LMFDB - Embedded newform 912.3.be.g.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.520060207104.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 44x^{6} + 664x^{4} - 3528x^{2} + 8100 $ x^8 - 44x^6 + 664x^4 - 3528*x^2 + 8100
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$4.34148 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.g.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(3.03409 + 5.25521i) q^{5} +2.33275 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(3.03409 + 5.25521i) q^{5} +2.33275 q^{7} +(1.50000 - 2.59808i) q^{9} -12.7512 q^{11} +(7.42129 + 4.28468i) q^{13} +(-9.10228 - 5.25521i) q^{15} +(11.9982 + 20.7815i) q^{17} +(18.0402 - 5.96259i) q^{19} +(-3.49913 + 2.02022i) q^{21} +(-8.34061 + 14.4464i) q^{23} +(-5.91146 + 10.2390i) q^{25} +5.19615i q^{27} +(-15.3502 - 8.86245i) q^{29} +29.5265i q^{31} +(19.1267 - 11.0428i) q^{33} +(7.07779 + 12.2591i) q^{35} -25.8670i q^{37} -14.8426 q^{39} +(-28.6462 + 16.5389i) q^{41} +(30.3762 + 52.6131i) q^{43} +18.2046 q^{45} +(1.46918 - 2.54469i) q^{47} -43.5583 q^{49} +(-35.9946 - 20.7815i) q^{51} +(-40.1937 - 23.2058i) q^{53} +(-38.6882 - 67.0099i) q^{55} +(-21.8965 + 24.5671i) q^{57} +(93.0601 - 53.7283i) q^{59} +(21.4370 - 37.1300i) q^{61} +(3.49913 - 6.06067i) q^{63} +52.0006i q^{65} +(-3.21307 - 1.85507i) q^{67} -28.8927i q^{69} +(-95.4988 + 55.1362i) q^{71} +(53.3048 + 92.3265i) q^{73} -20.4779i q^{75} -29.7453 q^{77} +(-105.269 + 60.7773i) q^{79} +(-4.50000 - 7.79423i) q^{81} -112.963 q^{83} +(-72.8074 + 126.106i) q^{85} +30.7004 q^{87} +(-119.192 - 68.8154i) q^{89} +(17.3120 + 9.99511i) q^{91} +(-25.5707 - 44.2898i) q^{93} +(86.0702 + 76.7137i) q^{95} +(29.4189 - 16.9850i) q^{97} +(-19.1267 + 33.1285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9	$ 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9} + 8 q^{11} + 24 q^{13} - 12 q^{15} - 20 q^{17} - 24 q^{19} - 36 q^{21} - 40 q^{23} - 88 q^{25} - 48 q^{29} - 12 q^{33} - 32 q^{35} - 48 q^{39} + 60 q^{41} + 116 q^{43} + 24 q^{45} + 68 q^{47} - 120 q^{49} + 60 q^{51} - 168 q^{53} - 232 q^{55} + 84 q^{57} + 156 q^{59} + 72 q^{61} + 36 q^{63} + 108 q^{67} - 444 q^{71} - 68 q^{73} + 296 q^{77} - 420 q^{79} - 36 q^{81} - 424 q^{83} + 40 q^{85} + 96 q^{87} - 420 q^{89} + 228 q^{91} + 84 q^{93} + 272 q^{95} + 156 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9 + 8 * q^11 + 24 * q^13 - 12 * q^15 - 20 * q^17 - 24 * q^19 - 36 * q^21 - 40 * q^23 - 88 * q^25 - 48 * q^29 - 12 * q^33 - 32 * q^35 - 48 * q^39 + 60 * q^41 + 116 * q^43 + 24 * q^45 + 68 * q^47 - 120 * q^49 + 60 * q^51 - 168 * q^53 - 232 * q^55 + 84 * q^57 + 156 * q^59 + 72 * q^61 + 36 * q^63 + 108 * q^67 - 444 * q^71 - 68 * q^73 + 296 * q^77 - 420 * q^79 - 36 * q^81 - 424 * q^83 + 40 * q^85 + 96 * q^87 - 420 * q^89 + 228 * q^91 + 84 * q^93 + 272 * q^95 + 156 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	3.03409	+	5.25521i	0.606819	+	1.05104i	0.991761	+	0.128101i	$0.0408880\pi$
$5$	3.03409	+	5.25521i	0.606819	+	1.05104i	−0.384942	+	0.922941i	$0.625779\pi$
$6$		0			0
$7$	2.33275			0.333250			0.166625	−	0.986020i	$-0.446713\pi$
$7$	2.33275			0.333250			0.166625	+	0.986020i	$0.446713\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−12.7512			−1.15920			−0.579598	−	0.814903i	$-0.696790\pi$
$11$	−12.7512			−1.15920			−0.579598	+	0.814903i	$0.696790\pi$
$12$		0			0
$13$	7.42129	+	4.28468i	0.570869	+	0.329591i	0.757496	−	0.652840i	$-0.226422\pi$
$13$	7.42129	+	4.28468i	0.570869	+	0.329591i	−0.186628	+	0.982431i	$0.559756\pi$
$14$		0			0
$15$	−9.10228	−	5.25521i	−0.606819	−	0.350347i
$16$		0			0
$17$	11.9982	+	20.7815i	0.705777	+	1.22244i	0.966410	+	0.257004i	$0.0827353\pi$
$17$	11.9982	+	20.7815i	0.705777	+	1.22244i	−0.260633	+	0.965438i	$0.583931\pi$
$18$		0			0
$19$	18.0402	−	5.96259i	0.949482	−	0.313821i
$19$	18.0402	−	5.96259i	0.949482	−	0.313821i
$20$		0			0
$21$	−3.49913	+	2.02022i	−0.166625	+	0.0962011i
$22$		0			0
$23$	−8.34061	+	14.4464i	−0.362635	+	0.628103i	−0.988394	−	0.151914i	$-0.951456\pi$
$23$	−8.34061	+	14.4464i	−0.362635	+	0.628103i	0.625758	+	0.780017i	$0.284790\pi$
$24$		0			0
$25$	−5.91146	+	10.2390i	−0.236458	+	0.409558i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−15.3502	−	8.86245i	−0.529318	−	0.305602i	0.211421	−	0.977395i	$-0.432191\pi$
$29$	−15.3502	−	8.86245i	−0.529318	−	0.305602i	−0.740739	+	0.671793i	$0.765524\pi$
$30$		0			0
$31$			29.5265i			0.952469i	0.879318	+	0.476234i	$0.157999\pi$
$31$			29.5265i			0.952469i	−0.879318	+	0.476234i	$0.842001\pi$
$32$		0			0
$33$	19.1267	−	11.0428i	0.579598	−	0.334631i
$34$		0			0
$35$	7.07779	+	12.2591i	0.202223	+	0.350260i
$36$		0			0
$37$		−	25.8670i		−	0.699109i	−0.936916	−	0.349554i	$-0.886333\pi$
$37$		−	25.8670i		−	0.699109i	0.936916	−	0.349554i	$-0.113667\pi$
$38$		0			0
$39$	−14.8426			−0.380579
$40$		0			0
$41$	−28.6462	+	16.5389i	−0.698687	+	0.403387i	−0.806858	−	0.590745i	$-0.798834\pi$
$41$	−28.6462	+	16.5389i	−0.698687	+	0.403387i	0.108171	+	0.994132i	$0.465501\pi$
$42$		0			0
$43$	30.3762	+	52.6131i	0.706423	+	1.22356i	0.966176	+	0.257885i	$0.0830257\pi$
$43$	30.3762	+	52.6131i	0.706423	+	1.22356i	−0.259753	+	0.965675i	$0.583641\pi$
$44$		0			0
$45$	18.2046			0.404546
$46$		0			0
$47$	1.46918	−	2.54469i	0.0312591	−	0.0541423i	−0.849973	−	0.526827i	$-0.823382\pi$
$47$	1.46918	−	2.54469i	0.0312591	−	0.0541423i	0.881232	+	0.472685i	$0.156715\pi$
$48$		0			0
$49$	−43.5583			−0.888944
$50$		0			0
$51$	−35.9946	−	20.7815i	−0.705777	−	0.407481i
$52$		0			0
$53$	−40.1937	−	23.2058i	−0.758371	−	0.437846i	0.0703395	−	0.997523i	$-0.477592\pi$
$53$	−40.1937	−	23.2058i	−0.758371	−	0.437846i	−0.828711	+	0.559677i	$0.810925\pi$
$54$		0			0
$55$	−38.6882	−	67.0099i	−0.703422	−	1.21836i
$56$		0			0
$57$	−21.8965	+	24.5671i	−0.384149	+	0.431002i
$58$		0			0
$59$	93.0601	−	53.7283i	1.57729	−	0.910649i	0.582055	−	0.813150i	$-0.302249\pi$
$59$	93.0601	−	53.7283i	1.57729	−	0.910649i	0.995236	−	0.0974994i	$-0.0310844\pi$
$60$		0			0
$61$	21.4370	−	37.1300i	0.351426	−	0.608688i	−0.635073	−	0.772452i	$-0.719030\pi$
$61$	21.4370	−	37.1300i	0.351426	−	0.608688i	0.986500	+	0.163764i	$0.0523634\pi$
$62$		0			0
$63$	3.49913	−	6.06067i	0.0555417	−	0.0962011i
$64$		0			0
$65$			52.0006i			0.800009i
$66$		0			0
$67$	−3.21307	−	1.85507i	−0.0479563	−	0.0276876i	0.475830	−	0.879537i	$-0.342148\pi$
$67$	−3.21307	−	1.85507i	−0.0479563	−	0.0276876i	−0.523786	+	0.851850i	$0.675481\pi$
$68$		0			0
$69$		−	28.8927i		−	0.418735i
$70$		0			0
$71$	−95.4988	+	55.1362i	−1.34505	+	0.776567i	−0.987544	−	0.157343i	$-0.949707\pi$
$71$	−95.4988	+	55.1362i	−1.34505	+	0.776567i	−0.357509	+	0.933910i	$0.616374\pi$
$72$		0			0
$73$	53.3048	+	92.3265i	0.730202	+	1.26475i	0.956797	+	0.290758i	$0.0939075\pi$
$73$	53.3048	+	92.3265i	0.730202	+	1.26475i	−0.226594	+	0.973989i	$0.572759\pi$
$74$		0			0
$75$		−	20.4779i		−	0.273039i
$76$		0			0
$77$	−29.7453			−0.386302
$78$		0			0
$79$	−105.269	+	60.7773i	−1.33252	+	0.769333i	−0.985686	−	0.168592i	$-0.946078\pi$
$79$	−105.269	+	60.7773i	−1.33252	+	0.769333i	−0.346838	+	0.937925i	$0.612745\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−112.963			−1.36100			−0.680498	−	0.732750i	$-0.738236\pi$
$83$	−112.963			−1.36100			−0.680498	+	0.732750i	$0.738236\pi$
$84$		0			0
$85$	−72.8074	+	126.106i	−0.856558	+	1.48360i
$86$		0			0
$87$	30.7004			0.352878
$88$		0			0
$89$	−119.192	−	68.8154i	−1.33923	−	0.773207i	−0.352540	−	0.935797i	$-0.614682\pi$
$89$	−119.192	−	68.8154i	−1.33923	−	0.773207i	−0.986694	+	0.162590i	$0.948015\pi$
$90$		0			0
$91$	17.3120	+	9.99511i	0.190242	+	0.109836i
$92$		0			0
$93$	−25.5707	−	44.2898i	−0.274954	−	0.476234i
$94$		0			0
$95$	86.0702	+	76.7137i	0.906002	+	0.807513i
$96$		0			0
$97$	29.4189	−	16.9850i	0.303288	−	0.175103i	−0.340631	−	0.940197i	$-0.610641\pi$
$97$	29.4189	−	16.9850i	0.303288	−	0.175103i	0.643919	+	0.765094i	$0.277307\pi$
$98$		0			0
$99$	−19.1267	+	33.1285i	−0.193199	+	0.334631i
$100$		0			0
$101$	−85.3846	+	147.890i	−0.845392	+	1.46426i	0.0398888	+	0.999204i	$0.487300\pi$
$101$	−85.3846	+	147.890i	−0.845392	+	1.46426i	−0.885281	+	0.465057i	$0.846034\pi$
$102$		0			0
$103$			56.2367i			0.545987i	0.962016	+	0.272994i	$0.0880138\pi$
$103$			56.2367i			0.545987i	−0.962016	+	0.272994i	$0.911986\pi$
$104$		0			0
$105$	−21.2334	−	12.2591i	−0.202223	−	0.116753i
$106$		0			0
$107$			76.8536i			0.718258i	0.933288	+	0.359129i	$0.116926\pi$
$107$			76.8536i			0.718258i	−0.933288	+	0.359129i	$0.883074\pi$
$108$		0			0
$109$	12.6796	−	7.32057i	0.116327	−	0.0671612i	−0.440708	−	0.897651i	$-0.645272\pi$
$109$	12.6796	−	7.32057i	0.116327	−	0.0671612i	0.557034	+	0.830489i	$0.311939\pi$
$110$		0			0
$111$	22.4015	+	38.8005i	0.201815	+	0.349554i
$112$		0			0
$113$			113.484i			1.00428i	0.864786	+	0.502140i	$0.167454\pi$
$113$			113.484i			1.00428i	−0.864786	+	0.502140i	$0.832546\pi$
$114$		0			0
$115$	−101.225			−0.880216
$116$		0			0
$117$	22.2639	−	12.8541i	0.190290	−	0.109864i
$118$		0			0
$119$	27.9889	+	48.4781i	0.235200	+	0.407379i
$120$		0			0
$121$	41.5919			0.343735
$122$		0			0
$123$	28.6462	−	49.6166i	0.232896	−	0.403387i
$124$		0			0
$125$	79.9610			0.639688
$126$		0			0
$127$	22.5059	+	12.9938i	0.177212	+	0.102313i	0.585982	−	0.810324i	$-0.300709\pi$
$127$	22.5059	+	12.9938i	0.177212	+	0.102313i	−0.408770	+	0.912637i	$0.634042\pi$
$128$		0			0
$129$	−91.1286	−	52.6131i	−0.706423	−	0.407853i
$130$		0			0
$131$	26.7545	+	46.3402i	0.204233	+	0.353742i	0.949888	−	0.312590i	$-0.101197\pi$
$131$	26.7545	+	46.3402i	0.204233	+	0.353742i	−0.745655	+	0.666332i	$0.767863\pi$
$132$		0			0
$133$	42.0832	−	13.9092i	0.316415	−	0.104581i
$134$		0			0
$135$	−27.3069	+	15.7656i	−0.202273	+	0.116782i
$136$		0			0
$137$	−36.3765	+	63.0059i	−0.265522	+	0.459897i	−0.967700	−	0.252104i	$-0.918878\pi$
$137$	−36.3765	+	63.0059i	−0.265522	+	0.459897i	0.702178	+	0.712001i	$0.252211\pi$
$138$		0			0
$139$	67.3061	−	116.578i	0.484216	−	0.838687i	−0.515619	−	0.856818i	$-0.672438\pi$
$139$	67.3061	−	116.578i	0.484216	−	0.838687i	0.999836	+	0.0181305i	$0.00577143\pi$
$140$		0			0
$141$			5.08938i			0.0360949i
$142$		0			0
$143$	−94.6300	−	54.6347i	−0.661748	−	0.382061i
$144$		0			0
$145$		−	107.558i		−	0.741780i
$146$		0			0
$147$	65.3374	−	37.7226i	0.444472	−	0.256616i
$148$		0			0
$149$	63.3404	+	109.709i	0.425104	+	0.736301i	0.996430	−	0.0844218i	$-0.0269043\pi$
$149$	63.3404	+	109.709i	0.425104	+	0.736301i	−0.571326	+	0.820723i	$0.693571\pi$
$150$		0			0
$151$			17.4246i			0.115394i	0.998334	+	0.0576972i	$0.0183758\pi$
$151$			17.4246i			0.115394i	−0.998334	+	0.0576972i	$0.981624\pi$
$152$		0			0
$153$	71.9893			0.470518
$154$		0			0
$155$	−155.168	+	89.5863i	−1.00108	+	0.577976i
$156$		0			0
$157$	−24.3134	−	42.1120i	−0.154862	−	0.268229i	0.778147	−	0.628083i	$-0.216160\pi$
$157$	−24.3134	−	42.1120i	−0.154862	−	0.268229i	−0.933009	+	0.359854i	$0.882827\pi$
$158$		0			0
$159$	80.3873			0.505581
$160$		0			0
$161$	−19.4566	+	33.6998i	−0.120848	+	0.209315i
$162$		0			0
$163$	−225.931			−1.38608			−0.693041	−	0.720898i	$-0.743729\pi$
$163$	−225.931			−1.38608			−0.693041	+	0.720898i	$0.743729\pi$
$164$		0			0
$165$	116.065	+	67.0099i	0.703422	+	0.406121i
$166$		0			0
$167$	229.833	+	132.694i	1.37625	+	0.794576i	0.991705	−	0.128532i	$-0.0410265\pi$
$167$	229.833	+	132.694i	1.37625	+	0.794576i	0.384541	+	0.923108i	$0.374360\pi$
$168$		0			0
$169$	−47.7830	−	82.7625i	−0.282739	−	0.489719i
$170$		0			0
$171$	11.5690	−	55.8136i	0.0676549	−	0.326395i
$172$		0			0
$173$	120.608	−	69.6333i	0.697159	−	0.402505i	−0.109130	−	0.994028i	$-0.534806\pi$
$173$	120.608	−	69.6333i	0.697159	−	0.402505i	0.806288	+	0.591523i	$0.201473\pi$
$174$		0			0
$175$	−13.7900	+	23.8849i	−0.0787998	+	0.136485i
$176$		0			0
$177$	−93.0601	+	161.185i	−0.525763	+	0.910649i
$178$		0			0
$179$			4.92297i			0.0275026i	0.999905	+	0.0137513i	$0.00437732\pi$
$179$			4.92297i			0.0275026i	−0.999905	+	0.0137513i	$0.995623\pi$
$180$		0			0
$181$	−223.841	−	129.235i	−1.23669	−	0.714004i	−0.268274	−	0.963343i	$-0.586453\pi$
$181$	−223.841	−	129.235i	−1.23669	−	0.714004i	−0.968416	+	0.249339i	$0.919787\pi$
$182$		0			0
$183$			74.2600i			0.405792i
$184$		0			0
$185$	135.937	−	78.4830i	0.734792	−	0.424233i
$186$		0			0
$187$	−152.991	−	264.988i	−0.818134	−	1.41705i
$188$		0			0
$189$			12.1213i			0.0641341i
$190$		0			0
$191$	−25.3250			−0.132592			−0.0662959	−	0.997800i	$-0.521118\pi$
$191$	−25.3250			−0.132592			−0.0662959	+	0.997800i	$0.521118\pi$
$192$		0			0
$193$	255.340	−	147.420i	1.32300	−	0.763837i	0.338797	−	0.940860i	$-0.389980\pi$
$193$	255.340	−	147.420i	1.32300	−	0.763837i	0.984207	+	0.177023i	$0.0566467\pi$
$194$		0			0
$195$	−45.0338	−	78.0008i	−0.230943	−	0.400004i
$196$		0			0
$197$	345.057			1.75156			0.875780	−	0.482711i	$-0.160348\pi$
$197$	345.057			1.75156			0.875780	+	0.482711i	$0.160348\pi$
$198$		0			0
$199$	176.271	−	305.310i	0.885784	−	1.53422i	0.0409720	−	0.999160i	$-0.486955\pi$
$199$	176.271	−	305.310i	0.885784	−	1.53422i	0.844812	−	0.535063i	$-0.179712\pi$
$200$		0			0
$201$	6.42614			0.0319708
$202$		0			0
$203$	−35.8082	−	20.6739i	−0.176395	−	0.101842i
$204$		0			0
$205$	−173.830	−	100.361i	−0.847953	−	0.489566i
$206$		0			0
$207$	25.0218	+	43.3391i	0.120878	+	0.209368i
$208$		0			0
$209$	−230.033	+	76.0299i	−1.10064	+	0.363779i
$210$		0			0
$211$	319.914	−	184.702i	1.51618	−	0.875366i	0.516358	−	0.856373i	$-0.327287\pi$
$211$	319.914	−	184.702i	1.51618	−	0.875366i	0.999820	−	0.0189930i	$-0.00604604\pi$
$212$		0			0
$213$	95.4988	−	165.409i	0.448351	−	0.776567i
$214$		0			0
$215$	−184.328	+	319.266i	−0.857342	+	1.48496i
$216$		0			0
$217$			68.8781i			0.317411i
$218$		0			0
$219$	−159.914	−	92.3265i	−0.730202	−	0.421582i
$220$		0			0
$221$			205.634i			0.930472i
$222$		0			0
$223$	81.5215	−	47.0664i	0.365567	−	0.211060i	−0.305953	−	0.952047i	$-0.598975\pi$
$223$	81.5215	−	47.0664i	0.365567	−	0.211060i	0.671520	+	0.740986i	$0.265642\pi$
$224$		0			0
$225$	17.7344	+	30.7169i	0.0788195	+	0.136519i
$226$		0			0
$227$		−	246.669i		−	1.08665i	−0.839524	−	0.543323i	$-0.817166\pi$
$227$		−	246.669i		−	1.08665i	0.839524	−	0.543323i	$-0.182834\pi$
$228$		0			0
$229$	−288.388			−1.25934			−0.629668	−	0.776865i	$-0.716809\pi$
$229$	−288.388			−1.25934			−0.629668	+	0.776865i	$0.716809\pi$
$230$		0			0
$231$	44.6179	−	25.7602i	0.193151	−	0.111516i
$232$		0			0
$233$	99.2994	+	171.992i	0.426178	+	0.738162i	0.996530	−	0.0832389i	$-0.0265265\pi$
$233$	99.2994	+	171.992i	0.426178	+	0.738162i	−0.570352	+	0.821401i	$0.693193\pi$
$234$		0			0
$235$	17.8305			0.0758744
$236$		0			0
$237$	105.269	−	182.332i	0.444175	−	0.769333i
$238$		0			0
$239$	−68.2746			−0.285668			−0.142834	−	0.989747i	$-0.545621\pi$
$239$	−68.2746			−0.285668			−0.142834	+	0.989747i	$0.545621\pi$
$240$		0			0
$241$	291.271	+	168.165i	1.20859	+	0.697781i	0.962452	−	0.271453i	$-0.0875042\pi$
$241$	291.271	+	168.165i	1.20859	+	0.697781i	0.246141	+	0.969234i	$0.420837\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−132.160	−	228.908i	−0.539428	−	0.934317i
$246$		0			0
$247$	159.429	+	33.0463i	0.645462	+	0.133791i
$248$		0			0
$249$	169.444	−	97.8285i	0.680498	−	0.392886i
$250$		0			0
$251$	−11.8076	+	20.4514i	−0.0470423	+	0.0814797i	−0.888588	−	0.458707i	$-0.848313\pi$
$251$	−11.8076	+	20.4514i	−0.0470423	+	0.0814797i	0.841545	+	0.540186i	$0.181646\pi$
$252$		0			0
$253$	106.352	−	184.208i	0.420365	−	0.728094i
$254$		0			0
$255$		−	252.212i		−	0.989068i
$256$		0			0
$257$	−148.757	−	85.8849i	−0.578821	−	0.334183i	0.181844	−	0.983327i	$-0.441794\pi$
$257$	−148.757	−	85.8849i	−0.578821	−	0.334183i	−0.760665	+	0.649145i	$0.775127\pi$
$258$		0			0
$259$		−	60.3414i		−	0.232978i
$260$		0			0
$261$	−46.0506	+	26.5873i	−0.176439	+	0.101867i
$262$		0			0
$263$	65.4480	+	113.359i	0.248852	+	0.431024i	0.963208	−	0.268759i	$-0.0866134\pi$
$263$	65.4480	+	113.359i	0.248852	+	0.431024i	−0.714356	+	0.699783i	$0.753280\pi$
$264$		0			0
$265$		−	281.635i		−	1.06277i
$266$		0			0
$267$	238.384			0.892822
$268$		0			0
$269$	328.569	−	189.700i	1.22145	−	0.705203i	0.256221	−	0.966618i	$-0.417523\pi$
$269$	328.569	−	189.700i	1.22145	−	0.705203i	0.965226	+	0.261416i	$0.0841893\pi$
$270$		0			0
$271$	235.196	+	407.372i	0.867883	+	1.50322i	0.864156	+	0.503224i	$0.167853\pi$
$271$	235.196	+	407.372i	0.867883	+	1.50322i	0.00372642	+	0.999993i	$0.498814\pi$
$272$		0			0
$273$	−34.6241			−0.126828
$274$		0			0
$275$	75.3779	−	130.558i	0.274102	−	0.474758i
$276$		0			0
$277$	−291.139			−1.05104			−0.525522	−	0.850780i	$-0.676130\pi$
$277$	−291.139			−1.05104			−0.525522	+	0.850780i	$0.676130\pi$
$278$		0			0
$279$	76.7122	+	44.2898i	0.274954	+	0.158745i
$280$		0			0
$281$	−272.146	−	157.124i	−0.968492	−	0.559159i	−0.0697155	−	0.997567i	$-0.522209\pi$
$281$	−272.146	−	157.124i	−0.968492	−	0.559159i	−0.898776	+	0.438408i	$0.855542\pi$
$282$		0			0
$283$	−103.981	−	180.100i	−0.367424	−	0.636396i	0.621738	−	0.783225i	$-0.286427\pi$
$283$	−103.981	−	180.100i	−0.367424	−	0.636396i	−0.989162	+	0.146829i	$0.953093\pi$
$284$		0			0
$285$	−195.541	−	40.5316i	−0.686110	−	0.142216i
$286$		0			0
$287$	−66.8244	+	38.5811i	−0.232838	+	0.134429i
$288$		0			0
$289$	−143.414	+	248.401i	−0.496243	+	0.859518i
$290$		0			0
$291$	−29.4189	+	50.9550i	−0.101096	+	0.175103i
$292$		0			0
$293$			392.921i			1.34103i	0.741897	+	0.670514i	$0.233926\pi$
$293$			392.921i			1.34103i	−0.741897	+	0.670514i	$0.766074\pi$
$294$		0			0
$295$	564.706	+	326.033i	1.91426	+	1.10520i
$296$		0			0
$297$		−	66.2569i		−	0.223087i
$298$		0			0
$299$	−123.796	+	71.4738i	−0.414034	+	0.239043i
$300$		0			0
$301$	70.8601	+	122.733i	0.235416	+	0.407752i
$302$		0			0
$303$		−	295.781i		−	0.976174i
$304$		0			0
$305$	260.168			0.853009
$306$		0			0
$307$	187.357	−	108.171i	0.610284	−	0.352347i	−0.162793	−	0.986660i	$-0.552050\pi$
$307$	187.357	−	108.171i	0.610284	−	0.352347i	0.773076	+	0.634313i	$0.218717\pi$
$308$		0			0
$309$	−48.7024	−	84.3550i	−0.157613	−	0.272994i
$310$		0			0
$311$	103.938			0.334205			0.167102	−	0.985940i	$-0.446559\pi$
$311$	103.938			0.334205			0.167102	+	0.985940i	$0.446559\pi$
$312$		0			0
$313$	259.062	−	448.708i	0.827673	−	1.43357i	−0.0721867	−	0.997391i	$-0.522998\pi$
$313$	259.062	−	448.708i	0.827673	−	1.43357i	0.899859	−	0.436180i	$-0.143669\pi$
$314$		0			0
$315$	42.4667			0.134815
$316$		0			0
$317$	244.167	+	140.970i	0.770242	+	0.444699i	0.832961	−	0.553332i	$-0.186644\pi$
$317$	244.167	+	140.970i	0.770242	+	0.444699i	−0.0627190	+	0.998031i	$0.519977\pi$
$318$		0			0
$319$	195.733	+	113.006i	0.613583	+	0.354252i
$320$		0			0
$321$	−66.5571	−	115.280i	−0.207343	−	0.359129i
$322$		0			0
$323$	340.361	+	303.361i	1.05375	+	0.939200i
$324$		0			0
$325$	−87.7413	+	50.6575i	−0.269973	+	0.155869i
$326$		0			0
$327$	−12.6796	+	21.9617i	−0.0387755	+	0.0671612i
$328$		0			0
$329$	3.42722	−	5.93613i	0.0104171	−	0.0180429i
$330$		0			0
$331$		−	114.928i		−	0.347213i	−0.984815	−	0.173607i	$-0.944458\pi$
$331$		−	114.928i		−	0.347213i	0.984815	−	0.173607i	$-0.0555421\pi$
$332$		0			0
$333$	−67.2045	−	38.8005i	−0.201815	−	0.116518i
$334$		0			0
$335$		−	22.5138i		−	0.0672053i
$336$		0			0
$337$	−241.393	+	139.368i	−0.716300	+	0.413556i	−0.813389	−	0.581720i	$-0.802380\pi$
$337$	−241.393	+	139.368i	−0.716300	+	0.413556i	0.0970896	+	0.995276i	$0.469047\pi$
$338$		0			0
$339$	−98.2797	−	170.225i	−0.289911	−	0.502140i
$340$		0			0
$341$		−	376.497i		−	1.10410i
$342$		0			0
$343$	−215.916			−0.629491
$344$		0			0
$345$	151.837	−	87.6633i	0.440108	−	0.254096i
$346$		0			0
$347$	−230.969	−	400.051i	−0.665618	−	1.15288i	−0.979117	−	0.203296i	$-0.934835\pi$
$347$	−230.969	−	400.051i	−0.665618	−	1.15288i	0.313499	−	0.949588i	$-0.398499\pi$
$348$		0			0
$349$	587.424			1.68316			0.841581	−	0.540131i	$-0.181625\pi$
$349$	587.424			1.68316			0.841581	+	0.540131i	$0.181625\pi$
$350$		0			0
$351$	−22.2639	+	38.5622i	−0.0634298	+	0.109864i
$352$		0			0
$353$	−78.1456			−0.221376			−0.110688	−	0.993855i	$-0.535305\pi$
$353$	−78.1456			−0.221376			−0.110688	+	0.993855i	$0.535305\pi$
$354$		0			0
$355$	−579.505	−	334.577i	−1.63241	−	0.942471i
$356$		0			0
$357$	−83.9666	−	48.4781i	−0.235200	−	0.135793i
$358$		0			0
$359$	169.340	+	293.306i	0.471700	+	0.817009i	0.999476	−	0.0323749i	$-0.0103070\pi$
$359$	169.340	+	293.306i	0.471700	+	0.817009i	−0.527775	+	0.849384i	$0.676974\pi$
$360$		0			0
$361$	289.895	−	215.132i	0.803033	−	0.595934i
$362$		0			0
$363$	−62.3879	+	36.0197i	−0.171867	+	0.0992277i
$364$		0			0
$365$	−323.463	+	560.255i	−0.886201	+	1.53495i
$366$		0			0
$367$	−298.459	+	516.946i	−0.813239	+	1.40857i	0.0973465	+	0.995251i	$0.468964\pi$
$367$	−298.459	+	516.946i	−0.813239	+	1.40857i	−0.910586	+	0.413321i	$0.864369\pi$
$368$		0			0
$369$			99.2332i			0.268925i
$370$		0			0
$371$	−93.7619	−	54.1334i	−0.252727	−	0.145912i
$372$		0			0
$373$			87.4003i			0.234317i	0.993113	+	0.117159i	$0.0373786\pi$
$373$			87.4003i			0.234317i	−0.993113	+	0.117159i	$0.962621\pi$
$374$		0			0
$375$	−119.942	+	69.2483i	−0.319844	+	0.184662i
$376$		0			0
$377$	−75.9456	−	131.542i	−0.201447	−	0.348917i
$378$		0			0
$379$		−	376.413i		−	0.993175i	−0.867987	−	0.496588i	$-0.834586\pi$
$379$		−	376.413i		−	0.993175i	0.867987	−	0.496588i	$-0.165414\pi$
$380$		0			0
$381$	−45.0118			−0.118141
$382$		0			0
$383$	293.419	−	169.405i	0.766106	−	0.442312i	−0.0653776	−	0.997861i	$-0.520825\pi$
$383$	293.419	−	169.405i	0.766106	−	0.442312i	0.831484	+	0.555549i	$0.187492\pi$
$384$		0			0
$385$	−90.2500	−	156.318i	−0.234416	−	0.406020i
$386$		0			0
$387$	182.257			0.470949
$388$		0			0
$389$	−291.059	+	504.129i	−0.748224	+	1.29596i	0.200449	+	0.979704i	$0.435760\pi$
$389$	−291.059	+	504.129i	−0.748224	+	1.29596i	−0.948673	+	0.316258i	$0.897573\pi$
$390$		0			0
$391$	−400.290			−1.02376
$392$		0			0
$393$	−80.2636	−	46.3402i	−0.204233	−	0.117914i
$394$		0			0
$395$	−638.795	−	368.808i	−1.61720	−	0.933692i
$396$		0			0
$397$	338.426	+	586.170i	0.852457	+	1.47650i	0.878984	+	0.476852i	$0.158222\pi$
$397$	338.426	+	586.170i	0.852457	+	1.47650i	−0.0265264	+	0.999648i	$0.508445\pi$
$398$		0			0
$399$	−51.0791	+	57.3090i	−0.128018	+	0.143632i
$400$		0			0
$401$	19.8001	−	11.4316i	0.0493767	−	0.0285076i	−0.475108	−	0.879927i	$-0.657591\pi$
$401$	19.8001	−	11.4316i	0.0493767	−	0.0285076i	0.524485	+	0.851420i	$0.324258\pi$
$402$		0			0
$403$	−126.512	+	219.125i	−0.313925	+	0.543734i
$404$		0			0
$405$	27.3069	−	47.2969i	0.0674243	−	0.116782i
$406$		0			0
$407$			329.835i			0.810404i
$408$		0			0
$409$	686.586	+	396.401i	1.67870	+	0.969195i	0.962494	+	0.271301i	$0.0874540\pi$
$409$	686.586	+	396.401i	1.67870	+	0.969195i	0.716201	+	0.697894i	$0.245879\pi$
$410$		0			0
$411$		−	126.012i		−	0.306598i
$412$		0			0
$413$	217.086	−	125.335i	0.525633	−	0.303474i
$414$		0			0
$415$	−342.739	−	593.642i	−0.825878	−	1.43046i
$416$		0			0
$417$			233.155i			0.559125i
$418$		0			0
$419$	72.6180			0.173313			0.0866563	−	0.996238i	$-0.472382\pi$
$419$	72.6180			0.173313			0.0866563	+	0.996238i	$0.472382\pi$
$420$		0			0
$421$	212.967	−	122.956i	0.505859	−	0.292058i	−0.225271	−	0.974296i	$-0.572327\pi$
$421$	212.967	−	122.956i	0.505859	−	0.292058i	0.731130	+	0.682238i	$0.238993\pi$
$422$		0			0
$423$	−4.40753	−	7.63407i	−0.0104197	−	0.0180474i
$424$		0			0
$425$	−283.708			−0.667548
$426$		0			0
$427$	50.0072	−	86.6151i	0.117113	−	0.202846i
$428$		0			0
$429$	189.260			0.441166
$430$		0			0
$431$	256.472	+	148.074i	0.595062	+	0.343559i	0.767096	−	0.641532i	$-0.221701\pi$
$431$	256.472	+	148.074i	0.595062	+	0.343559i	−0.172035	+	0.985091i	$0.555034\pi$
$432$		0			0
$433$	407.814	+	235.451i	0.941833	+	0.543767i	0.890534	−	0.454916i	$-0.150331\pi$
$433$	407.814	+	235.451i	0.941833	+	0.543767i	0.0512985	+	0.998683i	$0.483664\pi$
$434$		0			0
$435$	93.1480	+	161.337i	0.214133	+	0.370890i
$436$		0			0
$437$	−64.3283	+	310.346i	−0.147204	+	0.710175i
$438$		0			0
$439$	336.154	−	194.079i	0.765728	−	0.442093i	−0.0656208	−	0.997845i	$-0.520903\pi$
$439$	336.154	−	194.079i	0.765728	−	0.442093i	0.831348	+	0.555752i	$0.187569\pi$
$440$		0			0
$441$	−65.3374	+	113.168i	−0.148157	+	0.256616i
$442$		0			0
$443$	−5.59129	+	9.68441i	−0.0126214	+	0.0218610i	−0.872267	−	0.489030i	$-0.837351\pi$
$443$	−5.59129	+	9.68441i	−0.0126214	+	0.0218610i	0.859646	+	0.510891i	$0.170684\pi$
$444$		0			0
$445$		−	835.170i		−	1.87679i
$446$		0			0
$447$	−190.021	−	109.709i	−0.425104	−	0.245434i
$448$		0			0
$449$		−	508.975i		−	1.13357i	−0.823864	−	0.566787i	$-0.808186\pi$
$449$		−	508.975i		−	1.13357i	0.823864	−	0.566787i	$-0.191814\pi$
$450$		0			0
$451$	365.272	−	210.890i	0.809915	−	0.467605i
$452$		0			0
$453$	−15.0901	−	26.1368i	−0.0333115	−	0.0576972i
$454$		0			0
$455$			121.304i			0.266603i
$456$		0			0
$457$	−546.954			−1.19684			−0.598418	−	0.801184i	$-0.704204\pi$
$457$	−546.954			−1.19684			−0.598418	+	0.801184i	$0.704204\pi$
$458$		0			0
$459$	−107.984	+	62.3445i	−0.235259	+	0.135827i
$460$		0			0
$461$	−182.237	−	315.643i	−0.395308	−	0.684693i	0.597833	−	0.801621i	$-0.296029\pi$
$461$	−182.237	−	315.643i	−0.395308	−	0.684693i	−0.993140	+	0.116928i	$0.962695\pi$
$462$		0			0
$463$	−283.061			−0.611363			−0.305681	−	0.952134i	$-0.598884\pi$
$463$	−283.061			−0.611363			−0.305681	+	0.952134i	$0.598884\pi$
$464$		0			0
$465$	155.168	−	268.759i	0.333695	−	0.577976i
$466$		0			0
$467$	716.445			1.53414			0.767072	−	0.641561i	$-0.221713\pi$
$467$	716.445			1.53414			0.767072	+	0.641561i	$0.221713\pi$
$468$		0			0
$469$	−7.49529	−	4.32741i	−0.0159814	−	0.00922689i
$470$		0			0
$471$	72.9401	+	42.1120i	0.154862	+	0.0894097i
$472$		0			0
$473$	−387.331	−	670.878i	−0.818883	−	1.41835i
$474$		0			0
$475$	−45.5931	+	219.960i	−0.0959854	+	0.463074i
$476$		0			0
$477$	−120.581	+	69.6175i	−0.252790	+	0.145949i
$478$		0			0
$479$	−11.2934	+	19.5607i	−0.0235769	+	0.0408365i	−0.877573	−	0.479443i	$-0.840839\pi$
$479$	−11.2934	+	19.5607i	−0.0235769	+	0.0408365i	0.853996	+	0.520279i	$0.174172\pi$
$480$		0			0
$481$	110.832	−	191.967i	0.230420	−	0.399099i
$482$		0			0
$483$		−	67.3996i		−	0.139544i
$484$		0			0
$485$	178.519	+	103.068i	0.368081	+	0.212512i
$486$		0			0
$487$		−	464.306i		−	0.953400i	−0.879066	−	0.476700i	$-0.841833\pi$
$487$		−	464.306i		−	0.953400i	0.879066	−	0.476700i	$-0.158167\pi$
$488$		0			0
$489$	338.897	−	195.662i	0.693041	−	0.400127i
$490$		0			0
$491$	93.3533	+	161.693i	0.190129	+	0.329313i	0.945293	−	0.326223i	$-0.105776\pi$
$491$	93.3533	+	161.693i	0.190129	+	0.329313i	−0.755164	+	0.655536i	$0.772443\pi$
$492$		0			0
$493$		−	425.334i		−	0.862747i
$494$		0			0
$495$	−232.129			−0.468948
$496$		0			0
$497$	−222.775	+	128.619i	−0.448239	+	0.258791i
$498$		0			0
$499$	397.435	+	688.377i	0.796462	+	1.37951i	0.921906	+	0.387413i	$0.126631\pi$
$499$	397.435	+	688.377i	0.796462	+	1.37951i	−0.125444	+	0.992101i	$0.540036\pi$
$500$		0			0
$501$	−459.666			−0.917497
$502$		0			0
$503$	211.931	−	367.076i	0.421335	−	0.729773i	−0.574736	−	0.818339i	$-0.694895\pi$
$503$	211.931	−	367.076i	0.421335	−	0.729773i	0.996070	+	0.0885661i	$0.0282284\pi$
$504$		0			0
$505$	−1036.26			−2.05200
$506$		0			0
$507$	143.349	+	82.7625i	0.282739	+	0.163240i
$508$		0			0
$509$	332.991	+	192.252i	0.654206	+	0.377706i	0.790066	−	0.613022i	$-0.210046\pi$
$509$	332.991	+	192.252i	0.654206	+	0.377706i	−0.135860	+	0.990728i	$0.543380\pi$
$510$		0			0
$511$	124.347	+	215.375i	0.243340	+	0.421477i
$512$		0			0
$513$	30.9825	+	93.7394i	0.0603948	+	0.182728i
$514$		0			0
$515$	−295.535	+	170.627i	−0.573855	+	0.331315i
$516$		0			0
$517$	−18.7337	+	32.4477i	−0.0362354	+	0.0627615i
$518$		0			0
$519$	−120.608	+	208.900i	−0.232386	+	0.402505i
$520$		0			0
$521$		−	129.324i		−	0.248223i	−0.992268	−	0.124111i	$-0.960392\pi$
$521$		−	129.324i		−	0.248223i	0.992268	−	0.124111i	$-0.0396080\pi$
$522$		0			0
$523$	−276.385	−	159.571i	−0.528461	−	0.305107i	0.211928	−	0.977285i	$-0.432026\pi$
$523$	−276.385	−	159.571i	−0.528461	−	0.305107i	−0.740390	+	0.672178i	$0.765359\pi$
$524$		0			0
$525$		−	47.7699i		−	0.0909902i
$526$		0			0
$527$	−613.606	+	354.266i	−1.16434	+	0.672231i
$528$		0			0
$529$	125.368	+	217.144i	0.236991	+	0.410481i
$530$		0			0
$531$		−	322.370i		−	0.607099i
$532$		0			0
$533$	−283.455			−0.531811
$534$		0			0
$535$	−403.881	+	233.181i	−0.754918	+	0.435852i
$536$		0			0
$537$	−4.26342	−	7.38446i	−0.00793933	−	0.0137513i
$538$		0			0
$539$	555.418			1.03046
$540$		0			0
$541$	−39.5504	+	68.5033i	−0.0731061	+	0.126624i	−0.900261	−	0.435350i	$-0.856625\pi$
$541$	−39.5504	+	68.5033i	−0.0731061	+	0.126624i	0.827155	+	0.561974i	$0.189958\pi$
$542$		0			0
$543$	447.682			0.824460
$544$		0			0
$545$	76.9422	+	44.4226i	0.141178	+	0.0815094i
$546$		0			0
$547$	254.651	+	147.023i	0.465541	+	0.268780i	0.714371	−	0.699767i	$-0.246713\pi$
$547$	254.651	+	147.023i	0.465541	+	0.268780i	−0.248830	+	0.968547i	$0.580046\pi$
$548$		0			0
$549$	−64.3110	−	111.390i	−0.117142	−	0.202896i
$550$		0			0
$551$	−329.764	−	68.3530i	−0.598482	−	0.124053i
$552$		0			0
$553$	−245.567	+	141.778i	−0.444064	+	0.256381i
$554$		0			0
$555$	−135.937	+	235.449i	−0.244931	+	0.424233i
$556$		0			0
$557$	−225.519	+	390.611i	−0.404882	+	0.701276i	−0.994308	−	0.106546i	$-0.966021\pi$
$557$	−225.519	+	390.611i	−0.404882	+	0.701276i	0.589426	+	0.807823i	$0.299354\pi$
$558$		0			0
$559$			520.610i			0.931323i
$560$		0			0
$561$	458.973	+	264.988i	0.818134	+	0.472350i
$562$		0			0
$563$		−	871.835i		−	1.54855i	−0.632848	−	0.774276i	$-0.718114\pi$
$563$		−	871.835i		−	1.54855i	0.632848	−	0.774276i	$-0.281886\pi$
$564$		0			0
$565$	−596.380	+	344.320i	−1.05554	+	0.609416i
$566$		0			0
$567$	−10.4974	−	18.1820i	−0.0185139	−	0.0320670i
$568$		0			0
$569$			885.978i			1.55708i	0.627596	+	0.778539i	$0.284039\pi$
$569$			885.978i			1.55708i	−0.627596	+	0.778539i	$0.715961\pi$
$570$		0			0
$571$	198.079			0.346898			0.173449	−	0.984843i	$-0.444509\pi$
$571$	198.079			0.346898			0.173449	+	0.984843i	$0.444509\pi$
$572$		0			0
$573$	37.9875	−	21.9321i	0.0662959	−	0.0382759i
$574$		0			0
$575$	−98.6104	−	170.798i	−0.171496	−	0.297040i
$576$		0			0
$577$	178.142			0.308739			0.154369	−	0.988013i	$-0.450665\pi$
$577$	178.142			0.308739			0.154369	+	0.988013i	$0.450665\pi$
$578$		0			0
$579$	−255.340	+	442.261i	−0.441001	+	0.763837i
$580$		0			0
$581$	−263.514			−0.453552
$582$		0			0
$583$	512.516	+	295.901i	0.879101	+	0.507549i
$584$		0			0
$585$	135.101	+	78.0008i	0.230943	+	0.133335i
$586$		0			0
$587$	181.796	+	314.880i	0.309704	+	0.536423i	0.978298	−	0.207205i	$-0.0664367\pi$
$587$	181.796	+	314.880i	0.309704	+	0.536423i	−0.668593	+	0.743628i	$0.733103\pi$
$588$		0			0
$589$	176.055	+	532.663i	0.298904	+	0.904352i
$590$		0			0
$591$	−517.586	+	298.828i	−0.875780	+	0.505632i
$592$		0			0
$593$	−312.692	+	541.599i	−0.527306	+	0.913321i	0.472187	+	0.881498i	$0.343465\pi$
$593$	−312.692	+	541.599i	−0.527306	+	0.913321i	−0.999494	+	0.0318227i	$0.989869\pi$
$594$		0			0
$595$	−169.842	+	294.174i	−0.285448	+	0.494411i
$596$		0			0
$597$			610.621i			1.02282i
$598$		0			0
$599$	76.5813	+	44.2143i	0.127849	+	0.0738134i	0.562560	−	0.826756i	$-0.309816\pi$
$599$	76.5813	+	44.2143i	0.127849	+	0.0738134i	−0.434712	+	0.900570i	$0.643150\pi$
$600$		0			0
$601$			463.310i			0.770898i	0.922729	+	0.385449i	$0.125953\pi$
$601$			463.310i			0.770898i	−0.922729	+	0.385449i	$0.874047\pi$
$602$		0			0
$603$	−9.63921	+	5.56520i	−0.0159854	+	0.00922919i
$604$		0			0
$605$	126.194	+	218.574i	0.208585	+	0.361280i
$606$		0			0
$607$		−	436.122i		−	0.718487i	−0.933244	−	0.359244i	$-0.883035\pi$
$607$		−	436.122i		−	0.718487i	0.933244	−	0.359244i	$-0.116965\pi$
$608$		0			0
$609$	71.6165			0.117597
$610$		0			0
$611$	21.8064	−	12.5899i	0.0356896	−	0.0206054i
$612$		0			0
$613$	−437.468	−	757.717i	−0.713651	−	1.23608i	−0.963477	−	0.267790i	$-0.913707\pi$
$613$	−437.468	−	757.717i	−0.713651	−	1.23608i	0.249826	−	0.968291i	$-0.419627\pi$
$614$		0			0
$615$	347.661			0.565302
$616$		0			0
$617$	401.768	−	695.883i	0.651164	−	1.12785i	−0.331676	−	0.943393i	$-0.607614\pi$
$617$	401.768	−	695.883i	0.651164	−	1.12785i	0.982841	−	0.184457i	$-0.0590525\pi$
$618$		0			0
$619$	−37.6874			−0.0608843			−0.0304421	−	0.999537i	$-0.509692\pi$
$619$	−37.6874			−0.0608843			−0.0304421	+	0.999537i	$0.509692\pi$
$620$		0			0
$621$	−75.0655	−	43.3391i	−0.120878	−	0.0697892i
$622$		0			0
$623$	−278.045	−	160.529i	−0.446300	−	0.257671i
$624$		0			0
$625$	390.396	+	676.185i	0.624633	+	1.08190i
$626$		0			0
$627$	279.206	−	313.259i	0.445304	−	0.499616i
$628$		0			0
$629$	537.556	−	310.358i	0.854620	−	0.493415i
$630$		0			0
$631$	−352.654	+	610.814i	−0.558880	+	0.968009i	0.438710	+	0.898629i	$0.355436\pi$
$631$	−352.654	+	610.814i	−0.558880	+	0.968009i	−0.997590	+	0.0693806i	$0.977898\pi$
$632$		0			0
$633$	−319.914	+	554.106i	−0.505393	+	0.875366i
$634$		0			0
$635$			157.697i			0.248342i
$636$		0			0
$637$	−323.259	−	186.633i	−0.507470	−	0.292988i
$638$		0			0
$639$			330.817i			0.517711i
$640$		0			0
$641$	896.054	−	517.337i	1.39790	−	0.807078i	0.403728	−	0.914879i	$-0.367714\pi$
$641$	896.054	−	517.337i	1.39790	−	0.807078i	0.994173	+	0.107801i	$0.0343809\pi$
$642$		0			0
$643$	453.785	+	785.979i	0.705732	+	1.22236i	0.966427	+	0.256942i	$0.0827149\pi$
$643$	453.785	+	785.979i	0.705732	+	1.22236i	−0.260695	+	0.965421i	$0.583952\pi$
$644$		0			0
$645$		−	638.533i		−	0.989973i
$646$		0			0
$647$	−428.493			−0.662276			−0.331138	−	0.943582i	$-0.607433\pi$
$647$	−428.493			−0.662276			−0.331138	+	0.943582i	$0.607433\pi$
$648$		0			0
$649$	−1186.62	+	685.098i	−1.82839	+	1.05562i
$650$		0			0
$651$	−59.6502	−	103.317i	−0.0916285	−	0.158705i
$652$		0			0
$653$	120.487			0.184513			0.0922563	−	0.995735i	$-0.470592\pi$
$653$	120.487			0.184513			0.0922563	+	0.995735i	$0.470592\pi$
$654$		0			0
$655$	−162.352	+	281.201i	−0.247865	+	0.429315i
$656$		0			0
$657$	319.829			0.486801
$658$		0			0
$659$	−396.938	−	229.172i	−0.602333	−	0.347757i	0.167626	−	0.985851i	$-0.446390\pi$
$659$	−396.938	−	229.172i	−0.602333	−	0.347757i	−0.769959	+	0.638093i	$0.779723\pi$
$660$		0			0
$661$	507.845	+	293.204i	0.768297	+	0.443577i	0.832267	−	0.554375i	$-0.187043\pi$
$661$	507.845	+	293.204i	0.768297	+	0.443577i	−0.0639696	+	0.997952i	$0.520376\pi$
$662$		0			0
$663$	−178.084	−	308.451i	−0.268604	−	0.465236i
$664$		0			0
$665$	200.780	+	178.954i	0.301926	+	0.269104i
$666$		0			0
$667$	256.060	−	147.836i	0.383898	−	0.221644i
$668$		0			0
$669$	−81.5215	+	141.199i	−0.121856	+	0.211060i
$670$		0			0
$671$	−273.347	+	473.450i	−0.407372	+	0.705589i
$672$		0			0
$673$		−	1156.52i		−	1.71845i	−0.511595	−	0.859227i	$-0.670945\pi$
$673$		−	1156.52i		−	1.71845i	0.511595	−	0.859227i	$-0.329055\pi$
$674$		0			0
$675$	−53.2031	−	30.7169i	−0.0788195	−	0.0455064i
$676$		0			0
$677$			19.9791i			0.0295113i	0.999891	+	0.0147556i	$0.00469704\pi$
$677$			19.9791i			0.0295113i	−0.999891	+	0.0147556i	$0.995303\pi$
$678$		0			0
$679$	68.6270	−	39.6218i	0.101071	−	0.0583532i
$680$		0			0
$681$	213.621	+	370.003i	0.313688	+	0.543323i
$682$		0			0
$683$		−	885.326i		−	1.29623i	−0.761542	−	0.648116i	$-0.775557\pi$
$683$		−	885.326i		−	1.29623i	0.761542	−	0.648116i	$-0.224443\pi$
$684$		0			0
$685$	−441.479			−0.644495
$686$		0			0
$687$	432.582	−	249.751i	0.629668	−	0.363539i
$688$		0			0
$689$	−198.859	−	344.434i	−0.288620	−	0.499905i
$690$		0			0
$691$	−1201.89			−1.73935			−0.869675	−	0.493625i	$-0.835672\pi$
$691$	−1201.89			−1.73935			−0.869675	+	0.493625i	$0.835672\pi$
$692$		0			0
$693$	−44.6179	+	77.2805i	−0.0643837	+	0.111516i
$694$		0			0
$695$	816.852			1.17533
$696$		0			0
$697$	−687.405	−	396.874i	−0.986234	−	0.569403i
$698$		0			0
$699$	−297.898	−	171.992i	−0.426178	−	0.246054i
$700$		0			0
$701$	476.867	+	825.957i	0.680266	+	1.17826i	0.974900	+	0.222645i	$0.0714691\pi$
$701$	476.867	+	825.957i	0.680266	+	1.17826i	−0.294633	+	0.955610i	$0.595198\pi$
$702$		0			0
$703$	−154.235	−	466.645i	−0.219395	−	0.663792i
$704$		0			0
$705$	−26.7457	+	15.4417i	−0.0379372	+	0.0219031i
$706$		0			0
$707$	−199.181	+	344.992i	−0.281727	+	0.487966i
$708$		0			0
$709$	−283.929	+	491.779i	−0.400464	+	0.693624i	−0.993782	−	0.111344i	$-0.964484\pi$
$709$	−283.929	+	491.779i	−0.400464	+	0.693624i	0.593318	+	0.804968i	$0.297818\pi$
$710$		0			0
$711$			364.664i			0.512889i
$712$		0			0
$713$	−426.551	−	246.269i	−0.598248	−	0.345399i
$714$		0			0
$715$		−	663.067i		−	0.927367i
$716$		0			0
$717$	102.412	−	59.1276i	0.142834	−	0.0824652i
$718$		0			0
$719$	309.532	+	536.126i	0.430504	+	0.745655i	0.996917	−	0.0784671i	$-0.0250026\pi$
$719$	309.532	+	536.126i	0.430504	+	0.745655i	−0.566413	+	0.824122i	$0.691669\pi$
$720$		0			0
$721$			131.186i			0.181950i
$722$		0			0
$723$	−582.542			−0.805728
$724$		0			0
$725$	181.484	−	104.780i	0.250323	−	0.144524i
$726$		0			0
$727$	−491.712	−	851.671i	−0.676358	−	1.17149i	−0.976070	−	0.217457i	$-0.930224\pi$
$727$	−491.712	−	851.671i	−0.676358	−	1.17149i	0.299712	−	0.954030i	$-0.403109\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−728.920	+	1262.53i	−0.997154	+	1.72712i
$732$		0			0
$733$	116.933			0.159527			0.0797635	−	0.996814i	$-0.474583\pi$
$733$	116.933			0.159527			0.0797635	+	0.996814i	$0.474583\pi$
$734$		0			0
$735$	396.480	+	228.908i	0.539428	+	0.311439i
$736$		0			0
$737$	40.9703	+	23.6542i	0.0555907	+	0.0320953i
$738$		0			0
$739$	−114.723	−	198.707i	−0.155241	−	0.268886i	0.777906	−	0.628381i	$-0.216282\pi$
$739$	−114.723	−	198.707i	−0.155241	−	0.268886i	−0.933147	+	0.359495i	$0.882949\pi$
$740$		0			0
$741$	−267.763	+	88.5002i	−0.361353	+	0.119434i
$742$		0			0
$743$	368.354	−	212.669i	0.495766	−	0.286231i	−0.231197	−	0.972907i	$-0.574264\pi$
$743$	368.354	−	212.669i	0.495766	−	0.286231i	0.726963	+	0.686676i	$0.240931\pi$
$744$		0			0
$745$	−384.362	+	665.734i	−0.515922	+	0.893603i
$746$		0			0
$747$	−169.444	+	293.486i	−0.226833	+	0.392886i
$748$		0			0
$749$			179.280i			0.239360i
$750$		0			0
$751$	250.213	+	144.461i	0.333173	+	0.192358i	0.657249	−	0.753673i	$-0.271720\pi$
$751$	250.213	+	144.461i	0.333173	+	0.192358i	−0.324076	+	0.946031i	$0.605053\pi$
$752$		0			0
$753$		−	40.9028i		−	0.0543198i
$754$		0			0
$755$	−91.5696	+	52.8678i	−0.121284	+	0.0700235i
$756$		0			0
$757$	−449.147	−	777.945i	−0.593325	−	1.02767i	−0.993781	−	0.111353i	$-0.964482\pi$
$757$	−449.147	−	777.945i	−0.593325	−	1.02767i	0.400456	−	0.916316i	$-0.368852\pi$
$758$		0			0
$759$			368.416i			0.485396i
$760$		0			0
$761$	−842.483			−1.10707			−0.553537	−	0.832825i	$-0.686722\pi$
$761$	−842.483			−1.10707			−0.553537	+	0.832825i	$0.686722\pi$
$762$		0			0
$763$	29.5784	−	17.0771i	0.0387659	−	0.0223815i
$764$		0			0
$765$	218.422	+	378.318i	0.285519	+	0.494534i
$766$		0			0
$767$	920.835			1.20057
$768$		0			0
$769$	−229.391	+	397.317i	−0.298298	+	0.516667i	−0.975747	−	0.218903i	$-0.929752\pi$
$769$	−229.391	+	397.317i	−0.298298	+	0.516667i	0.677449	+	0.735570i	$0.263086\pi$
$770$		0			0
$771$	297.514			0.385881
$772$		0			0
$773$	−581.409	−	335.677i	−0.752146	−	0.434252i	0.0743228	−	0.997234i	$-0.476320\pi$
$773$	−581.409	−	335.677i	−0.752146	−	0.434252i	−0.826469	+	0.562983i	$0.809654\pi$
$774$		0			0
$775$	−302.321	−	174.545i	−0.390091	−	0.225219i
$776$		0			0
$777$	52.2572	+	90.5121i	0.0672550	+	0.116489i
$778$		0			0
$779$	−418.167	+	469.169i	−0.536800	+	0.602271i
$780$		0			0
$781$	1217.72	−	703.051i	1.55918	−	0.900193i
$782$		0			0
$783$	46.0506	−	79.7620i	0.0588131	−	0.101867i
$784$		0			0
$785$	147.538	−	255.543i	0.187947	−	0.325533i
$786$		0			0
$787$			765.723i			0.972964i	0.873691	+	0.486482i	$0.161720\pi$
$787$			765.723i			0.972964i	−0.873691	+	0.486482i	$0.838280\pi$
$788$		0			0
$789$	−196.344	−	113.359i	−0.248852	−	0.143675i
$790$		0			0
$791$			264.729i			0.334677i
$792$		0			0
$793$	318.181	−	183.702i	0.401237	−	0.231654i
$794$		0			0
$795$	243.903	+	422.452i	0.306796	+	0.531386i
$796$		0			0
$797$			132.597i			0.166370i	0.996534	+	0.0831851i	$0.0265093\pi$
$797$			132.597i			0.166370i	−0.996534	+	0.0831851i	$0.973491\pi$
$798$		0			0
$799$	70.5100			0.0882478
$800$		0			0
$801$	−357.575	+	206.446i	−0.446411	+	0.257736i
$802$		0			0
$803$	−679.697	−	1177.27i	−0.846447	−	1.46609i
$804$		0			0
$805$	−236.132			−0.293332
$806$		0			0
$807$	−328.569	+	569.099i	−0.407149	+	0.705203i
$808$		0			0
$809$	−820.855			−1.01465			−0.507327	−	0.861754i	$-0.669366\pi$
$809$	−820.855			−1.01465			−0.507327	+	0.861754i	$0.669366\pi$
$810$		0			0
$811$	−1037.69	−	599.108i	−1.27951	−	0.738728i	−0.302755	−	0.953068i	$-0.597906\pi$
$811$	−1037.69	−	599.108i	−1.27951	−	0.738728i	−0.976759	+	0.214341i	$0.931240\pi$
$812$		0			0
$813$	−705.589	−	407.372i	−0.867883	−	0.501072i
$814$		0			0
$815$	−685.497	−	1187.32i	−0.841101	−	1.45683i
$816$		0			0
$817$	861.702	+	768.028i	1.05471	+	0.940059i
$818$		0			0
$819$	51.9361	−	29.9853i	0.0634140	−	0.0366121i
$820$		0			0
$821$	306.495	−	530.864i	0.373319	−	0.646607i	−0.616755	−	0.787155i	$-0.711553\pi$
$821$	306.495	−	530.864i	0.373319	−	0.646607i	0.990074	+	0.140548i	$0.0448865\pi$
$822$		0			0
$823$	−135.178	+	234.136i	−0.164251	+	0.284491i	−0.936389	−	0.350964i	$-0.885854\pi$
$823$	−135.178	+	234.136i	−0.164251	+	0.284491i	0.772138	+	0.635455i	$0.219187\pi$
$824$		0			0
$825$			261.117i			0.316505i
$826$		0			0
$827$	280.576	+	161.991i	0.339270	+	0.195877i	0.659949	−	0.751310i	$-0.270578\pi$
$827$	280.576	+	161.991i	0.339270	+	0.195877i	−0.320679	+	0.947188i	$0.603911\pi$
$828$		0			0
$829$			853.335i			1.02935i	0.857384	+	0.514677i	$0.172088\pi$
$829$			853.335i			1.02935i	−0.857384	+	0.514677i	$0.827912\pi$
$830$		0			0
$831$	436.708	−	252.134i	0.525522	−	0.303410i
$832$		0			0
$833$	−522.621	−	905.207i	−0.627396	−	1.08668i
$834$		0			0
$835$			1610.43i			1.92866i
$836$		0			0
$837$	−153.424			−0.183303
$838$		0			0
$839$	−978.627	+	565.011i	−1.16642	+	0.673433i	−0.952834	−	0.303491i	$-0.901848\pi$
$839$	−978.627	+	565.011i	−1.16642	+	0.673433i	−0.213587	+	0.976924i	$0.568515\pi$
$840$		0			0
$841$	−263.414	−	456.246i	−0.313215	−	0.542505i
$842$		0			0
$843$	544.292			0.645661
$844$		0			0
$845$	289.956	−	502.219i	0.343143	−	0.594341i
$846$		0			0
$847$	97.0237			0.114550
$848$		0			0
$849$	311.943	+	180.100i	0.367424	+	0.212132i
$850$		0			0
$851$	373.684	+	215.747i	0.439112	+	0.253522i
$852$		0			0
$853$	261.610	+	453.122i	0.306694	+	0.531210i	0.977637	−	0.210299i	$-0.0674439\pi$
$853$	261.610	+	453.122i	0.306694	+	0.531210i	−0.670943	+	0.741509i	$0.734111\pi$
$854$		0			0
$855$	328.413	−	108.546i	0.384109	−	0.126955i
$856$		0			0
$857$	−117.980	+	68.1158i	−0.137666	+	0.0794817i	−0.567251	−	0.823545i	$-0.691993\pi$
$857$	−117.980	+	68.1158i	−0.137666	+	0.0794817i	0.429585	+	0.903026i	$0.358660\pi$
$858$		0			0
$859$	189.094	−	327.521i	0.220133	−	0.381282i	−0.734715	−	0.678376i	$-0.762684\pi$
$859$	189.094	−	327.521i	0.220133	−	0.381282i	0.954848	+	0.297094i	$0.0960175\pi$
$860$		0			0
$861$	66.8244	−	115.743i	0.0776125	−	0.134429i
$862$		0			0
$863$		−	1008.90i		−	1.16906i	−0.811373	−	0.584529i	$-0.801279\pi$
$863$		−	1008.90i		−	1.16906i	0.811373	−	0.584529i	$-0.198721\pi$
$864$		0			0
$865$	731.875	+	422.548i	0.846098	+	0.488495i
$866$		0			0
$867$		−	496.801i		−	0.573012i
$868$		0			0
$869$	1342.31	−	774.981i	1.54466	−	0.891808i
$870$		0			0
$871$	−15.8967	−	27.5340i	−0.0182511	−	0.0316119i
$872$		0			0
$873$		−	101.910i		−	0.116735i
$874$		0			0
$875$	186.529			0.213176
$876$		0			0
$877$	−216.476	+	124.982i	−0.246836	+	0.142511i	−0.618315	−	0.785931i	$-0.712184\pi$
$877$	−216.476	+	124.982i	−0.246836	+	0.142511i	0.371478	+	0.928442i	$0.378851\pi$
$878$		0			0
$879$	−340.280	−	589.382i	−0.387121	−	0.670514i
$880$		0			0
$881$	1012.94			1.14977			0.574884	−	0.818235i	$-0.305047\pi$
$881$	1012.94			1.14977			0.574884	+	0.818235i	$0.305047\pi$
$882$		0			0
$883$	474.892	−	822.538i	0.537817	−	0.931527i	−0.461204	−	0.887294i	$-0.652582\pi$
$883$	474.892	−	822.538i	0.537817	−	0.931527i	0.999021	−	0.0442325i	$-0.0140842\pi$
$884$		0			0
$885$	−1129.41			−1.27617
$886$		0			0
$887$	−151.364	−	87.3903i	−0.170648	−	0.0985234i	0.412244	−	0.911074i	$-0.364745\pi$
$887$	−151.364	−	87.3903i	−0.170648	−	0.0985234i	−0.582891	+	0.812550i	$0.698079\pi$
$888$		0			0
$889$	52.5007	+	30.3113i	0.0590559	+	0.0340959i
$890$		0			0
$891$	57.3802	+	99.3854i	0.0643998	+	0.111544i
$892$		0			0
$893$	11.3313	−	54.6667i	0.0126890	−	0.0612169i
$894$		0			0
$895$	−25.8712	+	14.9368i	−0.0289064	+	0.0166891i
$896$		0			0
$897$	123.796	−	214.421i	0.138011	−	0.239043i
$898$		0			0
$899$	261.677	−	453.239i	0.291076	−	0.504159i
$900$		0			0
$901$		−	1113.71i		−	1.23609i
$902$		0			0
$903$	−212.580	−	122.733i	−0.235416	−	0.135917i
$904$		0			0
$905$		−	1568.44i		−	1.73308i
$906$		0			0
$907$	697.582	−	402.749i	0.769109	−	0.444045i	−0.0634475	−	0.997985i	$-0.520210\pi$
$907$	697.582	−	402.749i	0.769109	−	0.444045i	0.832557	+	0.553940i	$0.186876\pi$
$908$		0			0
$909$	256.154	+	443.671i	0.281797	+	0.488087i
$910$		0			0
$911$		−	1374.83i		−	1.50915i	−0.656216	−	0.754573i	$-0.727844\pi$
$911$		−	1374.83i		−	1.50915i	0.656216	−	0.754573i	$-0.272156\pi$
$912$		0			0
$913$	1440.40			1.57766
$914$		0			0
$915$	−390.251	+	225.312i	−0.426504	+	0.246242i
$916$		0			0
$917$	62.4117	+	108.100i	0.0680607	+	0.117885i
$918$		0			0
$919$	433.425			0.471627			0.235813	−	0.971798i	$-0.424225\pi$
$919$	433.425			0.471627			0.235813	+	0.971798i	$0.424225\pi$
$920$		0			0
$921$	−187.357	+	324.512i	−0.203428	+	0.352347i
$922$		0			0
$923$	−944.966			−1.02380
$924$		0			0
$925$	264.851	+	152.912i	0.286326	+	0.165310i
$926$		0			0
$927$	146.107	+	84.3550i	0.157613	+	0.0909978i
$928$		0			0
$929$	−352.328	−	610.250i	−0.379255	−	0.656889i	0.611699	−	0.791090i	$-0.290486\pi$
$929$	−352.328	−	610.250i	−0.379255	−	0.656889i	−0.990954	+	0.134202i	$0.957153\pi$
$930$		0			0
$931$	−785.798	+	259.720i	−0.844037	+	0.278969i
$932$		0			0
$933$	−155.906	+	90.0126i	−0.167102	+	0.0964765i
$934$		0			0
$935$	928.379	−	1608.00i	0.992918	−	1.71978i
$936$		0			0
$937$	5.90757	−	10.2322i	0.00630477	−	0.0109202i	−0.862856	−	0.505450i	$-0.831326\pi$
$937$	5.90757	−	10.2322i	0.00630477	−	0.0109202i	0.869161	+	0.494530i	$0.164660\pi$
$938$		0			0
$939$			897.416i			0.955714i
$940$		0			0
$941$	715.298	+	412.978i	0.760147	+	0.438871i	0.829349	−	0.558732i	$-0.188712\pi$
$941$	715.298	+	412.978i	0.760147	+	0.438871i	−0.0692015	+	0.997603i	$0.522045\pi$
$942$		0			0
$943$		−	551.777i		−	0.585129i
$944$		0			0
$945$	−63.7001	+	36.7773i	−0.0674075	+	0.0389178i
$946$		0			0
$947$	−198.426	−	343.684i	−0.209531	−	0.362918i	0.742036	−	0.670360i	$-0.233860\pi$
$947$	−198.426	−	343.684i	−0.209531	−	0.362918i	−0.951567	+	0.307442i	$0.900527\pi$
$948$		0			0
$949$			913.576i			0.962673i
$950$		0			0
$951$	−488.333			−0.513495
$952$		0			0
$953$	−701.008	+	404.727i	−0.735581	+	0.424688i	−0.820460	−	0.571704i	$-0.806283\pi$
$953$	−701.008	+	404.727i	−0.735581	+	0.424688i	0.0848797	+	0.996391i	$0.472949\pi$
$954$		0			0
$955$	−76.8385	−	133.088i	−0.0804592	−	0.139359i
$956$		0			0
$957$	−391.466			−0.409055
$958$		0			0
$959$	−84.8573	+	146.977i	−0.0884852	+	0.153261i
$960$		0			0
$961$	89.1839			0.0928033
$962$		0			0
$963$	199.671	+	115.280i	0.207343	+	0.119710i
$964$		0			0
$965$	1549.45	+	894.575i	1.60565	+	0.927021i
$966$		0			0
$967$	517.936	+	897.092i	0.535611	+	0.927706i	0.999133	+	0.0416208i	$0.0132521\pi$
$967$	517.936	+	897.092i	0.535611	+	0.927706i	−0.463522	+	0.886085i	$0.653415\pi$
$968$		0			0
$969$	−773.261	−	160.281i	−0.797999	−	0.165408i
$970$		0			0
$971$	608.776	−	351.477i	0.626958	−	0.361974i	−0.152615	−	0.988286i	$-0.548770\pi$
$971$	608.776	−	351.477i	0.626958	−	0.361974i	0.779573	+	0.626312i	$0.215436\pi$
$972$		0			0
$973$	157.008	−	271.947i	0.161365	−	0.279493i
$974$		0			0
$975$	87.7413	−	151.972i	0.0899911	−	0.155869i
$976$		0			0
$977$			60.2420i			0.0616602i	0.999525	+	0.0308301i	$0.00981508\pi$
$977$			60.2420i			0.0616602i	−0.999525	+	0.0308301i	$0.990185\pi$
$978$		0			0
$979$	1519.83	+	877.476i	1.55243	+	0.896298i
$980$		0			0
$981$		−	43.9234i		−	0.0447741i
$982$		0			0
$983$	1152.30	−	665.283i	1.17223	−	0.676788i	0.218027	−	0.975943i	$-0.430038\pi$
$983$	1152.30	−	665.283i	1.17223	−	0.676788i	0.954205	+	0.299154i	$0.0967045\pi$
$984$		0			0
$985$	1046.94	+	1813.35i	1.06288	+	1.84096i
$986$		0			0
$987$			11.8723i			0.0120286i
$988$		0			0
$989$	−1013.42			−1.02470
$990$		0			0
$991$	−624.323	+	360.453i	−0.629993	+	0.363727i	−0.780749	−	0.624844i	$-0.785162\pi$
$991$	−624.323	+	360.453i	−0.629993	+	0.363727i	0.150756	+	0.988571i	$0.451829\pi$
$992$		0			0
$993$	99.5302	+	172.391i	0.100232	+	0.173607i
$994$		0			0
$995$	2139.29			2.15004
$996$		0			0
$997$	907.197	−	1571.31i	0.909926	−	1.57604i	0.0957619	−	0.995404i	$-0.469471\pi$
$997$	907.197	−	1571.31i	0.909926	−	1.57604i	0.814164	−	0.580634i	$-0.197195\pi$
$998$		0			0
$999$	134.409			0.134544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.g.145.3		8
4.3	odd	2		114.3.f.b.31.2	✓	8
12.11	even	2		342.3.m.b.145.3		8
19.8	odd	6	inner	912.3.be.g.673.3		8
76.27	even	6		114.3.f.b.103.2	yes	8
228.179	odd	6		342.3.m.b.217.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.3.f.b.31.2	✓	8	4.3	odd	2
114.3.f.b.103.2	yes	8	76.27	even	6
342.3.m.b.145.3		8	12.11	even	2
342.3.m.b.217.3		8	228.179	odd	6
912.3.be.g.145.3		8	1.1	even	1	trivial
912.3.be.g.673.3		8	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(3.03409 + 5.25521i) q^{5} +2.33275 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(3.03409 + 5.25521i) q^{5} +2.33275 q^{7} +(1.50000 - 2.59808i) q^{9} -12.7512 q^{11} +(7.42129 + 4.28468i) q^{13} +(-9.10228 - 5.25521i) q^{15} +(11.9982 + 20.7815i) q^{17} +(18.0402 - 5.96259i) q^{19} +(-3.49913 + 2.02022i) q^{21} +(-8.34061 + 14.4464i) q^{23} +(-5.91146 + 10.2390i) q^{25} +5.19615i q^{27} +(-15.3502 - 8.86245i) q^{29} +29.5265i q^{31} +(19.1267 - 11.0428i) q^{33} +(7.07779 + 12.2591i) q^{35} -25.8670i q^{37} -14.8426 q^{39} +(-28.6462 + 16.5389i) q^{41} +(30.3762 + 52.6131i) q^{43} +18.2046 q^{45} +(1.46918 - 2.54469i) q^{47} -43.5583 q^{49} +(-35.9946 - 20.7815i) q^{51} +(-40.1937 - 23.2058i) q^{53} +(-38.6882 - 67.0099i) q^{55} +(-21.8965 + 24.5671i) q^{57} +(93.0601 - 53.7283i) q^{59} +(21.4370 - 37.1300i) q^{61} +(3.49913 - 6.06067i) q^{63} +52.0006i q^{65} +(-3.21307 - 1.85507i) q^{67} -28.8927i q^{69} +(-95.4988 + 55.1362i) q^{71} +(53.3048 + 92.3265i) q^{73} -20.4779i q^{75} -29.7453 q^{77} +(-105.269 + 60.7773i) q^{79} +(-4.50000 - 7.79423i) q^{81} -112.963 q^{83} +(-72.8074 + 126.106i) q^{85} +30.7004 q^{87} +(-119.192 - 68.8154i) q^{89} +(17.3120 + 9.99511i) q^{91} +(-25.5707 - 44.2898i) q^{93} +(86.0702 + 76.7137i) q^{95} +(29.4189 - 16.9850i) q^{97} +(-19.1267 + 33.1285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9	\( 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9} + 8 q^{11} + 24 q^{13} - 12 q^{15} - 20 q^{17} - 24 q^{19} - 36 q^{21} - 40 q^{23} - 88 q^{25} - 48 q^{29} - 12 q^{33} - 32 q^{35} - 48 q^{39} + 60 q^{41} + 116 q^{43} + 24 q^{45} + 68 q^{47} - 120 q^{49} + 60 q^{51} - 168 q^{53} - 232 q^{55} + 84 q^{57} + 156 q^{59} + 72 q^{61} + 36 q^{63} + 108 q^{67} - 444 q^{71} - 68 q^{73} + 296 q^{77} - 420 q^{79} - 36 q^{81} - 424 q^{83} + 40 q^{85} + 96 q^{87} - 420 q^{89} + 228 q^{91} + 84 q^{93} + 272 q^{95} + 156 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9 + 8 * q^11 + 24 * q^13 - 12 * q^15 - 20 * q^17 - 24 * q^19 - 36 * q^21 - 40 * q^23 - 88 * q^25 - 48 * q^29 - 12 * q^33 - 32 * q^35 - 48 * q^39 + 60 * q^41 + 116 * q^43 + 24 * q^45 + 68 * q^47 - 120 * q^49 + 60 * q^51 - 168 * q^53 - 232 * q^55 + 84 * q^57 + 156 * q^59 + 72 * q^61 + 36 * q^63 + 108 * q^67 - 444 * q^71 - 68 * q^73 + 296 * q^77 - 420 * q^79 - 36 * q^81 - 424 * q^83 + 40 * q^85 + 96 * q^87 - 420 * q^89 + 228 * q^91 + 84 * q^93 + 272 * q^95 + 156 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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