	+	0.102907i	−0.472597	−	0.881279i	$-0.656683\pi$
$983$	−638.687	+	101.158i	−0.649732	+	0.102907i	−0.177136	+	0.984186i	$0.556683\pi$
$984$		0			0
$985$	−874.412	−	247.213i	−0.887728	−	0.250978i
$986$		0			0
$987$	91.3204	−	46.5300i	0.0925232	−	0.0471429i
$988$		0			0
$989$	415.325	−	134.947i	0.419945	−	0.136448i
$990$		0			0
$991$	473.302	−	1456.67i	0.477600	−	1.46990i	−0.364818	−	0.931079i	$-0.618869\pi$
$991$	473.302	−	1456.67i	0.477600	−	1.46990i	0.842419	−	0.538824i	$-0.181131\pi$
$992$		0			0
$993$	−826.695	+	826.695i	−0.832523	+	0.832523i
$994$		0			0
$995$	−136.623	+	1148.03i	−0.137309	+	1.15380i
$996$		0			0
$997$	−1057.47	−	167.487i	−1.06065	−	0.167991i	−0.398354	−	0.917232i	$-0.630418\pi$
$997$	−1057.47	−	167.487i	−1.06065	−	0.167991i	−0.662297	+	0.749241i	$0.730418\pi$
$998$		0			0
$999$			399.018i			0.399417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.17.6		64
4.3	odd	2		200.3.u.b.17.3	✓	64
25.3	odd	20	inner	400.3.bg.f.353.6		64
100.3	even	20		200.3.u.b.153.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.17.3	✓	64	4.3	odd	2
200.3.u.b.153.3	yes	64	100.3	even	20
400.3.bg.f.17.6		64	1.1	even	1	trivial
400.3.bg.f.353.6		64	25.3	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.298963 - 1.88758i) q^{3} +(4.96497 + 0.590862i) q^{5} +(0.603173 + 0.603173i) q^{7} +(5.08593 + 1.65252i) q^{9} +O(q^{10})\)	\(q+(0.298963 - 1.88758i) q^{3} +(4.96497 + 0.590862i) q^{5} +(0.603173 + 0.603173i) q^{7} +(5.08593 + 1.65252i) q^{9} +(1.32991 + 4.09306i) q^{11} +(5.11090 + 10.0307i) q^{13} +(2.59964 - 9.19513i) q^{15} +(1.48017 + 9.34543i) q^{17} +(4.55381 - 6.26779i) q^{19} +(1.31886 - 0.958211i) q^{21} +(-11.6689 - 5.94559i) q^{23} +(24.3018 + 5.86721i) q^{25} +(12.4484 - 24.4314i) q^{27} +(5.20126 + 7.15892i) q^{29} +(0.874688 + 0.635498i) q^{31} +(8.12357 - 1.28665i) q^{33} +(2.63834 + 3.35112i) q^{35} +(-12.9660 + 6.60651i) q^{37} +(20.4618 - 6.64843i) q^{39} +(19.9807 - 61.4943i) q^{41} +(-23.5787 + 23.5787i) q^{43} +(24.2750 + 11.2098i) q^{45} +(62.0961 + 9.83505i) q^{47} -48.2724i q^{49} +18.0828 q^{51} +(-0.0161839 + 0.102181i) q^{53} +(4.18455 + 21.1077i) q^{55} +(-10.4695 - 10.4695i) q^{57} +(47.1252 + 15.3119i) q^{59} +(-26.7093 - 82.2027i) q^{61} +(2.07094 + 4.06445i) q^{63} +(19.4487 + 52.8220i) q^{65} +(-6.94118 - 43.8249i) q^{67} +(-14.7114 + 20.2484i) q^{69} +(-18.7104 + 13.5939i) q^{71} +(-2.93919 - 1.49759i) q^{73} +(18.3402 - 44.1175i) q^{75} +(-1.66665 + 3.27099i) q^{77} +(83.1987 + 114.513i) q^{79} +(-3.45743 - 2.51197i) q^{81} +(-127.531 + 20.1989i) q^{83} +(1.82714 + 47.2743i) q^{85} +(15.0680 - 7.67755i) q^{87} +(-71.6570 + 23.2828i) q^{89} +(-2.96750 + 9.13301i) q^{91} +(1.46105 - 1.46105i) q^{93} +(26.3129 - 28.4287i) q^{95} +(-90.2730 - 14.2978i) q^{97} +23.0147i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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