LMFDB - Embedded newform 256.3.h.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,3,Mod(31,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("256.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	256.h (of order $8$, degree $4$, 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:	$6.97549476762$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	256.31
Dual form			256.3.h.a.223.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.35131 - 1.80237i) q^{3} +(2.81639 + 1.16659i) q^{5} +(6.23443 - 6.23443i) q^{7} +(9.32143 - 9.32143i) q^{9} +O(q^{10})$	\(q+(4.35131 - 1.80237i) q^{3} +(2.81639 + 1.16659i) q^{5} +(6.23443 - 6.23443i) q^{7} +(9.32143 - 9.32143i) q^{9} +(-8.06262 - 3.33965i) q^{11} +(-13.3208 + 5.51766i) q^{13} +14.3576 q^{15} -4.56488i q^{17} +(13.4421 + 32.4522i) q^{19} +(15.8912 - 38.3647i) q^{21} +(6.75277 + 6.75277i) q^{23} +(-11.1065 - 11.1065i) q^{25} +(7.53841 - 18.1993i) q^{27} +(0.266504 + 0.643399i) q^{29} +0.326715i q^{31} -41.1023 q^{33} +(24.8316 - 10.2856i) q^{35} +(-31.5133 - 13.0532i) q^{37} +(-48.0182 + 48.0182i) q^{39} +(15.7509 - 15.7509i) q^{41} +(4.83274 + 2.00179i) q^{43} +(37.1271 - 15.3785i) q^{45} +49.7096 q^{47} -28.7362i q^{49} +(-8.22762 - 19.8632i) q^{51} +(-4.45882 + 10.7645i) q^{53} +(-18.8115 - 18.8115i) q^{55} +(116.982 + 116.982i) q^{57} +(13.1268 - 31.6909i) q^{59} +(35.4023 + 85.4687i) q^{61} -116.228i q^{63} -43.9535 q^{65} +(-41.3348 + 17.1214i) q^{67} +(41.5545 + 17.2124i) q^{69} +(-37.6381 + 37.6381i) q^{71} +(-52.2302 + 52.2302i) q^{73} +(-68.3461 - 28.3099i) q^{75} +(-71.0866 + 29.4450i) q^{77} -26.9061 q^{79} +25.8643i q^{81} +(10.6315 + 25.6667i) q^{83} +(5.32533 - 12.8565i) q^{85} +(2.31929 + 2.31929i) q^{87} +(-103.292 - 103.292i) q^{89} +(-48.6482 + 117.447i) q^{91} +(0.588862 + 1.42164i) q^{93} +107.080i q^{95} +77.9778 q^{97} +(-106.285 + 44.0249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{19} + 4 q^{21} + 68 q^{23} - 4 q^{25} - 100 q^{27} + 4 q^{29} - 8 q^{33} + 92 q^{35} + 4 q^{37} - 188 q^{39} - 4 q^{41} + 92 q^{43} + 40 q^{45} + 8 q^{47} + 224 q^{51} + 164 q^{53} - 252 q^{55} - 4 q^{57} + 124 q^{59} + 68 q^{61} - 8 q^{65} - 164 q^{67} - 188 q^{69} + 260 q^{71} - 4 q^{73} - 488 q^{75} - 220 q^{77} + 520 q^{79} - 484 q^{83} - 96 q^{85} + 452 q^{87} - 4 q^{89} - 196 q^{91} - 32 q^{93} - 8 q^{97} + 216 q^{99}+O(q^{100}) $ 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^19 + 4 * q^21 + 68 * q^23 - 4 * q^25 - 100 * q^27 + 4 * q^29 - 8 * q^33 + 92 * q^35 + 4 * q^37 - 188 * q^39 - 4 * q^41 + 92 * q^43 + 40 * q^45 + 8 * q^47 + 224 * q^51 + 164 * q^53 - 252 * q^55 - 4 * q^57 + 124 * q^59 + 68 * q^61 - 8 * q^65 - 164 * q^67 - 188 * q^69 + 260 * q^71 - 4 * q^73 - 488 * q^75 - 220 * q^77 + 520 * q^79 - 484 * q^83 - 96 * q^85 + 452 * q^87 - 4 * q^89 - 196 * q^91 - 32 * q^93 - 8 * q^97 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

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
$3$	4.35131	−	1.80237i	1.45044	−	0.600791i	0.488135	−	0.872768i	$-0.337678\pi$
$3$	4.35131	−	1.80237i	1.45044	−	0.600791i	0.962304	+	0.271977i	$0.0876775\pi$
$4$		0			0
$5$	2.81639	+	1.16659i	0.563278	+	0.233318i	0.646108	−	0.763246i	$-0.276396\pi$
$5$	2.81639	+	1.16659i	0.563278	+	0.233318i	−0.0828294	+	0.996564i	$0.526396\pi$
$6$		0			0
$7$	6.23443	−	6.23443i	0.890633	−	0.890633i	−0.103950	−	0.994583i	$-0.533148\pi$
$7$	6.23443	−	6.23443i	0.890633	−	0.890633i	0.994583	+	0.103950i	$0.0331481\pi$
$8$		0			0
$9$	9.32143	−	9.32143i	1.03571	−	1.03571i
$10$		0			0
$11$	−8.06262	−	3.33965i	−0.732965	−	0.303604i	−0.0151955	−	0.999885i	$-0.504837\pi$
$11$	−8.06262	−	3.33965i	−0.732965	−	0.303604i	−0.717770	+	0.696280i	$0.754837\pi$
$12$		0			0
$13$	−13.3208	+	5.51766i	−1.02468	+	0.424436i	−0.830789	−	0.556588i	$-0.812110\pi$
$13$	−13.3208	+	5.51766i	−1.02468	+	0.424436i	−0.193889	+	0.981023i	$0.562110\pi$
$14$		0			0
$15$	14.3576			0.957176
$16$		0			0
$17$		−	4.56488i		−	0.268522i	−0.990946	−	0.134261i	$-0.957134\pi$
$17$		−	4.56488i		−	0.268522i	0.990946	−	0.134261i	$-0.0428661\pi$
$18$		0			0
$19$	13.4421	+	32.4522i	0.707481	+	1.70801i	0.706201	+	0.708011i	$0.250407\pi$
$19$	13.4421	+	32.4522i	0.707481	+	1.70801i	0.00128016	+	0.999999i	$0.499593\pi$
$20$		0			0
$21$	15.8912	−	38.3647i	0.756724	−	1.82689i
$22$		0			0
$23$	6.75277	+	6.75277i	0.293599	+	0.293599i	0.838500	−	0.544901i	$-0.183433\pi$
$23$	6.75277	+	6.75277i	0.293599	+	0.293599i	−0.544901	+	0.838500i	$0.683433\pi$
$24$		0			0
$25$	−11.1065	−	11.1065i	−0.444261	−	0.444261i
$26$		0			0
$27$	7.53841	−	18.1993i	0.279200	−	0.674050i
$28$		0			0
$29$	0.266504	+	0.643399i	0.00918981	+	0.0221862i	0.928408	−	0.371563i	$-0.121178\pi$
$29$	0.266504	+	0.643399i	0.00918981	+	0.0221862i	−0.919218	+	0.393749i	$0.871178\pi$
$30$		0			0
$31$			0.326715i			0.0105392i	0.999986	+	0.00526959i	$0.00167737\pi$
$31$			0.326715i			0.0105392i	−0.999986	+	0.00526959i	$0.998323\pi$
$32$		0			0
$33$	−41.1023			−1.24552
$34$		0			0
$35$	24.8316	−	10.2856i	0.709475	−	0.293874i
$36$		0			0
$37$	−31.5133	−	13.0532i	−0.851710	−	0.352790i	−0.0862502	−	0.996274i	$-0.527488\pi$
$37$	−31.5133	−	13.0532i	−0.851710	−	0.352790i	−0.765460	+	0.643484i	$0.777488\pi$
$38$		0			0
$39$	−48.0182	+	48.0182i	−1.23124	+	1.23124i
$40$		0			0
$41$	15.7509	−	15.7509i	0.384169	−	0.384169i	−0.488433	−	0.872601i	$-0.662431\pi$
$41$	15.7509	−	15.7509i	0.384169	−	0.384169i	0.872601	+	0.488433i	$0.162431\pi$
$42$		0			0
$43$	4.83274	+	2.00179i	0.112389	+	0.0465531i	0.438170	−	0.898892i	$-0.355627\pi$
$43$	4.83274	+	2.00179i	0.112389	+	0.0465531i	−0.325780	+	0.945446i	$0.605627\pi$
$44$		0			0
$45$	37.1271	−	15.3785i	0.825046	−	0.341745i
$46$		0			0
$47$	49.7096			1.05765			0.528825	−	0.848731i	$-0.322633\pi$
$47$	49.7096			1.05765			0.528825	+	0.848731i	$0.322633\pi$
$48$		0			0
$49$		−	28.7362i		−	0.586454i
$50$		0			0
$51$	−8.22762	−	19.8632i	−0.161326	−	0.389475i
$52$		0			0
$53$	−4.45882	+	10.7645i	−0.0841286	+	0.203105i	−0.960346	−	0.278812i	$-0.910059\pi$
$53$	−4.45882	+	10.7645i	−0.0841286	+	0.203105i	0.876217	+	0.481917i	$0.160059\pi$
$54$		0			0
$55$	−18.8115	−	18.8115i	−0.342027	−	0.342027i
$56$		0			0
$57$	116.982	+	116.982i	2.05232	+	2.05232i
$58$		0			0
$59$	13.1268	−	31.6909i	0.222488	−	0.537134i	−0.772739	−	0.634724i	$-0.781114\pi$
$59$	13.1268	−	31.6909i	0.222488	−	0.537134i	0.995227	+	0.0975907i	$0.0311136\pi$
$60$		0			0
$61$	35.4023	+	85.4687i	0.580366	+	1.40113i	0.892482	+	0.451083i	$0.148962\pi$
$61$	35.4023	+	85.4687i	0.580366	+	1.40113i	−0.312116	+	0.950044i	$0.601038\pi$
$62$		0			0
$63$		−	116.228i		−	1.84488i
$64$		0			0
$65$	−43.9535			−0.676207
$66$		0			0
$67$	−41.3348	+	17.1214i	−0.616938	+	0.255544i	−0.669192	−	0.743090i	$-0.733359\pi$
$67$	−41.3348	+	17.1214i	−0.616938	+	0.255544i	0.0522539	+	0.998634i	$0.483359\pi$
$68$		0			0
$69$	41.5545	+	17.2124i	0.602239	+	0.249455i
$70$		0			0
$71$	−37.6381	+	37.6381i	−0.530114	+	0.530114i	−0.920606	−	0.390492i	$-0.872305\pi$
$71$	−37.6381	+	37.6381i	−0.530114	+	0.530114i	0.390492	+	0.920606i	$0.372305\pi$
$72$		0			0
$73$	−52.2302	+	52.2302i	−0.715482	+	0.715482i	−0.967677	−	0.252195i	$-0.918848\pi$
$73$	−52.2302	+	52.2302i	−0.715482	+	0.715482i	0.252195	+	0.967677i	$0.418848\pi$
$74$		0			0
$75$	−68.3461	−	28.3099i	−0.911282	−	0.377465i
$76$		0			0
$77$	−71.0866	+	29.4450i	−0.923203	+	0.382403i
$78$		0			0
$79$	−26.9061			−0.340583			−0.170292	−	0.985394i	$-0.554471\pi$
$79$	−26.9061			−0.340583			−0.170292	+	0.985394i	$0.554471\pi$
$80$		0			0
$81$			25.8643i			0.319313i
$82$		0			0
$83$	10.6315	+	25.6667i	0.128090	+	0.309237i	0.974894	−	0.222667i	$-0.0714764\pi$
$83$	10.6315	+	25.6667i	0.128090	+	0.309237i	−0.846804	+	0.531905i	$0.821476\pi$
$84$		0			0
$85$	5.32533	−	12.8565i	0.0626510	−	0.151253i
$86$		0			0
$87$	2.31929	+	2.31929i	0.0266585	+	0.0266585i
$88$		0			0
$89$	−103.292	−	103.292i	−1.16058	−	1.16058i	−0.984348	−	0.176234i	$-0.943609\pi$
$89$	−103.292	−	103.292i	−1.16058	−	1.16058i	−0.176234	−	0.984348i	$-0.556391\pi$
$90$		0			0
$91$	−48.6482	+	117.447i	−0.534596	+	1.29063i
$92$		0			0
$93$	0.588862	+	1.42164i	0.00633185	+	0.0152864i
$94$		0			0
$95$			107.080i			1.12715i
$96$		0			0
$97$	77.9778			0.803895			0.401948	−	0.915663i	$-0.368333\pi$
$97$	77.9778			0.803895			0.401948	+	0.915663i	$0.368333\pi$
$98$		0			0
$99$	−106.285	+	44.0249i	−1.07359	+	0.444696i
$100$		0			0
$101$	−104.064	−	43.1046i	−1.03033	−	0.426778i	−0.197500	−	0.980303i	$-0.563282\pi$
$101$	−104.064	−	43.1046i	−1.03033	−	0.426778i	−0.832833	+	0.553525i	$0.813282\pi$
$102$		0			0
$103$	76.6571	−	76.6571i	0.744243	−	0.744243i	−0.229148	−	0.973392i	$-0.573594\pi$
$103$	76.6571	−	76.6571i	0.744243	−	0.744243i	0.973392	+	0.229148i	$0.0735940\pi$
$104$		0			0
$105$	89.5117	−	89.5117i	0.852492	−	0.852492i
$106$		0			0
$107$	−40.9728	−	16.9715i	−0.382923	−	0.158612i	0.182914	−	0.983129i	$-0.441447\pi$
$107$	−40.9728	−	16.9715i	−0.382923	−	0.158612i	−0.565837	+	0.824517i	$0.691447\pi$
$108$		0			0
$109$	−102.183	+	42.3255i	−0.937456	+	0.388307i	−0.798502	−	0.601992i	$-0.794374\pi$
$109$	−102.183	+	42.3255i	−0.937456	+	0.388307i	−0.138954	+	0.990299i	$0.544374\pi$
$110$		0			0
$111$	−160.651			−1.44731
$112$		0			0
$113$			123.602i			1.09383i	0.837190	+	0.546913i	$0.184197\pi$
$113$			123.602i			1.09383i	−0.837190	+	0.546913i	$0.815803\pi$
$114$		0			0
$115$	11.1408	+	26.8962i	0.0968761	+	0.233880i
$116$		0			0
$117$	−72.7365	+	175.602i	−0.621680	+	1.50087i
$118$		0			0
$119$	−28.4594	−	28.4594i	−0.239155	−	0.239155i
$120$		0			0
$121$	−31.7073	−	31.7073i	−0.262044	−	0.262044i
$122$		0			0
$123$	40.1481	−	96.9262i	0.326408	−	0.788018i
$124$		0			0
$125$	−47.4883	−	114.647i	−0.379906	−	0.917175i
$126$		0			0
$127$			133.213i			1.04892i	0.851434	+	0.524462i	$0.175734\pi$
$127$			133.213i			1.04892i	−0.851434	+	0.524462i	$0.824266\pi$
$128$		0			0
$129$	24.6367			0.190982
$130$		0			0
$131$	228.056	−	94.4640i	1.74089	−	0.721100i	0.742185	−	0.670195i	$-0.233790\pi$
$131$	228.056	−	94.4640i	1.74089	−	0.721100i	0.998704	−	0.0509041i	$-0.0162103\pi$
$132$		0			0
$133$	286.125	+	118.517i	2.15132	+	0.891104i
$134$		0			0
$135$	42.4622	−	42.4622i	0.314535	−	0.314535i
$136$		0			0
$137$	−111.817	+	111.817i	−0.816180	+	0.816180i	−0.985552	−	0.169372i	$-0.945826\pi$
$137$	−111.817	+	111.817i	−0.816180	+	0.816180i	0.169372	+	0.985552i	$0.445826\pi$
$138$		0			0
$139$	31.7750	+	13.1616i	0.228597	+	0.0946880i	0.494042	−	0.869438i	$-0.335519\pi$
$139$	31.7750	+	13.1616i	0.228597	+	0.0946880i	−0.265445	+	0.964126i	$0.585519\pi$
$140$		0			0
$141$	216.302	−	89.5952i	1.53406	−	0.635427i
$142$		0			0
$143$	125.828			0.879914
$144$		0			0
$145$			2.12296i			0.0146411i
$146$		0			0
$147$	−51.7934	−	125.040i	−0.352336	−	0.850615i
$148$		0			0
$149$	108.344	−	261.565i	0.727140	−	1.75547i	0.0752422	−	0.997165i	$-0.476027\pi$
$149$	108.344	−	261.565i	0.727140	−	1.75547i	0.651898	−	0.758307i	$-0.273973\pi$
$150$		0			0
$151$	−51.5292	−	51.5292i	−0.341253	−	0.341253i	0.515585	−	0.856838i	$-0.327575\pi$
$151$	−51.5292	−	51.5292i	−0.341253	−	0.341253i	−0.856838	+	0.515585i	$0.827575\pi$
$152$		0			0
$153$	−42.5512	−	42.5512i	−0.278112	−	0.278112i
$154$		0			0
$155$	−0.381142	+	0.920157i	−0.00245898	+	0.00593650i
$156$		0			0
$157$	−39.3450	−	94.9872i	−0.250605	−	0.605014i	0.747648	−	0.664095i	$-0.231183\pi$
$157$	−39.3450	−	94.9872i	−0.250605	−	0.605014i	−0.998253	+	0.0590811i	$0.981183\pi$
$158$		0			0
$159$			54.8764i			0.345134i
$160$		0			0
$161$	84.1994			0.522978
$162$		0			0
$163$	−4.97467	+	2.06057i	−0.0305194	+	0.0126416i	−0.397891	−	0.917433i	$-0.630258\pi$
$163$	−4.97467	+	2.06057i	−0.0305194	+	0.0126416i	0.367372	+	0.930074i	$0.380258\pi$
$164$		0			0
$165$	−115.760	−	47.9494i	−0.701577	−	0.290603i
$166$		0			0
$167$	165.012	−	165.012i	0.988097	−	0.988097i	−0.0118333	−	0.999930i	$-0.503767\pi$
$167$	165.012	−	165.012i	0.988097	−	0.988097i	0.999930	+	0.0118333i	$0.00376674\pi$
$168$		0			0
$169$	27.4985	−	27.4985i	0.162713	−	0.162713i
$170$		0			0
$171$	427.801	+	177.201i	2.50176	+	1.03626i
$172$		0			0
$173$	115.760	−	47.9493i	0.669132	−	0.277163i	−0.0221438	−	0.999755i	$-0.507049\pi$
$173$	115.760	−	47.9493i	0.669132	−	0.277163i	0.691275	+	0.722591i	$0.257049\pi$
$174$		0			0
$175$	−138.486			−0.791348
$176$		0			0
$177$		−	161.556i		−	0.912748i
$178$		0			0
$179$	−44.8368	−	108.246i	−0.250485	−	0.604724i	0.747758	−	0.663971i	$-0.231130\pi$
$179$	−44.8368	−	108.246i	−0.250485	−	0.604724i	−0.998243	+	0.0592467i	$0.981130\pi$
$180$		0			0
$181$	−80.3652	+	194.019i	−0.444007	+	1.07193i	0.530524	+	0.847670i	$0.321995\pi$
$181$	−80.3652	+	194.019i	−0.444007	+	1.07193i	−0.974530	+	0.224256i	$0.928005\pi$
$182$		0			0
$183$	308.093	+	308.093i	1.68357	+	1.68357i
$184$		0			0
$185$	−73.5260	−	73.5260i	−0.397438	−	0.397438i
$186$		0			0
$187$	−15.2451	+	36.8049i	−0.0815245	+	0.196818i
$188$		0			0
$189$	−66.4648	−	160.460i	−0.351666	−	0.848996i
$190$		0			0
$191$		−	338.117i		−	1.77025i	−0.465357	−	0.885123i	$-0.654074\pi$
$191$		−	338.117i		−	1.77025i	0.465357	−	0.885123i	$-0.345926\pi$
$192$		0			0
$193$	234.508			1.21507			0.607533	−	0.794295i	$-0.292159\pi$
$193$	234.508			1.21507			0.607533	+	0.794295i	$0.292159\pi$
$194$		0			0
$195$	−191.255	+	79.2206i	−0.980797	+	0.406259i
$196$		0			0
$197$	−237.007	−	98.1713i	−1.20308	−	0.498332i	−0.311086	−	0.950382i	$-0.600693\pi$
$197$	−237.007	−	98.1713i	−1.20308	−	0.498332i	−0.891993	+	0.452050i	$0.850693\pi$
$198$		0			0
$199$	−39.2172	+	39.2172i	−0.197071	+	0.197071i	−0.798743	−	0.601672i	$-0.794501\pi$
$199$	−39.2172	+	39.2172i	−0.197071	+	0.197071i	0.601672	+	0.798743i	$0.294501\pi$
$200$		0			0
$201$	−149.002	+	149.002i	−0.741302	+	0.741302i
$202$		0			0
$203$	5.67273	+	2.34972i	0.0279445	+	0.0115750i
$204$		0			0
$205$	62.7356	−	25.9859i	0.306027	−	0.126761i
$206$		0			0
$207$	125.891			0.608169
$208$		0			0
$209$		−	306.542i		−	1.46671i
$210$		0			0
$211$	−79.9026	−	192.902i	−0.378685	−	0.914227i	−0.992213	−	0.124554i	$-0.960250\pi$
$211$	−79.9026	−	192.902i	−0.378685	−	0.914227i	0.613528	−	0.789673i	$-0.289750\pi$
$212$		0			0
$213$	−95.9373	+	231.613i	−0.450410	+	1.08739i
$214$		0			0
$215$	11.2756	+	11.2756i	0.0524448	+	0.0524448i
$216$		0			0
$217$	2.03688	+	2.03688i	0.00938655	+	0.00938655i
$218$		0			0
$219$	−133.132	+	321.408i	−0.607907	+	1.46762i
$220$		0			0
$221$	25.1875	+	60.8079i	0.113970	+	0.275149i
$222$		0			0
$223$			344.421i			1.54449i	0.635326	+	0.772244i	$0.280866\pi$
$223$			344.421i			1.54449i	−0.635326	+	0.772244i	$0.719134\pi$
$224$		0			0
$225$	−207.058			−0.920256
$226$		0			0
$227$	68.2639	−	28.2758i	0.300722	−	0.124563i	−0.227220	−	0.973843i	$-0.572964\pi$
$227$	68.2639	−	28.2758i	0.300722	−	0.124563i	0.527942	+	0.849280i	$0.322964\pi$
$228$		0			0
$229$	41.8202	+	17.3225i	0.182621	+	0.0756440i	0.472120	−	0.881534i	$-0.343489\pi$
$229$	41.8202	+	17.3225i	0.182621	+	0.0756440i	−0.289499	+	0.957178i	$0.593489\pi$
$230$		0			0
$231$	−256.249	+	256.249i	−1.10930	+	1.10930i
$232$		0			0
$233$	203.044	−	203.044i	0.871432	−	0.871432i	−0.121197	−	0.992629i	$-0.538673\pi$
$233$	203.044	−	203.044i	0.871432	−	0.871432i	0.992629	+	0.121197i	$0.0386731\pi$
$234$		0			0
$235$	140.002	+	57.9906i	0.595752	+	0.246768i
$236$		0			0
$237$	−117.077	+	48.4948i	−0.493995	+	0.204619i
$238$		0			0
$239$	−87.6710			−0.366824			−0.183412	−	0.983036i	$-0.558714\pi$
$239$	−87.6710			−0.366824			−0.183412	+	0.983036i	$0.558714\pi$
$240$		0			0
$241$		−	15.4754i		−	0.0642135i	−0.999484	−	0.0321067i	$-0.989778\pi$
$241$		−	15.4754i		−	0.0642135i	0.999484	−	0.0321067i	$-0.0102216\pi$
$242$		0			0
$243$	114.463	+	276.338i	0.471041	+	1.13719i
$244$		0			0
$245$	33.5233	−	80.9325i	0.136830	−	0.330337i
$246$		0			0
$247$	−358.121	−	358.121i	−1.44988	−	1.44988i
$248$		0			0
$249$	92.5220	+	92.5220i	0.371574	+	0.371574i
$250$		0			0
$251$	95.9530	−	231.651i	0.382283	−	0.922913i	−0.609241	−	0.792985i	$-0.708526\pi$
$251$	95.9530	−	231.651i	0.382283	−	0.922913i	0.991524	−	0.129927i	$-0.0414743\pi$
$252$		0			0
$253$	−31.8932	−	76.9969i	−0.126060	−	0.304336i
$254$		0			0
$255$		−	65.5409i		−	0.257023i
$256$		0			0
$257$	−131.142			−0.510282			−0.255141	−	0.966904i	$-0.582122\pi$
$257$	−131.142			−0.510282			−0.255141	+	0.966904i	$0.582122\pi$
$258$		0			0
$259$	−277.847	+	115.088i	−1.07277	+	0.444355i
$260$		0			0
$261$	8.48160	+	3.51319i	0.0324965	+	0.0134605i
$262$		0			0
$263$	281.350	−	281.350i	1.06977	−	1.06977i	0.0723955	−	0.997376i	$-0.476936\pi$
$263$	281.350	−	281.350i	1.06977	−	1.06977i	0.997376	−	0.0723955i	$-0.0230644\pi$
$264$		0			0
$265$	−25.1156	+	25.1156i	−0.0947757	+	0.0947757i
$266$		0			0
$267$	−635.626	−	263.285i	−2.38062	−	0.986085i
$268$		0			0
$269$	−133.290	+	55.2107i	−0.495503	+	0.205244i	−0.616419	−	0.787419i	$-0.711417\pi$
$269$	−133.290	+	55.2107i	−0.495503	+	0.205244i	0.120915	+	0.992663i	$0.461417\pi$
$270$		0			0
$271$	368.673			1.36042			0.680208	−	0.733019i	$-0.261889\pi$
$271$	368.673			1.36042			0.680208	+	0.733019i	$0.261889\pi$
$272$		0			0
$273$			598.732i			2.19316i
$274$		0			0
$275$	52.4559	+	126.640i	0.190749	+	0.460508i
$276$		0			0
$277$	−21.6001	+	52.1472i	−0.0779786	+	0.188257i	−0.958061	−	0.286564i	$-0.907487\pi$
$277$	−21.6001	+	52.1472i	−0.0779786	+	0.188257i	0.880083	+	0.474821i	$0.157487\pi$
$278$		0			0
$279$	3.04545	+	3.04545i	0.0109156	+	0.0109156i
$280$		0			0
$281$	85.0605	+	85.0605i	0.302706	+	0.302706i	0.842072	−	0.539365i	$-0.181336\pi$
$281$	85.0605	+	85.0605i	0.302706	+	0.302706i	−0.539365	+	0.842072i	$0.681336\pi$
$282$		0			0
$283$	27.0948	−	65.4127i	0.0957414	−	0.231140i	−0.868752	−	0.495248i	$-0.835077\pi$
$283$	27.0948	−	65.4127i	0.0957414	−	0.231140i	0.964493	+	0.264107i	$0.0850773\pi$
$284$		0			0
$285$	192.997	+	465.937i	0.677184	+	1.63487i
$286$		0			0
$287$		−	196.396i		−	0.684306i
$288$		0			0
$289$	268.162			0.927896
$290$		0			0
$291$	339.306	−	140.545i	1.16600	−	0.482973i
$292$		0			0
$293$	321.033	+	132.976i	1.09568	+	0.453844i	0.855983	−	0.517005i	$-0.172953\pi$
$293$	321.033	+	132.976i	1.09568	+	0.453844i	0.239694	+	0.970849i	$0.422953\pi$
$294$		0			0
$295$	73.9404	−	73.9404i	0.250645	−	0.250645i
$296$		0			0
$297$	−121.559	+	121.559i	−0.409289	+	0.409289i
$298$		0			0
$299$	−127.212	−	52.6929i	−0.425458	−	0.176231i
$300$		0			0
$301$	42.6094	−	17.6494i	0.141559	−	0.0586358i
$302$		0			0
$303$	−530.504			−1.75084
$304$		0			0
$305$			282.013i			0.924634i
$306$		0			0
$307$	−92.6973	−	223.791i	−0.301946	−	0.728961i	−0.999918	−	0.0128360i	$-0.995914\pi$
$307$	−92.6973	−	223.791i	−0.301946	−	0.728961i	0.697972	−	0.716125i	$-0.254086\pi$
$308$		0			0
$309$	195.394	−	471.724i	0.632344	−	1.52661i
$310$		0			0
$311$	44.5768	+	44.5768i	0.143334	+	0.143334i	0.775133	−	0.631799i	$-0.217683\pi$
$311$	44.5768	+	44.5768i	0.143334	+	0.143334i	−0.631799	+	0.775133i	$0.717683\pi$
$312$		0			0
$313$	−27.9303	−	27.9303i	−0.0892343	−	0.0892343i	0.661081	−	0.750315i	$-0.270098\pi$
$313$	−27.9303	−	27.9303i	−0.0892343	−	0.0892343i	−0.750315	+	0.661081i	$0.770098\pi$
$314$		0			0
$315$	135.590	−	327.342i	0.430443	−	1.03918i
$316$		0			0
$317$	125.850	+	303.829i	0.397003	+	0.958450i	0.988373	+	0.152049i	$0.0485873\pi$
$317$	125.850	+	303.829i	0.397003	+	0.958450i	−0.591370	+	0.806400i	$0.701413\pi$
$318$		0			0
$319$		−	6.07751i		−	0.0190518i
$320$		0			0
$321$	−208.874			−0.650699
$322$		0			0
$323$	148.140	−	61.3618i	0.458639	−	0.189975i
$324$		0			0
$325$	209.230	+	86.6660i	0.643785	+	0.266665i
$326$		0			0
$327$	−368.343	+	368.343i	−1.12643	+	1.12643i
$328$		0			0
$329$	309.911	−	309.911i	0.941978	−	0.941978i
$330$		0			0
$331$	−169.515	−	70.2155i	−0.512131	−	0.212131i	0.111626	−	0.993750i	$-0.464394\pi$
$331$	−169.515	−	70.2155i	−0.512131	−	0.212131i	−0.623756	+	0.781619i	$0.714394\pi$
$332$		0			0
$333$	−415.423	+	172.074i	−1.24752	+	0.516739i
$334$		0			0
$335$	−136.389			−0.407131
$336$		0			0
$337$			67.3116i			0.199738i	0.995001	+	0.0998689i	$0.0318423\pi$
$337$			67.3116i			0.199738i	−0.995001	+	0.0998689i	$0.968158\pi$
$338$		0			0
$339$	222.778	+	537.833i	0.657161	+	1.58653i
$340$		0			0
$341$	1.09111	−	2.63418i	0.00319974	−	0.00772486i
$342$		0			0
$343$	126.333	+	126.333i	0.368318	+	0.368318i
$344$		0			0
$345$	96.9538	+	96.9538i	0.281026	+	0.281026i
$346$		0			0
$347$	−107.157	+	258.699i	−0.308809	+	0.745530i	0.690935	+	0.722916i	$0.257199\pi$
$347$	−107.157	+	258.699i	−0.308809	+	0.745530i	−0.999744	+	0.0226140i	$0.992801\pi$
$348$		0			0
$349$	−165.558	−	399.692i	−0.474378	−	1.14525i	−0.962209	−	0.272311i	$-0.912212\pi$
$349$	−165.558	−	399.692i	−0.474378	−	1.14525i	0.487831	−	0.872938i	$-0.337788\pi$
$350$		0			0
$351$			284.024i			0.809187i
$352$		0			0
$353$	−574.524			−1.62755			−0.813773	−	0.581183i	$-0.802590\pi$
$353$	−574.524			−1.62755			−0.813773	+	0.581183i	$0.802590\pi$
$354$		0			0
$355$	−149.912	+	62.0955i	−0.422287	+	0.174917i
$356$		0			0
$357$	−175.130	−	72.5414i	−0.490562	−	0.203197i
$358$		0			0
$359$	−499.243	+	499.243i	−1.39065	+	1.39065i	−0.566782	+	0.823868i	$0.691812\pi$
$359$	−499.243	+	499.243i	−1.39065	+	1.39065i	−0.823868	+	0.566782i	$0.808188\pi$
$360$		0			0
$361$	−617.189	+	617.189i	−1.70966	+	1.70966i
$362$		0			0
$363$	−195.117	−	80.8201i	−0.537512	−	0.222645i
$364$		0			0
$365$	−208.032	+	86.1696i	−0.569950	+	0.236081i
$366$		0			0
$367$	−295.566			−0.805357			−0.402679	−	0.915341i	$-0.631921\pi$
$367$	−295.566			−0.805357			−0.402679	+	0.915341i	$0.631921\pi$
$368$		0			0
$369$		−	293.642i		−	0.795778i
$370$		0			0
$371$	39.3126	+	94.9090i	0.105964	+	0.255819i
$372$		0			0
$373$	133.878	−	323.209i	0.358921	−	0.866512i	−0.636531	−	0.771251i	$-0.719631\pi$
$373$	133.878	−	323.209i	0.358921	−	0.866512i	0.995452	−	0.0952612i	$-0.0303686\pi$
$374$		0			0
$375$	−413.273	−	413.273i	−1.10206	−	1.10206i
$376$		0			0
$377$	−7.10011	−	7.10011i	−0.0188332	−	0.0188332i
$378$		0			0
$379$	170.642	−	411.967i	0.450244	−	1.08698i	−0.521986	−	0.852954i	$-0.674809\pi$
$379$	170.642	−	411.967i	0.450244	−	1.08698i	0.972229	−	0.234030i	$-0.0751915\pi$
$380$		0			0
$381$	240.100	+	579.654i	0.630185	+	1.52140i
$382$		0			0
$383$		−	254.902i		−	0.665540i	−0.943008	−	0.332770i	$-0.892017\pi$
$383$		−	254.902i		−	0.665540i	0.943008	−	0.332770i	$-0.107983\pi$
$384$		0			0
$385$	−234.558			−0.609242
$386$		0			0
$387$	63.7075	−	26.3885i	0.164619	−	0.0681874i
$388$		0			0
$389$	−687.246	−	284.667i	−1.76670	−	0.731791i	−0.995453	−	0.0952550i	$-0.969633\pi$
$389$	−687.246	−	284.667i	−1.76670	−	0.731791i	−0.771247	−	0.636536i	$-0.780367\pi$
$390$		0			0
$391$	30.8256	−	30.8256i	0.0788379	−	0.0788379i
$392$		0			0
$393$	822.086	−	822.086i	2.09182	−	2.09182i
$394$		0			0
$395$	−75.7781	−	31.3883i	−0.191843	−	0.0794640i
$396$		0			0
$397$	56.8981	−	23.5679i	0.143320	−	0.0593651i	−0.309871	−	0.950779i	$-0.600286\pi$
$397$	56.8981	−	23.5679i	0.143320	−	0.0593651i	0.453191	+	0.891414i	$0.350286\pi$
$398$		0			0
$399$	1458.63			3.65572
$400$		0			0
$401$		−	704.010i		−	1.75564i	−0.478994	−	0.877818i	$-0.658999\pi$
$401$		−	704.010i		−	1.75564i	0.478994	−	0.877818i	$-0.341001\pi$
$402$		0			0
$403$	−1.80270	−	4.35211i	−0.00447321	−	0.0107993i
$404$		0			0
$405$	−30.1730	+	72.8441i	−0.0745013	+	0.179862i
$406$		0			0
$407$	210.486	+	210.486i	0.517166	+	0.517166i
$408$		0			0
$409$	528.488	+	528.488i	1.29215	+	1.29215i	0.933457	+	0.358690i	$0.116776\pi$
$409$	528.488	+	528.488i	1.29215	+	1.29215i	0.358690	+	0.933457i	$0.383224\pi$
$410$		0			0
$411$	−285.014	+	688.085i	−0.693465	+	1.67417i
$412$		0			0
$413$	−115.737	−	279.413i	−0.280234	−	0.676544i
$414$		0			0
$415$			84.6901i			0.204072i
$416$		0			0
$417$	161.985			0.388453
$418$		0			0
$419$	−153.485	+	63.5754i	−0.366312	+	0.151731i	−0.558244	−	0.829677i	$-0.688525\pi$
$419$	−153.485	+	63.5754i	−0.366312	+	0.151731i	0.191932	+	0.981408i	$0.438525\pi$
$420$		0			0
$421$	240.175	+	99.4838i	0.570487	+	0.236304i	0.649231	−	0.760591i	$-0.275091\pi$
$421$	240.175	+	99.4838i	0.570487	+	0.236304i	−0.0787437	+	0.996895i	$0.525091\pi$
$422$		0			0
$423$	463.364	−	463.364i	1.09542	−	1.09542i
$424$		0			0
$425$	−50.7000	+	50.7000i	−0.119294	+	0.119294i
$426$		0			0
$427$	753.562	+	312.136i	1.76478	+	0.730997i
$428$		0			0
$429$	547.516	−	226.789i	1.27626	−	0.528645i
$430$		0			0
$431$	607.318			1.40909			0.704546	−	0.709659i	$-0.251151\pi$
$431$	607.318			1.40909			0.704546	+	0.709659i	$0.251151\pi$
$432$		0			0
$433$		−	233.380i		−	0.538984i	−0.963003	−	0.269492i	$-0.913144\pi$
$433$		−	233.380i		−	0.538984i	0.963003	−	0.269492i	$-0.0868557\pi$
$434$		0			0
$435$	3.82637	+	9.23768i	0.00879626	+	0.0212361i
$436$		0			0
$437$	−128.371	+	309.914i	−0.293754	+	0.709185i
$438$		0			0
$439$	496.850	+	496.850i	1.13178	+	1.13178i	0.989882	+	0.141896i	$0.0453200\pi$
$439$	496.850	+	496.850i	1.13178	+	1.13178i	0.141896	+	0.989882i	$0.454680\pi$
$440$		0			0
$441$	−267.863	−	267.863i	−0.607399	−	0.607399i
$442$		0			0
$443$	59.8483	−	144.487i	0.135098	−	0.326155i	−0.841824	−	0.539752i	$-0.818518\pi$
$443$	59.8483	−	144.487i	0.135098	−	0.326155i	0.976922	+	0.213597i	$0.0685180\pi$
$444$		0			0
$445$	−170.411	−	411.409i	−0.382947	−	0.924515i
$446$		0			0
$447$		−	1333.43i		−	2.98306i
$448$		0			0
$449$	−15.4530			−0.0344165			−0.0172082	−	0.999852i	$-0.505478\pi$
$449$	−15.4530			−0.0344165			−0.0172082	+	0.999852i	$0.505478\pi$
$450$		0			0
$451$	−179.596	+	74.3911i	−0.398217	+	0.164947i
$452$		0			0
$453$	−317.095	−	131.345i	−0.699989	−	0.289945i
$454$		0			0
$455$	−274.025	+	274.025i	−0.602253	+	0.602253i
$456$		0			0
$457$	−93.8365	+	93.8365i	−0.205332	+	0.205332i	−0.802280	−	0.596948i	$-0.796380\pi$
$457$	−93.8365	+	93.8365i	−0.205332	+	0.205332i	0.596948	+	0.802280i	$0.296380\pi$
$458$		0			0
$459$	−83.0778	−	34.4120i	−0.180997	−	0.0749716i
$460$		0			0
$461$	574.348	−	237.903i	1.24588	−	0.516058i	0.340329	−	0.940306i	$-0.389462\pi$
$461$	574.348	−	237.903i	1.24588	−	0.516058i	0.905546	+	0.424248i	$0.139462\pi$
$462$		0			0
$463$	−568.089			−1.22697			−0.613487	−	0.789705i	$-0.710234\pi$
$463$	−568.089			−1.22697			−0.613487	+	0.789705i	$0.710234\pi$
$464$		0			0
$465$			4.69085i			0.0100879i
$466$		0			0
$467$	−156.459	−	377.726i	−0.335030	−	0.808835i	−0.998178	−	0.0603459i	$-0.980780\pi$
$467$	−156.459	−	377.726i	−0.335030	−	0.808835i	0.663147	−	0.748489i	$-0.269220\pi$
$468$		0			0
$469$	−150.957	+	364.442i	−0.321869	+	0.777061i
$470$		0			0
$471$	−342.405	−	342.405i	−0.726974	−	0.726974i
$472$		0			0
$473$	−32.2793	−	32.2793i	−0.0682437	−	0.0682437i
$474$		0			0
$475$	211.136	−	509.727i	0.444497	−	1.07311i
$476$		0			0
$477$	58.7783	+	141.903i	0.123225	+	0.297492i
$478$		0			0
$479$			327.880i			0.684509i	0.939607	+	0.342254i	$0.111190\pi$
$479$			327.880i			0.684509i	−0.939607	+	0.342254i	$0.888810\pi$
$480$		0			0
$481$	491.806			1.02247
$482$		0			0
$483$	366.378	−	151.759i	0.758547	−	0.314200i
$484$		0			0
$485$	219.616	+	90.9680i	0.452817	+	0.187563i
$486$		0			0
$487$	147.493	−	147.493i	0.302861	−	0.302861i	−0.539271	−	0.842132i	$-0.681300\pi$
$487$	147.493	−	147.493i	0.302861	−	0.302861i	0.842132	+	0.539271i	$0.181300\pi$
$488$		0			0
$489$	−17.9324	+	17.9324i	−0.0366716	+	0.0366716i
$490$		0			0
$491$	598.802	+	248.032i	1.21956	+	0.505157i	0.897269	−	0.441485i	$-0.145548\pi$
$491$	598.802	+	248.032i	1.21956	+	0.505157i	0.322288	+	0.946642i	$0.395548\pi$
$492$		0			0
$493$	2.93704	−	1.21656i	0.00595748	−	0.00246767i
$494$		0			0
$495$	−350.700			−0.708485
$496$		0			0
$497$			469.304i			0.944274i
$498$		0			0
$499$	58.1446	+	140.373i	0.116522	+	0.281309i	0.971371	−	0.237568i	$-0.0763502\pi$
$499$	58.1446	+	140.373i	0.116522	+	0.281309i	−0.854849	+	0.518877i	$0.826350\pi$
$500$		0			0
$501$	420.606	−	1015.43i	0.839533	−	2.02681i
$502$		0			0
$503$	256.204	+	256.204i	0.509351	+	0.509351i	0.914327	−	0.404976i	$-0.132720\pi$
$503$	256.204	+	256.204i	0.509351	+	0.509351i	−0.404976	+	0.914327i	$0.632720\pi$
$504$		0			0
$505$	−242.799	−	242.799i	−0.480789	−	0.480789i
$506$		0			0
$507$	70.0921	−	169.217i	0.138249	−	0.333762i
$508$		0			0
$509$	229.271	+	553.510i	0.450435	+	1.08745i	0.972157	+	0.234331i	$0.0752898\pi$
$509$	229.271	+	553.510i	0.450435	+	1.08745i	−0.521722	+	0.853115i	$0.674710\pi$
$510$		0			0
$511$			651.251i			1.27446i
$512$		0			0
$513$	691.941			1.34881
$514$		0			0
$515$	305.324	−	126.469i	0.592861	−	0.245571i
$516$		0			0
$517$	−400.789	−	166.012i	−0.775221	−	0.321107i
$518$		0			0
$519$	417.285	−	417.285i	0.804017	−	0.804017i
$520$		0			0
$521$	80.7376	−	80.7376i	0.154967	−	0.154967i	−0.625365	−	0.780332i	$-0.715050\pi$
$521$	80.7376	−	80.7376i	0.154967	−	0.154967i	0.780332	+	0.625365i	$0.215050\pi$
$522$		0			0
$523$	123.197	+	51.0300i	0.235559	+	0.0975717i	0.497341	−	0.867555i	$-0.334310\pi$
$523$	123.197	+	51.0300i	0.235559	+	0.0975717i	−0.261781	+	0.965127i	$0.584310\pi$
$524$		0			0
$525$	−602.595	+	249.603i	−1.14780	+	0.475435i
$526$		0			0
$527$	1.49141			0.00283001
$528$		0			0
$529$		−	437.800i		−	0.827599i
$530$		0			0
$531$	−173.044	−	417.765i	−0.325883	−	0.786751i
$532$		0			0
$533$	−122.907	+	296.723i	−0.230594	+	0.556704i
$534$		0			0
$535$	−95.5966	−	95.5966i	−0.178685	−	0.178685i
$536$		0			0
$537$	−390.198	−	390.198i	−0.726626	−	0.726626i
$538$		0			0
$539$	−95.9689	+	231.689i	−0.178050	+	0.429850i
$540$		0			0
$541$	−184.993	−	446.613i	−0.341947	−	0.825532i	−0.997519	−	0.0703996i	$-0.977573\pi$
$541$	−184.993	−	446.613i	−0.341947	−	0.825532i	0.655572	−	0.755132i	$-0.272427\pi$
$542$		0			0
$543$			989.085i			1.82152i
$544$		0			0
$545$	−337.163			−0.618648
$546$		0			0
$547$	−570.529	+	236.321i	−1.04302	+	0.432031i	−0.837394	−	0.546600i	$-0.815922\pi$
$547$	−570.529	+	236.321i	−1.04302	+	0.432031i	−0.205622	+	0.978632i	$0.565922\pi$
$548$		0			0
$549$	1126.69	+	466.691i	2.05226	+	0.850074i
$550$		0			0
$551$	−17.2973	+	17.2973i	−0.0313926	+	0.0313926i
$552$		0			0
$553$	−167.744	+	167.744i	−0.303335	+	0.303335i
$554$		0			0
$555$	−452.456	−	187.413i	−0.815236	−	0.337682i
$556$		0			0
$557$	−340.362	+	140.983i	−0.611063	+	0.253111i	−0.666683	−	0.745341i	$-0.732286\pi$
$557$	−340.362	+	140.983i	−0.611063	+	0.253111i	0.0556199	+	0.998452i	$0.482286\pi$
$558$		0			0
$559$	−75.4212			−0.134922
$560$		0			0
$561$			187.627i			0.334451i
$562$		0			0
$563$	241.885	+	583.963i	0.429637	+	1.03723i	0.979403	+	0.201916i	$0.0647168\pi$
$563$	241.885	+	583.963i	0.429637	+	1.03723i	−0.549766	+	0.835319i	$0.685283\pi$
$564$		0			0
$565$	−144.193	+	348.113i	−0.255209	+	0.616128i
$566$		0			0
$567$	161.249	+	161.249i	0.284390	+	0.284390i
$568$		0			0
$569$	88.6373	+	88.6373i	0.155777	+	0.155777i	0.780693	−	0.624915i	$-0.214866\pi$
$569$	88.6373	+	88.6373i	0.155777	+	0.155777i	−0.624915	+	0.780693i	$0.714866\pi$
$570$		0			0
$571$	−160.453	+	387.367i	−0.281003	+	0.678401i	−0.999860	−	0.0167573i	$-0.994666\pi$
$571$	−160.453	+	387.367i	−0.281003	+	0.678401i	0.718857	+	0.695158i	$0.244666\pi$
$572$		0			0
$573$	−609.413	−	1471.25i	−1.06355	−	2.56763i
$574$		0			0
$575$		−	150.000i		−	0.260869i
$576$		0			0
$577$	−501.285			−0.868778			−0.434389	−	0.900725i	$-0.643036\pi$
$577$	−501.285			−0.868778			−0.434389	+	0.900725i	$0.643036\pi$
$578$		0			0
$579$	1020.42	−	422.670i	1.76238	−	0.730000i
$580$		0			0
$581$	226.299	+	93.7360i	0.389498	+	0.161336i
$582$		0			0
$583$	71.8995	−	71.8995i	0.123327	−	0.123327i
$584$		0			0
$585$	−409.709	+	409.709i	−0.700358	+	0.700358i
$586$		0			0
$587$	−805.600	−	333.691i	−1.37240	−	0.568468i	−0.429964	−	0.902846i	$-0.641474\pi$
$587$	−805.600	−	333.691i	−1.37240	−	0.568468i	−0.942439	+	0.334378i	$0.891474\pi$
$588$		0			0
$589$	−10.6026	+	4.39175i	−0.0180010	+	0.00745628i
$590$		0			0
$591$	−1208.23			−2.04438
$592$		0			0
$593$			1035.33i			1.74591i	0.487798	+	0.872957i	$0.337800\pi$
$593$			1035.33i			1.74591i	−0.487798	+	0.872957i	$0.662200\pi$
$594$		0			0
$595$	−46.9525	−	113.353i	−0.0789117	−	0.190510i
$596$		0			0
$597$	−99.9623	+	241.330i	−0.167441	+	0.404238i
$598$		0			0
$599$	−361.938	−	361.938i	−0.604237	−	0.604237i	0.337197	−	0.941434i	$-0.390521\pi$
$599$	−361.938	−	361.938i	−0.604237	−	0.604237i	−0.941434	+	0.337197i	$0.890521\pi$
$600$		0			0
$601$	−221.839	−	221.839i	−0.369116	−	0.369116i	0.498039	−	0.867155i	$-0.334054\pi$
$601$	−221.839	−	221.839i	−0.369116	−	0.369116i	−0.867155	+	0.498039i	$0.834054\pi$
$602$		0			0
$603$	−225.703	+	544.896i	−0.374301	+	0.903642i
$604$		0			0
$605$	−52.3109	−	126.290i	−0.0864642	−	0.208743i
$606$		0			0
$607$			465.834i			0.767437i	0.923450	+	0.383719i	$0.125357\pi$
$607$			465.834i			0.767437i	−0.923450	+	0.383719i	$0.874643\pi$
$608$		0			0
$609$	28.9189			0.0474859
$610$		0			0
$611$	−662.172	+	274.281i	−1.08375	+	0.448905i
$612$		0			0
$613$	−292.579	−	121.190i	−0.477290	−	0.197700i	0.131051	−	0.991376i	$-0.458165\pi$
$613$	−292.579	−	121.190i	−0.477290	−	0.197700i	−0.608341	+	0.793676i	$0.708165\pi$
$614$		0			0
$615$	226.146	−	226.146i	0.367717	−	0.367717i
$616$		0			0
$617$	−226.657	+	226.657i	−0.367354	+	0.367354i	−0.866511	−	0.499158i	$-0.833643\pi$
$617$	−226.657	+	226.657i	−0.367354	+	0.367354i	0.499158	+	0.866511i	$0.333643\pi$
$618$		0			0
$619$	756.530	+	313.365i	1.22218	+	0.506244i	0.898102	−	0.439787i	$-0.144946\pi$
$619$	756.530	+	313.365i	1.22218	+	0.506244i	0.324078	+	0.946030i	$0.394946\pi$
$620$		0			0
$621$	173.801	−	71.9908i	0.279873	−	0.115927i
$622$		0			0
$623$	−1287.93			−2.06730
$624$		0			0
$625$			14.3854i			0.0230167i
$626$		0			0
$627$	−552.503	−	1333.86i	−0.881185	−	2.12737i
$628$		0			0
$629$	−59.5864	+	143.854i	−0.0947320	+	0.228703i
$630$		0			0
$631$	−338.810	−	338.810i	−0.536941	−	0.536941i	0.385688	−	0.922629i	$-0.373964\pi$
$631$	−338.810	−	338.810i	−0.536941	−	0.536941i	−0.922629	+	0.385688i	$0.873964\pi$
$632$		0			0
$633$	−695.363	−	695.363i	−1.09852	−	1.09852i
$634$		0			0
$635$	−155.405	+	375.181i	−0.244733	+	0.590837i
$636$		0			0
$637$	158.557	+	382.790i	0.248912	+	0.600927i
$638$		0			0
$639$			701.682i			1.09809i
$640$		0			0
$641$	729.839			1.13859			0.569297	−	0.822132i	$-0.307215\pi$
$641$	729.839			1.13859			0.569297	+	0.822132i	$0.307215\pi$
$642$		0			0
$643$	−370.578	+	153.498i	−0.576327	+	0.238722i	−0.651756	−	0.758429i	$-0.725967\pi$
$643$	−370.578	+	153.498i	−0.576327	+	0.238722i	0.0754293	+	0.997151i	$0.475967\pi$
$644$		0			0
$645$	69.3867	+	28.7409i	0.107576	+	0.0445595i
$646$		0			0
$647$	179.567	−	179.567i	0.277538	−	0.277538i	−0.554587	−	0.832126i	$-0.687124\pi$
$647$	179.567	−	179.567i	0.277538	−	0.277538i	0.832126	+	0.554587i	$0.187124\pi$
$648$		0			0
$649$	−211.673	+	211.673i	−0.326152	+	0.326152i
$650$		0			0
$651$	12.5343	+	5.19189i	0.0192540	+	0.00797525i
$652$		0			0
$653$	964.894	−	399.672i	1.47763	−	0.612056i	0.509048	−	0.860738i	$-0.329998\pi$
$653$	964.894	−	399.672i	1.47763	−	0.612056i	0.968585	+	0.248683i	$0.0799976\pi$
$654$		0			0
$655$	752.497			1.14885
$656$		0			0
$657$			973.720i			1.48207i
$658$		0			0
$659$	233.939	+	564.778i	0.354990	+	0.857023i	0.995989	+	0.0894804i	$0.0285206\pi$
$659$	233.939	+	564.778i	0.354990	+	0.857023i	−0.640998	+	0.767542i	$0.721479\pi$
$660$		0			0
$661$	−281.181	+	678.831i	−0.425387	+	1.02698i	0.555345	+	0.831620i	$0.312586\pi$
$661$	−281.181	+	678.831i	−0.425387	+	1.02698i	−0.980732	+	0.195356i	$0.937414\pi$
$662$		0			0
$663$	219.197	+	219.197i	0.330614	+	0.330614i
$664$		0			0
$665$	667.580	+	667.580i	1.00388	+	1.00388i
$666$		0			0
$667$	−2.54508	+	6.14437i	−0.00381571	+	0.00921195i
$668$		0			0
$669$	620.775	+	1498.68i	0.927915	+	2.24018i
$670$		0			0
$671$		−	807.333i		−	1.20318i
$672$		0			0
$673$	705.345			1.04806			0.524031	−	0.851699i	$-0.324428\pi$
$673$	705.345			1.04806			0.524031	+	0.851699i	$0.324428\pi$
$674$		0			0
$675$	−285.857	+	118.406i	−0.423492	+	0.175416i
$676$		0			0
$677$	10.4550	+	4.33061i	0.0154432	+	0.00639676i	0.390392	−	0.920649i	$-0.372340\pi$
$677$	10.4550	+	4.33061i	0.0154432	+	0.00639676i	−0.374948	+	0.927046i	$0.622340\pi$
$678$		0			0
$679$	486.147	−	486.147i	0.715976	−	0.715976i
$680$		0			0
$681$	246.074	−	246.074i	0.361342	−	0.361342i
$682$		0			0
$683$	−307.101	−	127.205i	−0.449635	−	0.186245i	0.146363	−	0.989231i	$-0.453243\pi$
$683$	−307.101	−	127.205i	−0.449635	−	0.186245i	−0.595998	+	0.802986i	$0.703243\pi$
$684$		0			0
$685$	−445.364	+	184.476i	−0.650166	+	0.269308i
$686$		0			0
$687$	213.194			0.310327
$688$		0			0
$689$		−	167.995i		−	0.243824i
$690$		0			0
$691$	−243.176	−	587.078i	−0.351919	−	0.849607i	−0.996383	−	0.0849727i	$-0.972920\pi$
$691$	−243.176	−	587.078i	−0.351919	−	0.849607i	0.644465	−	0.764634i	$-0.277080\pi$
$692$		0			0
$693$	−388.159	+	937.099i	−0.560114	+	1.35224i
$694$		0			0
$695$	74.1366	+	74.1366i	0.106671	+	0.106671i
$696$		0			0
$697$	−71.9010	−	71.9010i	−0.103158	−	0.103158i
$698$		0			0
$699$	517.546	−	1249.47i	0.740410	−	1.78751i
$700$		0			0
$701$	−65.7383	−	158.706i	−0.0937779	−	0.226400i	0.870029	−	0.493000i	$-0.164100\pi$
$701$	−65.7383	−	158.706i	−0.0937779	−	0.226400i	−0.963807	+	0.266600i	$0.914100\pi$
$702$		0			0
$703$		−	1198.14i		−	1.70432i
$704$		0			0
$705$	713.712			1.01236
$706$		0			0
$707$	−917.510	+	380.045i	−1.29775	+	0.537546i
$708$		0			0
$709$	1029.00	+	426.228i	1.45135	+	0.601167i	0.962519	−	0.271214i	$-0.0874250\pi$
$709$	1029.00	+	426.228i	1.45135	+	0.601167i	0.488827	+	0.872381i	$0.337425\pi$
$710$		0			0
$711$	−250.803	+	250.803i	−0.352747	+	0.352747i
$712$		0			0
$713$	−2.20623	+	2.20623i	−0.00309429	+	0.00309429i
$714$		0			0
$715$	354.380	+	146.789i	0.495637	+	0.205299i
$716$		0			0
$717$	−381.484	+	158.016i	−0.532056	+	0.220385i
$718$		0			0
$719$	439.735			0.611592			0.305796	−	0.952097i	$-0.401077\pi$
$719$	439.735			0.611592			0.305796	+	0.952097i	$0.401077\pi$
$720$		0			0
$721$		−	955.826i		−	1.32570i
$722$		0			0
$723$	−27.8925	−	67.3385i	−0.0385789	−	0.0931377i
$724$		0			0
$725$	4.18599	−	10.1059i	0.00577378	−	0.0139391i
$726$		0			0
$727$	−137.308	−	137.308i	−0.188869	−	0.188869i	0.606338	−	0.795207i	$-0.292638\pi$
$727$	−137.308	−	137.308i	−0.188869	−	0.188869i	−0.795207	+	0.606338i	$0.792638\pi$
$728$		0			0
$729$	831.529	+	831.529i	1.14064	+	1.14064i
$730$		0			0
$731$	9.13791	−	22.0609i	0.0125006	−	0.0301790i
$732$		0			0
$733$	−57.7693	−	139.467i	−0.0788121	−	0.190269i	0.879562	−	0.475784i	$-0.157836\pi$
$733$	−57.7693	−	139.467i	−0.0788121	−	0.190269i	−0.958374	+	0.285514i	$0.907836\pi$
$734$		0			0
$735$		−	412.584i		−	0.561339i
$736$		0			0
$737$	390.447			0.529778
$738$		0			0
$739$	536.590	−	222.263i	0.726103	−	0.300762i	0.0111538	−	0.999938i	$-0.496450\pi$
$739$	536.590	−	222.263i	0.726103	−	0.300762i	0.714950	+	0.699176i	$0.246450\pi$
$740$		0			0
$741$	−2203.76	−	912.828i	−2.97404	−	1.23189i
$742$		0			0
$743$	−907.324	+	907.324i	−1.22116	+	1.22116i	−0.253944	+	0.967219i	$0.581728\pi$
$743$	−907.324	+	907.324i	−1.22116	+	1.22116i	−0.967219	+	0.253944i	$0.918272\pi$
$744$		0			0
$745$	610.278	−	610.278i	0.819165	−	0.819165i
$746$		0			0
$747$	338.351	+	140.150i	0.452947	+	0.187617i
$748$		0			0
$749$	−361.249	+	149.634i	−0.482309	+	0.199779i
$750$		0			0
$751$	662.862			0.882639			0.441320	−	0.897350i	$-0.354511\pi$
$751$	662.862			0.882639			0.441320	+	0.897350i	$0.354511\pi$
$752$		0			0
$753$		−	1180.93i		−	1.56830i
$754$		0			0
$755$	−85.0132	−	205.240i	−0.112600	−	0.271841i
$756$		0			0
$757$	−76.1190	+	183.767i	−0.100553	+	0.242757i	−0.966148	−	0.257988i	$-0.916941\pi$
$757$	−76.1190	+	183.767i	−0.100553	+	0.242757i	0.865595	+	0.500745i	$0.166941\pi$
$758$		0			0
$759$	−277.554	−	277.554i	−0.365684	−	0.365684i
$760$		0			0
$761$	435.811	+	435.811i	0.572683	+	0.572683i	0.932877	−	0.360195i	$-0.117290\pi$
$761$	435.811	+	435.811i	0.572683	+	0.572683i	−0.360195	+	0.932877i	$0.617290\pi$
$762$		0			0
$763$	−373.176	+	900.926i	−0.489090	+	1.18077i
$764$		0			0
$765$	−70.2012	−	169.481i	−0.0917662	−	0.221543i
$766$		0			0
$767$			494.578i			0.644821i
$768$		0			0
$769$	−1422.48			−1.84978			−0.924889	−	0.380237i	$-0.875843\pi$
$769$	−1422.48			−1.84978			−0.924889	+	0.380237i	$0.875843\pi$
$770$		0			0
$771$	−570.642	+	236.368i	−0.740132	+	0.306573i
$772$		0			0
$773$	0.439715	+	0.182136i	0.000568842	+	0.000235622i	0.382968	−	0.923762i	$-0.374902\pi$
$773$	0.439715	+	0.182136i	0.000568842	+	0.000235622i	−0.382399	+	0.923997i	$0.624902\pi$
$774$		0			0
$775$	3.62867	−	3.62867i	0.00468215	−	0.00468215i
$776$		0			0
$777$	−1001.57	+	1001.57i	−1.28902	+	1.28902i
$778$		0			0
$779$	722.878	+	299.426i	0.927956	+	0.384372i
$780$		0			0
$781$	429.160	−	177.764i	0.549500	−	0.227610i
$782$		0			0
$783$	13.7184			0.0175204
$784$		0			0
$785$		−	313.420i		−	0.399262i
$786$		0			0
$787$	23.0303	+	55.6002i	0.0292635	+	0.0706482i	0.937836	−	0.347079i	$-0.112827\pi$
$787$	23.0303	+	55.6002i	0.0292635	+	0.0706482i	−0.908572	+	0.417728i	$0.862827\pi$
$788$		0			0
$789$	717.144	−	1731.34i	0.908928	−	2.19435i
$790$		0			0
$791$	770.590	+	770.590i	0.974197	+	0.974197i
$792$		0			0
$793$	−943.175	−	943.175i	−1.18938	−	1.18938i
$794$		0			0
$795$	−64.0181	+	154.553i	−0.0805259	+	0.194407i
$796$		0			0
$797$	−49.3444	−	119.128i	−0.0619127	−	0.149470i	0.889895	−	0.456165i	$-0.150777\pi$
$797$	−49.3444	−	119.128i	−0.0619127	−	0.149470i	−0.951808	+	0.306694i	$0.900777\pi$
$798$		0			0
$799$		−	226.918i		−	0.284003i
$800$		0			0
$801$	−1925.65			−2.40406
$802$		0			0
$803$	595.542	−	246.682i	0.741647	−	0.307200i
$804$		0			0
$805$	237.138	+	98.2260i	0.294582	+	0.122020i
$806$		0			0
$807$	−480.478	+	480.478i	−0.595388	+	0.595388i
$808$		0			0
$809$	29.6470	−	29.6470i	0.0366465	−	0.0366465i	−0.688546	−	0.725193i	$-0.741751\pi$
$809$	29.6470	−	29.6470i	0.0366465	−	0.0366465i	0.725193	+	0.688546i	$0.241751\pi$
$810$		0			0
$811$	−755.209	−	312.818i	−0.931207	−	0.385719i	−0.135071	−	0.990836i	$-0.543126\pi$
$811$	−755.209	−	312.818i	−0.931207	−	0.385719i	−0.796136	+	0.605117i	$0.793126\pi$
$812$		0			0
$813$	1604.21	−	664.486i	1.97320	−	0.817326i
$814$		0			0
$815$	−16.4144			−0.0201404
$816$		0			0
$817$			183.741i			0.224897i
$818$		0			0
$819$	641.305	+	1548.25i	0.783034	+	1.89041i
$820$		0			0
$821$	−120.712	+	291.425i	−0.147031	+	0.354964i	−0.980187	−	0.198074i	$-0.936531\pi$
$821$	−120.712	+	291.425i	−0.147031	+	0.354964i	0.833156	+	0.553038i	$0.186531\pi$
$822$		0			0
$823$	−173.105	−	173.105i	−0.210334	−	0.210334i	0.594076	−	0.804409i	$-0.297518\pi$
$823$	−173.105	−	173.105i	−0.210334	−	0.210334i	−0.804409	+	0.594076i	$0.797518\pi$
$824$		0			0
$825$	456.504	+	456.504i	0.553338	+	0.553338i
$826$		0			0
$827$	−59.9551	+	144.744i	−0.0724971	+	0.175023i	−0.955974	−	0.293451i	$-0.905196\pi$
$827$	−59.9551	+	144.744i	−0.0724971	+	0.175023i	0.883477	+	0.468475i	$0.155196\pi$
$828$		0			0
$829$	−259.829	−	627.283i	−0.313425	−	0.756674i	−0.999573	−	0.0292124i	$-0.990700\pi$
$829$	−259.829	−	627.283i	−0.313425	−	0.756674i	0.686149	−	0.727461i	$-0.259300\pi$
$830$		0			0
$831$			265.840i			0.319904i
$832$		0			0
$833$	−131.178			−0.157476
$834$		0			0
$835$	657.240	−	272.238i	0.787114	−	0.326033i
$836$		0			0
$837$	5.94599	+	2.46291i	0.00710394	+	0.00294255i
$838$		0			0
$839$	−182.343	+	182.343i	−0.217333	+	0.217333i	−0.807374	−	0.590040i	$-0.799112\pi$
$839$	−182.343	+	182.343i	−0.217333	+	0.217333i	0.590040	+	0.807374i	$0.299112\pi$
$840$		0			0
$841$	594.334	−	594.334i	0.706699	−	0.706699i
$842$		0			0
$843$	523.436	+	216.814i	0.620920	+	0.257194i
$844$		0			0
$845$	109.526	−	45.3671i	0.129617	−	0.0536889i
$846$		0			0
$847$	−395.354			−0.466770
$848$		0			0
$849$		−	333.466i		−	0.392775i
$850$		0			0
$851$	−124.657	−	300.947i	−0.146482	−	0.353640i
$852$		0			0
$853$	300.757	−	726.092i	0.352588	−	0.851222i	−0.643712	−	0.765268i	$-0.722606\pi$
$853$	300.757	−	726.092i	0.352588	−	0.851222i	0.996299	−	0.0859535i	$-0.0273936\pi$
$854$		0			0
$855$	998.134	+	998.134i	1.16741	+	1.16741i
$856$		0			0
$857$	−545.430	−	545.430i	−0.636441	−	0.636441i	0.313235	−	0.949676i	$-0.398587\pi$
$857$	−545.430	−	545.430i	−0.636441	−	0.636441i	−0.949676	+	0.313235i	$0.898587\pi$
$858$		0			0
$859$	230.652	−	556.843i	0.268512	−	0.648246i	−0.730901	−	0.682483i	$-0.760900\pi$
$859$	230.652	−	556.843i	0.268512	−	0.648246i	0.999414	+	0.0342370i	$0.0109001\pi$
$860$		0			0
$861$	−353.979	−	854.580i	−0.411125	−	0.992544i
$862$		0			0
$863$			980.846i			1.13655i	0.822837	+	0.568277i	$0.192390\pi$
$863$			980.846i			1.13655i	−0.822837	+	0.568277i	$0.807610\pi$
$864$		0			0
$865$	381.962			0.441574
$866$		0			0
$867$	1166.86	−	483.328i	1.34586	−	0.557472i
$868$		0			0
$869$	216.933	+	89.8568i	0.249636	+	0.103403i
$870$		0			0
$871$	456.143	−	456.143i	0.523701	−	0.523701i
$872$		0			0
$873$	726.865	−	726.865i	0.832606	−	0.832606i
$874$		0			0
$875$	−1010.82	−	418.696i	−1.15522	−	0.478509i
$876$		0			0
$877$	−1395.56	+	578.059i	−1.59129	+	0.659132i	−0.990150	−	0.140014i	$-0.955285\pi$
$877$	−1395.56	+	578.059i	−1.59129	+	0.659132i	−0.601137	+	0.799146i	$0.705285\pi$
$878$		0			0
$879$	1636.59			1.86188
$880$		0			0
$881$			1513.62i			1.71807i	0.511914	+	0.859037i	$0.328937\pi$
$881$			1513.62i			1.71807i	−0.511914	+	0.859037i	$0.671063\pi$
$882$		0			0
$883$	−91.3318	−	220.494i	−0.103434	−	0.249711i	0.863687	−	0.504028i	$-0.168149\pi$
$883$	−91.3318	−	220.494i	−0.103434	−	0.249711i	−0.967121	+	0.254317i	$0.918149\pi$
$884$		0			0
$885$	188.470	−	455.006i	0.212960	−	0.514131i
$886$		0			0
$887$	−892.828	−	892.828i	−1.00657	−	1.00657i	−0.999978	−	0.00659168i	$-0.997902\pi$
$887$	−892.828	−	892.828i	−1.00657	−	1.00657i	−0.00659168	−	0.999978i	$-0.502098\pi$
$888$		0			0
$889$	830.510	+	830.510i	0.934207	+	0.934207i
$890$		0			0
$891$	86.3777	−	208.534i	0.0969447	−	0.234045i
$892$		0			0
$893$	668.203	+	1613.19i	0.748268	+	1.80648i
$894$		0			0
$895$		−	357.168i		−	0.399071i
$896$		0			0
$897$	−648.512			−0.722978
$898$		0			0
$899$	−0.210208	+	0.0870710i	−0.000233824	+	9.68531e-5i
$900$		0			0
$901$	49.1388	+	20.3540i	0.0545381	+	0.0225904i
$902$		0			0
$903$	153.596	−	153.596i	0.170095	−	0.170095i
$904$		0			0
$905$	−452.680	+	452.680i	−0.500199	+	0.500199i
$906$		0			0
$907$	−469.078	−	194.298i	−0.517175	−	0.214221i	0.108800	−	0.994064i	$-0.465299\pi$
$907$	−469.078	−	194.298i	−0.517175	−	0.214221i	−0.625976	+	0.779843i	$0.715299\pi$
$908$		0			0
$909$	−1371.82	+	568.226i	−1.50915	+	0.625111i
$910$		0			0
$911$	−469.566			−0.515441			−0.257720	−	0.966220i	$-0.582971\pi$
$911$	−469.566			−0.515441			−0.257720	+	0.966220i	$0.582971\pi$
$912$		0			0
$913$		−	242.446i		−	0.265549i
$914$		0			0
$915$	508.293	+	1227.13i	0.555512	+	1.34112i
$916$		0			0
$917$	832.872	−	2010.73i	0.908257	−	2.19273i
$918$		0			0
$919$	−737.868	−	737.868i	−0.802903	−	0.802903i	0.180645	−	0.983548i	$-0.442181\pi$
$919$	−737.868	−	737.868i	−0.802903	−	0.802903i	−0.983548	+	0.180645i	$0.942181\pi$
$920$		0			0
$921$	−806.710	−	806.710i	−0.875907	−	0.875907i
$922$		0			0
$923$	293.696	−	709.045i	0.318197	−	0.768196i
$924$		0			0
$925$	205.027	+	494.979i	0.221651	+	0.535113i
$926$		0			0
$927$		−	1429.11i		−	1.54165i
$928$		0			0
$929$	796.539			0.857416			0.428708	−	0.903443i	$-0.358969\pi$
$929$	796.539			0.857416			0.428708	+	0.903443i	$0.358969\pi$
$930$		0			0
$931$	932.554	−	386.277i	1.00167	−	0.414905i
$932$		0			0
$933$	274.312	+	113.624i	0.294011	+	0.121783i
$934$		0			0
$935$	−85.8723	+	85.8723i	−0.0918420	+	0.0918420i
$936$		0			0
$937$	764.262	−	764.262i	0.815648	−	0.815648i	−0.169826	−	0.985474i	$-0.554321\pi$
$937$	764.262	−	764.262i	0.815648	−	0.815648i	0.985474	+	0.169826i	$0.0543206\pi$
$938$		0			0
$939$	−171.875	−	71.1927i	−0.183040	−	0.0758176i
$940$		0			0
$941$	−113.549	+	47.0336i	−0.120669	+	0.0499826i	−0.442201	−	0.896916i	$-0.645802\pi$
$941$	−113.549	+	47.0336i	−0.120669	+	0.0499826i	0.321532	+	0.946899i	$0.395802\pi$
$942$		0			0
$943$	212.725			0.225583
$944$		0			0
$945$		−	529.456i		−	0.560271i
$946$		0			0
$947$	396.726	+	957.782i	0.418930	+	1.01139i	0.982658	+	0.185425i	$0.0593663\pi$
$947$	396.726	+	957.782i	0.418930	+	1.01139i	−0.563729	+	0.825960i	$0.690634\pi$
$948$		0			0
$949$	407.560	−	983.937i	0.429463	−	1.03681i
$950$		0			0
$951$	1095.23	+	1095.23i	1.15166	+	1.15166i
$952$		0			0
$953$	391.136	+	391.136i	0.410426	+	0.410426i	0.881887	−	0.471461i	$-0.156273\pi$
$953$	391.136	+	391.136i	0.410426	+	0.410426i	−0.471461	+	0.881887i	$0.656273\pi$
$954$		0			0
$955$	394.443	−	952.270i	0.413030	−	0.997142i
$956$		0			0
$957$	−10.9539	−	26.4452i	−0.0114461	−	0.0276334i
$958$		0			0
$959$			1394.23i			1.45383i
$960$		0			0
$961$	960.893			0.999889
$962$		0			0
$963$	−540.123	+	223.726i	−0.560875	+	0.232322i
$964$		0			0
$965$	660.465	+	273.574i	0.684420	+	0.283496i
$966$		0			0
$967$	22.8939	−	22.8939i	0.0236752	−	0.0236752i	−0.695170	−	0.718845i	$-0.744671\pi$
$967$	22.8939	−	22.8939i	0.0236752	−	0.0236752i	0.718845	+	0.695170i	$0.244671\pi$
$968$		0			0
$969$	534.009	−	534.009i	0.551093	−	0.551093i
$970$		0			0
$971$	−619.006	−	256.401i	−0.637493	−	0.264058i	0.0404399	−	0.999182i	$-0.487124\pi$
$971$	−619.006	−	256.401i	−0.637493	−	0.264058i	−0.677933	+	0.735124i	$0.737124\pi$
$972$		0			0
$973$	280.154	−	116.044i	0.287928	−	0.119264i
$974$		0			0
$975$	1066.63			1.09398
$976$		0			0
$977$		−	430.856i		−	0.440999i	−0.975387	−	0.220500i	$-0.929231\pi$
$977$		−	430.856i		−	0.440999i	0.975387	−	0.220500i	$-0.0707688\pi$
$978$		0			0
$979$	487.844	+	1177.76i	0.498309	+	1.20302i
$980$		0			0
$981$	−557.955	+	1347.02i	−0.568762	+	1.37311i
$982$		0			0
$983$	−154.209	−	154.209i	−0.156876	−	0.156876i	0.624305	−	0.781181i	$-0.285382\pi$
$983$	−154.209	−	154.209i	−0.156876	−	0.156876i	−0.781181	+	0.624305i	$0.785382\pi$
$984$		0			0
$985$	−552.978	−	552.978i	−0.561399	−	0.561399i
$986$		0			0
$987$	789.945	−	1907.09i	0.800349	−	1.93221i
$988$		0			0
$989$	19.1168	+	46.1520i	0.0193294	+	0.0466653i
$990$		0			0
$991$		−	966.543i		−	0.975320i	−0.873033	−	0.487660i	$-0.837850\pi$
$991$		−	966.543i		−	0.975320i	0.873033	−	0.487660i	$-0.162150\pi$
$992$		0			0
$993$	−864.169			−0.870260
$994$		0			0
$995$	−156.201	+	64.7007i	−0.156986	+	0.0650258i
$996$		0			0
$997$	−732.694	−	303.492i	−0.734899	−	0.304405i	−0.0163357	−	0.999867i	$-0.505200\pi$
$997$	−732.694	−	303.492i	−0.734899	−	0.304405i	−0.718564	+	0.695461i	$0.755200\pi$
$998$		0			0
$999$	−475.120	+	475.120i	−0.475596	+	0.475596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.3.h.a.31.7		28
4.3	odd	2		256.3.h.b.31.1		28
8.3	odd	2		32.3.h.a.27.4	yes	28
8.5	even	2		128.3.h.a.15.1		28
24.11	even	2		288.3.u.a.91.4		28
32.3	odd	8		128.3.h.a.111.1		28
32.13	even	8		256.3.h.b.223.1		28
32.19	odd	8	inner	256.3.h.a.223.7		28
32.29	even	8		32.3.h.a.19.4	✓	28
96.29	odd	8		288.3.u.a.19.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.4	✓	28	32.29	even	8
32.3.h.a.27.4	yes	28	8.3	odd	2
128.3.h.a.15.1		28	8.5	even	2
128.3.h.a.111.1		28	32.3	odd	8
256.3.h.a.31.7		28	1.1	even	1	trivial
256.3.h.a.223.7		28	32.19	odd	8	inner
256.3.h.b.31.1		28	4.3	odd	2
256.3.h.b.223.1		28	32.13	even	8
288.3.u.a.19.4		28	96.29	odd	8
288.3.u.a.91.4		28	24.11	even	2

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	256.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.35131 - 1.80237i) q^{3} +(2.81639 + 1.16659i) q^{5} +(6.23443 - 6.23443i) q^{7} +(9.32143 - 9.32143i) q^{9} +O(q^{10})\)	\(q+(4.35131 - 1.80237i) q^{3} +(2.81639 + 1.16659i) q^{5} +(6.23443 - 6.23443i) q^{7} +(9.32143 - 9.32143i) q^{9} +(-8.06262 - 3.33965i) q^{11} +(-13.3208 + 5.51766i) q^{13} +14.3576 q^{15} -4.56488i q^{17} +(13.4421 + 32.4522i) q^{19} +(15.8912 - 38.3647i) q^{21} +(6.75277 + 6.75277i) q^{23} +(-11.1065 - 11.1065i) q^{25} +(7.53841 - 18.1993i) q^{27} +(0.266504 + 0.643399i) q^{29} +0.326715i q^{31} -41.1023 q^{33} +(24.8316 - 10.2856i) q^{35} +(-31.5133 - 13.0532i) q^{37} +(-48.0182 + 48.0182i) q^{39} +(15.7509 - 15.7509i) q^{41} +(4.83274 + 2.00179i) q^{43} +(37.1271 - 15.3785i) q^{45} +49.7096 q^{47} -28.7362i q^{49} +(-8.22762 - 19.8632i) q^{51} +(-4.45882 + 10.7645i) q^{53} +(-18.8115 - 18.8115i) q^{55} +(116.982 + 116.982i) q^{57} +(13.1268 - 31.6909i) q^{59} +(35.4023 + 85.4687i) q^{61} -116.228i q^{63} -43.9535 q^{65} +(-41.3348 + 17.1214i) q^{67} +(41.5545 + 17.2124i) q^{69} +(-37.6381 + 37.6381i) q^{71} +(-52.2302 + 52.2302i) q^{73} +(-68.3461 - 28.3099i) q^{75} +(-71.0866 + 29.4450i) q^{77} -26.9061 q^{79} +25.8643i q^{81} +(10.6315 + 25.6667i) q^{83} +(5.32533 - 12.8565i) q^{85} +(2.31929 + 2.31929i) q^{87} +(-103.292 - 103.292i) q^{89} +(-48.6482 + 117.447i) q^{91} +(0.588862 + 1.42164i) q^{93} +107.080i q^{95} +77.9778 q^{97} +(-106.285 + 44.0249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{19} + 4 q^{21} + 68 q^{23} - 4 q^{25} - 100 q^{27} + 4 q^{29} - 8 q^{33} + 92 q^{35} + 4 q^{37} - 188 q^{39} - 4 q^{41} + 92 q^{43} + 40 q^{45} + 8 q^{47} + 224 q^{51} + 164 q^{53} - 252 q^{55} - 4 q^{57} + 124 q^{59} + 68 q^{61} - 8 q^{65} - 164 q^{67} - 188 q^{69} + 260 q^{71} - 4 q^{73} - 488 q^{75} - 220 q^{77} + 520 q^{79} - 484 q^{83} - 96 q^{85} + 452 q^{87} - 4 q^{89} - 196 q^{91} - 32 q^{93} - 8 q^{97} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^19 + 4 * q^21 + 68 * q^23 - 4 * q^25 - 100 * q^27 + 4 * q^29 - 8 * q^33 + 92 * q^35 + 4 * q^37 - 188 * q^39 - 4 * q^41 + 92 * q^43 + 40 * q^45 + 8 * q^47 + 224 * q^51 + 164 * q^53 - 252 * q^55 - 4 * q^57 + 124 * q^59 + 68 * q^61 - 8 * q^65 - 164 * q^67 - 188 * q^69 + 260 * q^71 - 4 * q^73 - 488 * q^75 - 220 * q^77 + 520 * q^79 - 484 * q^83 - 96 * q^85 + 452 * q^87 - 4 * q^89 - 196 * q^91 - 32 * q^93 - 8 * q^97 + 216 * q^99

Introduction

L-functions

Modular forms

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Database

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