LMFDB - Embedded newform 459.2.f.c.217.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(55,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			217.10
Character	$\chi$	$=$	459.217
Dual form			459.2.f.c.55.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.61349i q^{2} -0.603350 q^{4} +(-0.576993 - 0.576993i) q^{5} +(1.78620 - 1.78620i) q^{7} +2.25348i q^{8} +(0.930973 - 0.930973i) q^{10} +(2.53389 - 2.53389i) q^{11} +5.59275 q^{13} +(2.88202 + 2.88202i) q^{14} -4.84267 q^{16} +(-1.62990 + 3.78727i) q^{17} +2.56848i q^{19} +(0.348129 + 0.348129i) q^{20} +(4.08841 + 4.08841i) q^{22} +(-1.41302 + 1.41302i) q^{23} -4.33416i q^{25} +9.02385i q^{26} +(-1.07771 + 1.07771i) q^{28} +(4.14738 + 4.14738i) q^{29} +(0.839455 + 0.839455i) q^{31} -3.30664i q^{32} +(-6.11072 - 2.62983i) q^{34} -2.06126 q^{35} +(-4.76750 - 4.76750i) q^{37} -4.14421 q^{38} +(1.30024 - 1.30024i) q^{40} +(6.73408 - 6.73408i) q^{41} +9.26834i q^{43} +(-1.52883 + 1.52883i) q^{44} +(-2.27990 - 2.27990i) q^{46} -9.21835 q^{47} +0.618947i q^{49} +6.99312 q^{50} -3.37439 q^{52} +1.17050i q^{53} -2.92408 q^{55} +(4.02518 + 4.02518i) q^{56} +(-6.69176 + 6.69176i) q^{58} -7.67537i q^{59} +(-2.97041 + 2.97041i) q^{61} +(-1.35445 + 1.35445i) q^{62} -4.35011 q^{64} +(-3.22698 - 3.22698i) q^{65} -4.68034 q^{67} +(0.983402 - 2.28505i) q^{68} -3.32582i q^{70} +(-5.93842 - 5.93842i) q^{71} +(0.390513 + 0.390513i) q^{73} +(7.69232 - 7.69232i) q^{74} -1.54969i q^{76} -9.05211i q^{77} +(9.32159 - 9.32159i) q^{79} +(2.79419 + 2.79419i) q^{80} +(10.8654 + 10.8654i) q^{82} -8.60839i q^{83} +(3.12567 - 1.24479i) q^{85} -14.9544 q^{86} +(5.71008 + 5.71008i) q^{88} -10.5202 q^{89} +(9.98980 - 9.98980i) q^{91} +(0.852548 - 0.852548i) q^{92} -14.8737i q^{94} +(1.48199 - 1.48199i) q^{95} +(2.34993 + 2.34993i) q^{97} -0.998664 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 16 q^{10} + 8 q^{13} + 40 q^{16} - 32 q^{22} - 40 q^{28} + 16 q^{31} + 40 q^{34} - 24 q^{37} - 40 q^{40} - 24 q^{46} + 16 q^{52} + 8 q^{55} - 40 q^{58} - 56 q^{61} - 80 q^{64} - 16 q^{67}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q - 24 * q^4 + 16 * q^10 + 8 * q^13 + 40 * q^16 - 32 * q^22 - 40 * q^28 + 16 * q^31 + 40 * q^34 - 24 * q^37 - 40 * q^40 - 24 * q^46 + 16 * q^52 + 8 * q^55 - 40 * q^58 - 56 * q^61 - 80 * q^64 - 16 * q^67 + 72 * q^73 + 32 * q^82 + 16 * q^85 + 64 * q^88 + 88 * q^91 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			1.61349i			1.14091i	0.821329	+	0.570455i	$0.193233\pi$
$2$			1.61349i			1.14091i	−0.821329	+	0.570455i	$0.806767\pi$
$3$		0			0
$3$		0			0
$4$	−0.603350			−0.301675
$5$	−0.576993	−	0.576993i	−0.258039	−	0.258039i	0.566217	−	0.824256i	$-0.308406\pi$
$5$	−0.576993	−	0.576993i	−0.258039	−	0.258039i	−0.824256	+	0.566217i	$0.808406\pi$
$6$		0			0
$7$	1.78620	−	1.78620i	0.675122	−	0.675122i	−0.283770	−	0.958892i	$-0.591585\pi$
$7$	1.78620	−	1.78620i	0.675122	−	0.675122i	0.958892	+	0.283770i	$0.0915854\pi$
$8$			2.25348i			0.796726i
$9$		0			0
$10$	0.930973	−	0.930973i	0.294399	−	0.294399i
$11$	2.53389	−	2.53389i	0.763998	−	0.763998i	−0.213045	−	0.977042i	$-0.568338\pi$
$11$	2.53389	−	2.53389i	0.763998	−	0.763998i	0.977042	+	0.213045i	$0.0683380\pi$
$12$		0			0
$13$	5.59275			1.55115			0.775575	−	0.631255i	$-0.217460\pi$
$13$	5.59275			1.55115			0.775575	+	0.631255i	$0.217460\pi$
$14$	2.88202	+	2.88202i	0.770253	+	0.770253i
$15$		0			0
$16$	−4.84267			−1.21067
$17$	−1.62990	+	3.78727i	−0.395309	+	0.918548i
$17$	−1.62990	+	3.78727i	−0.395309	+	0.918548i
$18$		0			0
$19$			2.56848i			0.589249i	0.955613	+	0.294625i	$0.0951946\pi$
$19$			2.56848i			0.589249i	−0.955613	+	0.294625i	$0.904805\pi$
$20$	0.348129	+	0.348129i	0.0778440	+	0.0778440i
$21$		0			0
$22$	4.08841	+	4.08841i	0.871653	+	0.871653i
$23$	−1.41302	+	1.41302i	−0.294636	+	0.294636i	−0.838908	−	0.544273i	$-0.816806\pi$
$23$	−1.41302	+	1.41302i	−0.294636	+	0.294636i	0.544273	+	0.838908i	$0.316806\pi$
$24$		0			0
$25$		−	4.33416i		−	0.866832i
$26$			9.02385i			1.76972i
$27$		0			0
$28$	−1.07771	+	1.07771i	−0.203667	+	0.203667i
$29$	4.14738	+	4.14738i	0.770150	+	0.770150i	0.978133	−	0.207983i	$-0.0666897\pi$
$29$	4.14738	+	4.14738i	0.770150	+	0.770150i	−0.207983	+	0.978133i	$0.566690\pi$
$30$		0			0
$31$	0.839455	+	0.839455i	0.150771	+	0.150771i	0.778462	−	0.627692i	$-0.216000\pi$
$31$	0.839455	+	0.839455i	0.150771	+	0.150771i	−0.627692	+	0.778462i	$0.716000\pi$
$32$		−	3.30664i		−	0.584536i
$33$		0			0
$34$	−6.11072	−	2.62983i	−1.04798	−	0.451012i
$35$	−2.06126			−0.348416
$36$		0			0
$37$	−4.76750	−	4.76750i	−0.783773	−	0.783773i	0.196692	−	0.980465i	$-0.436980\pi$
$37$	−4.76750	−	4.76750i	−0.783773	−	0.783773i	−0.980465	+	0.196692i	$0.936980\pi$
$38$	−4.14421			−0.672280
$39$		0			0
$40$	1.30024	−	1.30024i	0.205586	−	0.205586i
$41$	6.73408	−	6.73408i	1.05169	−	1.05169i	0.0530979	−	0.998589i	$-0.483090\pi$
$41$	6.73408	−	6.73408i	1.05169	−	1.05169i	0.998589	−	0.0530979i	$-0.0169095\pi$
$42$		0			0
$43$			9.26834i			1.41341i	0.707509	+	0.706705i	$0.249819\pi$
$43$			9.26834i			1.41341i	−0.707509	+	0.706705i	$0.750181\pi$
$44$	−1.52883	+	1.52883i	−0.230479	+	0.230479i
$45$		0			0
$46$	−2.27990	−	2.27990i	−0.336153	−	0.336153i
$47$	−9.21835			−1.34463			−0.672317	−	0.740263i	$-0.734701\pi$
$47$	−9.21835			−1.34463			−0.672317	+	0.740263i	$0.734701\pi$
$48$		0			0
$49$			0.618947i			0.0884209i
$50$	6.99312			0.988977
$51$		0			0
$52$	−3.37439			−0.467943
$53$			1.17050i			0.160781i	0.996763	+	0.0803905i	$0.0256167\pi$
$53$			1.17050i			0.160781i	−0.996763	+	0.0803905i	$0.974383\pi$
$54$		0			0
$55$	−2.92408			−0.394283
$56$	4.02518	+	4.02518i	0.537887	+	0.537887i
$57$		0			0
$58$	−6.69176	+	6.69176i	−0.878672	+	0.878672i
$59$		−	7.67537i		−	0.999248i	−0.866242	−	0.499624i	$-0.833471\pi$
$59$		−	7.67537i		−	0.999248i	0.866242	−	0.499624i	$-0.166529\pi$
$60$		0			0
$61$	−2.97041	+	2.97041i	−0.380323	+	0.380323i	−0.871218	−	0.490896i	$-0.836670\pi$
$61$	−2.97041	+	2.97041i	−0.380323	+	0.380323i	0.490896	+	0.871218i	$0.336670\pi$
$62$	−1.35445	+	1.35445i	−0.172016	+	0.172016i
$63$		0			0
$64$	−4.35011			−0.543764
$65$	−3.22698	−	3.22698i	−0.400258	−	0.400258i
$66$		0			0
$67$	−4.68034			−0.571794			−0.285897	−	0.958260i	$-0.592292\pi$
$67$	−4.68034			−0.571794			−0.285897	+	0.958260i	$0.592292\pi$
$68$	0.983402	−	2.28505i	0.119255	−	0.277103i
$69$		0			0
$70$		−	3.32582i		−	0.397511i
$71$	−5.93842	−	5.93842i	−0.704761	−	0.704761i	0.260668	−	0.965429i	$-0.416057\pi$
$71$	−5.93842	−	5.93842i	−0.704761	−	0.704761i	−0.965429	+	0.260668i	$0.916057\pi$
$72$		0			0
$73$	0.390513	+	0.390513i	0.0457060	+	0.0457060i	0.729590	−	0.683884i	$-0.239711\pi$
$73$	0.390513	+	0.390513i	0.0457060	+	0.0457060i	−0.683884	+	0.729590i	$0.739711\pi$
$74$	7.69232	−	7.69232i	0.894214	−	0.894214i
$75$		0			0
$76$		−	1.54969i		−	0.177762i
$77$		−	9.05211i		−	1.03158i
$78$		0			0
$79$	9.32159	−	9.32159i	1.04876	−	1.04876i	0.0500128	−	0.998749i	$-0.484074\pi$
$79$	9.32159	−	9.32159i	1.04876	−	1.04876i	0.998749	−	0.0500128i	$-0.0159262\pi$
$80$	2.79419	+	2.79419i	0.312400	+	0.312400i
$81$		0			0
$82$	10.8654	+	10.8654i	1.19988	+	1.19988i
$83$		−	8.60839i		−	0.944893i	−0.881359	−	0.472447i	$-0.843371\pi$
$83$		−	8.60839i		−	0.944893i	0.881359	−	0.472447i	$-0.156629\pi$
$84$		0			0
$85$	3.12567	−	1.24479i	0.339027	−	0.135016i
$86$	−14.9544			−1.61257
$87$		0			0
$88$	5.71008	+	5.71008i	0.608697	+	0.608697i
$89$	−10.5202			−1.11514			−0.557570	−	0.830130i	$-0.688266\pi$
$89$	−10.5202			−1.11514			−0.557570	+	0.830130i	$0.688266\pi$
$90$		0			0
$91$	9.98980	−	9.98980i	1.04722	−	1.04722i
$92$	0.852548	−	0.852548i	0.0888842	−	0.0888842i
$93$		0			0
$94$		−	14.8737i		−	1.53411i
$95$	1.48199	−	1.48199i	0.152049	−	0.152049i
$96$		0			0
$97$	2.34993	+	2.34993i	0.238599	+	0.238599i	0.816270	−	0.577671i	$-0.196038\pi$
$97$	2.34993	+	2.34993i	0.238599	+	0.238599i	−0.577671	+	0.816270i	$0.696038\pi$
$98$	−0.998664			−0.100880
$99$		0			0
$100$			2.61501i			0.261501i
$101$	2.16031			0.214959			0.107479	−	0.994207i	$-0.465722\pi$
$101$	2.16031			0.214959			0.107479	+	0.994207i	$0.465722\pi$
$102$		0			0
$103$	5.73949			0.565529			0.282764	−	0.959189i	$-0.408749\pi$
$103$	5.73949			0.565529			0.282764	+	0.959189i	$0.408749\pi$
$104$			12.6032i			1.23584i
$105$		0			0
$106$	−1.88860			−0.183437
$107$	7.82035	+	7.82035i	0.756022	+	0.756022i	0.975596	−	0.219574i	$-0.0704666\pi$
$107$	7.82035	+	7.82035i	0.756022	+	0.756022i	−0.219574	+	0.975596i	$0.570467\pi$
$108$		0			0
$109$	−7.22298	+	7.22298i	−0.691836	+	0.691836i	−0.962636	−	0.270800i	$-0.912712\pi$
$109$	−7.22298	+	7.22298i	−0.691836	+	0.691836i	0.270800	+	0.962636i	$0.412712\pi$
$110$		−	4.71797i		−	0.449841i
$111$		0			0
$112$	−8.65000	+	8.65000i	−0.817348	+	0.817348i
$113$	10.7640	−	10.7640i	1.01259	−	1.01259i	0.0126702	−	0.999920i	$-0.495967\pi$
$113$	10.7640	−	10.7640i	1.01259	−	1.01259i	0.999920	−	0.0126702i	$-0.00403316\pi$
$114$		0			0
$115$	1.63061			0.152055
$116$	−2.50232	−	2.50232i	−0.232335	−	0.232335i
$117$		0			0
$118$	12.3841			1.14005
$119$	3.85350	+	9.67618i	0.353250	+	0.887014i
$120$		0			0
$121$		−	1.84124i		−	0.167386i
$122$	−4.79273	−	4.79273i	−0.433914	−	0.433914i
$123$		0			0
$124$	−0.506486	−	0.506486i	−0.0454837	−	0.0454837i
$125$	−5.38574	+	5.38574i	−0.481716	+	0.481716i
$126$		0			0
$127$		−	4.45909i		−	0.395680i	−0.980234	−	0.197840i	$-0.936607\pi$
$127$		−	4.45909i		−	0.395680i	0.980234	−	0.197840i	$-0.0633927\pi$
$128$		−	13.6321i		−	1.20492i
$129$		0			0
$130$	5.20670	−	5.20670i	0.456658	−	0.456658i
$131$	−15.3735	−	15.3735i	−1.34319	−	1.34319i	−0.892869	−	0.450316i	$-0.851311\pi$
$131$	−15.3735	−	15.3735i	−1.34319	−	1.34319i	−0.450316	−	0.892869i	$-0.648689\pi$
$132$		0			0
$133$	4.58783	+	4.58783i	0.397815	+	0.397815i
$134$		−	7.55168i		−	0.652366i
$135$		0			0
$136$	−8.53454	−	3.67295i	−0.731831	−	0.314953i
$137$	−12.8727			−1.09979			−0.549896	−	0.835233i	$-0.685333\pi$
$137$	−12.8727			−1.09979			−0.549896	+	0.835233i	$0.685333\pi$
$138$		0			0
$139$	−9.49356	−	9.49356i	−0.805234	−	0.805234i	0.178675	−	0.983908i	$-0.442819\pi$
$139$	−9.49356	−	9.49356i	−0.805234	−	0.805234i	−0.983908	+	0.178675i	$0.942819\pi$
$140$	1.24366			0.105108
$141$		0			0
$142$	9.58158	−	9.58158i	0.804068	−	0.804068i
$143$	14.1714	−	14.1714i	1.18508	−	1.18508i
$144$		0			0
$145$		−	4.78602i		−	0.397458i
$146$	−0.630088	+	0.630088i	−0.0521465	+	0.0521465i
$147$		0			0
$148$	2.87647	+	2.87647i	0.236445	+	0.236445i
$149$	10.0770			0.825541			0.412770	−	0.910835i	$-0.364561\pi$
$149$	10.0770			0.825541			0.412770	+	0.910835i	$0.364561\pi$
$150$		0			0
$151$			17.4518i			1.42021i	0.704097	+	0.710104i	$0.251352\pi$
$151$			17.4518i			1.42021i	−0.704097	+	0.710104i	$0.748648\pi$
$152$	−5.78801			−0.469470
$153$		0			0
$154$	14.6055			1.17694
$155$		−	0.968720i		−	0.0778095i
$156$		0			0
$157$	−16.5280			−1.31908			−0.659538	−	0.751671i	$-0.729248\pi$
$157$	−16.5280			−1.31908			−0.659538	+	0.751671i	$0.729248\pi$
$158$	15.0403	+	15.0403i	1.19654	+	1.19654i
$159$		0			0
$160$	−1.90791	+	1.90791i	−0.150833	+	0.150833i
$161$			5.04790i			0.397830i
$162$		0			0
$163$	−7.85866	+	7.85866i	−0.615538	+	0.615538i	−0.944384	−	0.328846i	$-0.893340\pi$
$163$	−7.85866	+	7.85866i	−0.615538	+	0.615538i	0.328846	+	0.944384i	$0.393340\pi$
$164$	−4.06301	+	4.06301i	−0.317268	+	0.317268i
$165$		0			0
$166$	13.8895			1.07804
$167$	−1.55337	−	1.55337i	−0.120204	−	0.120204i	0.644446	−	0.764650i	$-0.277088\pi$
$167$	−1.55337	−	1.55337i	−0.120204	−	0.120204i	−0.764650	+	0.644446i	$0.777088\pi$
$168$		0			0
$169$	18.2789			1.40607
$170$	2.00845	+	5.04324i	0.154041	+	0.386799i
$171$		0			0
$172$		−	5.59206i		−	0.426390i
$173$	5.39609	+	5.39609i	0.410257	+	0.410257i	0.881828	−	0.471571i	$-0.156313\pi$
$173$	5.39609	+	5.39609i	0.410257	+	0.410257i	−0.471571	+	0.881828i	$0.656313\pi$
$174$		0			0
$175$	−7.74169	−	7.74169i	−0.585217	−	0.585217i
$176$	−12.2708	+	12.2708i	−0.924947	+	0.924947i
$177$		0			0
$178$		−	16.9742i		−	1.27227i
$179$		−	16.9787i		−	1.26905i	−0.772902	−	0.634525i	$-0.781196\pi$
$179$		−	16.9787i		−	1.26905i	0.772902	−	0.634525i	$-0.218804\pi$
$180$		0			0
$181$	−6.89057	+	6.89057i	−0.512172	+	0.512172i	−0.915191	−	0.403019i	$-0.867961\pi$
$181$	−6.89057	+	6.89057i	−0.512172	+	0.512172i	0.403019	+	0.915191i	$0.367961\pi$
$182$	16.1184	+	16.1184i	1.19478	+	1.19478i
$183$		0			0
$184$	−3.18422	−	3.18422i	−0.234744	−	0.234744i
$185$			5.50163i			0.404488i
$186$		0			0
$187$	5.46654	+	13.7265i	0.399753	+	1.00378i
$188$	5.56189			0.405643
$189$		0			0
$190$	2.39118	+	2.39118i	0.173475	+	0.173475i
$191$	−26.1154			−1.88964			−0.944821	−	0.327588i	$-0.893764\pi$
$191$	−26.1154			−1.88964			−0.944821	+	0.327588i	$0.893764\pi$
$192$		0			0
$193$	−12.6090	+	12.6090i	−0.907615	+	0.907615i	−0.996079	−	0.0884639i	$-0.971804\pi$
$193$	−12.6090	+	12.6090i	−0.907615	+	0.907615i	0.0884639	+	0.996079i	$0.471804\pi$
$194$	−3.79159	+	3.79159i	−0.272220	+	0.272220i
$195$		0			0
$196$		−	0.373442i		−	0.0266744i
$197$	−10.4155	+	10.4155i	−0.742073	+	0.742073i	−0.972977	−	0.230903i	$-0.925832\pi$
$197$	−10.4155	+	10.4155i	−0.742073	+	0.742073i	0.230903	+	0.972977i	$0.425832\pi$
$198$		0			0
$199$	−7.36863	−	7.36863i	−0.522349	−	0.522349i	0.395932	−	0.918280i	$-0.370422\pi$
$199$	−7.36863	−	7.36863i	−0.522349	−	0.522349i	−0.918280	+	0.395932i	$0.870422\pi$
$200$	9.76694			0.690627
$201$		0			0
$202$			3.48564i			0.245249i
$203$	14.8162			1.03989
$204$		0			0
$205$	−7.77104			−0.542753
$206$			9.26061i			0.645217i
$207$		0			0
$208$	−27.0839			−1.87793
$209$	6.50825	+	6.50825i	0.450185	+	0.450185i
$210$		0			0
$211$	−9.85702	+	9.85702i	−0.678585	+	0.678585i	−0.959680	−	0.281095i	$-0.909302\pi$
$211$	−9.85702	+	9.85702i	−0.678585	+	0.678585i	0.281095	+	0.959680i	$0.409302\pi$
$212$		−	0.706224i		−	0.0485036i
$213$		0			0
$214$	−12.6181	+	12.6181i	−0.862553	+	0.862553i
$215$	5.34777	−	5.34777i	0.364715	−	0.364715i
$216$		0			0
$217$	2.99888			0.203577
$218$	−11.6542	−	11.6542i	−0.789323	−	0.789323i
$219$		0			0
$220$	1.76424			0.118945
$221$	−9.11564	+	21.1813i	−0.613184	+	1.42481i
$222$		0			0
$223$		−	18.9731i		−	1.27054i	−0.772292	−	0.635268i	$-0.780890\pi$
$223$		−	18.9731i		−	1.27054i	0.772292	−	0.635268i	$-0.219110\pi$
$224$	−5.90633	−	5.90633i	−0.394633	−	0.394633i
$225$		0			0
$226$	17.3676	+	17.3676i	1.15527	+	1.15527i
$227$	6.66313	−	6.66313i	0.442248	−	0.442248i	−0.450519	−	0.892767i	$-0.648761\pi$
$227$	6.66313	−	6.66313i	0.442248	−	0.442248i	0.892767	+	0.450519i	$0.148761\pi$
$228$		0			0
$229$		−	20.5779i		−	1.35982i	−0.733294	−	0.679912i	$-0.762018\pi$
$229$		−	20.5779i		−	1.35982i	0.733294	−	0.679912i	$-0.237982\pi$
$230$			2.63097i			0.173481i
$231$		0			0
$232$	−9.34605	+	9.34605i	−0.613598	+	0.613598i
$233$	17.6969	+	17.6969i	1.15936	+	1.15936i	0.984613	+	0.174751i	$0.0559121\pi$
$233$	17.6969	+	17.6969i	1.15936	+	1.15936i	0.174751	+	0.984613i	$0.444088\pi$
$234$		0			0
$235$	5.31892	+	5.31892i	0.346968	+	0.346968i
$236$			4.63094i			0.301448i
$237$		0			0
$238$	−15.6124	+	6.21759i	−1.01200	+	0.403026i
$239$	5.18719			0.335532			0.167766	−	0.985827i	$-0.446345\pi$
$239$	5.18719			0.335532			0.167766	+	0.985827i	$0.446345\pi$
$240$		0			0
$241$	0.899602	+	0.899602i	0.0579484	+	0.0579484i	0.735487	−	0.677539i	$-0.236953\pi$
$241$	0.899602	+	0.899602i	0.0579484	+	0.0579484i	−0.677539	+	0.735487i	$0.736953\pi$
$242$	2.97082			0.190972
$243$		0			0
$244$	1.79220	−	1.79220i	0.114734	−	0.114734i
$245$	0.357128	−	0.357128i	0.0228161	−	0.0228161i
$246$		0			0
$247$			14.3649i			0.914014i
$248$	−1.89170	+	1.89170i	−0.120123	+	0.120123i
$249$		0			0
$250$	−8.68985	−	8.68985i	−0.549594	−	0.549594i
$251$	3.84757			0.242857			0.121428	−	0.992600i	$-0.461253\pi$
$251$	3.84757			0.242857			0.121428	+	0.992600i	$0.461253\pi$
$252$		0			0
$253$			7.16090i			0.450202i
$254$	7.19469			0.451435
$255$		0			0
$256$	13.2951			0.830943
$257$			30.3426i			1.89272i	0.323118	+	0.946359i	$0.395269\pi$
$257$			30.3426i			1.89272i	−0.323118	+	0.946359i	$0.604731\pi$
$258$		0			0
$259$	−17.0315			−1.05828
$260$	1.94700	+	1.94700i	0.120748	+	0.120748i
$261$		0			0
$262$	24.8049	−	24.8049i	1.53245	−	1.53245i
$263$			27.1948i			1.67690i	0.544977	+	0.838451i	$0.316539\pi$
$263$			27.1948i			1.67690i	−0.544977	+	0.838451i	$0.683461\pi$
$264$		0			0
$265$	0.675373	−	0.675373i	0.0414878	−	0.0414878i
$266$	−7.40241	+	7.40241i	−0.453871	+	0.453871i
$267$		0			0
$268$	2.82388			0.172496
$269$	0.316559	+	0.316559i	0.0193010	+	0.0193010i	0.716691	−	0.697390i	$-0.245656\pi$
$269$	0.316559	+	0.316559i	0.0193010	+	0.0193010i	−0.697390	+	0.716691i	$0.745656\pi$
$270$		0			0
$271$	−15.0696			−0.915411			−0.457705	−	0.889104i	$-0.651329\pi$
$271$	−15.0696			−0.915411			−0.457705	+	0.889104i	$0.651329\pi$
$272$	7.89308	−	18.3405i	0.478588	−	1.11206i
$273$		0			0
$274$		−	20.7700i		−	1.25476i
$275$	−10.9823	−	10.9823i	−0.662258	−	0.662258i
$276$		0			0
$277$	−1.39925	−	1.39925i	−0.0840730	−	0.0840730i	0.663820	−	0.747893i	$-0.268934\pi$
$277$	−1.39925	−	1.39925i	−0.0840730	−	0.0840730i	−0.747893	+	0.663820i	$0.768934\pi$
$278$	15.3178	−	15.3178i	0.918699	−	0.918699i
$279$		0			0
$280$		−	4.64500i		−	0.277592i
$281$			29.1820i			1.74085i	0.492297	+	0.870427i	$0.336157\pi$
$281$			29.1820i			1.74085i	−0.492297	+	0.870427i	$0.663843\pi$
$282$		0			0
$283$	14.6481	−	14.6481i	0.870738	−	0.870738i	−0.121815	−	0.992553i	$-0.538871\pi$
$283$	14.6481	−	14.6481i	0.870738	−	0.870738i	0.992553	+	0.121815i	$0.0388714\pi$
$284$	3.58295	+	3.58295i	0.212609	+	0.212609i
$285$		0			0
$286$	22.8655	+	22.8655i	1.35206	+	1.35206i
$287$		−	24.0569i		−	1.42003i
$288$		0			0
$289$	−11.6868	−	12.3458i	−0.687461	−	0.726221i
$290$	7.72220			0.453463
$291$		0			0
$292$	−0.235616	−	0.235616i	−0.0137884	−	0.0137884i
$293$	5.05564			0.295354			0.147677	−	0.989036i	$-0.452820\pi$
$293$	5.05564			0.295354			0.147677	+	0.989036i	$0.452820\pi$
$294$		0			0
$295$	−4.42864	+	4.42864i	−0.257845	+	0.257845i
$296$	10.7435	−	10.7435i	0.624452	−	0.624452i
$297$		0			0
$298$			16.2592i			0.941867i
$299$	−7.90269	+	7.90269i	−0.457024	+	0.457024i
$300$		0			0
$301$	16.5552	+	16.5552i	0.954223	+	0.954223i
$302$	−28.1583			−1.62033
$303$		0			0
$304$		−	12.4383i		−	0.713385i
$305$	3.42782			0.196276
$306$		0			0
$307$	−6.69816			−0.382284			−0.191142	−	0.981562i	$-0.561219\pi$
$307$	−6.69816			−0.382284			−0.191142	+	0.981562i	$0.561219\pi$
$308$			5.46159i			0.311203i
$309$		0			0
$310$	1.56302			0.0887736
$311$	−3.72825	−	3.72825i	−0.211409	−	0.211409i	0.593457	−	0.804866i	$-0.297763\pi$
$311$	−3.72825	−	3.72825i	−0.211409	−	0.211409i	−0.804866	+	0.593457i	$0.797763\pi$
$312$		0			0
$313$	−5.73323	+	5.73323i	−0.324061	+	0.324061i	−0.850323	−	0.526261i	$-0.823593\pi$
$313$	−5.73323	+	5.73323i	−0.324061	+	0.324061i	0.526261	+	0.850323i	$0.323593\pi$
$314$		−	26.6677i		−	1.50495i
$315$		0			0
$316$	−5.62419	+	5.62419i	−0.316385	+	0.316385i
$317$	−2.77944	+	2.77944i	−0.156109	+	0.156109i	−0.780840	−	0.624731i	$-0.785209\pi$
$317$	−2.77944	+	2.77944i	−0.156109	+	0.156109i	0.624731	+	0.780840i	$0.285209\pi$
$318$		0			0
$319$	21.0181			1.17679
$320$	2.50998	+	2.50998i	0.140312	+	0.140312i
$321$		0			0
$322$	−8.14473			−0.453888
$323$	−9.72752	−	4.18637i	−0.541254	−	0.232936i
$324$		0			0
$325$		−	24.2399i		−	1.34459i
$326$	−12.6799	−	12.6799i	−0.702273	−	0.702273i
$327$		0			0
$328$	15.1751	+	15.1751i	0.837906	+	0.837906i
$329$	−16.4659	+	16.4659i	−0.907792	+	0.907792i
$330$		0			0
$331$		−	19.9729i		−	1.09781i	−0.835884	−	0.548906i	$-0.815045\pi$
$331$		−	19.9729i		−	1.09781i	0.835884	−	0.548906i	$-0.184955\pi$
$332$			5.19387i			0.285051i
$333$		0			0
$334$	2.50635	−	2.50635i	0.137142	−	0.137142i
$335$	2.70052	+	2.70052i	0.147545	+	0.147545i
$336$		0			0
$337$	21.8065	+	21.8065i	1.18788	+	1.18788i	0.977654	+	0.210222i	$0.0674186\pi$
$337$	21.8065	+	21.8065i	1.18788	+	1.18788i	0.210222	+	0.977654i	$0.432581\pi$
$338$			29.4928i			1.60420i
$339$		0			0
$340$	−1.88587	+	0.751042i	−0.102276	+	0.0407310i
$341$	4.25418			0.230377
$342$		0			0
$343$	13.6090	+	13.6090i	0.734817	+	0.734817i
$344$	−20.8860			−1.12610
$345$		0			0
$346$	−8.70653	+	8.70653i	−0.468066	+	0.468066i
$347$	11.9027	−	11.9027i	0.638971	−	0.638971i	−0.311331	−	0.950302i	$-0.600775\pi$
$347$	11.9027	−	11.9027i	0.638971	−	0.638971i	0.950302	+	0.311331i	$0.100775\pi$
$348$		0			0
$349$		−	27.9391i		−	1.49555i	−0.663954	−	0.747774i	$-0.731123\pi$
$349$		−	27.9391i		−	1.49555i	0.663954	−	0.747774i	$-0.268877\pi$
$350$	12.4911	−	12.4911i	0.667680	−	0.667680i
$351$		0			0
$352$	−8.37867	−	8.37867i	−0.446585	−	0.446585i
$353$	22.5616			1.20083			0.600416	−	0.799688i	$-0.295002\pi$
$353$	22.5616			1.20083			0.600416	+	0.799688i	$0.295002\pi$
$354$		0			0
$355$			6.85285i			0.363712i
$356$	6.34737			0.336410
$357$		0			0
$358$	27.3950			1.44787
$359$		−	2.62410i		−	0.138495i	−0.997600	−	0.0692474i	$-0.977940\pi$
$359$		−	2.62410i		−	0.138495i	0.997600	−	0.0692474i	$-0.0220598\pi$
$360$		0			0
$361$	12.4029			0.652786
$362$	−11.1179	−	11.1179i	−0.584342	−	0.584342i
$363$		0			0
$364$	−6.02735	+	6.02735i	−0.315919	+	0.315919i
$365$		−	0.450646i		−	0.0235879i
$366$		0			0
$367$	−11.7818	+	11.7818i	−0.615004	+	0.615004i	−0.944246	−	0.329242i	$-0.893207\pi$
$367$	−11.7818	+	11.7818i	−0.615004	+	0.615004i	0.329242	+	0.944246i	$0.393207\pi$
$368$	6.84280	−	6.84280i	0.356706	−	0.356706i
$369$		0			0
$370$	−8.87683			−0.461485
$371$	2.09076	+	2.09076i	0.108547	+	0.108547i
$372$		0			0
$373$	26.4354			1.36877			0.684386	−	0.729120i	$-0.260070\pi$
$373$	26.4354			1.36877			0.684386	+	0.729120i	$0.260070\pi$
$374$	−22.1476	+	8.82021i	−1.14523	+	0.456082i
$375$		0			0
$376$		−	20.7734i		−	1.07130i
$377$	23.1953	+	23.1953i	1.19462	+	1.19462i
$378$		0			0
$379$	10.8285	+	10.8285i	0.556221	+	0.556221i	0.928229	−	0.372009i	$-0.121331\pi$
$379$	10.8285	+	10.8285i	0.556221	+	0.556221i	−0.372009	+	0.928229i	$0.621331\pi$
$380$	−0.894161	+	0.894161i	−0.0458695	+	0.0458695i
$381$		0			0
$382$		−	42.1369i		−	2.15591i
$383$		−	21.9992i		−	1.12411i	−0.827101	−	0.562053i	$-0.810012\pi$
$383$		−	21.9992i		−	1.12411i	0.827101	−	0.562053i	$-0.189988\pi$
$384$		0			0
$385$	−5.22300	+	5.22300i	−0.266189	+	0.266189i
$386$	−20.3445	−	20.3445i	−1.03551	−	1.03551i
$387$		0			0
$388$	−1.41783	−	1.41783i	−0.0719795	−	0.0719795i
$389$		−	29.0749i		−	1.47415i	−0.675809	−	0.737077i	$-0.736206\pi$
$389$		−	29.0749i		−	1.47415i	0.675809	−	0.737077i	$-0.263794\pi$
$390$		0			0
$391$	−3.04841	−	7.65459i	−0.154165	−	0.387109i
$392$	−1.39478			−0.0704472
$393$		0			0
$394$	−16.8053	−	16.8053i	−0.846639	−	0.846639i
$395$	−10.7570			−0.541243
$396$		0			0
$397$	23.5680	−	23.5680i	1.18284	−	1.18284i	0.203839	−	0.979004i	$-0.434658\pi$
$397$	23.5680	−	23.5680i	1.18284	−	1.18284i	0.979004	−	0.203839i	$-0.0653419\pi$
$398$	11.8892	−	11.8892i	0.595953	−	0.595953i
$399$		0			0
$400$			20.9889i			1.04944i
$401$	14.9313	−	14.9313i	0.745631	−	0.745631i	−0.228024	−	0.973655i	$-0.573227\pi$
$401$	14.9313	−	14.9313i	0.745631	−	0.745631i	0.973655	+	0.228024i	$0.0732265\pi$
$402$		0			0
$403$	4.69487	+	4.69487i	0.233868	+	0.233868i
$404$	−1.30342			−0.0648477
$405$		0			0
$406$			23.9057i			1.18642i
$407$	−24.1607			−1.19760
$408$		0			0
$409$	−16.0388			−0.793066			−0.396533	−	0.918020i	$-0.629787\pi$
$409$	−16.0388			−0.793066			−0.396533	+	0.918020i	$0.629787\pi$
$410$		−	12.5385i		−	0.619232i
$411$		0			0
$412$	−3.46292			−0.170606
$413$	−13.7098	−	13.7098i	−0.674614	−	0.674614i
$414$		0			0
$415$	−4.96698	+	4.96698i	−0.243819	+	0.243819i
$416$		−	18.4932i		−	0.906704i
$417$		0			0
$418$	−10.5010	+	10.5010i	−0.513621	+	0.513621i
$419$	21.4445	−	21.4445i	1.04763	−	1.04763i	0.0488243	−	0.998807i	$-0.484453\pi$
$419$	21.4445	−	21.4445i	1.04763	−	1.04763i	0.998807	−	0.0488243i	$-0.0155475\pi$
$420$		0			0
$421$	3.28147			0.159929			0.0799645	−	0.996798i	$-0.474519\pi$
$421$	3.28147			0.159929			0.0799645	+	0.996798i	$0.474519\pi$
$422$	−15.9042	−	15.9042i	−0.774204	−	0.774204i
$423$		0			0
$424$	−2.63771			−0.128098
$425$	16.4146	+	7.06425i	0.796226	+	0.342667i
$426$		0			0
$427$			10.6115i			0.513528i
$428$	−4.71841	−	4.71841i	−0.228073	−	0.228073i
$429$		0			0
$430$	8.62857	+	8.62857i	0.416107	+	0.416107i
$431$	−0.450359	+	0.450359i	−0.0216930	+	0.0216930i	−0.717870	−	0.696177i	$-0.754883\pi$
$431$	−0.450359	+	0.450359i	−0.0216930	+	0.0216930i	0.696177	+	0.717870i	$0.254883\pi$
$432$		0			0
$433$			38.8945i			1.86915i	0.355764	+	0.934576i	$0.384221\pi$
$433$			38.8945i			1.86915i	−0.355764	+	0.934576i	$0.615779\pi$
$434$			4.83866i			0.232263i
$435$		0			0
$436$	4.35799	−	4.35799i	0.208710	−	0.208710i
$437$	−3.62932	−	3.62932i	−0.173614	−	0.173614i
$438$		0			0
$439$	−12.8705	−	12.8705i	−0.614276	−	0.614276i	0.329781	−	0.944057i	$-0.393025\pi$
$439$	−12.8705	−	12.8705i	−0.614276	−	0.614276i	−0.944057	+	0.329781i	$0.893025\pi$
$440$		−	6.58936i		−	0.314135i
$441$		0			0
$442$	−34.1758	−	14.7080i	−1.62558	−	0.699588i
$443$	−14.4462			−0.686361			−0.343181	−	0.939269i	$-0.611504\pi$
$443$	−14.4462			−0.686361			−0.343181	+	0.939269i	$0.611504\pi$
$444$		0			0
$445$	6.07009	+	6.07009i	0.287750	+	0.287750i
$446$	30.6130			1.44957
$447$		0			0
$448$	−7.77019	+	7.77019i	−0.367107	+	0.367107i
$449$	−26.1717	+	26.1717i	−1.23512	+	1.23512i	−0.273144	+	0.961973i	$0.588063\pi$
$449$	−26.1717	+	26.1717i	−1.23512	+	1.23512i	−0.961973	+	0.273144i	$0.911937\pi$
$450$		0			0
$451$		−	34.1269i		−	1.60697i
$452$	−6.49445	+	6.49445i	−0.305473	+	0.305473i
$453$		0			0
$454$	10.7509	+	10.7509i	0.504565	+	0.504565i
$455$	−11.5281			−0.540445
$456$		0			0
$457$		−	15.0383i		−	0.703461i	−0.936101	−	0.351731i	$-0.885593\pi$
$457$		−	15.0383i		−	0.703461i	0.936101	−	0.351731i	$-0.114407\pi$
$458$	33.2022			1.55144
$459$		0			0
$460$	−0.983828			−0.0458712
$461$		−	13.9905i		−	0.651604i	−0.945438	−	0.325802i	$-0.894366\pi$
$461$		−	13.9905i		−	0.651604i	0.945438	−	0.325802i	$-0.105634\pi$
$462$		0			0
$463$	−2.40768			−0.111895			−0.0559473	−	0.998434i	$-0.517818\pi$
$463$	−2.40768			−0.111895			−0.0559473	+	0.998434i	$0.517818\pi$
$464$	−20.0844	−	20.0844i	−0.932395	−	0.932395i
$465$		0			0
$466$	−28.5538	+	28.5538i	−1.32273	+	1.32273i
$467$			12.7577i			0.590354i	0.955443	+	0.295177i	$0.0953786\pi$
$467$			12.7577i			0.590354i	−0.955443	+	0.295177i	$0.904621\pi$
$468$		0			0
$469$	−8.36004	+	8.36004i	−0.386031	+	0.386031i
$470$	−8.58203	+	8.58203i	−0.395859	+	0.395859i
$471$		0			0
$472$	17.2963			0.796127
$473$	23.4850	+	23.4850i	1.07984	+	1.07984i
$474$		0			0
$475$	11.1322			0.510780
$476$	−2.32501	−	5.83812i	−0.106567	−	0.267590i
$477$		0			0
$478$			8.36949i			0.382811i
$479$	23.2946	+	23.2946i	1.06436	+	1.06436i	0.997781	+	0.0665743i	$0.0212069\pi$
$479$	23.2946	+	23.2946i	1.06436	+	1.06436i	0.0665743	+	0.997781i	$0.478793\pi$
$480$		0			0
$481$	−26.6635	−	26.6635i	−1.21575	−	1.21575i
$482$	−1.45150	+	1.45150i	−0.0661139	+	0.0661139i
$483$		0			0
$484$			1.11091i			0.0504961i
$485$		−	2.71179i		−	0.123136i
$486$		0			0
$487$	12.4152	−	12.4152i	0.562587	−	0.562587i	−0.367455	−	0.930041i	$-0.619771\pi$
$487$	12.4152	−	12.4152i	0.562587	−	0.562587i	0.930041	+	0.367455i	$0.119771\pi$
$488$	−6.69377	−	6.69377i	−0.303013	−	0.303013i
$489$		0			0
$490$	0.576222	+	0.576222i	0.0260311	+	0.0260311i
$491$			35.8504i			1.61790i	0.587874	+	0.808952i	$0.299965\pi$
$491$			35.8504i			1.61790i	−0.587874	+	0.808952i	$0.700035\pi$
$492$		0			0
$493$	−22.4671	+	8.94743i	−1.01187	+	0.402972i
$494$	−23.1776			−1.04281
$495$		0			0
$496$	−4.06520	−	4.06520i	−0.182533	−	0.182533i
$497$	−21.2145			−0.951599
$498$		0			0
$499$	19.7717	−	19.7717i	0.885102	−	0.885102i	−0.108946	−	0.994048i	$-0.534748\pi$
$499$	19.7717	−	19.7717i	0.885102	−	0.885102i	0.994048	+	0.108946i	$0.0347476\pi$
$500$	3.24949	−	3.24949i	0.145322	−	0.145322i
$501$		0			0
$502$			6.20802i			0.277077i
$503$	18.2007	−	18.2007i	0.811529	−	0.811529i	−0.173334	−	0.984863i	$-0.555454\pi$
$503$	18.2007	−	18.2007i	0.811529	−	0.811529i	0.984863	+	0.173334i	$0.0554540\pi$
$504$		0			0
$505$	−1.24648	−	1.24648i	−0.0554678	−	0.0554678i
$506$	−11.5540			−0.513640
$507$		0			0
$508$			2.69039i			0.119367i
$509$	−39.9728			−1.77176			−0.885882	−	0.463910i	$-0.846446\pi$
$509$	−39.9728			−1.77176			−0.885882	+	0.463910i	$0.846446\pi$
$510$		0			0
$511$	1.39507			0.0617143
$512$		−	5.81277i		−	0.256891i
$513$		0			0
$514$	−48.9574			−2.15942
$515$	−3.31165	−	3.31165i	−0.145929	−	0.145929i
$516$		0			0
$517$	−23.3583	+	23.3583i	−1.02730	+	1.02730i
$518$		−	27.4801i		−	1.20741i
$519$		0			0
$520$	7.27194	−	7.27194i	0.318896	−	0.318896i
$521$	−9.18599	+	9.18599i	−0.402446	+	0.402446i	−0.879094	−	0.476648i	$-0.841851\pi$
$521$	−9.18599	+	9.18599i	−0.402446	+	0.402446i	0.476648	+	0.879094i	$0.341851\pi$
$522$		0			0
$523$	−1.53869			−0.0672822			−0.0336411	−	0.999434i	$-0.510710\pi$
$523$	−1.53869			−0.0672822			−0.0336411	+	0.999434i	$0.510710\pi$
$524$	9.27558	+	9.27558i	0.405205	+	0.405205i
$525$		0			0
$526$	−43.8785			−1.91319
$527$	−4.54748	+	1.81101i	−0.198091	+	0.0788890i
$528$		0			0
$529$			19.0067i			0.826380i
$530$	1.08971	+	1.08971i	0.0473339	+	0.0473339i
$531$		0			0
$532$	−2.76807	−	2.76807i	−0.120011	−	0.120011i
$533$	37.6621	−	37.6621i	1.63133	−	1.63133i
$534$		0			0
$535$		−	9.02458i		−	0.390167i
$536$		−	10.5471i		−	0.455563i
$537$		0			0
$538$	−0.510765	+	0.510765i	−0.0220207	+	0.0220207i
$539$	1.56835	+	1.56835i	0.0675534	+	0.0675534i
$540$		0			0
$541$	20.3855	+	20.3855i	0.876439	+	0.876439i	0.993164	−	0.116725i	$-0.0372396\pi$
$541$	20.3855	+	20.3855i	0.876439	+	0.876439i	−0.116725	+	0.993164i	$0.537240\pi$
$542$		−	24.3146i		−	1.04440i
$543$		0			0
$544$	12.5231	+	5.38950i	0.536925	+	0.231073i
$545$	8.33522			0.357042
$546$		0			0
$547$	−4.43261	−	4.43261i	−0.189525	−	0.189525i	0.605966	−	0.795491i	$-0.292787\pi$
$547$	−4.43261	−	4.43261i	−0.189525	−	0.189525i	−0.795491	+	0.605966i	$0.792787\pi$
$548$	7.76677			0.331780
$549$		0			0
$550$	17.7198	−	17.7198i	0.755576	−	0.755576i
$551$	−10.6525	+	10.6525i	−0.453810	+	0.453810i
$552$		0			0
$553$		−	33.3006i		−	1.41608i
$554$	2.25768	−	2.25768i	0.0959197	−	0.0959197i
$555$		0			0
$556$	5.72794	+	5.72794i	0.242919	+	0.242919i
$557$	5.26768			0.223199			0.111599	−	0.993753i	$-0.464403\pi$
$557$	5.26768			0.223199			0.111599	+	0.993753i	$0.464403\pi$
$558$		0			0
$559$			51.8356i			2.19241i
$560$	9.98198			0.421816
$561$		0			0
$562$	−47.0849			−1.98616
$563$		−	12.7777i		−	0.538515i	−0.963068	−	0.269257i	$-0.913222\pi$
$563$		−	12.7777i		−	0.538515i	0.963068	−	0.269257i	$-0.0867782\pi$
$564$		0			0
$565$	−12.4215			−0.522576
$566$	23.6345	+	23.6345i	0.993433	+	0.993433i
$567$		0			0
$568$	13.3821	−	13.3821i	0.561501	−	0.561501i
$569$			6.91475i			0.289881i	0.989440	+	0.144941i	$0.0462991\pi$
$569$			6.91475i			0.289881i	−0.989440	+	0.144941i	$0.953701\pi$
$570$		0			0
$571$	−6.37349	+	6.37349i	−0.266722	+	0.266722i	−0.827778	−	0.561056i	$-0.810395\pi$
$571$	−6.37349	+	6.37349i	−0.266722	+	0.266722i	0.561056	+	0.827778i	$0.310395\pi$
$572$	−8.55034	+	8.55034i	−0.357508	+	0.357508i
$573$		0			0
$574$	38.8156			1.62013
$575$	6.12427	+	6.12427i	0.255400	+	0.255400i
$576$		0			0
$577$	37.5084			1.56149			0.780747	−	0.624848i	$-0.214839\pi$
$577$	37.5084			1.56149			0.780747	+	0.624848i	$0.214839\pi$
$578$	19.9198	−	18.8566i	0.828553	−	0.784331i
$579$		0			0
$580$			2.88765i			0.119903i
$581$	−15.3763	−	15.3763i	−0.637918	−	0.637918i
$582$		0			0
$583$	2.96593	+	2.96593i	0.122836	+	0.122836i
$584$	−0.880013	+	0.880013i	−0.0364152	+	0.0364152i
$585$		0			0
$586$			8.15723i			0.336972i
$587$			20.8834i			0.861950i	0.902364	+	0.430975i	$0.141830\pi$
$587$			20.8834i			0.861950i	−0.902364	+	0.430975i	$0.858170\pi$
$588$		0			0
$589$	−2.15612	+	2.15612i	−0.0888415	+	0.0888415i
$590$	−7.14556	−	7.14556i	−0.294178	−	0.294178i
$591$		0			0
$592$	23.0874	+	23.0874i	0.948888	+	0.948888i
$593$			27.8291i			1.14280i	0.820670	+	0.571402i	$0.193600\pi$
$593$			27.8291i			1.14280i	−0.820670	+	0.571402i	$0.806400\pi$
$594$		0			0
$595$	3.35965	−	7.80653i	0.137732	−	0.320037i
$596$	−6.07996			−0.249045
$597$		0			0
$598$	−12.7509	−	12.7509i	−0.521424	−	0.521424i
$599$	38.9632			1.59199			0.795997	−	0.605300i	$-0.206947\pi$
$599$	38.9632			1.59199			0.795997	+	0.605300i	$0.206947\pi$
$600$		0			0
$601$	17.3489	−	17.3489i	0.707675	−	0.707675i	−0.258371	−	0.966046i	$-0.583186\pi$
$601$	17.3489	−	17.3489i	0.707675	−	0.707675i	0.966046	+	0.258371i	$0.0831856\pi$
$602$	−26.7116	+	26.7116i	−1.08868	+	1.08868i
$603$		0			0
$604$		−	10.5296i		−	0.428441i
$605$	−1.06238	+	1.06238i	−0.0431920	+	0.0431920i
$606$		0			0
$607$	11.1714	+	11.1714i	0.453434	+	0.453434i	0.896493	−	0.443058i	$-0.146107\pi$
$607$	11.1714	+	11.1714i	0.453434	+	0.453434i	−0.443058	+	0.896493i	$0.646107\pi$
$608$	8.49302			0.344437
$609$		0			0
$610$			5.53075i			0.223934i
$611$	−51.5559			−2.08573
$612$		0			0
$613$	13.1247			0.530103			0.265052	−	0.964234i	$-0.414611\pi$
$613$	13.1247			0.530103			0.265052	+	0.964234i	$0.414611\pi$
$614$		−	10.8074i		−	0.436152i
$615$		0			0
$616$	20.3987			0.821889
$617$	10.1808	+	10.1808i	0.409864	+	0.409864i	0.881691	−	0.471827i	$-0.156405\pi$
$617$	10.1808	+	10.1808i	0.409864	+	0.409864i	−0.471827	+	0.881691i	$0.656405\pi$
$618$		0			0
$619$	14.3437	−	14.3437i	0.576522	−	0.576522i	−0.357421	−	0.933943i	$-0.616344\pi$
$619$	14.3437	−	14.3437i	0.576522	−	0.576522i	0.933943	+	0.357421i	$0.116344\pi$
$620$			0.584477i			0.0234732i
$621$		0			0
$622$	6.01549	−	6.01549i	0.241199	−	0.241199i
$623$	−18.7912	+	18.7912i	−0.752855	+	0.752855i
$624$		0			0
$625$	−15.4557			−0.618229
$626$	−9.25051	−	9.25051i	−0.369725	−	0.369725i
$627$		0			0
$628$	9.97216			0.397933
$629$	25.8264	−	10.2853i	1.02977	−	0.410100i
$630$		0			0
$631$			0.933597i			0.0371659i	0.999827	+	0.0185830i	$0.00591548\pi$
$631$			0.933597i			0.0371659i	−0.999827	+	0.0185830i	$0.994085\pi$
$632$	21.0060	+	21.0060i	0.835575	+	0.835575i
$633$		0			0
$634$	−4.48461	−	4.48461i	−0.178106	−	0.178106i
$635$	−2.57286	+	2.57286i	−0.102101	+	0.102101i
$636$		0			0
$637$			3.46162i			0.137154i
$638$			33.9124i			1.34261i
$639$		0			0
$640$	−7.86565	+	7.86565i	−0.310917	+	0.310917i
$641$	4.02977	+	4.02977i	0.159166	+	0.159166i	0.782197	−	0.623031i	$-0.214099\pi$
$641$	4.02977	+	4.02977i	0.159166	+	0.159166i	−0.623031	+	0.782197i	$0.714099\pi$
$642$		0			0
$643$	−1.94154	−	1.94154i	−0.0765667	−	0.0765667i	0.667786	−	0.744353i	$-0.267242\pi$
$643$	−1.94154	−	1.94154i	−0.0765667	−	0.0765667i	−0.744353	+	0.667786i	$0.767242\pi$
$644$		−	3.04565i		−	0.120015i
$645$		0			0
$646$	6.75466	−	15.6953i	0.265759	−	0.617521i
$647$	8.48539			0.333595			0.166798	−	0.985991i	$-0.446657\pi$
$647$	8.48539			0.333595			0.166798	+	0.985991i	$0.446657\pi$
$648$		0			0
$649$	−19.4486	−	19.4486i	−0.763424	−	0.763424i
$650$	39.1108			1.53405
$651$		0			0
$652$	4.74152	−	4.74152i	0.185692	−	0.185692i
$653$	−6.79935	+	6.79935i	−0.266079	+	0.266079i	−0.827518	−	0.561439i	$-0.810248\pi$
$653$	−6.79935	+	6.79935i	−0.266079	+	0.266079i	0.561439	+	0.827518i	$0.310248\pi$
$654$		0			0
$655$			17.7408i			0.693189i
$656$	−32.6109	+	32.6109i	−1.27324	+	1.27324i
$657$		0			0
$658$	−26.5675	−	26.5675i	−1.03571	−	1.03571i
$659$	16.9543			0.660446			0.330223	−	0.943903i	$-0.392876\pi$
$659$	16.9543			0.660446			0.330223	+	0.943903i	$0.392876\pi$
$660$		0			0
$661$		−	22.8810i		−	0.889968i	−0.895539	−	0.444984i	$-0.853209\pi$
$661$		−	22.8810i		−	0.889968i	0.895539	−	0.444984i	$-0.146791\pi$
$662$	32.2261			1.25250
$663$		0			0
$664$	19.3988			0.752821
$665$		−	5.29429i		−	0.205304i
$666$		0			0
$667$	−11.7207			−0.453827
$668$	0.937229	+	0.937229i	0.0362625	+	0.0362625i
$669$		0			0
$670$	−4.35727	+	4.35727i	−0.168336	+	0.168336i
$671$			15.0534i			0.581131i
$672$		0			0
$673$	−0.687686	+	0.687686i	−0.0265084	+	0.0265084i	−0.720237	−	0.693728i	$-0.755967\pi$
$673$	−0.687686	+	0.687686i	−0.0265084	+	0.0265084i	0.693728	+	0.720237i	$0.255967\pi$
$674$	−35.1846	+	35.1846i	−1.35526	+	1.35526i
$675$		0			0
$676$	−11.0286			−0.424176
$677$	−14.6325	−	14.6325i	−0.562372	−	0.562372i	0.367608	−	0.929981i	$-0.380177\pi$
$677$	−14.6325	−	14.6325i	−0.562372	−	0.562372i	−0.929981	+	0.367608i	$0.880177\pi$
$678$		0			0
$679$	8.39492			0.322167
$680$	2.80510	+	7.04364i	0.107571	+	0.270111i
$681$		0			0
$682$			6.86408i			0.262839i
$683$	15.5089	+	15.5089i	0.593430	+	0.593430i	0.938556	−	0.345126i	$-0.112164\pi$
$683$	15.5089	+	15.5089i	0.593430	+	0.593430i	−0.345126	+	0.938556i	$0.612164\pi$
$684$		0			0
$685$	7.42748	+	7.42748i	0.283790	+	0.283790i
$686$	−21.9580	+	21.9580i	−0.838360	+	0.838360i
$687$		0			0
$688$		−	44.8835i		−	1.71117i
$689$			6.54634i			0.249396i
$690$		0			0
$691$	21.2206	−	21.2206i	0.807270	−	0.807270i	−0.176950	−	0.984220i	$-0.556623\pi$
$691$	21.2206	−	21.2206i	0.807270	−	0.807270i	0.984220	+	0.176950i	$0.0566229\pi$
$692$	−3.25573	−	3.25573i	−0.123764	−	0.123764i
$693$		0			0
$694$	19.2049	+	19.2049i	0.729008	+	0.729008i
$695$			10.9554i			0.415564i
$696$		0			0
$697$	14.5279	+	36.4797i	0.550283	+	1.38177i
$698$	45.0795			1.70628
$699$		0			0
$700$	4.67095	+	4.67095i	0.176545	+	0.176545i
$701$	13.0830			0.494140			0.247070	−	0.968998i	$-0.420532\pi$
$701$	13.0830			0.494140			0.247070	+	0.968998i	$0.420532\pi$
$702$		0			0
$703$	12.2452	−	12.2452i	0.461837	−	0.461837i
$704$	−11.0227	+	11.0227i	−0.415435	+	0.415435i
$705$		0			0
$706$			36.4029i			1.37004i
$707$	3.85876	−	3.85876i	0.145123	−	0.145123i
$708$		0			0
$709$	23.2261	+	23.2261i	0.872276	+	0.872276i	0.992720	−	0.120444i	$-0.0384319\pi$
$709$	23.2261	+	23.2261i	0.872276	+	0.872276i	−0.120444	+	0.992720i	$0.538432\pi$
$710$	−11.0570			−0.414962
$711$		0			0
$712$		−	23.7071i		−	0.888460i
$713$	−2.37234			−0.0888448
$714$		0			0
$715$	−16.3537			−0.611592
$716$			10.2441i			0.382841i
$717$		0			0
$718$	4.23396			0.158010
$719$	−9.63837	−	9.63837i	−0.359450	−	0.359450i	0.504160	−	0.863610i	$-0.331802\pi$
$719$	−9.63837	−	9.63837i	−0.359450	−	0.359450i	−0.863610	+	0.504160i	$0.831802\pi$
$720$		0			0
$721$	10.2519	−	10.2519i	0.381801	−	0.381801i
$722$			20.0120i			0.744769i
$723$		0			0
$724$	4.15743	−	4.15743i	0.154510	−	0.154510i
$725$	17.9754	−	17.9754i	0.667590	−	0.667590i
$726$		0			0
$727$	−8.12446			−0.301320			−0.150660	−	0.988586i	$-0.548140\pi$
$727$	−8.12446			−0.301320			−0.150660	+	0.988586i	$0.548140\pi$
$728$	22.5118	+	22.5118i	0.834344	+	0.834344i
$729$		0			0
$730$	0.727113			0.0269117
$731$	−35.1017	−	15.1065i	−1.29828	−	0.558734i
$732$		0			0
$733$		−	31.1522i		−	1.15063i	−0.817931	−	0.575316i	$-0.804879\pi$
$733$		−	31.1522i		−	1.15063i	0.817931	−	0.575316i	$-0.195121\pi$
$734$	−19.0098	−	19.0098i	−0.701664	−	0.701664i
$735$		0			0
$736$	4.67235	+	4.67235i	0.172225	+	0.172225i
$737$	−11.8595	+	11.8595i	−0.436850	+	0.436850i
$738$		0			0
$739$			34.6895i			1.27607i	0.770005	+	0.638037i	$0.220253\pi$
$739$			34.6895i			1.27607i	−0.770005	+	0.638037i	$0.779747\pi$
$740$		−	3.31941i		−	0.122024i
$741$		0			0
$742$	−3.37342	+	3.37342i	−0.123842	+	0.123842i
$743$	−34.3846	−	34.3846i	−1.26145	−	1.26145i	−0.950391	−	0.311058i	$-0.899317\pi$
$743$	−34.3846	−	34.3846i	−1.26145	−	1.26145i	−0.311058	−	0.950391i	$-0.600683\pi$
$744$		0			0
$745$	−5.81436	−	5.81436i	−0.213022	−	0.213022i
$746$			42.6532i			1.56164i
$747$		0			0
$748$	−3.29824	−	8.28191i	−0.120596	−	0.302817i
$749$	27.9375			1.02081
$750$		0			0
$751$	−29.6482	−	29.6482i	−1.08188	−	1.08188i	−0.996334	−	0.0855453i	$-0.972737\pi$
$751$	−29.6482	−	29.6482i	−1.08188	−	1.08188i	−0.0855453	−	0.996334i	$-0.527263\pi$
$752$	44.6414			1.62790
$753$		0			0
$754$	−37.4254	+	37.4254i	−1.36295	+	1.36295i
$755$	10.0696	−	10.0696i	0.366469	−	0.366469i
$756$		0			0
$757$			10.7455i			0.390553i	0.980748	+	0.195277i	$0.0625605\pi$
$757$			10.7455i			0.390553i	−0.980748	+	0.195277i	$0.937439\pi$
$758$	−17.4716	+	17.4716i	−0.634598	+	0.634598i
$759$		0			0
$760$	3.33964	+	3.33964i	0.121142	+	0.121142i
$761$	−7.39335			−0.268009			−0.134004	−	0.990981i	$-0.542784\pi$
$761$	−7.39335			−0.268009			−0.134004	+	0.990981i	$0.542784\pi$
$762$		0			0
$763$			25.8034i			0.934148i
$764$	15.7567			0.570058
$765$		0			0
$766$	35.4955			1.28250
$767$		−	42.9265i		−	1.54998i
$768$		0			0
$769$	17.4382			0.628838			0.314419	−	0.949284i	$-0.398190\pi$
$769$	17.4382			0.628838			0.314419	+	0.949284i	$0.398190\pi$
$770$	−8.42726	−	8.42726i	−0.303698	−	0.303698i
$771$		0			0
$772$	7.60764	−	7.60764i	0.273805	−	0.273805i
$773$			31.1238i			1.11945i	0.828680	+	0.559723i	$0.189093\pi$
$773$			31.1238i			1.11945i	−0.828680	+	0.559723i	$0.810907\pi$
$774$		0			0
$775$	3.63833	−	3.63833i	0.130693	−	0.130693i
$776$	−5.29553	+	5.29553i	−0.190098	+	0.190098i
$777$		0			0
$778$	46.9120			1.68188
$779$	17.2963	+	17.2963i	0.619706	+	0.619706i
$780$		0			0
$781$	−30.0947			−1.07687
$782$	12.3506	−	4.91858i	0.441657	−	0.175888i
$783$		0			0
$784$		−	2.99735i		−	0.107048i
$785$	9.53653	+	9.53653i	0.340373	+	0.340373i
$786$		0			0
$787$	5.09881	+	5.09881i	0.181753	+	0.181753i	0.792119	−	0.610366i	$-0.208978\pi$
$787$	5.09881	+	5.09881i	0.181753	+	0.181753i	−0.610366	+	0.792119i	$0.708978\pi$
$788$	6.28419	−	6.28419i	0.223865	−	0.223865i
$789$		0			0
$790$		−	17.3563i		−	0.617509i
$791$		−	38.4533i		−	1.36724i
$792$		0			0
$793$	−16.6128	+	16.6128i	−0.589938	+	0.589938i
$794$	38.0267	+	38.0267i	1.34952	+	1.34952i
$795$		0			0
$796$	4.44587	+	4.44587i	0.157580	+	0.157580i
$797$		−	7.58702i		−	0.268746i	−0.990931	−	0.134373i	$-0.957098\pi$
$797$		−	7.58702i		−	0.268746i	0.990931	−	0.134373i	$-0.0429020\pi$
$798$		0			0
$799$	15.0250	−	34.9124i	0.531546	−	1.23511i
$800$	−14.3315			−0.506695
$801$		0			0
$802$	24.0914	+	24.0914i	0.850698	+	0.850698i
$803$	1.97904			0.0698386
$804$		0			0
$805$	2.91260	−	2.91260i	0.102656	−	0.102656i
$806$	−7.57512	+	7.57512i	−0.266822	+	0.266822i
$807$		0			0
$808$			4.86822i			0.171263i
$809$	−3.76972	+	3.76972i	−0.132536	+	0.132536i	−0.770263	−	0.637727i	$-0.779875\pi$
$809$	−3.76972	+	3.76972i	−0.132536	+	0.132536i	0.637727	+	0.770263i	$0.279875\pi$
$810$		0			0
$811$	−33.1839	−	33.1839i	−1.16524	−	1.16524i	−0.983311	−	0.181932i	$-0.941765\pi$
$811$	−33.1839	−	33.1839i	−1.16524	−	1.16524i	−0.181932	−	0.983311i	$-0.558235\pi$
$812$	−8.93933			−0.313709
$813$		0			0
$814$		−	38.9831i		−	1.36636i
$815$	9.06879			0.317666
$816$		0			0
$817$	−23.8055			−0.832850
$818$		−	25.8784i		−	0.904817i
$819$		0			0
$820$	4.68866			0.163735
$821$	−14.4341	−	14.4341i	−0.503754	−	0.503754i	0.408848	−	0.912602i	$-0.365931\pi$
$821$	−14.4341	−	14.4341i	−0.503754	−	0.503754i	−0.912602	+	0.408848i	$0.865931\pi$
$822$		0			0
$823$	−23.7916	+	23.7916i	−0.829322	+	0.829322i	−0.987423	−	0.158101i	$-0.949463\pi$
$823$	−23.7916	+	23.7916i	−0.829322	+	0.829322i	0.158101	+	0.987423i	$0.449463\pi$
$824$			12.9338i			0.450571i
$825$		0			0
$826$	22.1206	−	22.1206i	0.769674	−	0.769674i
$827$	9.83370	−	9.83370i	0.341951	−	0.341951i	−0.515149	−	0.857100i	$-0.672264\pi$
$827$	9.83370	−	9.83370i	0.341951	−	0.341951i	0.857100	+	0.515149i	$0.172264\pi$
$828$		0			0
$829$	−41.0730			−1.42652			−0.713262	−	0.700897i	$-0.752783\pi$
$829$	−41.0730			−1.42652			−0.713262	+	0.700897i	$0.752783\pi$
$830$	−8.01417	−	8.01417i	−0.278176	−	0.278176i
$831$		0			0
$832$	−24.3291			−0.843460
$833$	−2.34412	−	1.00882i	−0.0812189	−	0.0349536i
$834$		0			0
$835$			1.79257i			0.0620345i
$836$	−3.92675	−	3.92675i	−0.135810	−	0.135810i
$837$		0			0
$838$	34.6005	+	34.6005i	1.19525	+	1.19525i
$839$	10.5482	−	10.5482i	0.364164	−	0.364164i	−0.501179	−	0.865343i	$-0.667100\pi$
$839$	10.5482	−	10.5482i	0.364164	−	0.364164i	0.865343	+	0.501179i	$0.167100\pi$
$840$		0			0
$841$			5.40160i			0.186262i
$842$			5.29462i			0.182465i
$843$		0			0
$844$	5.94723	−	5.94723i	0.204712	−	0.204712i
$845$	−10.5468	−	10.5468i	−0.362821	−	0.362821i
$846$		0			0
$847$	−3.28883	−	3.28883i	−0.113006	−	0.113006i
$848$		−	5.66836i		−	0.194652i
$849$		0			0
$850$	−11.3981	+	26.4848i	−0.390952	+	0.908422i
$851$	13.4732			0.461855
$852$		0			0
$853$	−8.60401	−	8.60401i	−0.294596	−	0.294596i	0.544297	−	0.838893i	$-0.316796\pi$
$853$	−8.60401	−	8.60401i	−0.294596	−	0.294596i	−0.838893	+	0.544297i	$0.816796\pi$
$854$	−17.1216			−0.585889
$855$		0			0
$856$	−17.6230	+	17.6230i	−0.602342	+	0.602342i
$857$	−32.1255	+	32.1255i	−1.09739	+	1.09739i	−0.102672	+	0.994715i	$0.532739\pi$
$857$	−32.1255	+	32.1255i	−1.09739	+	1.09739i	−0.994715	+	0.102672i	$0.967261\pi$
$858$		0			0
$859$			24.5741i			0.838458i	0.907880	+	0.419229i	$0.137700\pi$
$859$			24.5741i			0.838458i	−0.907880	+	0.419229i	$0.862300\pi$
$860$	−3.22658	+	3.22658i	−0.110025	+	0.110025i
$861$		0			0
$862$	−0.726649	−	0.726649i	−0.0247498	−	0.0247498i
$863$	2.35798			0.0802667			0.0401334	−	0.999194i	$-0.487222\pi$
$863$	2.35798			0.0802667			0.0401334	+	0.999194i	$0.487222\pi$
$864$		0			0
$865$		−	6.22701i		−	0.211725i
$866$	−62.7559			−2.13253
$867$		0			0
$868$	−1.80937			−0.0614141
$869$		−	47.2399i		−	1.60250i
$870$		0			0
$871$	−26.1760			−0.886939
$872$	−16.2769	−	16.2769i	−0.551204	−	0.551204i
$873$		0			0
$874$	5.85587	−	5.85587i	0.198078	−	0.198078i
$875$			19.2401i			0.650434i
$876$		0			0
$877$	−26.2297	+	26.2297i	−0.885713	+	0.885713i	−0.994108	−	0.108395i	$-0.965429\pi$
$877$	−26.2297	+	26.2297i	−0.885713	+	0.885713i	0.108395	+	0.994108i	$0.465429\pi$
$878$	20.7665	−	20.7665i	0.700834	−	0.700834i
$879$		0			0
$880$	14.1603			0.477345
$881$	24.7512	+	24.7512i	0.833889	+	0.833889i	0.988046	−	0.154158i	$-0.0492664\pi$
$881$	24.7512	+	24.7512i	0.833889	+	0.833889i	−0.154158	+	0.988046i	$0.549266\pi$
$882$		0			0
$883$	−4.09966			−0.137964			−0.0689822	−	0.997618i	$-0.521975\pi$
$883$	−4.09966			−0.137964			−0.0689822	+	0.997618i	$0.521975\pi$
$884$	5.49992	−	12.7797i	0.184982	−	0.429829i
$885$		0			0
$886$		−	23.3089i		−	0.783076i
$887$	−3.21314	−	3.21314i	−0.107887	−	0.107887i	0.651103	−	0.758990i	$-0.274307\pi$
$887$	−3.21314	−	3.21314i	−0.107887	−	0.107887i	−0.758990	+	0.651103i	$0.774307\pi$
$888$		0			0
$889$	−7.96484	−	7.96484i	−0.267132	−	0.267132i
$890$	−9.79402	+	9.79402i	−0.328296	+	0.328296i
$891$		0			0
$892$			11.4474i			0.383289i
$893$		−	23.6771i		−	0.792324i
$894$		0			0
$895$	−9.79661	+	9.79661i	−0.327465	+	0.327465i
$896$	−24.3498	−	24.3498i	−0.813469	−	0.813469i
$897$		0			0
$898$	−42.2277	−	42.2277i	−1.40916	−	1.40916i
$899$			6.96309i			0.232232i
$900$		0			0
$901$	−4.43301	−	1.90781i	−0.147685	−	0.0635583i
$902$	55.0634			1.83341
$903$		0			0
$904$	24.2564	+	24.2564i	0.806756	+	0.806756i
$905$	7.95163			0.264321
$906$		0			0
$907$	−6.14695	+	6.14695i	−0.204106	+	0.204106i	−0.801757	−	0.597651i	$-0.796101\pi$
$907$	−6.14695	+	6.14695i	−0.204106	+	0.204106i	0.597651	+	0.801757i	$0.296101\pi$
$908$	−4.02020	+	4.02020i	−0.133415	+	0.133415i
$909$		0			0
$910$		−	18.6005i		−	0.616599i
$911$	32.4259	−	32.4259i	1.07432	−	1.07432i	0.0773122	−	0.997007i	$-0.475366\pi$
$911$	32.4259	−	32.4259i	1.07432	−	1.07432i	0.997007	−	0.0773122i	$-0.0246338\pi$
$912$		0			0
$913$	−21.8127	−	21.8127i	−0.721896	−	0.721896i
$914$	24.2641			0.802586
$915$		0			0
$916$			12.4157i			0.410225i
$917$	−54.9203			−1.81363
$918$		0			0
$919$	36.9580			1.21913			0.609566	−	0.792735i	$-0.291344\pi$
$919$	36.9580			1.21913			0.609566	+	0.792735i	$0.291344\pi$
$920$			3.67455i			0.121146i
$921$		0			0
$922$	22.5736			0.743421
$923$	−33.2121	−	33.2121i	−1.09319	−	1.09319i
$924$		0			0
$925$	−20.6631	+	20.6631i	−0.679399	+	0.679399i
$926$		−	3.88477i		−	0.127662i
$927$		0			0
$928$	13.7139	−	13.7139i	0.450181	−	0.450181i
$929$	26.2591	−	26.2591i	0.861532	−	0.861532i	−0.129984	−	0.991516i	$-0.541493\pi$
$929$	26.2591	−	26.2591i	0.861532	−	0.861532i	0.991516	+	0.129984i	$0.0414927\pi$
$930$		0			0
$931$	−1.58975			−0.0521020
$932$	−10.6774	−	10.6774i	−0.349751	−	0.349751i
$933$		0			0
$934$	−20.5844			−0.673541
$935$	4.76596	−	11.0743i	0.155864	−	0.362168i
$936$		0			0
$937$			20.2047i			0.660058i	0.943971	+	0.330029i	$0.107059\pi$
$937$			20.2047i			0.660058i	−0.943971	+	0.330029i	$0.892941\pi$
$938$	−13.4888	−	13.4888i	−0.440426	−	0.440426i
$939$		0			0
$940$	−3.20917	−	3.20917i	−0.104672	−	0.104672i
$941$	−34.0034	+	34.0034i	−1.10848	+	1.10848i	−0.115130	+	0.993350i	$0.536728\pi$
$941$	−34.0034	+	34.0034i	−1.10848	+	1.10848i	−0.993350	+	0.115130i	$0.963272\pi$
$942$		0			0
$943$			19.0308i			0.619729i
$944$			37.1693i			1.20976i
$945$		0			0
$946$	−37.8928	+	37.8928i	−1.23200	+	1.23200i
$947$	−16.2726	−	16.2726i	−0.528790	−	0.528790i	0.391422	−	0.920211i	$-0.371983\pi$
$947$	−16.2726	−	16.2726i	−0.528790	−	0.528790i	−0.920211	+	0.391422i	$0.871983\pi$
$948$		0			0
$949$	2.18404	+	2.18404i	0.0708970	+	0.0708970i
$950$			17.9617i			0.582754i
$951$		0			0
$952$	−21.8051	+	8.68379i	−0.706707	+	0.281443i
$953$	0.0564747			0.00182940			0.000914698	−	1.00000i	$-0.499709\pi$
$953$	0.0564747			0.00182940			0.000914698		1.00000i	$0.499709\pi$
$954$		0			0
$955$	15.0684	+	15.0684i	0.487601	+	0.487601i
$956$	−3.12969			−0.101222
$957$		0			0
$958$	−37.5855	+	37.5855i	−1.21433	+	1.21433i
$959$	−22.9933	+	22.9933i	−0.742494	+	0.742494i
$960$		0			0
$961$		−	29.5906i		−	0.954536i
$962$	43.0213	−	43.0213i	1.38706	−	1.38706i
$963$		0			0
$964$	−0.542775	−	0.542775i	−0.0174816	−	0.0174816i
$965$	14.5506			0.468401
$966$		0			0
$967$		−	0.706923i		−	0.0227331i	−0.999935	−	0.0113666i	$-0.996382\pi$
$967$		−	0.706923i		−	0.0227331i	0.999935	−	0.0113666i	$-0.00361816\pi$
$968$	4.14920			0.133360
$969$		0			0
$970$	4.37545			0.140487
$971$			10.5257i			0.337785i	0.985634	+	0.168892i	$0.0540190\pi$
$971$			10.5257i			0.337785i	−0.985634	+	0.168892i	$0.945981\pi$
$972$		0			0
$973$	−33.9149			−1.08726
$974$	20.0318	+	20.0318i	0.641860	+	0.641860i
$975$		0			0
$976$	14.3847	−	14.3847i	0.460444	−	0.460444i
$977$			13.9176i			0.445264i	0.974903	+	0.222632i	$0.0714648\pi$
$977$			13.9176i			0.445264i	−0.974903	+	0.222632i	$0.928535\pi$
$978$		0			0
$979$	−26.6571	+	26.6571i	−0.851964	+	0.851964i
$980$	−0.215473	+	0.215473i	−0.00688304	+	0.00688304i
$981$		0			0
$982$	−57.8442			−1.84588
$983$	−13.2245	−	13.2245i	−0.421795	−	0.421795i	0.464026	−	0.885822i	$-0.346404\pi$
$983$	−13.2245	−	13.2245i	−0.421795	−	0.421795i	−0.885822	+	0.464026i	$0.846404\pi$
$984$		0			0
$985$	12.0193			0.382968
$986$	−14.4366	−	36.2504i	−0.459755	−	1.15445i
$987$		0			0
$988$		−	8.66704i		−	0.275735i
$989$	−13.0964	−	13.0964i	−0.416441	−	0.416441i
$990$		0			0
$991$	−23.6334	−	23.6334i	−0.750741	−	0.750741i	0.223877	−	0.974617i	$-0.428129\pi$
$991$	−23.6334	−	23.6334i	−0.750741	−	0.750741i	−0.974617	+	0.223877i	$0.928129\pi$
$992$	2.77577	−	2.77577i	0.0881309	−	0.0881309i
$993$		0			0
$994$		−	34.2293i		−	1.08569i
$995$			8.50330i			0.269573i
$996$		0			0
$997$	29.5670	−	29.5670i	0.936397	−	0.936397i	−0.0616976	−	0.998095i	$-0.519651\pi$
$997$	29.5670	−	29.5670i	0.936397	−	0.936397i	0.998095	+	0.0616976i	$0.0196514\pi$
$998$	31.9014	+	31.9014i	1.00982	+	1.00982i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.f.c.217.10	yes	24
3.2	odd	2	inner	459.2.f.c.217.3	yes	24
17.2	even	8		7803.2.a.bw.1.3		12
17.4	even	4	inner	459.2.f.c.55.3	✓	24
17.15	even	8		7803.2.a.bv.1.3		12
51.2	odd	8		7803.2.a.bw.1.10		12
51.32	odd	8		7803.2.a.bv.1.10		12
51.38	odd	4	inner	459.2.f.c.55.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.f.c.55.3	✓	24	17.4	even	4	inner
459.2.f.c.55.10	yes	24	51.38	odd	4	inner
459.2.f.c.217.3	yes	24	3.2	odd	2	inner
459.2.f.c.217.10	yes	24	1.1	even	1	trivial
7803.2.a.bv.1.3		12	17.15	even	8
7803.2.a.bv.1.10		12	51.32	odd	8
7803.2.a.bw.1.3		12	17.2	even	8
7803.2.a.bw.1.10		12	51.2	odd	8

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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.61349i q^{2} -0.603350 q^{4} +(-0.576993 - 0.576993i) q^{5} +(1.78620 - 1.78620i) q^{7} +2.25348i q^{8} +(0.930973 - 0.930973i) q^{10} +(2.53389 - 2.53389i) q^{11} +5.59275 q^{13} +(2.88202 + 2.88202i) q^{14} -4.84267 q^{16} +(-1.62990 + 3.78727i) q^{17} +2.56848i q^{19} +(0.348129 + 0.348129i) q^{20} +(4.08841 + 4.08841i) q^{22} +(-1.41302 + 1.41302i) q^{23} -4.33416i q^{25} +9.02385i q^{26} +(-1.07771 + 1.07771i) q^{28} +(4.14738 + 4.14738i) q^{29} +(0.839455 + 0.839455i) q^{31} -3.30664i q^{32} +(-6.11072 - 2.62983i) q^{34} -2.06126 q^{35} +(-4.76750 - 4.76750i) q^{37} -4.14421 q^{38} +(1.30024 - 1.30024i) q^{40} +(6.73408 - 6.73408i) q^{41} +9.26834i q^{43} +(-1.52883 + 1.52883i) q^{44} +(-2.27990 - 2.27990i) q^{46} -9.21835 q^{47} +0.618947i q^{49} +6.99312 q^{50} -3.37439 q^{52} +1.17050i q^{53} -2.92408 q^{55} +(4.02518 + 4.02518i) q^{56} +(-6.69176 + 6.69176i) q^{58} -7.67537i q^{59} +(-2.97041 + 2.97041i) q^{61} +(-1.35445 + 1.35445i) q^{62} -4.35011 q^{64} +(-3.22698 - 3.22698i) q^{65} -4.68034 q^{67} +(0.983402 - 2.28505i) q^{68} -3.32582i q^{70} +(-5.93842 - 5.93842i) q^{71} +(0.390513 + 0.390513i) q^{73} +(7.69232 - 7.69232i) q^{74} -1.54969i q^{76} -9.05211i q^{77} +(9.32159 - 9.32159i) q^{79} +(2.79419 + 2.79419i) q^{80} +(10.8654 + 10.8654i) q^{82} -8.60839i q^{83} +(3.12567 - 1.24479i) q^{85} -14.9544 q^{86} +(5.71008 + 5.71008i) q^{88} -10.5202 q^{89} +(9.98980 - 9.98980i) q^{91} +(0.852548 - 0.852548i) q^{92} -14.8737i q^{94} +(1.48199 - 1.48199i) q^{95} +(2.34993 + 2.34993i) q^{97} -0.998664 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 16 q^{10} + 8 q^{13} + 40 q^{16} - 32 q^{22} - 40 q^{28} + 16 q^{31} + 40 q^{34} - 24 q^{37} - 40 q^{40} - 24 q^{46} + 16 q^{52} + 8 q^{55} - 40 q^{58} - 56 q^{61} - 80 q^{64} - 16 q^{67}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q - 24 * q^4 + 16 * q^10 + 8 * q^13 + 40 * q^16 - 32 * q^22 - 40 * q^28 + 16 * q^31 + 40 * q^34 - 24 * q^37 - 40 * q^40 - 24 * q^46 + 16 * q^52 + 8 * q^55 - 40 * q^58 - 56 * q^61 - 80 * q^64 - 16 * q^67 + 72 * q^73 + 32 * q^82 + 16 * q^85 + 64 * q^88 + 88 * q^91 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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