LMFDB - Embedded newform 1224.2.f.c.613.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1224,2,Mod(613,1224)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1224, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1224.613"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,1,0,1,0,0,-12,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4469724736.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 2x^{5} - 4x^{4} + 4x^{3} - 8x + 16 $ x^8 - x^7 + 2x^5 - 4x^4 + 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			613.6
Root			$0.733159 + 1.20933i$ of defining polynomial
Character	$\chi$	$=$	1224.613
Dual form			1224.2.f.c.613.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.733159 + 1.20933i) q^{2} +(-0.924955 + 1.77326i) q^{4} -1.12786i q^{5} +1.74755 q^{7} +(-2.82260 + 0.181508i) q^{8} +(1.36396 - 0.826905i) q^{10} -5.05364i q^{11} -3.09887i q^{13} +(1.28123 + 2.11337i) q^{14} +(-2.28892 - 3.28038i) q^{16} -1.00000 q^{17} -1.04322i q^{19} +(2.00000 + 1.04322i) q^{20} +(6.11151 - 3.70512i) q^{22} +7.54284 q^{23} +3.72792 q^{25} +(3.74755 - 2.27196i) q^{26} +(-1.61641 + 3.09887i) q^{28} +1.12786i q^{29} -2.68019 q^{31} +(2.28892 - 5.17309i) q^{32} +(-0.733159 - 1.20933i) q^{34} -1.97100i q^{35} -9.14869i q^{37} +(1.26160 - 0.764850i) q^{38} +(0.204716 + 3.18351i) q^{40} +4.72792 q^{41} -1.52970i q^{43} +(8.96142 + 4.67439i) q^{44} +(5.53010 + 9.12177i) q^{46} -7.66056 q^{47} -3.94606 q^{49} +(2.73316 + 4.50828i) q^{50} +(5.49510 + 2.86631i) q^{52} +3.90954i q^{53} -5.69982 q^{55} +(-4.93264 + 0.317194i) q^{56} +(-1.36396 + 0.826905i) q^{58} +11.0351i q^{59} -1.12786i q^{61} +(-1.96501 - 3.24123i) q^{62} +(7.93411 - 1.02465i) q^{64} -3.49510 q^{65} -2.86631i q^{67} +(0.924955 - 1.77326i) q^{68} +(2.38359 - 1.44506i) q^{70} +3.01963 q^{71} +12.2230 q^{73} +(11.0638 - 6.70745i) q^{74} +(1.84991 + 0.964936i) q^{76} -8.83150i q^{77} +3.95227 q^{79} +(-3.69982 + 2.58159i) q^{80} +(3.46632 + 5.71761i) q^{82} +9.34878i q^{83} +1.12786i q^{85} +(1.84991 - 1.12151i) q^{86} +(0.917274 + 14.2644i) q^{88} +18.2672 q^{89} -5.41543i q^{91} +(-6.97679 + 13.3754i) q^{92} +(-5.61641 - 9.26414i) q^{94} -1.17662 q^{95} -1.13735 q^{97} +(-2.89309 - 4.77209i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} - 12 q^{7} - 5 q^{8} - 8 q^{10} - 6 q^{14} + 9 q^{16} - 8 q^{17} + 16 q^{20} + 4 q^{22} + 16 q^{23} - 8 q^{25} + 4 q^{26} - 20 q^{28} + 24 q^{31} - 9 q^{32} - q^{34} - 18 q^{38} + 20 q^{40}+ \cdots + 57 q^{98}+O(q^{100}) $ 8 * q + q^2 + q^4 - 12 * q^7 - 5 * q^8 - 8 * q^10 - 6 * q^14 + 9 * q^16 - 8 * q^17 + 16 * q^20 + 4 * q^22 + 16 * q^23 - 8 * q^25 + 4 * q^26 - 20 * q^28 + 24 * q^31 - 9 * q^32 - q^34 - 18 * q^38 + 20 * q^40 + 10 * q^44 - 18 * q^46 - 4 * q^47 + 8 * q^49 + 17 * q^50 - 8 * q^52 - 12 * q^55 - 20 * q^56 + 8 * q^58 - 26 * q^62 + q^64 + 24 * q^65 - q^68 + 12 * q^70 + 36 * q^71 + 8 * q^73 + 36 * q^74 - 2 * q^76 + 24 * q^79 + 4 * q^80 + 18 * q^82 - 2 * q^86 + 10 * q^88 - 8 * q^89 + 28 * q^92 - 52 * q^94 - 32 * q^95 - 8 * q^97 + 57 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	0.733159	+	1.20933i	0.518422	+	0.855125i
$2$	0.733159	+	1.20933i	0.518422	+	0.855125i
$3$		0			0
$3$		0			0
$4$	−0.924955	+	1.77326i	−0.462478	+	0.886631i
$5$		−	1.12786i		−	0.504397i	−0.967676	−	0.252198i	$-0.918846\pi$
$5$		−	1.12786i		−	0.504397i	0.967676	−	0.252198i	$-0.0811535\pi$
$6$		0			0
$7$	1.74755			0.660513			0.330256	−	0.943891i	$-0.392865\pi$
$7$	1.74755			0.660513			0.330256	+	0.943891i	$0.392865\pi$
$8$	−2.82260	+	0.181508i	−0.997939	+	0.0641726i
$9$		0			0
$10$	1.36396	−	0.826905i	0.431322	−	0.261490i
$11$		−	5.05364i		−	1.52373i	−0.647736	−	0.761865i	$-0.724284\pi$
$11$		−	5.05364i		−	1.52373i	0.647736	−	0.761865i	$-0.275716\pi$
$12$		0			0
$13$		−	3.09887i		−	0.859471i	−0.902955	−	0.429736i	$-0.858607\pi$
$13$		−	3.09887i		−	0.859471i	0.902955	−	0.429736i	$-0.141393\pi$
$14$	1.28123	+	2.11337i	0.342424	+	0.564821i
$15$		0			0
$16$	−2.28892	−	3.28038i	−0.572229	−	0.820094i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$		0			0
$19$		−	1.04322i		−	0.239332i	−0.992814	−	0.119666i	$-0.961818\pi$
$19$		−	1.04322i		−	0.239332i	0.992814	−	0.119666i	$-0.0381824\pi$
$20$	2.00000	+	1.04322i	0.447214	+	0.233272i
$21$		0			0
$22$	6.11151	−	3.70512i	1.30298	−	0.789934i
$23$	7.54284			1.57279			0.786395	−	0.617724i	$-0.211945\pi$
$23$	7.54284			1.57279			0.786395	+	0.617724i	$0.211945\pi$
$24$		0			0
$25$	3.72792			0.745584
$26$	3.74755	−	2.27196i	0.734956	−	0.445569i
$27$		0			0
$28$	−1.61641	+	3.09887i	−0.305472	+	0.585631i
$29$			1.12786i			0.209439i	0.994502	+	0.104720i	$0.0333945\pi$
$29$			1.12786i			0.209439i	−0.994502	+	0.104720i	$0.966605\pi$
$30$		0			0
$31$	−2.68019			−0.481376			−0.240688	−	0.970603i	$-0.577373\pi$
$31$	−2.68019			−0.481376			−0.240688	+	0.970603i	$0.577373\pi$
$32$	2.28892	−	5.17309i	0.404627	−	0.914482i
$33$		0			0
$34$	−0.733159	−	1.20933i	−0.125736	−	0.207398i
$35$		−	1.97100i		−	0.333160i
$36$		0			0
$37$		−	9.14869i		−	1.50404i	−0.659143	−	0.752018i	$-0.729081\pi$
$37$		−	9.14869i		−	1.50404i	0.659143	−	0.752018i	$-0.270919\pi$
$38$	1.26160	−	0.764850i	0.204659	−	0.124075i
$39$		0			0
$40$	0.204716	+	3.18351i	0.0323685	+	0.503357i
$41$	4.72792			0.738377			0.369189	−	0.929355i	$-0.379636\pi$
$41$	4.72792			0.738377			0.369189	+	0.929355i	$0.379636\pi$
$42$		0			0
$43$		−	1.52970i		−	0.233277i	−0.993174	−	0.116638i	$-0.962788\pi$
$43$		−	1.52970i		−	0.233277i	0.993174	−	0.116638i	$-0.0372119\pi$
$44$	8.96142	+	4.67439i	1.35099	+	0.704691i
$45$		0			0
$46$	5.53010	+	9.12177i	0.815369	+	1.34493i
$47$	−7.66056			−1.11741			−0.558704	−	0.829367i	$-0.688701\pi$
$47$	−7.66056			−1.11741			−0.558704	+	0.829367i	$0.688701\pi$
$48$		0			0
$49$	−3.94606			−0.563723
$50$	2.73316	+	4.50828i	0.386527	+	0.637568i
$51$		0			0
$52$	5.49510	+	2.86631i	0.762034	+	0.397486i
$53$			3.90954i			0.537016i	0.963277	+	0.268508i	$0.0865307\pi$
$53$			3.90954i			0.537016i	−0.963277	+	0.268508i	$0.913469\pi$
$54$		0			0
$55$	−5.69982			−0.768564
$56$	−4.93264	+	0.317194i	−0.659151	+	0.0423868i
$57$		0			0
$58$	−1.36396	+	0.826905i	−0.179097	+	0.108578i
$59$			11.0351i			1.43664i	0.695712	+	0.718321i	$0.255089\pi$
$59$			11.0351i			1.43664i	−0.695712	+	0.718321i	$0.744911\pi$
$60$		0			0
$61$		−	1.12786i		−	0.144408i	−0.997390	−	0.0722042i	$-0.976997\pi$
$61$		−	1.12786i		−	0.144408i	0.997390	−	0.0722042i	$-0.0230033\pi$
$62$	−1.96501	−	3.24123i	−0.249556	−	0.411637i
$63$		0			0
$64$	7.93411	−	1.02465i	0.991764	−	0.128081i
$65$	−3.49510			−0.433514
$66$		0			0
$67$		−	2.86631i		−	0.350176i	−0.984553	−	0.175088i	$-0.943979\pi$
$67$		−	2.86631i		−	0.350176i	0.984553	−	0.175088i	$-0.0560210\pi$
$68$	0.924955	−	1.77326i	0.112167	−	0.215040i
$69$		0			0
$70$	2.38359	−	1.44506i	0.284894	−	0.172718i
$71$	3.01963			0.358364			0.179182	−	0.983816i	$-0.442655\pi$
$71$	3.01963			0.358364			0.179182	+	0.983816i	$0.442655\pi$
$72$		0			0
$73$	12.2230			1.43060			0.715298	−	0.698819i	$-0.246291\pi$
$73$	12.2230			1.43060			0.715298	+	0.698819i	$0.246291\pi$
$74$	11.0638	−	6.70745i	1.28614	−	0.779725i
$75$		0			0
$76$	1.84991	+	0.964936i	0.212199	+	0.110686i
$77$		−	8.83150i		−	1.00644i
$78$		0			0
$79$	3.95227			0.444665			0.222332	−	0.974971i	$-0.428633\pi$
$79$	3.95227			0.444665			0.222332	+	0.974971i	$0.428633\pi$
$80$	−3.69982	+	2.58159i	−0.413653	+	0.288630i
$81$		0			0
$82$	3.46632	+	5.71761i	0.382791	+	0.631405i
$83$			9.34878i			1.02616i	0.858340	+	0.513081i	$0.171496\pi$
$83$			9.34878i			1.02616i	−0.858340	+	0.513081i	$0.828504\pi$
$84$		0			0
$85$			1.12786i			0.122334i
$86$	1.84991	−	1.12151i	0.199481	−	0.120936i
$87$		0			0
$88$	0.917274	+	14.2644i	0.0977817	+	1.52059i
$89$	18.2672			1.93632			0.968158	−	0.250339i	$-0.0805420\pi$
$89$	18.2672			1.93632			0.968158	+	0.250339i	$0.0805420\pi$
$90$		0			0
$91$		−	5.41543i		−	0.567692i
$92$	−6.97679	+	13.3754i	−0.727380	+	1.39448i
$93$		0			0
$94$	−5.61641	−	9.26414i	−0.579288	−	0.955523i
$95$	−1.17662			−0.120718
$96$		0			0
$97$	−1.13735			−0.115481			−0.0577403	−	0.998332i	$-0.518390\pi$
$97$	−1.13735			−0.115481			−0.0577403	+	0.998332i	$0.518390\pi$
$98$	−2.89309	−	4.77209i	−0.292246	−	0.482054i
$99$		0			0
$100$	−3.44816	+	6.61058i	−0.344816	+	0.661058i
$101$		−	15.1985i		−	1.51231i	−0.654393	−	0.756154i	$-0.727076\pi$
$101$		−	15.1985i		−	1.51231i	0.654393	−	0.756154i	$-0.272924\pi$
$102$		0			0
$103$	−14.6325			−1.44178			−0.720889	−	0.693050i	$-0.756266\pi$
$103$	−14.6325			−1.44178			−0.720889	+	0.693050i	$0.756266\pi$
$104$	0.562468	+	8.74686i	0.0551545	+	0.857700i
$105$		0			0
$106$	−4.72792	+	2.86631i	−0.459216	+	0.278401i
$107$		−	3.08263i		−	0.298010i	−0.988836	−	0.149005i	$-0.952393\pi$
$107$		−	3.08263i		−	0.298010i	0.988836	−	0.149005i	$-0.0476070\pi$
$108$		0			0
$109$			17.6022i			1.68598i	0.537929	+	0.842990i	$0.319207\pi$
$109$			17.6022i			1.68598i	−0.537929	+	0.842990i	$0.680793\pi$
$110$	−4.17888	−	6.89296i	−0.398440	−	0.657218i
$111$		0			0
$112$	−4.00000	−	5.73263i	−0.377964	−	0.541683i
$113$	−5.49510			−0.516936			−0.258468	−	0.966020i	$-0.583218\pi$
$113$	−5.49510			−0.516936			−0.258468	+	0.966020i	$0.583218\pi$
$114$		0			0
$115$		−	8.50730i		−	0.793310i
$116$	−2.00000	−	1.04322i	−0.185695	−	0.0968610i
$117$		0			0
$118$	−13.3450	+	8.09045i	−1.22851	+	0.744786i
$119$	−1.74755			−0.160198
$120$		0			0
$121$	−14.5393			−1.32175
$122$	1.36396	−	0.826905i	0.123487	−	0.0748644i
$123$		0			0
$124$	2.47906	−	4.75268i	0.222626	−	0.426803i
$125$		−	9.84392i		−	0.880467i
$126$		0			0
$127$	14.7279			1.30689			0.653446	−	0.756973i	$-0.273323\pi$
$127$	14.7279			1.30689			0.653446	+	0.756973i	$0.273323\pi$
$128$	7.05610	+	8.84372i	0.623677	+	0.781682i
$129$		0			0
$130$	−2.56247	−	4.22673i	−0.224743	−	0.370709i
$131$			10.5015i			0.917524i	0.888559	+	0.458762i	$0.151707\pi$
$131$			10.5015i			0.917524i	−0.888559	+	0.458762i	$0.848293\pi$
$132$		0			0
$133$		−	1.82309i		−	0.158082i
$134$	3.46632	−	2.10146i	0.299444	−	0.181539i
$135$		0			0
$136$	2.82260	−	0.181508i	0.242036	−	0.0155642i
$137$	−5.31623			−0.454196			−0.227098	−	0.973872i	$-0.572924\pi$
$137$	−5.31623			−0.454196			−0.227098	+	0.973872i	$0.572924\pi$
$138$		0			0
$139$			2.36527i			0.200619i	0.994956	+	0.100310i	$0.0319834\pi$
$139$			2.36527i			0.200619i	−0.994956	+	0.100310i	$0.968017\pi$
$140$	3.49510	+	1.82309i	0.295390	+	0.154079i
$141$		0			0
$142$	2.21387	+	3.65173i	0.185784	+	0.306446i
$143$	−15.6606			−1.30960
$144$		0			0
$145$	1.27208			0.105640
$146$	8.96142	+	14.7817i	0.741653	+	1.22334i
$147$		0			0
$148$	16.2230	+	8.46213i	1.33352	+	0.695583i
$149$		−	21.4357i		−	1.75608i	−0.478585	−	0.878041i	$-0.658850\pi$
$149$		−	21.4357i		−	1.75608i	0.478585	−	0.878041i	$-0.341150\pi$
$150$		0			0
$151$	−18.1276			−1.47520			−0.737600	−	0.675238i	$-0.764041\pi$
$151$	−18.1276			−1.47520			−0.737600	+	0.675238i	$0.764041\pi$
$152$	0.189353	+	2.94460i	0.0153586	+	0.238839i
$153$		0			0
$154$	10.6802	−	6.47489i	0.860634	−	0.521762i
$155$			3.02289i			0.242804i
$156$		0			0
$157$		−	14.6187i		−	1.16670i	−0.812220	−	0.583351i	$-0.801741\pi$
$157$		−	14.6187i		−	1.16670i	0.812220	−	0.583351i	$-0.198259\pi$
$158$	2.89764	+	4.77959i	0.230524	+	0.380244i
$159$		0			0
$160$	−5.83455	−	2.58159i	−0.461261	−	0.204092i
$161$	13.1815			1.03885
$162$		0			0
$163$			19.4090i			1.52023i	0.649788	+	0.760116i	$0.274858\pi$
$163$			19.4090i			1.52023i	−0.649788	+	0.760116i	$0.725142\pi$
$164$	−4.37311	+	8.38384i	−0.341483	+	0.654668i
$165$		0			0
$166$	−11.3058	+	6.85414i	−0.877497	+	0.531985i
$167$	−11.8751			−0.918924			−0.459462	−	0.888197i	$-0.651958\pi$
$167$	−11.8751			−0.918924			−0.459462	+	0.888197i	$0.651958\pi$
$168$		0			0
$169$	3.39702			0.261309
$170$	−1.36396	+	0.826905i	−0.104611	+	0.0634207i
$171$		0			0
$172$	2.71256	+	1.41490i	0.206831	+	0.107885i
$173$			18.0197i			1.37001i	0.728539	+	0.685005i	$0.240200\pi$
$173$			18.0197i			1.37001i	−0.728539	+	0.685005i	$0.759800\pi$
$174$		0			0
$175$	6.51474			0.492468
$176$	−16.5778	+	11.5673i	−1.24960	+	0.871922i
$177$		0			0
$178$	13.3927	+	22.0910i	1.00383	+	1.65579i
$179$		−	15.8637i		−	1.18571i	−0.805310	−	0.592855i	$-0.798001\pi$
$179$		−	15.8637i		−	1.18571i	0.805310	−	0.592855i	$-0.201999\pi$
$180$		0			0
$181$		−	11.0659i		−	0.822519i	−0.911518	−	0.411259i	$-0.865089\pi$
$181$		−	11.0659i		−	0.822519i	0.911518	−	0.411259i	$-0.134911\pi$
$182$	6.54904	−	3.97038i	0.485447	−	0.294304i
$183$		0			0
$184$	−21.2904	+	1.36908i	−1.56955	+	0.100930i
$185$	−10.3185			−0.758630
$186$		0			0
$187$			5.05364i			0.369559i
$188$	7.08567	−	13.5842i	0.516776	−	0.990728i
$189$		0			0
$190$	−0.862647	−	1.42292i	−0.0625830	−	0.103229i
$191$	−14.2930			−1.03421			−0.517103	−	0.855923i	$-0.672990\pi$
$191$	−14.2930			−1.03421			−0.517103	+	0.855923i	$0.672990\pi$
$192$		0			0
$193$	−21.3480			−1.53666			−0.768330	−	0.640054i	$-0.778912\pi$
$193$	−21.3480			−1.53666			−0.768330	+	0.640054i	$0.778912\pi$
$194$	−0.833861	−	1.37543i	−0.0598677	−	0.0987504i
$195$		0			0
$196$	3.64993	−	6.99740i	0.260709	−	0.499814i
$197$		−	22.8269i		−	1.62635i	−0.582018	−	0.813176i	$-0.697737\pi$
$197$		−	22.8269i		−	1.62635i	0.582018	−	0.813176i	$-0.302263\pi$
$198$		0			0
$199$	−8.81492			−0.624873			−0.312436	−	0.949939i	$-0.601145\pi$
$199$	−8.81492			−0.624873			−0.312436	+	0.949939i	$0.601145\pi$
$200$	−10.5224	+	0.676646i	−0.744047	+	0.0478461i
$201$		0			0
$202$	18.3800	−	11.1429i	1.29321	−	0.784014i
$203$			1.97100i			0.138337i
$204$		0			0
$205$		−	5.33246i		−	0.372435i
$206$	−10.7279	−	17.6955i	−0.747450	−	1.23290i
$207$		0			0
$208$	−10.1655	+	7.09305i	−0.704847	+	0.491814i
$209$	−5.27208			−0.364677
$210$		0			0
$211$		−	8.67845i		−	0.597449i	−0.954339	−	0.298725i	$-0.903439\pi$
$211$		−	8.67845i		−	0.597449i	0.954339	−	0.298725i	$-0.0965612\pi$
$212$	−6.93264	−	3.61615i	−0.476135	−	0.248358i
$213$		0			0
$214$	3.72792	−	2.26006i	0.254835	−	0.154495i
$215$	−1.72529			−0.117664
$216$		0			0
$217$	−4.68377			−0.317955
$218$	−21.2868	+	12.9052i	−1.44172	+	0.874049i
$219$		0			0
$220$	5.27208	−	10.1073i	0.355444	−	0.681432i
$221$			3.09887i			0.208452i
$222$		0			0
$223$	−4.33228			−0.290111			−0.145055	−	0.989424i	$-0.546336\pi$
$223$	−4.33228			−0.290111			−0.145055	+	0.989424i	$0.546336\pi$
$224$	4.00000	−	9.04025i	0.267261	−	0.604027i
$225$		0			0
$226$	−4.02879	−	6.64539i	−0.267991	−	0.442045i
$227$			25.6392i			1.70173i	0.525381	+	0.850867i	$0.323923\pi$
$227$			25.6392i			1.70173i	−0.525381	+	0.850867i	$0.676077\pi$
$228$		0			0
$229$		−	2.46448i		−	0.162857i	−0.996679	−	0.0814287i	$-0.974052\pi$
$229$		−	2.46448i		−	0.162857i	0.996679	−	0.0814287i	$-0.0259483\pi$
$230$	10.2881	−	6.23721i	0.678379	−	0.411269i
$231$		0			0
$232$	−0.204716	−	3.18351i	−0.0134403	−	0.209008i
$233$	2.67172			0.175030			0.0875151	−	0.996163i	$-0.472107\pi$
$233$	2.67172			0.175030			0.0875151	+	0.996163i	$0.472107\pi$
$234$		0			0
$235$			8.64007i			0.563616i
$236$	−19.5680	−	10.2069i	−1.27377	−	0.664415i
$237$		0			0
$238$	−1.28123	−	2.11337i	−0.0830501	−	0.136989i
$239$	2.89337			0.187157			0.0935784	−	0.995612i	$-0.470169\pi$
$239$	2.89337			0.187157			0.0935784	+	0.995612i	$0.470169\pi$
$240$		0			0
$241$	13.8260			0.890612			0.445306	−	0.895379i	$-0.353095\pi$
$241$	13.8260			0.890612			0.445306	+	0.895379i	$0.353095\pi$
$242$	−10.6596	−	17.5827i	−0.685224	−	1.13026i
$243$		0			0
$244$	2.00000	+	1.04322i	0.128037	+	0.0667856i
$245$			4.45062i			0.284340i
$246$		0			0
$247$	−3.23282			−0.205699
$248$	7.56509	−	0.486475i	0.480384	−	0.0308912i
$249$		0			0
$250$	11.9045	−	7.21716i	0.752909	−	0.456453i
$251$			26.7270i			1.68700i	0.537132	+	0.843498i	$0.319508\pi$
$251$			26.7270i			1.68700i	−0.537132	+	0.843498i	$0.680492\pi$
$252$		0			0
$253$		−	38.1188i		−	2.39651i
$254$	10.7979	+	17.8109i	0.677521	+	1.11756i
$255$		0			0
$256$	−5.52173	+	15.0170i	−0.345108	+	0.938563i
$257$	0.460746			0.0287405			0.0143703	−	0.999897i	$-0.495426\pi$
$257$	0.460746			0.0287405			0.0143703	+	0.999897i	$0.495426\pi$
$258$		0			0
$259$		−	15.9878i		−	0.993435i
$260$	3.23282	−	6.19774i	0.200491	−	0.384367i
$261$		0			0
$262$	−12.6998	+	7.69930i	−0.784598	+	0.475664i
$263$	16.2623			1.00278			0.501388	−	0.865223i	$-0.332823\pi$
$263$	16.2623			1.00278			0.501388	+	0.865223i	$0.332823\pi$
$264$		0			0
$265$	4.40943			0.270869
$266$	2.20472	−	1.33662i	0.135180	−	0.0819531i
$267$		0			0
$268$	5.08273	+	2.65121i	0.310477	+	0.161949i
$269$			20.0596i			1.22306i	0.791222	+	0.611529i	$0.209445\pi$
$269$			20.0596i			1.22306i	−0.791222	+	0.611529i	$0.790555\pi$
$270$		0			0
$271$	0.670347			0.0407207			0.0203604	−	0.999793i	$-0.493519\pi$
$271$	0.670347			0.0407207			0.0203604	+	0.999793i	$0.493519\pi$
$272$	2.28892	+	3.28038i	0.138786	+	0.198902i
$273$		0			0
$274$	−3.89764	−	6.42907i	−0.235465	−	0.388394i
$275$		−	18.8396i		−	1.13607i
$276$		0			0
$277$		−	3.58534i		−	0.215422i	−0.994182	−	0.107711i	$-0.965648\pi$
$277$		−	3.58534i		−	0.215422i	0.994182	−	0.107711i	$-0.0343522\pi$
$278$	−2.86039	+	1.73412i	−0.171555	+	0.104005i
$279$		0			0
$280$	0.357752	+	5.56335i	0.0213798	+	0.332474i
$281$	−0.397016			−0.0236840			−0.0118420	−	0.999930i	$-0.503770\pi$
$281$	−0.397016			−0.0236840			−0.0118420	+	0.999930i	$0.503770\pi$
$282$		0			0
$283$			9.96859i			0.592571i	0.955099	+	0.296286i	$0.0957481\pi$
$283$			9.96859i			0.592571i	−0.955099	+	0.296286i	$0.904252\pi$
$284$	−2.79302	+	5.35460i	−0.165736	+	0.317737i
$285$		0			0
$286$	−11.4817	−	18.9388i	−0.678926	−	1.11987i
$287$	8.26229			0.487708
$288$		0			0
$289$	1.00000			0.0588235
$290$	0.932637	+	1.53836i	0.0547663	+	0.0903358i
$291$		0			0
$292$	−11.3058	+	21.6746i	−0.661619	+	1.26841i
$293$		−	5.39407i		−	0.315125i	−0.987509	−	0.157562i	$-0.949636\pi$
$293$		−	5.39407i		−	0.315125i	0.987509	−	0.157562i	$-0.0503635\pi$
$294$		0			0
$295$	12.4461			0.724637
$296$	1.66056	+	25.8231i	0.0965179	+	1.50094i
$297$		0			0
$298$	25.9228	−	15.7158i	1.50167	−	0.910392i
$299$		−	23.3743i		−	1.35177i
$300$		0			0
$301$		−	2.67323i		−	0.154082i
$302$	−13.2904	−	21.9222i	−0.764776	−	1.26148i
$303$		0			0
$304$	−3.42217	+	2.38785i	−0.196275	+	0.136953i
$305$	−1.27208			−0.0728391
$306$		0			0
$307$			28.9614i			1.65291i	0.562999	+	0.826457i	$0.309647\pi$
$307$			28.9614i			1.65291i	−0.562999	+	0.826457i	$0.690353\pi$
$308$	15.6606	+	8.16874i	0.892343	+	0.465457i
$309$		0			0
$310$	−3.65567	+	2.21626i	−0.207628	+	0.125875i
$311$	13.5049			0.765795			0.382898	−	0.923791i	$-0.374926\pi$
$311$	13.5049			0.765795			0.382898	+	0.923791i	$0.374926\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	17.6789	−	10.7179i	0.997676	−	0.604844i
$315$		0			0
$316$	−3.65567	+	7.00841i	−0.205648	+	0.394254i
$317$		−	14.7272i		−	0.827161i	−0.910468	−	0.413580i	$-0.864278\pi$
$317$		−	14.7272i		−	0.827161i	0.910468	−	0.413580i	$-0.135722\pi$
$318$		0			0
$319$	5.69982			0.319129
$320$	−1.15566	−	8.94860i	−0.0646035	−	0.500242i
$321$		0			0
$322$	9.66414	+	15.9408i	0.538561	+	0.888345i
$323$			1.04322i			0.0580466i
$324$		0			0
$325$		−	11.5523i		−	0.640808i
$326$	−23.4719	+	14.2299i	−1.29999	+	0.788121i
$327$		0			0
$328$	−13.3450	+	0.858154i	−0.736855	+	0.0473836i
$329$	−13.3872			−0.738062
$330$		0			0
$331$		−	2.58159i		−	0.141897i	−0.997480	−	0.0709484i	$-0.977397\pi$
$331$		−	2.58159i		−	0.141897i	0.997480	−	0.0709484i	$-0.0226026\pi$
$332$	−16.5778	−	8.64720i	−0.909827	−	0.474577i
$333$		0			0
$334$	−8.70635	−	14.3609i	−0.476390	−	0.785795i
$335$	−3.23282			−0.176628
$336$		0			0
$337$	7.00263			0.381457			0.190729	−	0.981643i	$-0.438915\pi$
$337$	7.00263			0.381457			0.190729	+	0.981643i	$0.438915\pi$
$338$	2.49055	+	4.10811i	0.135468	+	0.223452i
$339$		0			0
$340$	−2.00000	−	1.04322i	−0.108465	−	0.0565768i
$341$			13.5447i			0.733487i
$342$		0			0
$343$	−19.1288			−1.03286
$344$	0.277652	+	4.31773i	0.0149700	+	0.232796i
$345$		0			0
$346$	−21.7917	+	13.2113i	−1.17153	+	0.710243i
$347$			1.76335i			0.0946614i	0.998879	+	0.0473307i	$0.0150715\pi$
$347$			1.76335i			0.0946614i	−0.998879	+	0.0473307i	$0.984929\pi$
$348$		0			0
$349$			36.8581i			1.97297i	0.163851	+	0.986485i	$0.447608\pi$
$349$			36.8581i			1.97297i	−0.163851	+	0.986485i	$0.552392\pi$
$350$	4.77634	+	7.87846i	0.255306	+	0.421122i
$351$		0			0
$352$	−26.1429	−	11.5673i	−1.39342	−	0.616542i
$353$	32.9830			1.75551			0.877755	−	0.479109i	$-0.159040\pi$
$353$	32.9830			1.75551			0.877755	+	0.479109i	$0.159040\pi$
$354$		0			0
$355$		−	3.40574i		−	0.180758i
$356$	−16.8963	+	32.3925i	−0.895503	+	1.71680i
$357$		0			0
$358$	19.1844	−	11.6306i	1.01393	−	0.614698i
$359$	−10.1093			−0.533546			−0.266773	−	0.963759i	$-0.585957\pi$
$359$	−10.1093			−0.533546			−0.266773	+	0.963759i	$0.585957\pi$
$360$		0			0
$361$	17.9117			0.942720
$362$	13.3823	−	8.11304i	0.703356	−	0.426412i
$363$		0			0
$364$	9.60298	+	5.00903i	0.503333	+	0.262545i
$365$		−	13.7859i		−	0.721588i
$366$		0			0
$367$	36.8261			1.92230			0.961152	−	0.276018i	$-0.0890150\pi$
$367$	36.8261			1.92230			0.961152	+	0.276018i	$0.0890150\pi$
$368$	−17.2649	−	24.7433i	−0.899996	−	1.28984i
$369$		0			0
$370$	−7.56509	−	12.4785i	−0.393291	−	0.648724i
$371$			6.83212i			0.354706i
$372$		0			0
$373$			15.2775i			0.791037i	0.918458	+	0.395518i	$0.129435\pi$
$373$			15.2775i			0.791037i	−0.918458	+	0.395518i	$0.870565\pi$
$374$	−6.11151	+	3.70512i	−0.316019	+	0.191587i
$375$		0			0
$376$	21.6227	−	1.39045i	1.11510	−	0.0717070i
$377$	3.49510			0.180007
$378$		0			0
$379$			14.9805i			0.769498i	0.923021	+	0.384749i	$0.125712\pi$
$379$			14.9805i			0.769498i	−0.923021	+	0.384749i	$0.874288\pi$
$380$	1.08832	−	2.08645i	0.0558295	−	0.107033i
$381$		0			0
$382$	−10.4791	−	17.2850i	−0.536155	−	0.884376i
$383$	5.19355			0.265378			0.132689	−	0.991158i	$-0.457639\pi$
$383$	5.19355			0.265378			0.132689	+	0.991158i	$0.457639\pi$
$384$		0			0
$385$	−9.96074			−0.507646
$386$	−15.6515	−	25.8167i	−0.796638	−	1.31404i
$387$		0			0
$388$	1.05200	−	2.01682i	0.0534072	−	0.102389i
$389$			9.29660i			0.471357i	0.971831	+	0.235678i	$0.0757312\pi$
$389$			9.29660i			0.471357i	−0.971831	+	0.235678i	$0.924269\pi$
$390$		0			0
$391$	−7.54284			−0.381458
$392$	11.1381	−	0.716240i	0.562561	−	0.0361756i
$393$		0			0
$394$	27.6053	−	16.7358i	1.39073	−	0.843137i
$395$		−	4.45763i		−	0.224287i
$396$		0			0
$397$			12.1177i			0.608172i	0.952645	+	0.304086i	$0.0983511\pi$
$397$			12.1177i			0.608172i	−0.952645	+	0.304086i	$0.901649\pi$
$398$	−6.46274	−	10.6601i	−0.323948	−	0.534344i
$399$		0			0
$400$	−8.53290	−	12.2290i	−0.426645	−	0.611449i
$401$	−30.3506			−1.51564			−0.757818	−	0.652466i	$-0.773735\pi$
$401$	−30.3506			−1.51564			−0.757818	+	0.652466i	$0.773735\pi$
$402$		0			0
$403$			8.30555i			0.413729i
$404$	26.9509	+	14.0579i	1.34086	+	0.699409i
$405$		0			0
$406$	−2.38359	+	1.44506i	−0.118296	+	0.0717171i
$407$	−46.2342			−2.29174
$408$		0			0
$409$	23.3015			1.15219			0.576093	−	0.817384i	$-0.304576\pi$
$409$	23.3015			1.15219			0.576093	+	0.817384i	$0.304576\pi$
$410$	6.44870	−	3.90954i	0.318478	−	0.193078i
$411$		0			0
$412$	13.5344	−	25.9472i	0.666790	−	1.27833i
$413$			19.2843i			0.948920i
$414$		0			0
$415$	10.5442			0.517592
$416$	−16.0307	−	7.09305i	−0.785971	−	0.347765i
$417$		0			0
$418$	−3.86527	−	6.37568i	−0.189057	−	0.311845i
$419$		−	8.50917i		−	0.415700i	−0.978161	−	0.207850i	$-0.933353\pi$
$419$		−	8.50917i		−	0.415700i	0.978161	−	0.207850i	$-0.0666466\pi$
$420$		0			0
$421$			31.3191i			1.52640i	0.646162	+	0.763200i	$0.276373\pi$
$421$			31.3191i			1.52640i	−0.646162	+	0.763200i	$0.723627\pi$
$422$	10.4951	−	6.36269i	0.510894	−	0.309731i
$423$		0			0
$424$	−0.709611	−	11.0351i	−0.0344618	−	0.535910i
$425$	−3.72792			−0.180831
$426$		0			0
$427$		−	1.97100i		−	0.0953835i
$428$	5.46632	+	2.85130i	0.264224	+	0.137823i
$429$		0			0
$430$	−1.26492	−	2.08645i	−0.0609996	−	0.100618i
$431$	−19.2734			−0.928366			−0.464183	−	0.885739i	$-0.653652\pi$
$431$	−19.2734			−0.928366			−0.464183	+	0.885739i	$0.653652\pi$
$432$		0			0
$433$	21.9363			1.05419			0.527095	−	0.849806i	$-0.323281\pi$
$433$	21.9363			1.05419			0.527095	+	0.849806i	$0.323281\pi$
$434$	−3.43395	−	5.66422i	−0.164835	−	0.271891i
$435$		0			0
$436$	−31.2132	−	16.2812i	−1.49484	−	0.779728i
$437$		−	7.86887i		−	0.376419i
$438$		0			0
$439$	−5.43358			−0.259331			−0.129665	−	0.991558i	$-0.541390\pi$
$439$	−5.43358			−0.259331			−0.129665	+	0.991558i	$0.541390\pi$
$440$	16.0883	−	1.03456i	0.766980	−	0.0493208i
$441$		0			0
$442$	−3.74755	+	2.27196i	−0.178253	+	0.108066i
$443$		−	5.06043i		−	0.240428i	−0.992748	−	0.120214i	$-0.961642\pi$
$443$		−	5.06043i		−	0.240428i	0.992748	−	0.120214i	$-0.0383581\pi$
$444$		0			0
$445$		−	20.6029i		−	0.976671i
$446$	−3.17625	−	5.23915i	−0.150400	−	0.248081i
$447$		0			0
$448$	13.8653	−	1.79062i	0.655073	−	0.0845990i
$449$	15.8653			0.748729			0.374364	−	0.927282i	$-0.377861\pi$
$449$	15.8653			0.748729			0.374364	+	0.927282i	$0.377861\pi$
$450$		0			0
$451$		−	23.8932i		−	1.12509i
$452$	5.08273	−	9.74426i	0.239071	−	0.458331i
$453$		0			0
$454$	−31.0063	+	18.7976i	−1.45520	+	0.882216i
$455$	−6.10788			−0.286342
$456$		0			0
$457$	−10.1272			−0.473730			−0.236865	−	0.971543i	$-0.576120\pi$
$457$	−10.1272			−0.473730			−0.236865	+	0.971543i	$0.576120\pi$
$458$	2.98037	−	1.80686i	0.139263	−	0.0844288i
$459$		0			0
$460$	15.0857	+	7.86887i	0.703373	+	0.366888i
$461$		−	22.6244i		−	1.05372i	−0.849951	−	0.526862i	$-0.823368\pi$
$461$		−	22.6244i		−	1.05372i	0.849951	−	0.526862i	$-0.176632\pi$
$462$		0			0
$463$	−7.18114			−0.333736			−0.166868	−	0.985979i	$-0.553365\pi$
$463$	−7.18114			−0.333736			−0.166868	+	0.985979i	$0.553365\pi$
$464$	3.69982	−	2.58159i	0.171760	−	0.119847i
$465$		0			0
$466$	1.95880	+	3.23099i	0.0907395	+	0.149673i
$467$			38.2074i			1.76803i	0.467459	+	0.884015i	$0.345170\pi$
$467$			38.2074i			1.76803i	−0.467459	+	0.884015i	$0.654830\pi$
$468$		0			0
$469$		−	5.00903i		−	0.231296i
$470$	−10.4487	+	6.33455i	−0.481962	+	0.292191i
$471$		0			0
$472$	−2.00295	−	31.1475i	−0.0921931	−	1.43368i
$473$	−7.73055			−0.355451
$474$		0			0
$475$		−	3.88906i		−	0.178442i
$476$	1.61641	−	3.09887i	0.0740879	−	0.142036i
$477$		0			0
$478$	2.12130	+	3.49904i	0.0970261	+	0.160042i
$479$	−0.136030			−0.00621538			−0.00310769	−	0.999995i	$-0.500989\pi$
$479$	−0.136030			−0.00621538			−0.00310769	+	0.999995i	$0.500989\pi$
$480$		0			0
$481$	−28.3506			−1.29268
$482$	10.1367	+	16.7202i	0.461712	+	0.761584i
$483$		0			0
$484$	13.4482	−	25.7819i	0.611280	−	1.17190i
$485$			1.28278i			0.0582481i
$486$		0			0
$487$	−38.5514			−1.74693			−0.873464	−	0.486888i	$-0.838132\pi$
$487$	−38.5514			−1.74693			−0.873464	+	0.486888i	$0.838132\pi$
$488$	0.204716	+	3.18351i	0.00926706	+	0.144111i
$489$		0			0
$490$	−5.38227	+	3.26302i	−0.243146	+	0.147408i
$491$		−	18.6889i		−	0.843418i	−0.906731	−	0.421709i	$-0.861430\pi$
$491$		−	18.6889i		−	0.843418i	0.906731	−	0.421709i	$-0.138570\pi$
$492$		0			0
$493$		−	1.12786i		−	0.0507965i
$494$	−2.37017	−	3.90954i	−0.106639	−	0.175898i
$495$		0			0
$496$	6.13473	+	8.79203i	0.275457	+	0.394774i
$497$	5.27697			0.236704
$498$		0			0
$499$			18.3033i			0.819368i	0.912228	+	0.409684i	$0.134361\pi$
$499$			18.3033i			0.819368i	−0.912228	+	0.409684i	$0.865639\pi$
$500$	17.4558	+	9.10518i	0.780649	+	0.407196i
$501$		0			0
$502$	−32.3218	+	19.5952i	−1.44259	+	0.874576i
$503$	26.6030			1.18617			0.593085	−	0.805140i	$-0.297910\pi$
$503$	26.6030			1.18617			0.593085	+	0.805140i	$0.297910\pi$
$504$		0			0
$505$	−17.1419			−0.762803
$506$	46.0981	−	27.9471i	2.04931	−	1.24240i
$507$		0			0
$508$	−13.6227	+	26.1165i	−0.604408	+	1.15873i
$509$		−	7.57086i		−	0.335572i	−0.985823	−	0.167786i	$-0.946338\pi$
$509$		−	7.57086i		−	0.335572i	0.985823	−	0.167786i	$-0.0536618\pi$
$510$		0			0
$511$	21.3604			0.944928
$512$	−22.2088	+	4.33226i	−0.981500	+	0.191461i
$513$		0			0
$514$	0.337800	+	0.557193i	0.0148997	+	0.0245767i
$515$			16.5034i			0.727228i
$516$		0			0
$517$			38.7137i			1.70263i
$518$	19.3345	−	11.7216i	0.849511	−	0.515018i
$519$		0			0
$520$	9.86527	−	0.634388i	0.432621	−	0.0278198i
$521$	22.4389			0.983065			0.491533	−	0.870859i	$-0.336437\pi$
$521$	22.4389			0.983065			0.491533	+	0.870859i	$0.336437\pi$
$522$		0			0
$523$		−	13.5755i		−	0.593616i	−0.954937	−	0.296808i	$-0.904078\pi$
$523$		−	13.5755i		−	0.593616i	0.954937	−	0.296808i	$-0.0959221\pi$
$524$	−18.6220	−	9.71345i	−0.813505	−	0.424334i
$525$		0			0
$526$	11.9228	+	19.6665i	0.519861	+	0.857499i
$527$	2.68019			0.116751
$528$		0			0
$529$	33.8944			1.47367
$530$	3.23282	+	5.33246i	0.140425	+	0.231627i
$531$		0			0
$532$	3.23282	+	1.68628i	0.140160	+	0.0731094i
$533$		−	14.6512i		−	0.634614i
$534$		0			0
$535$	−3.47680			−0.150315
$536$	0.520258	+	8.09045i	0.0224717	+	0.349454i
$537$		0			0
$538$	−24.2587	+	14.7069i	−1.04587	+	0.634060i
$539$			19.9420i			0.858961i
$540$		0			0
$541$			14.1426i			0.608037i	0.952666	+	0.304019i	$0.0983285\pi$
$541$			14.1426i			0.608037i	−0.952666	+	0.304019i	$0.901671\pi$
$542$	0.491471	+	0.810671i	0.0211105	+	0.0348213i
$543$		0			0
$544$	−2.28892	+	5.17309i	−0.0981364	+	0.221794i
$545$	19.8529			0.850403
$546$		0			0
$547$			29.0623i			1.24261i	0.783567	+	0.621307i	$0.213398\pi$
$547$			29.0623i			1.24261i	−0.783567	+	0.621307i	$0.786602\pi$
$548$	4.91727	−	9.42707i	0.210056	−	0.402704i
$549$		0			0
$550$	22.7832	−	13.8124i	0.971480	−	0.588963i
$551$	1.17662			0.0501255
$552$		0			0
$553$	6.90680			0.293707
$554$	4.33586	−	2.62863i	0.184213	−	0.111680i
$555$		0			0
$556$	−4.19424	−	2.18777i	−0.177875	−	0.0927820i
$557$			26.1386i			1.10753i	0.832674	+	0.553764i	$0.186809\pi$
$557$			26.1386i			1.10753i	−0.832674	+	0.553764i	$0.813191\pi$
$558$		0			0
$559$	−4.74034			−0.200495
$560$	−6.46563	+	4.51146i	−0.273223	+	0.190644i
$561$		0			0
$562$	−0.291076	−	0.480123i	−0.0122783	−	0.0202528i
$563$			17.8812i			0.753602i	0.926294	+	0.376801i	$0.122976\pi$
$563$			17.8812i			0.753602i	−0.926294	+	0.376801i	$0.877024\pi$
$564$		0			0
$565$			6.19774i			0.260741i
$566$	−12.0553	+	7.30857i	−0.506723	+	0.307202i
$567$		0			0
$568$	−8.52320	+	0.548086i	−0.357626	+	0.0229972i
$569$	21.4434			0.898955			0.449478	−	0.893292i	$-0.351610\pi$
$569$	21.4434			0.898955			0.449478	+	0.893292i	$0.351610\pi$
$570$		0			0
$571$		−	34.9469i		−	1.46248i	−0.682120	−	0.731240i	$-0.738942\pi$
$571$		−	34.9469i		−	1.46248i	0.682120	−	0.731240i	$-0.261058\pi$
$572$	14.4853	−	27.7703i	0.605661	−	1.16113i
$573$		0			0
$574$	6.05757	+	9.99183i	0.252838	+	0.417051i
$575$	28.1191			1.17265
$576$		0			0
$577$	−8.95848			−0.372946			−0.186473	−	0.982460i	$-0.559706\pi$
$577$	−8.95848			−0.372946			−0.186473	+	0.982460i	$0.559706\pi$
$578$	0.733159	+	1.20933i	0.0304954	+	0.0503015i
$579$		0			0
$580$	−1.17662	+	2.25573i	−0.0488563	+	0.0936641i
$581$			16.3375i			0.677793i
$582$		0			0
$583$	19.7574			0.818268
$584$	−34.5007	+	2.21857i	−1.42765	+	0.0918052i
$585$		0			0
$586$	6.52320	−	3.95471i	0.269471	−	0.163368i
$587$			6.94513i			0.286656i	0.989675	+	0.143328i	$0.0457804\pi$
$587$			6.94513i			0.286656i	−0.989675	+	0.143328i	$0.954220\pi$
$588$		0			0
$589$			2.79604i			0.115209i
$590$	9.12494	+	15.0514i	0.375668	+	0.619655i
$591$		0			0
$592$	−30.0111	+	20.9406i	−1.23345	+	0.860653i
$593$	−18.5932			−0.763531			−0.381765	−	0.924259i	$-0.624684\pi$
$593$	−18.5932			−0.763531			−0.381765	+	0.924259i	$0.624684\pi$
$594$		0			0
$595$			1.97100i			0.0808033i
$596$	38.0111	+	19.8271i	1.55700	+	0.812149i
$597$		0			0
$598$	28.2672	−	17.1370i	1.15593	−	0.700786i
$599$	−31.7057			−1.29546			−0.647730	−	0.761870i	$-0.724282\pi$
$599$	−31.7057			−1.29546			−0.647730	+	0.761870i	$0.724282\pi$
$600$		0			0
$601$	−29.2257			−1.19214			−0.596070	−	0.802933i	$-0.703272\pi$
$601$	−29.2257			−1.19214			−0.596070	+	0.802933i	$0.703272\pi$
$602$	3.23282	−	1.95990i	0.131760	−	0.0798797i
$603$		0			0
$604$	16.7672	−	32.1449i	0.682247	−	1.30796i
$605$			16.3983i			0.666686i
$606$		0			0
$607$	−4.90321			−0.199015			−0.0995077	−	0.995037i	$-0.531727\pi$
$607$	−4.90321			−0.199015			−0.0995077	+	0.995037i	$0.531727\pi$
$608$	−5.39670	−	2.38785i	−0.218865	−	0.0968402i
$609$		0			0
$610$	−0.932637	−	1.53836i	−0.0377614	−	0.0622865i
$611$			23.7391i			0.960379i
$612$		0			0
$613$		−	33.8739i		−	1.36816i	−0.729409	−	0.684078i	$-0.760205\pi$
$613$		−	33.8739i		−	1.36816i	0.729409	−	0.684078i	$-0.239795\pi$
$614$	−35.0239	+	21.2333i	−1.41345	+	0.856907i
$615$		0			0
$616$	1.60298	+	24.9278i	0.0645861	+	1.00437i
$617$	34.5174			1.38962			0.694809	−	0.719194i	$-0.255489\pi$
$617$	34.5174			1.38962			0.694809	+	0.719194i	$0.255489\pi$
$618$		0			0
$619$		−	21.3435i		−	0.857868i	−0.903336	−	0.428934i	$-0.858889\pi$
$619$		−	21.3435i		−	0.857868i	0.903336	−	0.428934i	$-0.141111\pi$
$620$	−5.36038	−	2.79604i	−0.215278	−	0.112292i
$621$		0			0
$622$	9.90128	+	16.3319i	0.397005	+	0.654851i
$623$	31.9228			1.27896
$624$		0			0
$625$	7.53699			0.301480
$626$	−4.39896	−	7.25598i	−0.175818	−	0.290007i
$627$		0			0
$628$	25.9228	+	13.5217i	1.03443	+	0.539574i
$629$			9.14869i			0.364782i
$630$		0			0
$631$	44.3689			1.76630			0.883149	−	0.469093i	$-0.155419\pi$
$631$	44.3689			1.76630			0.883149	+	0.469093i	$0.155419\pi$
$632$	−11.1557	+	0.717367i	−0.443748	+	0.0285353i
$633$		0			0
$634$	17.8100	−	10.7974i	0.707326	−	0.428818i
$635$		−	16.6111i		−	0.659192i
$636$		0			0
$637$			12.2283i			0.484504i
$638$	4.17888	+	6.89296i	0.165443	+	0.272895i
$639$		0			0
$640$	9.97453	−	7.95833i	0.394278	−	0.314581i
$641$	3.68151			0.145411			0.0727055	−	0.997353i	$-0.476837\pi$
$641$	3.68151			0.145411			0.0727055	+	0.997353i	$0.476837\pi$
$642$		0			0
$643$			30.6988i			1.21064i	0.795982	+	0.605321i	$0.206955\pi$
$643$			30.6988i			1.21064i	−0.795982	+	0.605321i	$0.793045\pi$
$644$	−12.1923	+	23.3743i	−0.480444	+	0.921075i
$645$		0			0
$646$	−1.26160	+	0.764850i	−0.0496371	+	0.0300926i
$647$	20.1066			0.790472			0.395236	−	0.918580i	$-0.370663\pi$
$647$	20.1066			0.790472			0.395236	+	0.918580i	$0.370663\pi$
$648$		0			0
$649$	55.7672			2.18905
$650$	13.9706	−	8.46970i	0.547971	−	0.332209i
$651$		0			0
$652$	−34.4173	−	17.9525i	−1.34788	−	0.703073i
$653$			4.85298i			0.189912i	0.995481	+	0.0949560i	$0.0302710\pi$
$653$			4.85298i			0.189912i	−0.995481	+	0.0949560i	$0.969729\pi$
$654$		0			0
$655$	11.8443			0.462796
$656$	−10.8218	−	15.5094i	−0.422521	−	0.605539i
$657$		0			0
$658$	−9.81497	−	16.1896i	−0.382627	−	0.631135i
$659$		−	0.820109i		−	0.0319469i	−0.999872	−	0.0159735i	$-0.994915\pi$
$659$		−	0.820109i		−	0.0319469i	0.999872	−	0.0159735i	$-0.00508473\pi$
$660$		0			0
$661$			33.6446i			1.30862i	0.756225	+	0.654311i	$0.227041\pi$
$661$			33.6446i			1.30862i	−0.756225	+	0.654311i	$0.772959\pi$
$662$	3.12199	−	1.89271i	0.121340	−	0.0735624i
$663$		0			0
$664$	−1.69687	−	26.3878i	−0.0658515	−	1.02405i
$665$	−2.05620			−0.0797360
$666$		0			0
$667$			8.50730i			0.329404i
$668$	10.9840	−	21.0577i	0.424982	−	0.814746i
$669$		0			0
$670$	−2.37017	−	3.90954i	−0.0915676	−	0.151039i
$671$	−5.69982			−0.220039
$672$		0			0
$673$	14.3061			0.551459			0.275729	−	0.961235i	$-0.411081\pi$
$673$	14.3061			0.551459			0.275729	+	0.961235i	$0.411081\pi$
$674$	5.13404	+	8.46848i	0.197756	+	0.326194i
$675$		0			0
$676$	−3.14209	+	6.02380i	−0.120850	+	0.231685i
$677$			25.2693i			0.971177i	0.874187	+	0.485589i	$0.161395\pi$
$677$			25.2693i			0.971177i	−0.874187	+	0.485589i	$0.838605\pi$
$678$		0			0
$679$	−1.98758			−0.0762765
$680$	−0.204716	−	3.18351i	−0.00785050	−	0.122082i
$681$		0			0
$682$	−16.3800	+	9.93042i	−0.627223	+	0.380256i
$683$		−	16.5149i		−	0.631923i	−0.948772	−	0.315962i	$-0.897673\pi$
$683$		−	16.5149i		−	0.631923i	0.948772	−	0.315962i	$-0.102327\pi$
$684$		0			0
$685$			5.99599i			0.229095i
$686$	−14.0245	−	23.1330i	−0.535457	−	0.883224i
$687$		0			0
$688$	−5.01799	+	3.50135i	−0.191309	+	0.133488i
$689$	12.1151			0.461550
$690$		0			0
$691$		−	3.61558i		−	0.137543i	−0.997632	−	0.0687716i	$-0.978092\pi$
$691$		−	3.61558i		−	0.137543i	0.997632	−	0.0687716i	$-0.0219080\pi$
$692$	−31.9536	−	16.6674i	−1.21469	−	0.633599i
$693$		0			0
$694$	−2.13247	+	1.29281i	−0.0809473	+	0.0490745i
$695$	2.66770			0.101192
$696$		0			0
$697$	−4.72792			−0.179083
$698$	−44.5736	+	27.0229i	−1.68714	+	1.02283i
$699$		0			0
$700$	−6.02584	+	11.5523i	−0.227755	+	0.436637i
$701$		−	20.4233i		−	0.771377i	−0.922629	−	0.385689i	$-0.873964\pi$
$701$		−	20.4233i		−	0.771377i	0.922629	−	0.385689i	$-0.126036\pi$
$702$		0			0
$703$	−9.54414			−0.359964
$704$	−5.17819	−	40.0961i	−0.195160	−	1.51118i
$705$		0			0
$706$	24.1818	+	39.8874i	0.910095	+	1.50118i
$707$		−	26.5602i		−	0.998899i
$708$		0			0
$709$			1.88393i			0.0707523i	0.999374	+	0.0353762i	$0.0112629\pi$
$709$			1.88393i			0.0707523i	−0.999374	+	0.0353762i	$0.988737\pi$
$710$	4.11866	−	2.49695i	0.154570	−	0.0937088i
$711$		0			0
$712$	−51.5609	+	3.31563i	−1.93233	+	0.124259i
$713$	−20.2162			−0.757104
$714$		0			0
$715$			17.6630i			0.660559i
$716$	28.1305	+	14.6732i	1.05129	+	0.548364i
$717$		0			0
$718$	−7.41169	−	12.2254i	−0.276602	−	0.456249i
$719$	29.2872			1.09223			0.546114	−	0.837711i	$-0.316107\pi$
$719$	29.2872			1.09223			0.546114	+	0.837711i	$0.316107\pi$
$720$		0			0
$721$	−25.5710			−0.952313
$722$	13.1321	+	21.6611i	0.488727	+	0.806144i
$723$		0			0
$724$	19.6227	+	10.2354i	0.729271	+	0.380397i
$725$			4.20459i			0.156155i
$726$		0			0
$727$	31.1485			1.15523			0.577617	−	0.816308i	$-0.303983\pi$
$727$	31.1485			1.15523			0.577617	+	0.816308i	$0.303983\pi$
$728$	0.982943	+	15.2856i	0.0364303	+	0.566522i
$729$		0			0
$730$	16.6717	−	10.1073i	0.617048	−	0.374087i
$731$			1.52970i			0.0565780i
$732$		0			0
$733$		−	6.44596i		−	0.238087i	−0.992889	−	0.119043i	$-0.962017\pi$
$733$		−	6.44596i		−	0.238087i	0.992889	−	0.119043i	$-0.0379828\pi$
$734$	26.9994	+	44.5348i	0.996565	+	1.64381i
$735$		0			0
$736$	17.2649	−	39.0198i	0.636393	−	1.43829i
$737$	−14.4853			−0.533573
$738$		0			0
$739$			19.5888i			0.720587i	0.932839	+	0.360293i	$0.117323\pi$
$739$			19.5888i			0.720587i	−0.932839	+	0.360293i	$0.882677\pi$
$740$	9.54414	−	18.2974i	0.350850	−	0.672625i
$741$		0			0
$742$	−8.26229	+	5.00903i	−0.303318	+	0.183887i
$743$	16.2315			0.595476			0.297738	−	0.954648i	$-0.403768\pi$
$743$	16.2315			0.595476			0.297738	+	0.954648i	$0.403768\pi$
$744$		0			0
$745$	−24.1766			−0.885762
$746$	−18.4755	+	11.2008i	−0.676435	+	0.410091i
$747$		0			0
$748$	−8.96142	−	4.67439i	−0.327662	−	0.170913i
$749$		−	5.38707i		−	0.196839i
$750$		0			0
$751$	2.87965			0.105080			0.0525400	−	0.998619i	$-0.483268\pi$
$751$	2.87965			0.105080			0.0525400	+	0.998619i	$0.483268\pi$
$752$	17.5344	+	25.1295i	0.639413	+	0.916379i
$753$		0			0
$754$	2.56247	+	4.22673i	0.0933196	+	0.153929i
$755$			20.4454i			0.744086i
$756$		0			0
$757$		−	19.8538i		−	0.721600i	−0.932643	−	0.360800i	$-0.882504\pi$
$757$		−	19.8538i		−	0.721600i	0.932643	−	0.360800i	$-0.117496\pi$
$758$	−18.1164	+	10.9831i	−0.658017	+	0.398925i
$759$		0			0
$760$	3.32111	−	0.213565i	0.120469	−	0.00774681i
$761$	−21.1619			−0.767119			−0.383560	−	0.923516i	$-0.625302\pi$
$761$	−21.1619			−0.767119			−0.383560	+	0.923516i	$0.625302\pi$
$762$		0			0
$763$			30.7607i			1.11361i
$764$	13.2204	−	25.3453i	0.478297	−	0.916959i
$765$		0			0
$766$	3.80770	+	6.28072i	0.137578	+	0.226931i
$767$	34.1962			1.23475
$768$		0			0
$769$	−28.0879			−1.01288			−0.506438	−	0.862276i	$-0.669038\pi$
$769$	−28.0879			−1.01288			−0.506438	+	0.862276i	$0.669038\pi$
$770$	−7.30281	−	12.0458i	−0.263175	−	0.434101i
$771$		0			0
$772$	19.7459	−	37.8555i	0.710671	−	1.36245i
$773$			21.4752i			0.772409i	0.922413	+	0.386204i	$0.126214\pi$
$773$			21.4752i			0.772409i	−0.922413	+	0.386204i	$0.873786\pi$
$774$		0			0
$775$	−9.99153			−0.358906
$776$	3.21029	−	0.206438i	0.115243	−	0.00741070i
$777$		0			0
$778$	−11.2427	+	6.81589i	−0.403069	+	0.244362i
$779$		−	4.93228i		−	0.176717i
$780$		0			0
$781$		−	15.2601i		−	0.546050i
$782$	−5.53010	−	9.12177i	−0.197756	−	0.326194i
$783$		0			0
$784$	9.03220	+	12.9446i	0.322579	+	0.462306i
$785$	−16.4880			−0.588481
$786$		0			0
$787$		−	1.22304i		−	0.0435966i	−0.999762	−	0.0217983i	$-0.993061\pi$
$787$		−	1.22304i		−	0.0435966i	0.999762	−	0.0217983i	$-0.00693916\pi$
$788$	40.4782	+	21.1139i	1.44197	+	0.752152i
$789$		0			0
$790$	5.39074	−	3.26815i	0.191794	−	0.116276i
$791$	−9.60298			−0.341443
$792$		0			0
$793$	−3.49510			−0.124115
$794$	−14.6543	+	8.88424i	−0.520063	+	0.315290i
$795$		0			0
$796$	8.15340	−	15.6312i	0.288990	−	0.554032i
$797$		−	27.2300i		−	0.964535i	−0.876024	−	0.482267i	$-0.839813\pi$
$797$		−	27.2300i		−	0.964535i	0.876024	−	0.482267i	$-0.160187\pi$
$798$		0			0
$799$	7.66056			0.271011
$800$	8.53290	−	19.2849i	0.301683	−	0.681823i
$801$		0			0
$802$	−22.2518	−	36.7039i	−0.785739	−	1.29606i
$803$		−	61.7707i		−	2.17984i
$804$		0			0
$805$		−	14.8670i		−	0.523991i
$806$	−10.0441	+	6.08929i	−0.353790	+	0.214486i
$807$		0			0
$808$	2.75865	+	42.8993i	0.0970488	+	1.50919i
$809$	−12.6939			−0.446294			−0.223147	−	0.974785i	$-0.571633\pi$
$809$	−12.6939			−0.446294			−0.223147	+	0.974785i	$0.571633\pi$
$810$		0			0
$811$			30.6006i			1.07453i	0.843412	+	0.537267i	$0.180543\pi$
$811$			30.6006i			1.07453i	−0.843412	+	0.537267i	$0.819457\pi$
$812$	−3.49510	−	1.82309i	−0.122654	−	0.0639779i
$813$		0			0
$814$	−33.8970	−	55.9123i	−1.18809	−	1.95973i
$815$	21.8907			0.766799
$816$		0			0
$817$	−1.59582			−0.0558307
$818$	17.0837	+	28.1792i	0.597319	+	0.985264i
$819$		0			0
$820$	9.45584	+	4.93228i	0.330212	+	0.172243i
$821$			34.8617i			1.21668i	0.793676	+	0.608340i	$0.208164\pi$
$821$			34.8617i			1.21668i	−0.793676	+	0.608340i	$0.791836\pi$
$822$		0			0
$823$	−25.7292			−0.896865			−0.448433	−	0.893817i	$-0.648018\pi$
$823$	−25.7292			−0.896865			−0.448433	+	0.893817i	$0.648018\pi$
$824$	41.3015	−	2.65590i	1.43881	−	0.0925228i
$825$		0			0
$826$	−23.3211	+	14.1385i	−0.811445	+	0.491941i
$827$			31.5024i			1.09545i	0.836659	+	0.547723i	$0.184505\pi$
$827$			31.5024i			1.09545i	−0.836659	+	0.547723i	$0.815495\pi$
$828$		0			0
$829$			24.2760i			0.843142i	0.906795	+	0.421571i	$0.138521\pi$
$829$			24.2760i			0.843142i	−0.906795	+	0.421571i	$0.861479\pi$
$830$	7.73055	+	12.7514i	0.268331	+	0.442606i
$831$		0			0
$832$	−3.17524	−	24.5868i	−0.110082	−	0.852393i
$833$	3.94606			0.136723
$834$		0			0
$835$			13.3935i			0.463502i
$836$	4.87644	−	9.34878i	0.168655	−	0.323334i
$837$		0			0
$838$	10.2904	−	6.23858i	0.355476	−	0.215508i
$839$	−34.6299			−1.19556			−0.597778	−	0.801662i	$-0.703950\pi$
$839$	−34.6299			−1.19556			−0.597778	+	0.801662i	$0.703950\pi$
$840$		0			0
$841$	27.7279			0.956135
$842$	−37.8751	+	22.9619i	−1.30526	+	0.791319i
$843$		0			0
$844$	15.3892	+	8.02718i	0.529717	+	0.276307i
$845$		−	3.83138i		−	0.131803i
$846$		0			0
$847$	−25.4081			−0.873033
$848$	12.8248	−	8.94860i	0.440404	−	0.307296i
$849$		0			0
$850$	−2.73316	−	4.50828i	−0.0937466	−	0.154633i
$851$		−	69.0071i		−	2.36553i
$852$		0			0
$853$			24.3542i			0.833872i	0.908936	+	0.416936i	$0.136896\pi$
$853$			24.3542i			0.833872i	−0.908936	+	0.416936i	$0.863104\pi$
$854$	2.38359	−	1.44506i	0.0815648	−	0.0494489i
$855$		0			0
$856$	0.559522	+	8.70104i	0.0191241	+	0.297395i
$857$	−1.86002			−0.0635371			−0.0317686	−	0.999495i	$-0.510114\pi$
$857$	−1.86002			−0.0635371			−0.0317686	+	0.999495i	$0.510114\pi$
$858$		0			0
$859$		−	20.8140i		−	0.710166i	−0.934835	−	0.355083i	$-0.884453\pi$
$859$		−	20.8140i		−	0.710166i	0.934835	−	0.355083i	$-0.115547\pi$
$860$	1.59582	−	3.05940i	0.0544170	−	0.104325i
$861$		0			0
$862$	−14.1305	−	23.3079i	−0.481285	−	0.793869i
$863$	31.1302			1.05968			0.529842	−	0.848096i	$-0.322251\pi$
$863$	31.1302			1.05968			0.529842	+	0.848096i	$0.322251\pi$
$864$		0			0
$865$	20.3237			0.691028
$866$	16.0828	+	26.5282i	0.546515	+	0.901464i
$867$		0			0
$868$	4.33228	−	8.30555i	0.147047	−	0.281909i
$869$		−	19.9733i		−	0.677549i
$870$		0			0
$871$	−8.88233			−0.300966
$872$	−3.19493	−	49.6838i	−0.108194	−	1.68251i
$873$		0			0
$874$	9.51606	−	5.76914i	0.321886	−	0.195144i
$875$		−	17.2028i		−	0.581559i
$876$		0			0
$877$			0.991052i			0.0334654i	0.999860	+	0.0167327i	$0.00532644\pi$
$877$			0.991052i			0.0334654i	−0.999860	+	0.0167327i	$0.994674\pi$
$878$	−3.98368	−	6.57099i	−0.134443	−	0.221760i
$879$		0			0
$880$	13.0464	+	18.6976i	0.439794	+	0.630294i
$881$	−19.3087			−0.650527			−0.325263	−	0.945623i	$-0.605453\pi$
$881$	−19.3087			−0.650527			−0.325263	+	0.945623i	$0.605453\pi$
$882$		0			0
$883$		−	23.9889i		−	0.807290i	−0.914916	−	0.403645i	$-0.867743\pi$
$883$		−	23.9889i		−	0.807290i	0.914916	−	0.403645i	$-0.132257\pi$
$884$	−5.49510	−	2.86631i	−0.184820	−	0.0964046i
$885$		0			0
$886$	6.11973	−	3.71010i	0.205596	−	0.124643i
$887$	−2.58473			−0.0867866			−0.0433933	−	0.999058i	$-0.513817\pi$
$887$	−2.58473			−0.0867866			−0.0433933	+	0.999058i	$0.513817\pi$
$888$		0			0
$889$	25.7378			0.863219
$890$	24.9157	−	15.1052i	0.835176	−	0.506328i
$891$		0			0
$892$	4.00716	−	7.68226i	0.134170	−	0.257221i
$893$			7.99168i			0.267431i
$894$		0			0
$895$	−17.8921			−0.598068
$896$	12.3309	+	15.4549i	0.411947	+	0.516311i
$897$		0			0
$898$	11.6318	+	19.1863i	0.388157	+	0.640257i
$899$		−	3.02289i		−	0.100819i
$900$		0			0
$901$		−	3.90954i		−	0.130246i
$902$	28.8947	−	17.5175i	0.962090	−	0.583270i
$903$		0			0
$904$	15.5105	−	0.997403i	0.515870	−	0.0331731i
$905$	−12.4808			−0.414876
$906$		0			0
$907$		−	42.7770i		−	1.42039i	−0.704006	−	0.710194i	$-0.748607\pi$
$907$		−	42.7770i		−	1.42039i	0.704006	−	0.710194i	$-0.251393\pi$
$908$	−45.4650	−	23.7151i	−1.50881	−	0.787014i
$909$		0			0
$910$	−4.47805	−	7.38644i	−0.148446	−	0.244858i
$911$	42.6128			1.41183			0.705913	−	0.708299i	$-0.250537\pi$
$911$	42.6128			1.41183			0.705913	+	0.708299i	$0.250537\pi$
$912$		0			0
$913$	47.2453			1.56359
$914$	−7.42485	−	12.2471i	−0.245592	−	0.405099i
$915$		0			0
$916$	4.37017	+	2.27953i	0.144394	+	0.0753179i
$917$			18.3520i			0.606036i
$918$		0			0
$919$	4.78549			0.157859			0.0789294	−	0.996880i	$-0.474850\pi$
$919$	4.78549			0.157859			0.0789294	+	0.996880i	$0.474850\pi$
$920$	1.54414	+	24.0127i	0.0509088	+	0.791675i
$921$		0			0
$922$	27.3604	−	16.5873i	0.901066	−	0.546274i
$923$		−	9.35744i		−	0.308004i
$924$		0			0
$925$		−	34.1056i		−	1.12139i
$926$	−5.26492	−	8.68436i	−0.173016	−	0.285386i
$927$		0			0
$928$	5.83455	+	2.58159i	0.191528	+	0.0847448i
$929$	−27.2819			−0.895088			−0.447544	−	0.894262i	$-0.647701\pi$
$929$	−27.2819			−0.895088			−0.447544	+	0.894262i	$0.647701\pi$
$930$		0			0
$931$			4.11663i			0.134917i
$932$	−2.47122	+	4.73766i	−0.0809476	+	0.155187i
$933$		0			0
$934$	−46.2054	+	28.0121i	−1.51189	+	0.916585i
$935$	5.69982			0.186404
$936$		0			0
$937$	0.0837798			0.00273697			0.00136848	−	0.999999i	$-0.499564\pi$
$937$	0.0837798			0.00273697			0.00136848	+	0.999999i	$0.499564\pi$
$938$	6.05757	−	3.67242i	0.197787	−	0.119909i
$939$		0			0
$940$	−15.3211	−	7.99168i	−0.499720	−	0.260660i
$941$		−	22.3002i		−	0.726967i	−0.931601	−	0.363483i	$-0.881587\pi$
$941$		−	22.3002i		−	0.726967i	0.931601	−	0.363483i	$-0.118413\pi$
$942$		0			0
$943$	35.6619			1.16131
$944$	36.1991	−	25.2583i	1.17818	−	0.822088i
$945$		0			0
$946$	−5.66772	−	9.34878i	−0.184274	−	0.303955i
$947$			18.5335i			0.602257i	0.953584	+	0.301128i	$0.0973633\pi$
$947$			18.5335i			0.602257i	−0.953584	+	0.301128i	$0.902637\pi$
$948$		0			0
$949$		−	37.8775i		−	1.22956i
$950$	4.70315	−	2.85130i	0.152590	−	0.0925084i
$951$		0			0
$952$	4.93264	−	0.317194i	0.159868	−	0.0102803i
$953$	20.9782			0.679549			0.339775	−	0.940507i	$-0.389649\pi$
$953$	20.9782			0.679549			0.339775	+	0.940507i	$0.389649\pi$
$954$		0			0
$955$			16.1206i			0.521650i
$956$	−2.67624	+	5.13071i	−0.0865558	+	0.165939i
$957$		0			0
$958$	−0.0997319	−	0.164505i	−0.00322219	−	0.00531493i
$959$	−9.29039			−0.300002
$960$		0			0
$961$	−23.8166			−0.768277
$962$	−20.7855	−	34.2852i	−0.670151	−	1.10540i
$963$		0			0
$964$	−12.7884	+	24.5171i	−0.411888	+	0.789644i
$965$			24.0776i			0.775086i
$966$		0			0
$967$	7.73192			0.248642			0.124321	−	0.992242i	$-0.460325\pi$
$967$	7.73192			0.248642			0.124321	+	0.992242i	$0.460325\pi$
$968$	41.0385	−	2.63899i	1.31903	−	0.0848202i
$969$		0			0
$970$	−1.55130	+	0.940482i	−0.0498094	+	0.0301971i
$971$		−	17.2155i		−	0.552471i	−0.961090	−	0.276235i	$-0.910913\pi$
$971$		−	17.2155i		−	0.552471i	0.961090	−	0.276235i	$-0.0890869\pi$
$972$		0			0
$973$			4.13343i			0.132512i
$974$	−28.2643	−	46.6213i	−0.905646	−	1.49384i
$975$		0			0
$976$	−3.69982	+	2.58159i	−0.118428	+	0.0826346i
$977$	−25.7377			−0.823422			−0.411711	−	0.911314i	$-0.635069\pi$
$977$	−25.7377			−0.823422			−0.411711	+	0.911314i	$0.635069\pi$
$978$		0			0
$979$		−	92.3157i		−	2.95042i
$980$	−7.89212	−	4.11663i	−0.252105	−	0.131501i
$981$		0			0
$982$	22.6010	−	13.7019i	0.721228	−	0.437246i
$983$	−33.9385			−1.08247			−0.541235	−	0.840872i	$-0.682043\pi$
$983$	−33.9385			−1.08247			−0.541235	+	0.840872i	$0.682043\pi$
$984$		0			0
$985$	−25.7457			−0.820327
$986$	1.36396	−	0.826905i	0.0434373	−	0.0263340i
$987$		0			0
$988$	2.99021	−	5.73263i	0.0951312	−	0.182379i
$989$		−	11.5383i		−	0.366896i
$990$		0			0
$991$	3.70829			0.117798			0.0588988	−	0.998264i	$-0.481241\pi$
$991$	3.70829			0.117798			0.0588988	+	0.998264i	$0.481241\pi$
$992$	−6.13473	+	13.8649i	−0.194778	+	0.440210i
$993$		0			0
$994$	3.86886	+	6.38159i	0.122713	+	0.202412i
$995$			9.94203i			0.315184i
$996$		0			0
$997$			26.8766i			0.851191i	0.904913	+	0.425596i	$0.139935\pi$
$997$			26.8766i			0.851191i	−0.904913	+	0.425596i	$0.860065\pi$
$998$	−22.1347	+	13.4192i	−0.700662	+	0.424778i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.f.c.613.6		8
3.2	odd	2		136.2.c.b.69.3	✓	8
4.3	odd	2		4896.2.f.d.2449.4		8
8.3	odd	2		4896.2.f.d.2449.5		8
8.5	even	2	inner	1224.2.f.c.613.5		8
12.11	even	2		544.2.c.b.273.3		8
24.5	odd	2		136.2.c.b.69.4	yes	8
24.11	even	2		544.2.c.b.273.6		8
48.5	odd	4		4352.2.a.bf.1.6		8
48.11	even	4		4352.2.a.bb.1.3		8
48.29	odd	4		4352.2.a.bf.1.3		8
48.35	even	4		4352.2.a.bb.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.c.b.69.3	✓	8	3.2	odd	2
136.2.c.b.69.4	yes	8	24.5	odd	2
544.2.c.b.273.3		8	12.11	even	2
544.2.c.b.273.6		8	24.11	even	2
1224.2.f.c.613.5		8	8.5	even	2	inner
1224.2.f.c.613.6		8	1.1	even	1	trivial
4352.2.a.bb.1.3		8	48.11	even	4
4352.2.a.bb.1.6		8	48.35	even	4
4352.2.a.bf.1.3		8	48.29	odd	4
4352.2.a.bf.1.6		8	48.5	odd	4
4896.2.f.d.2449.4		8	4.3	odd	2
4896.2.f.d.2449.5		8	8.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.733159 + 1.20933i) q^{2} +(-0.924955 + 1.77326i) q^{4} -1.12786i q^{5} +1.74755 q^{7} +(-2.82260 + 0.181508i) q^{8} +(1.36396 - 0.826905i) q^{10} -5.05364i q^{11} -3.09887i q^{13} +(1.28123 + 2.11337i) q^{14} +(-2.28892 - 3.28038i) q^{16} -1.00000 q^{17} -1.04322i q^{19} +(2.00000 + 1.04322i) q^{20} +(6.11151 - 3.70512i) q^{22} +7.54284 q^{23} +3.72792 q^{25} +(3.74755 - 2.27196i) q^{26} +(-1.61641 + 3.09887i) q^{28} +1.12786i q^{29} -2.68019 q^{31} +(2.28892 - 5.17309i) q^{32} +(-0.733159 - 1.20933i) q^{34} -1.97100i q^{35} -9.14869i q^{37} +(1.26160 - 0.764850i) q^{38} +(0.204716 + 3.18351i) q^{40} +4.72792 q^{41} -1.52970i q^{43} +(8.96142 + 4.67439i) q^{44} +(5.53010 + 9.12177i) q^{46} -7.66056 q^{47} -3.94606 q^{49} +(2.73316 + 4.50828i) q^{50} +(5.49510 + 2.86631i) q^{52} +3.90954i q^{53} -5.69982 q^{55} +(-4.93264 + 0.317194i) q^{56} +(-1.36396 + 0.826905i) q^{58} +11.0351i q^{59} -1.12786i q^{61} +(-1.96501 - 3.24123i) q^{62} +(7.93411 - 1.02465i) q^{64} -3.49510 q^{65} -2.86631i q^{67} +(0.924955 - 1.77326i) q^{68} +(2.38359 - 1.44506i) q^{70} +3.01963 q^{71} +12.2230 q^{73} +(11.0638 - 6.70745i) q^{74} +(1.84991 + 0.964936i) q^{76} -8.83150i q^{77} +3.95227 q^{79} +(-3.69982 + 2.58159i) q^{80} +(3.46632 + 5.71761i) q^{82} +9.34878i q^{83} +1.12786i q^{85} +(1.84991 - 1.12151i) q^{86} +(0.917274 + 14.2644i) q^{88} +18.2672 q^{89} -5.41543i q^{91} +(-6.97679 + 13.3754i) q^{92} +(-5.61641 - 9.26414i) q^{94} -1.17662 q^{95} -1.13735 q^{97} +(-2.89309 - 4.77209i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} - 12 q^{7} - 5 q^{8} - 8 q^{10} - 6 q^{14} + 9 q^{16} - 8 q^{17} + 16 q^{20} + 4 q^{22} + 16 q^{23} - 8 q^{25} + 4 q^{26} - 20 q^{28} + 24 q^{31} - 9 q^{32} - q^{34} - 18 q^{38} + 20 q^{40}+ \cdots + 57 q^{98}+O(q^{100}) \) 8 * q + q^2 + q^4 - 12 * q^7 - 5 * q^8 - 8 * q^10 - 6 * q^14 + 9 * q^16 - 8 * q^17 + 16 * q^20 + 4 * q^22 + 16 * q^23 - 8 * q^25 + 4 * q^26 - 20 * q^28 + 24 * q^31 - 9 * q^32 - q^34 - 18 * q^38 + 20 * q^40 + 10 * q^44 - 18 * q^46 - 4 * q^47 + 8 * q^49 + 17 * q^50 - 8 * q^52 - 12 * q^55 - 20 * q^56 + 8 * q^58 - 26 * q^62 + q^64 + 24 * q^65 - q^68 + 12 * q^70 + 36 * q^71 + 8 * q^73 + 36 * q^74 - 2 * q^76 + 24 * q^79 + 4 * q^80 + 18 * q^82 - 2 * q^86 + 10 * q^88 - 8 * q^89 + 28 * q^92 - 52 * q^94 - 32 * q^95 - 8 * q^97 + 57 * q^98

Introduction

L-functions

Modular forms

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Database

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