LMFDB - Embedded newform 1232.2.q.m.177.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1232,2,Mod(177,1232)] 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("1232.177"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1232, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,3,0,-6,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.3
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.m.529.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.43969 + 2.49362i) q^{3} +(-1.17365 + 2.03282i) q^{5} +(-2.05303 + 1.66885i) q^{7} +(-2.64543 + 4.58202i) q^{9} +(0.500000 + 0.866025i) q^{11} -0.184793 q^{13} -6.75877 q^{15} +(1.96064 + 3.39592i) q^{17} +(0.386659 - 0.669713i) q^{19} +(-7.11721 - 2.71686i) q^{21} +(4.17752 - 7.23567i) q^{23} +(-0.254900 - 0.441500i) q^{25} -6.59627 q^{27} -8.17024 q^{29} +(1.32635 + 2.29731i) q^{31} +(-1.43969 + 2.49362i) q^{33} +(-0.982926 - 6.13208i) q^{35} +(3.41147 - 5.90885i) q^{37} +(-0.266044 - 0.460802i) q^{39} +0.426022 q^{41} -1.18479 q^{43} +(-6.20961 - 10.7554i) q^{45} +(-3.84002 + 6.65111i) q^{47} +(1.42989 - 6.85240i) q^{49} +(-5.64543 + 9.77817i) q^{51} +(-3.27719 - 5.67626i) q^{53} -2.34730 q^{55} +2.22668 q^{57} +(0.102196 + 0.177009i) q^{59} +(-7.29086 + 12.6281i) q^{61} +(-2.21554 - 13.8219i) q^{63} +(0.216881 - 0.375650i) q^{65} +(1.87939 + 3.25519i) q^{67} +24.0574 q^{69} +9.96585 q^{71} +(-0.0603074 - 0.104455i) q^{73} +(0.733956 - 1.27125i) q^{75} +(-2.47178 - 0.943555i) q^{77} +(0.163848 - 0.283793i) q^{79} +(-1.56031 - 2.70253i) q^{81} -3.35504 q^{83} -9.20439 q^{85} +(-11.7626 - 20.3735i) q^{87} +(2.32635 - 4.02936i) q^{89} +(0.379385 - 0.308391i) q^{91} +(-3.81908 + 6.61484i) q^{93} +(0.907604 + 1.57202i) q^{95} +13.1206 q^{97} -5.29086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 6 q^{5} + 3 q^{11} + 6 q^{13} - 18 q^{15} + 3 q^{17} + 9 q^{19} - 12 q^{21} - 3 q^{25} - 12 q^{27} - 6 q^{29} + 9 q^{31} - 3 q^{33} + 15 q^{35} + 3 q^{39} + 18 q^{41} - 3 q^{45} - 3 q^{47}+ \cdots + 90 q^{97}+O(q^{100}) $ 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^11 + 6 * q^13 - 18 * q^15 + 3 * q^17 + 9 * q^19 - 12 * q^21 - 3 * q^25 - 12 * q^27 - 6 * q^29 + 9 * q^31 - 3 * q^33 + 15 * q^35 + 3 * q^39 + 18 * q^41 - 3 * q^45 - 3 * q^47 - 18 * q^51 - 9 * q^53 - 12 * q^55 - 12 * q^61 - 6 * q^63 - 15 * q^65 + 42 * q^69 + 18 * q^71 - 6 * q^73 + 9 * q^75 - 3 * q^79 - 15 * q^81 + 30 * q^83 - 54 * q^85 - 24 * q^87 + 15 * q^89 - 9 * q^91 - 6 * q^93 + 9 * q^95 + 90 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.43969	+	2.49362i	0.831207	+	1.43969i	0.897082	+	0.441865i	$0.145683\pi$
$3$	1.43969	+	2.49362i	0.831207	+	1.43969i	−0.0658748	+	0.997828i	$0.520984\pi$
$4$		0			0
$5$	−1.17365	+	2.03282i	−0.524871	+	0.909104i	0.474709	+	0.880143i	$0.342553\pi$
$5$	−1.17365	+	2.03282i	−0.524871	+	0.909104i	−0.999581	+	0.0289612i	$0.990780\pi$
$6$		0			0
$7$	−2.05303	+	1.66885i	−0.775974	+	0.630765i
$7$	−2.05303	+	1.66885i	−0.775974	+	0.630765i
$8$		0			0
$9$	−2.64543	+	4.58202i	−0.881810	+	1.52734i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−0.184793			−0.0512522			−0.0256261	−	0.999672i	$-0.508158\pi$
$13$	−0.184793			−0.0512522			−0.0256261	+	0.999672i	$0.508158\pi$
$14$		0			0
$15$	−6.75877			−1.74511
$16$		0			0
$17$	1.96064	+	3.39592i	0.475524	+	0.823632i	0.999607	−	0.0280351i	$-0.00892502\pi$
$17$	1.96064	+	3.39592i	0.475524	+	0.823632i	−0.524083	+	0.851667i	$0.675592\pi$
$18$		0			0
$19$	0.386659	−	0.669713i	0.0887057	−	0.153643i	−0.818259	−	0.574850i	$-0.805060\pi$
$19$	0.386659	−	0.669713i	0.0887057	−	0.153643i	0.906964	+	0.421208i	$0.138394\pi$
$20$		0			0
$21$	−7.11721	−	2.71686i	−1.55310	−	0.592867i
$22$		0			0
$23$	4.17752	−	7.23567i	0.871073	−	1.50874i	0.0101847	−	0.999948i	$-0.496758\pi$
$23$	4.17752	−	7.23567i	0.871073	−	1.50874i	0.860888	−	0.508794i	$-0.169909\pi$
$24$		0			0
$25$	−0.254900	−	0.441500i	−0.0509800	−	0.0883000i
$26$		0			0
$27$	−6.59627			−1.26945
$28$		0			0
$29$	−8.17024			−1.51718			−0.758588	−	0.651570i	$-0.774111\pi$
$29$	−8.17024			−1.51718			−0.758588	+	0.651570i	$0.774111\pi$
$30$		0			0
$31$	1.32635	+	2.29731i	0.238220	+	0.412609i	0.960204	−	0.279301i	$-0.0901028\pi$
$31$	1.32635	+	2.29731i	0.238220	+	0.412609i	−0.721984	+	0.691910i	$0.756769\pi$
$32$		0			0
$33$	−1.43969	+	2.49362i	−0.250618	+	0.434084i
$34$		0			0
$35$	−0.982926	−	6.13208i	−0.166145	−	1.03651i
$36$		0			0
$37$	3.41147	−	5.90885i	0.560843	−	0.971408i	−0.436580	−	0.899665i	$-0.643811\pi$
$37$	3.41147	−	5.90885i	0.560843	−	0.971408i	0.997423	−	0.0717431i	$-0.0228562\pi$
$38$		0			0
$39$	−0.266044	−	0.460802i	−0.0426012	−	0.0737875i
$40$		0			0
$41$	0.426022			0.0665335			0.0332667	−	0.999447i	$-0.489409\pi$
$41$	0.426022			0.0665335			0.0332667	+	0.999447i	$0.489409\pi$
$42$		0			0
$43$	−1.18479			−0.180679			−0.0903396	−	0.995911i	$-0.528795\pi$
$43$	−1.18479			−0.180679			−0.0903396	+	0.995911i	$0.528795\pi$
$44$		0			0
$45$	−6.20961	−	10.7554i	−0.925674	−	1.60331i
$46$		0			0
$47$	−3.84002	+	6.65111i	−0.560125	+	0.970165i	0.437360	+	0.899286i	$0.355914\pi$
$47$	−3.84002	+	6.65111i	−0.560125	+	0.970165i	−0.997485	+	0.0708782i	$0.977420\pi$
$48$		0			0
$49$	1.42989	−	6.85240i	0.204270	−	0.978915i
$50$		0			0
$51$	−5.64543	+	9.77817i	−0.790518	+	1.36922i
$52$		0			0
$53$	−3.27719	−	5.67626i	−0.450157	−	0.779694i	0.548239	−	0.836322i	$-0.315298\pi$
$53$	−3.27719	−	5.67626i	−0.450157	−	0.779694i	−0.998395	+	0.0566279i	$0.981965\pi$
$54$		0			0
$55$	−2.34730			−0.316509
$56$		0			0
$57$	2.22668			0.294931
$58$		0			0
$59$	0.102196	+	0.177009i	0.0133048	+	0.0230447i	0.872601	−	0.488433i	$-0.162431\pi$
$59$	0.102196	+	0.177009i	0.0133048	+	0.0230447i	−0.859296	+	0.511478i	$0.829098\pi$
$60$		0			0
$61$	−7.29086	+	12.6281i	−0.933499	+	1.61687i	−0.156210	+	0.987724i	$0.549928\pi$
$61$	−7.29086	+	12.6281i	−0.933499	+	1.61687i	−0.777289	+	0.629144i	$0.783406\pi$
$62$		0			0
$63$	−2.21554	−	13.8219i	−0.279131	−	1.74139i
$64$		0			0
$65$	0.216881	−	0.375650i	0.0269008	−	0.0465936i
$66$		0			0
$67$	1.87939	+	3.25519i	0.229603	+	0.397685i	0.957691	−	0.287800i	$-0.0929237\pi$
$67$	1.87939	+	3.25519i	0.229603	+	0.397685i	−0.728087	+	0.685485i	$0.759590\pi$
$68$		0			0
$69$	24.0574			2.89617
$70$		0			0
$71$	9.96585			1.18273			0.591365	−	0.806404i	$-0.298589\pi$
$71$	9.96585			1.18273			0.591365	+	0.806404i	$0.298589\pi$
$72$		0			0
$73$	−0.0603074	−	0.104455i	−0.00705844	−	0.0122256i	0.862475	−	0.506100i	$-0.168913\pi$
$73$	−0.0603074	−	0.104455i	−0.00705844	−	0.0122256i	−0.869533	+	0.493875i	$0.835580\pi$
$74$		0			0
$75$	0.733956	−	1.27125i	0.0847499	−	0.146791i
$76$		0			0
$77$	−2.47178	−	0.943555i	−0.281686	−	0.107528i
$78$		0			0
$79$	0.163848	−	0.283793i	0.0184343	−	0.0319292i	−0.856661	−	0.515880i	$-0.827465\pi$
$79$	0.163848	−	0.283793i	0.0184343	−	0.0319292i	0.875095	+	0.483950i	$0.160799\pi$
$80$		0			0
$81$	−1.56031	−	2.70253i	−0.173367	−	0.300281i
$82$		0			0
$83$	−3.35504			−0.368263			−0.184132	−	0.982902i	$-0.558947\pi$
$83$	−3.35504			−0.368263			−0.184132	+	0.982902i	$0.558947\pi$
$84$		0			0
$85$	−9.20439			−0.998357
$86$		0			0
$87$	−11.7626	−	20.3735i	−1.26109	−	2.18427i
$88$		0			0
$89$	2.32635	−	4.02936i	0.246593	−	0.427111i	−0.715985	−	0.698115i	$-0.754022\pi$
$89$	2.32635	−	4.02936i	0.246593	−	0.427111i	0.962578	+	0.271004i	$0.0873557\pi$
$90$		0			0
$91$	0.379385	−	0.308391i	0.0397704	−	0.0323281i
$92$		0			0
$93$	−3.81908	+	6.61484i	−0.396020	+	0.685927i
$94$		0			0
$95$	0.907604	+	1.57202i	0.0931182	+	0.161285i
$96$		0			0
$97$	13.1206			1.33220			0.666098	−	0.745864i	$-0.267963\pi$
$97$	13.1206			1.33220			0.666098	+	0.745864i	$0.267963\pi$
$98$		0			0
$99$	−5.29086			−0.531751
$100$		0			0
$101$	2.95084	+	5.11100i	0.293619	+	0.508563i	0.974663	−	0.223679i	$-0.0718069\pi$
$101$	2.95084	+	5.11100i	0.293619	+	0.508563i	−0.681044	+	0.732243i	$0.738474\pi$
$102$		0			0
$103$	0.460637	−	0.797847i	0.0453879	−	0.0786142i	−0.842439	−	0.538792i	$-0.818881\pi$
$103$	0.460637	−	0.797847i	0.0453879	−	0.0786142i	0.887827	+	0.460178i	$0.152214\pi$
$104$		0			0
$105$	13.8760	−	11.2794i	1.35416	−	1.10075i
$106$		0			0
$107$	−5.17365	+	8.96102i	−0.500155	+	0.866295i	0.499845	+	0.866115i	$0.333390\pi$
$107$	−5.17365	+	8.96102i	−0.500155	+	0.866295i	−1.00000		0.000179505i	$0.999943\pi$
$108$		0			0
$109$	−0.237826	−	0.411927i	−0.0227796	−	0.0394554i	0.854411	−	0.519598i	$-0.173918\pi$
$109$	−0.237826	−	0.411927i	−0.0227796	−	0.0394554i	−0.877190	+	0.480143i	$0.840585\pi$
$110$		0			0
$111$	19.6459			1.86471
$112$		0			0
$113$	−3.14290			−0.295659			−0.147830	−	0.989013i	$-0.547229\pi$
$113$	−3.14290			−0.295659			−0.147830	+	0.989013i	$0.547229\pi$
$114$		0			0
$115$	9.80587	+	16.9843i	0.914402	+	1.58379i
$116$		0			0
$117$	0.488856	−	0.846723i	0.0451947	−	0.0782796i
$118$		0			0
$119$	−9.69253	−	3.69994i	−0.888513	−	0.339173i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	0.613341	+	1.06234i	0.0553031	+	0.0957877i
$124$		0			0
$125$	−10.5398			−0.942711
$126$		0			0
$127$	0.445622			0.0395426			0.0197713	−	0.999805i	$-0.493706\pi$
$127$	0.445622			0.0395426			0.0197713	+	0.999805i	$0.493706\pi$
$128$		0			0
$129$	−1.70574	−	2.95442i	−0.150182	−	0.260122i
$130$		0			0
$131$	−6.04323	+	10.4672i	−0.528000	+	0.914522i	0.471467	+	0.881883i	$0.343724\pi$
$131$	−6.04323	+	10.4672i	−0.528000	+	0.914522i	−0.999467	+	0.0326389i	$0.989609\pi$
$132$		0			0
$133$	0.323826	+	2.02022i	0.0280792	+	0.175175i
$134$		0			0
$135$	7.74170	−	13.4090i	0.666299	−	1.15406i
$136$		0			0
$137$	8.17412	+	14.1580i	0.698362	+	1.20960i	0.969034	+	0.246927i	$0.0794206\pi$
$137$	8.17412	+	14.1580i	0.698362	+	1.20960i	−0.270672	+	0.962672i	$0.587246\pi$
$138$		0			0
$139$	20.7297			1.75827			0.879134	−	0.476575i	$-0.158122\pi$
$139$	20.7297			1.75827			0.879134	+	0.476575i	$0.158122\pi$
$140$		0			0
$141$	−22.1138			−1.86232
$142$		0			0
$143$	−0.0923963	−	0.160035i	−0.00772656	−	0.0133828i
$144$		0			0
$145$	9.58899	−	16.6086i	0.796322	−	1.37927i
$146$		0			0
$147$	19.1459	−	6.29974i	1.57913	−	0.519594i
$148$		0			0
$149$	0.357097	−	0.618509i	0.0292545	−	0.0506703i	−0.851027	−	0.525121i	$-0.824020\pi$
$149$	0.357097	−	0.618509i	0.0292545	−	0.0506703i	0.880282	+	0.474451i	$0.157353\pi$
$150$		0			0
$151$	−4.77244	−	8.26611i	−0.388376	−	0.672687i	0.603855	−	0.797094i	$-0.293630\pi$
$151$	−4.77244	−	8.26611i	−0.388376	−	0.672687i	−0.992231	+	0.124407i	$0.960297\pi$
$152$		0			0
$153$	−20.7469			−1.67729
$154$		0			0
$155$	−6.22668			−0.500139
$156$		0			0
$157$	−4.62061	−	8.00314i	−0.368765	−	0.638720i	0.620608	−	0.784121i	$-0.286886\pi$
$157$	−4.62061	−	8.00314i	−0.368765	−	0.638720i	−0.989373	+	0.145401i	$0.953553\pi$
$158$		0			0
$159$	9.43629	−	16.3441i	0.748346	−	1.29617i
$160$		0			0
$161$	3.49866	+	21.8267i	0.275733	+	1.72019i
$162$		0			0
$163$	−4.40167	+	7.62392i	−0.344766	+	0.597152i	−0.985311	−	0.170769i	$-0.945375\pi$
$163$	−4.40167	+	7.62392i	−0.344766	+	0.597152i	0.640545	+	0.767920i	$0.278708\pi$
$164$		0			0
$165$	−3.37939	−	5.85327i	−0.263085	−	0.455676i
$166$		0			0
$167$	−8.38238			−0.648648			−0.324324	−	0.945946i	$-0.605137\pi$
$167$	−8.38238			−0.648648			−0.324324	+	0.945946i	$0.605137\pi$
$168$		0			0
$169$	−12.9659			−0.997373
$170$		0			0
$171$	2.04576	+	3.54336i	0.156443	+	0.270967i
$172$		0			0
$173$	−2.72281	+	4.71605i	−0.207012	+	0.358554i	−0.950772	−	0.309892i	$-0.899707\pi$
$173$	−2.72281	+	4.71605i	−0.207012	+	0.358554i	0.743760	+	0.668446i	$0.233040\pi$
$174$		0			0
$175$	1.26011	+	0.481025i	0.0952557	+	0.0363620i
$176$		0			0
$177$	−0.294263	+	0.509678i	−0.0221182	+	0.0383098i
$178$		0			0
$179$	−5.04576	−	8.73951i	−0.377138	−	0.653222i	0.613507	−	0.789689i	$-0.289758\pi$
$179$	−5.04576	−	8.73951i	−0.377138	−	0.653222i	−0.990645	+	0.136468i	$0.956425\pi$
$180$		0			0
$181$	19.8794			1.47762			0.738812	−	0.673912i	$-0.235387\pi$
$181$	19.8794			1.47762			0.738812	+	0.673912i	$0.235387\pi$
$182$		0			0
$183$	−41.9864			−3.10372
$184$		0			0
$185$	8.00774	+	13.8698i	0.588741	+	1.01973i
$186$		0			0
$187$	−1.96064	+	3.39592i	−0.143376	+	0.248334i
$188$		0			0
$189$	13.5424	−	11.0082i	0.985061	−	0.800726i
$190$		0			0
$191$	−12.6925	+	21.9841i	−0.918399	+	1.59071i	−0.116553	+	0.993184i	$0.537184\pi$
$191$	−12.6925	+	21.9841i	−0.918399	+	1.59071i	−0.801846	+	0.597530i	$0.796149\pi$
$192$		0			0
$193$	3.86571	+	6.69561i	0.278260	+	0.481961i	0.970952	−	0.239272i	$-0.0769089\pi$
$193$	3.86571	+	6.69561i	0.278260	+	0.481961i	−0.692692	+	0.721233i	$0.743576\pi$
$194$		0			0
$195$	1.24897			0.0894406
$196$		0			0
$197$	−5.37464			−0.382927			−0.191464	−	0.981500i	$-0.561323\pi$
$197$	−5.37464			−0.382927			−0.191464	+	0.981500i	$0.561323\pi$
$198$		0			0
$199$	4.39053	+	7.60462i	0.311236	+	0.539077i	0.978630	−	0.205628i	$-0.0659236\pi$
$199$	4.39053	+	7.60462i	0.311236	+	0.539077i	−0.667394	+	0.744705i	$0.732590\pi$
$200$		0			0
$201$	−5.41147	+	9.37295i	−0.381696	+	0.661117i
$202$		0			0
$203$	16.7738	−	13.6349i	1.17729	−	0.956982i
$204$		0			0
$205$	−0.500000	+	0.866025i	−0.0349215	+	0.0604858i
$206$		0			0
$207$	22.1027	+	38.2829i	1.53624	+	2.66085i
$208$		0			0
$209$	0.773318			0.0534916
$210$		0			0
$211$	−4.24123			−0.291978			−0.145989	−	0.989286i	$-0.546636\pi$
$211$	−4.24123			−0.291978			−0.145989	+	0.989286i	$0.546636\pi$
$212$		0			0
$213$	14.3478	+	24.8511i	0.983093	+	1.70277i
$214$		0			0
$215$	1.39053	−	2.40847i	0.0948333	−	0.164256i
$216$		0			0
$217$	−6.55690	−	2.50297i	−0.445112	−	0.169913i
$218$		0			0
$219$	0.173648	−	0.300767i	0.0117341	−	0.0203240i
$220$		0			0
$221$	−0.362311	−	0.627541i	−0.0243717	−	0.0422130i
$222$		0			0
$223$	18.0351			1.20772			0.603859	−	0.797091i	$-0.293629\pi$
$223$	18.0351			1.20772			0.603859	+	0.797091i	$0.293629\pi$
$224$		0			0
$225$	2.69728			0.179819
$226$		0			0
$227$	9.10266	+	15.7663i	0.604165	+	1.04644i	0.992183	+	0.124793i	$0.0398265\pi$
$227$	9.10266	+	15.7663i	0.604165	+	1.04644i	−0.388018	+	0.921652i	$0.626840\pi$
$228$		0			0
$229$	−9.62061	+	16.6634i	−0.635748	+	1.10115i	0.350608	+	0.936522i	$0.385975\pi$
$229$	−9.62061	+	16.6634i	−0.635748	+	1.10115i	−0.986356	+	0.164626i	$0.947358\pi$
$230$		0			0
$231$	−1.20574	−	7.52211i	−0.0793317	−	0.494919i
$232$		0			0
$233$	−4.66250	+	8.07569i	−0.305451	+	0.529056i	−0.977362	−	0.211576i	$-0.932140\pi$
$233$	−4.66250	+	8.07569i	−0.305451	+	0.529056i	0.671911	+	0.740632i	$0.265474\pi$
$234$		0			0
$235$	−9.01367	−	15.6121i	−0.587987	−	1.01842i
$236$		0			0
$237$	0.943563			0.0612910
$238$		0			0
$239$	−11.1898			−0.723811			−0.361905	−	0.932215i	$-0.617874\pi$
$239$	−11.1898			−0.723811			−0.361905	+	0.932215i	$0.617874\pi$
$240$		0			0
$241$	−10.1022	−	17.4975i	−0.650740	−	1.12711i	−0.982944	−	0.183907i	$-0.941126\pi$
$241$	−10.1022	−	17.4975i	−0.650740	−	1.12711i	0.332204	−	0.943208i	$-0.392208\pi$
$242$		0			0
$243$	−5.40167	+	9.35597i	−0.346518	+	0.600186i
$244$		0			0
$245$	12.2515	+	10.9490i	0.782719	+	0.699507i
$246$		0			0
$247$	−0.0714517	+	0.123758i	−0.00454636	+	0.00787453i
$248$		0			0
$249$	−4.83022	−	8.36619i	−0.306103	−	0.530186i
$250$		0			0
$251$	5.89218			0.371911			0.185956	−	0.982558i	$-0.440462\pi$
$251$	5.89218			0.371911			0.185956	+	0.982558i	$0.440462\pi$
$252$		0			0
$253$	8.35504			0.525277
$254$		0			0
$255$	−13.2515	−	22.9523i	−0.829841	−	1.43733i
$256$		0			0
$257$	1.36824	−	2.36986i	0.0853485	−	0.147828i	−0.820191	−	0.572090i	$-0.806133\pi$
$257$	1.36824	−	2.36986i	0.0853485	−	0.147828i	0.905540	+	0.424262i	$0.139466\pi$
$258$		0			0
$259$	2.85710	+	17.8243i	0.177531	+	1.10755i
$260$		0			0
$261$	21.6138	−	37.4362i	1.33786	−	2.31724i
$262$		0			0
$263$	3.09879	+	5.36727i	0.191080	+	0.330960i	0.945608	−	0.325307i	$-0.105468\pi$
$263$	3.09879	+	5.36727i	0.191080	+	0.330960i	−0.754529	+	0.656267i	$0.772134\pi$
$264$		0			0
$265$	15.3851			0.945097
$266$		0			0
$267$	13.3969			0.819879
$268$		0			0
$269$	2.10472	+	3.64549i	0.128327	+	0.222269i	0.923029	−	0.384731i	$-0.125706\pi$
$269$	2.10472	+	3.64549i	0.128327	+	0.222269i	−0.794701	+	0.607001i	$0.792373\pi$
$270$		0			0
$271$	12.7909	−	22.1544i	0.776989	−	1.34579i	−0.156680	−	0.987649i	$-0.550079\pi$
$271$	12.7909	−	22.1544i	0.776989	−	1.34579i	0.933670	−	0.358136i	$-0.116587\pi$
$272$		0			0
$273$	1.31521	+	0.502055i	0.0796000	+	0.0303858i
$274$		0			0
$275$	0.254900	−	0.441500i	0.0153711	−	0.0266234i
$276$		0			0
$277$	7.67886	+	13.3002i	0.461378	+	0.799130i	0.999030	−	0.0440366i	$-0.0140218\pi$
$277$	7.67886	+	13.3002i	0.461378	+	0.799130i	−0.537652	+	0.843167i	$0.680688\pi$
$278$		0			0
$279$	−14.0351			−0.840258
$280$		0			0
$281$	19.2540			1.14860			0.574299	−	0.818645i	$-0.305275\pi$
$281$	19.2540			1.14860			0.574299	+	0.818645i	$0.305275\pi$
$282$		0			0
$283$	−13.5326	−	23.4391i	−0.804427	−	1.39331i	−0.916677	−	0.399628i	$-0.869139\pi$
$283$	−13.5326	−	23.4391i	−0.804427	−	1.39331i	0.112250	−	0.993680i	$-0.464194\pi$
$284$		0			0
$285$	−2.61334	+	4.52644i	−0.154801	+	0.268123i
$286$		0			0
$287$	−0.874638	+	0.710966i	−0.0516282	+	0.0419670i
$288$		0			0
$289$	0.811804	−	1.40609i	0.0477532	−	0.0827109i
$290$		0			0
$291$	18.8897	+	32.7178i	1.10733	+	1.91795i
$292$		0			0
$293$	4.03508			0.235732			0.117866	−	0.993030i	$-0.462395\pi$
$293$	4.03508			0.235732			0.117866	+	0.993030i	$0.462395\pi$
$294$		0			0
$295$	−0.479771			−0.0279333
$296$		0			0
$297$	−3.29813	−	5.71253i	−0.191377	−	0.331475i
$298$		0			0
$299$	−0.771974	+	1.33710i	−0.0446444	+	0.0773264i
$300$		0			0
$301$	2.43242	−	1.97724i	0.140202	−	0.113966i
$302$		0			0
$303$	−8.49660	+	14.7165i	−0.488117	+	0.845443i
$304$		0			0
$305$	−17.1138	−	29.6420i	−0.979934	−	1.69730i
$306$		0			0
$307$	−2.92902			−0.167168			−0.0835839	−	0.996501i	$-0.526637\pi$
$307$	−2.92902			−0.167168			−0.0835839	+	0.996501i	$0.526637\pi$
$308$		0			0
$309$	2.65270			0.150907
$310$		0			0
$311$	7.81180	+	13.5304i	0.442967	+	0.767241i	0.997908	−	0.0646486i	$-0.0205926\pi$
$311$	7.81180	+	13.5304i	0.442967	+	0.767241i	−0.554941	+	0.831889i	$0.687259\pi$
$312$		0			0
$313$	10.9880	−	19.0317i	0.621077	−	1.07574i	−0.368208	−	0.929743i	$-0.620029\pi$
$313$	10.9880	−	19.0317i	0.621077	−	1.07574i	0.989285	−	0.145994i	$-0.0466380\pi$
$314$		0			0
$315$	30.6976	+	11.7182i	1.72961	+	0.660247i
$316$		0			0
$317$	1.50593	−	2.60835i	0.0845814	−	0.146499i	−0.820631	−	0.571458i	$-0.806378\pi$
$317$	1.50593	−	2.60835i	0.0845814	−	0.146499i	0.905213	+	0.424959i	$0.139711\pi$
$318$		0			0
$319$	−4.08512	−	7.07564i	−0.228723	−	0.396160i
$320$		0			0
$321$	−29.7939			−1.66293
$322$		0			0
$323$	3.03239			0.168727
$324$		0			0
$325$	0.0471036	+	0.0815859i	0.00261284	+	0.00452557i
$326$		0			0
$327$	0.684793	−	1.18610i	0.0378691	−	0.0655912i
$328$		0			0
$329$	−3.21600	−	20.0634i	−0.177304	−	1.10613i
$330$		0			0
$331$	13.7344	−	23.7887i	0.754912	−	1.30755i	−0.190506	−	0.981686i	$-0.561013\pi$
$331$	13.7344	−	23.7887i	0.754912	−	1.30755i	0.945418	−	0.325860i	$-0.105654\pi$
$332$		0			0
$333$	18.0496	+	31.2629i	0.989114	+	1.71320i
$334$		0			0
$335$	−8.82295			−0.482049
$336$		0			0
$337$	17.2422			0.939240			0.469620	−	0.882869i	$-0.344391\pi$
$337$	17.2422			0.939240			0.469620	+	0.882869i	$0.344391\pi$
$338$		0			0
$339$	−4.52481	−	7.83721i	−0.245754	−	0.425659i
$340$		0			0
$341$	−1.32635	+	2.29731i	−0.0718260	+	0.124406i
$342$		0			0
$343$	8.50000	+	16.4545i	0.458957	+	0.888459i
$344$		0			0
$345$	−28.2349	+	48.9043i	−1.52012	+	2.63292i
$346$		0			0
$347$	−5.71554	−	9.89960i	−0.306826	−	0.531438i	0.670840	−	0.741602i	$-0.265934\pi$
$347$	−5.71554	−	9.89960i	−0.306826	−	0.531438i	−0.977666	+	0.210164i	$0.932600\pi$
$348$		0			0
$349$	28.3209			1.51598			0.757991	−	0.652265i	$-0.226181\pi$
$349$	28.3209			1.51598			0.757991	+	0.652265i	$0.226181\pi$
$350$		0			0
$351$	1.21894			0.0650622
$352$		0			0
$353$	−8.21806	−	14.2341i	−0.437403	−	0.757605i	0.560085	−	0.828435i	$-0.310768\pi$
$353$	−8.21806	−	14.2341i	−0.437403	−	0.757605i	−0.997488	+	0.0708303i	$0.977435\pi$
$354$		0			0
$355$	−11.6964	+	20.2588i	−0.620781	+	1.07522i
$356$		0			0
$357$	−4.72803	−	29.4963i	−0.250234	−	1.56111i
$358$		0			0
$359$	12.4315	−	21.5321i	0.656112	−	1.13642i	−0.325502	−	0.945541i	$-0.605533\pi$
$359$	12.4315	−	21.5321i	0.656112	−	1.13642i	0.981614	−	0.190877i	$-0.0611333\pi$
$360$		0			0
$361$	9.20099	+	15.9366i	0.484263	+	0.838767i
$362$		0			0
$363$	−2.87939			−0.151129
$364$		0			0
$365$	0.283119			0.0148191
$366$		0			0
$367$	2.14930	+	3.72270i	0.112193	+	0.194323i	0.916654	−	0.399682i	$-0.130879\pi$
$367$	2.14930	+	3.72270i	0.112193	+	0.194323i	−0.804461	+	0.594005i	$0.797546\pi$
$368$		0			0
$369$	−1.12701	+	1.95204i	−0.0586699	+	0.101619i
$370$		0			0
$371$	16.2010	+	6.18442i	0.841113	+	0.321079i
$372$		0			0
$373$	1.36484	−	2.36397i	0.0706686	−	0.122402i	−0.828526	−	0.559951i	$-0.810820\pi$
$373$	1.36484	−	2.36397i	0.0706686	−	0.122402i	0.899195	+	0.437549i	$0.144153\pi$
$374$		0			0
$375$	−15.1741	−	26.2823i	−0.783588	−	1.35721i
$376$		0			0
$377$	1.50980			0.0777587
$378$		0			0
$379$	16.4584			0.845412			0.422706	−	0.906267i	$-0.361080\pi$
$379$	16.4584			0.845412			0.422706	+	0.906267i	$0.361080\pi$
$380$		0			0
$381$	0.641559	+	1.11121i	0.0328681	+	0.0569292i
$382$		0			0
$383$	−3.92989	+	6.80677i	−0.200808	+	0.347810i	−0.948789	−	0.315910i	$-0.897690\pi$
$383$	−3.92989	+	6.80677i	−0.200808	+	0.347810i	0.747981	+	0.663720i	$0.231023\pi$
$384$		0			0
$385$	4.81908	−	3.91728i	0.245603	−	0.199643i
$386$		0			0
$387$	3.13429	−	5.42874i	0.159325	−	0.275958i
$388$		0			0
$389$	−4.82160	−	8.35126i	−0.244465	−	0.423426i	0.717516	−	0.696542i	$-0.245279\pi$
$389$	−4.82160	−	8.35126i	−0.244465	−	0.423426i	−0.961981	+	0.273116i	$0.911946\pi$
$390$		0			0
$391$	32.7624			1.65687
$392$		0			0
$393$	−34.8016			−1.75551
$394$		0			0
$395$	0.384600	+	0.666146i	0.0193513	+	0.0335175i
$396$		0			0
$397$	4.71688	−	8.16988i	0.236733	−	0.410034i	−0.723042	−	0.690805i	$-0.757257\pi$
$397$	4.71688	−	8.16988i	0.236733	−	0.410034i	0.959775	+	0.280770i	$0.0905898\pi$
$398$		0			0
$399$	−4.57145	+	3.71599i	−0.228859	+	0.186032i
$400$		0			0
$401$	9.10994	−	15.7789i	0.454929	−	0.787959i	−0.543756	−	0.839244i	$-0.682998\pi$
$401$	9.10994	−	15.7789i	0.454929	−	0.787959i	0.998684	+	0.0512843i	$0.0163315\pi$
$402$		0			0
$403$	−0.245100	−	0.424525i	−0.0122093	−	0.0211471i
$404$		0			0
$405$	7.32501			0.363983
$406$		0			0
$407$	6.82295			0.338201
$408$		0			0
$409$	−3.20574	−	5.55250i	−0.158513	−	0.274553i	0.775819	−	0.630955i	$-0.217337\pi$
$409$	−3.20574	−	5.55250i	−0.158513	−	0.274553i	−0.934333	+	0.356402i	$0.884003\pi$
$410$		0			0
$411$	−23.5364	+	40.7663i	−1.16097	+	2.01085i
$412$		0			0
$413$	−0.505215	−	0.192856i	−0.0248600	−	0.00948982i
$414$		0			0
$415$	3.93763	−	6.82018i	0.193291	−	0.334790i
$416$		0			0
$417$	29.8444	+	51.6919i	1.46148	+	2.53137i
$418$		0			0
$419$	−1.62092			−0.0791871			−0.0395935	−	0.999216i	$-0.512606\pi$
$419$	−1.62092			−0.0791871			−0.0395935	+	0.999216i	$0.512606\pi$
$420$		0			0
$421$	31.1489			1.51810			0.759052	−	0.651030i	$-0.225663\pi$
$421$	31.1489			1.51810			0.759052	+	0.651030i	$0.225663\pi$
$422$		0			0
$423$	−20.3170	−	35.1901i	−0.987847	−	1.71100i
$424$		0			0
$425$	0.999533	−	1.73124i	0.0484845	−	0.0839776i
$426$		0			0
$427$	−6.10607	−	38.0933i	−0.295493	−	1.84347i
$428$		0			0
$429$	0.266044	−	0.460802i	0.0128447	−	0.0222478i
$430$		0			0
$431$	17.1040	+	29.6250i	0.823871	+	1.42699i	0.902779	+	0.430105i	$0.141523\pi$
$431$	17.1040	+	29.6250i	0.823871	+	1.42699i	−0.0789080	+	0.996882i	$0.525143\pi$
$432$		0			0
$433$	−20.4979			−0.985068			−0.492534	−	0.870293i	$-0.663929\pi$
$433$	−20.4979			−0.985068			−0.492534	+	0.870293i	$0.663929\pi$
$434$		0			0
$435$	55.2208			2.64764
$436$		0			0
$437$	−3.23055	−	5.59548i	−0.154538	−	0.267668i
$438$		0			0
$439$	15.6609	−	27.1255i	0.747455	−	1.29463i	−0.201585	−	0.979471i	$-0.564609\pi$
$439$	15.6609	−	27.1255i	0.747455	−	1.29463i	0.949039	−	0.315158i	$-0.102058\pi$
$440$		0			0
$441$	27.6152	+	24.6793i	1.31501	+	1.17521i
$442$		0			0
$443$	−14.6989	+	25.4593i	−0.698367	+	1.20961i	0.270665	+	0.962674i	$0.412756\pi$
$443$	−14.6989	+	25.4593i	−0.698367	+	1.20961i	−0.969032	+	0.246934i	$0.920577\pi$
$444$		0			0
$445$	5.46064	+	9.45810i	0.258859	+	0.448357i
$446$		0			0
$447$	2.05644			0.0972661
$448$		0			0
$449$	−6.90074			−0.325666			−0.162833	−	0.986654i	$-0.552063\pi$
$449$	−6.90074			−0.325666			−0.162833	+	0.986654i	$0.552063\pi$
$450$		0			0
$451$	0.213011	+	0.368946i	0.0100303	+	0.0173730i
$452$		0			0
$453$	13.7417	−	23.8013i	0.645641	−	1.11828i
$454$		0			0
$455$	0.181637	+	1.13316i	0.00851529	+	0.0531235i
$456$		0			0
$457$	−6.18732	+	10.7168i	−0.289431	+	0.501308i	−0.973674	−	0.227945i	$-0.926799\pi$
$457$	−6.18732	+	10.7168i	−0.289431	+	0.501308i	0.684243	+	0.729254i	$0.260133\pi$
$458$		0			0
$459$	−12.9329	−	22.4004i	−0.603655	−	1.04556i
$460$		0			0
$461$	20.0942			0.935881			0.467940	−	0.883760i	$-0.344996\pi$
$461$	20.0942			0.935881			0.467940	+	0.883760i	$0.344996\pi$
$462$		0			0
$463$	−8.69190			−0.403947			−0.201974	−	0.979391i	$-0.564735\pi$
$463$	−8.69190			−0.403947			−0.201974	+	0.979391i	$0.564735\pi$
$464$		0			0
$465$	−8.96451	−	15.5270i	−0.415719	−	0.720047i
$466$		0			0
$467$	2.38460	−	4.13025i	0.110346	−	0.191125i	−0.805564	−	0.592509i	$-0.798137\pi$
$467$	2.38460	−	4.13025i	0.110346	−	0.191125i	0.915910	+	0.401384i	$0.131471\pi$
$468$		0			0
$469$	−9.29086	−	3.54661i	−0.429012	−	0.163767i
$470$		0			0
$471$	13.3045	−	23.0441i	0.613040	−	1.06182i
$472$		0			0
$473$	−0.592396	−	1.02606i	−0.0272384	−	0.0471783i
$474$		0			0
$475$	−0.394238			−0.0180889
$476$		0			0
$477$	34.6783			1.58781
$478$		0			0
$479$	−19.8071	−	34.3068i	−0.905007	−	1.56752i	−0.820907	−	0.571062i	$-0.806532\pi$
$479$	−19.8071	−	34.3068i	−0.905007	−	1.56752i	−0.0841003	−	0.996457i	$-0.526802\pi$
$480$		0			0
$481$	−0.630415	+	1.09191i	−0.0287444	+	0.0497868i
$482$		0			0
$483$	−49.3906	+	40.1481i	−2.24735	+	1.82680i
$484$		0			0
$485$	−15.3990	+	26.6718i	−0.699232	+	1.21111i
$486$		0			0
$487$	2.57785	+	4.46496i	0.116813	+	0.202327i	0.918503	−	0.395414i	$-0.129399\pi$
$487$	2.57785	+	4.46496i	0.116813	+	0.202327i	−0.801690	+	0.597740i	$0.796065\pi$
$488$		0			0
$489$	−25.3482			−1.14629
$490$		0			0
$491$	−10.1925			−0.459983			−0.229991	−	0.973193i	$-0.573870\pi$
$491$	−10.1925			−0.459983			−0.229991	+	0.973193i	$0.573870\pi$
$492$		0			0
$493$	−16.0189	−	27.7455i	−0.721454	−	1.24960i
$494$		0			0
$495$	6.20961	−	10.7554i	0.279101	−	0.483417i
$496$		0			0
$497$	−20.4602	+	16.6315i	−0.917767	+	0.746024i
$498$		0			0
$499$	2.94491	−	5.10073i	0.131832	−	0.228340i	−0.792551	−	0.609806i	$-0.791247\pi$
$499$	2.94491	−	5.10073i	0.131832	−	0.228340i	0.924383	+	0.381466i	$0.124581\pi$
$500$		0			0
$501$	−12.0680	−	20.9025i	−0.539161	−	0.933854i
$502$		0			0
$503$	12.8348			0.572276			0.286138	−	0.958188i	$-0.407628\pi$
$503$	12.8348			0.572276			0.286138	+	0.958188i	$0.407628\pi$
$504$		0			0
$505$	−13.8530			−0.616449
$506$		0			0
$507$	−18.6668	−	32.3319i	−0.829024	−	1.43591i
$508$		0			0
$509$	−16.1065	+	27.8973i	−0.713910	+	1.23653i	0.249469	+	0.968383i	$0.419744\pi$
$509$	−16.1065	+	27.8973i	−0.713910	+	1.23653i	−0.963379	+	0.268145i	$0.913589\pi$
$510$		0			0
$511$	0.298133	+	0.113807i	0.0131886	+	0.00503451i
$512$		0			0
$513$	−2.55051	+	4.41761i	−0.112608	+	0.195042i
$514$		0			0
$515$	1.08125	+	1.87278i	0.0476457	+	0.0825247i
$516$		0			0
$517$	−7.68004			−0.337768
$518$		0			0
$519$	−15.6800			−0.688278
$520$		0			0
$521$	−9.26399	−	16.0457i	−0.405863	−	0.702975i	0.588559	−	0.808454i	$-0.299696\pi$
$521$	−9.26399	−	16.0457i	−0.405863	−	0.702975i	−0.994421	+	0.105480i	$0.966362\pi$
$522$		0			0
$523$	−18.6211	+	32.2527i	−0.814243	+	1.41031i	0.0956271	+	0.995417i	$0.469514\pi$
$523$	−18.6211	+	32.2527i	−0.814243	+	1.41031i	−0.909870	+	0.414893i	$0.863819\pi$
$524$		0			0
$525$	0.614685	+	3.83478i	0.0268271	+	0.167363i
$526$		0			0
$527$	−5.20099	+	9.00838i	−0.226559	+	0.392411i
$528$		0			0
$529$	−23.4033	−	40.5357i	−1.01754	−	1.76242i
$530$		0			0
$531$	−1.08141			−0.0469294
$532$		0			0
$533$	−0.0787257			−0.00340999
$534$		0			0
$535$	−12.1441	−	21.0342i	−0.525035	−	0.909387i
$536$		0			0
$537$	14.5287	−	25.1644i	0.626959	−	1.08592i
$538$		0			0
$539$	6.64930	−	2.18788i	0.286406	−	0.0942386i
$540$		0			0
$541$	−18.0783	+	31.3126i	−0.777247	+	1.34623i	0.156275	+	0.987714i	$0.450051\pi$
$541$	−18.0783	+	31.3126i	−0.777247	+	1.34623i	−0.933523	+	0.358519i	$0.883282\pi$
$542$		0			0
$543$	28.6202	+	49.5716i	1.22821	+	2.12732i
$544$		0			0
$545$	1.11650			0.0478254
$546$		0			0
$547$	−12.7980			−0.547202			−0.273601	−	0.961843i	$-0.588215\pi$
$547$	−12.7980			−0.547202			−0.273601	+	0.961843i	$0.588215\pi$
$548$		0			0
$549$	−38.5749	−	66.8137i	−1.64634	−	2.85154i
$550$		0			0
$551$	−3.15910	+	5.47172i	−0.134582	+	0.233103i
$552$		0			0
$553$	0.137222	+	0.856074i	0.00583528	+	0.0364040i
$554$		0			0
$555$	−23.0574	+	39.9365i	−0.978731	+	1.69521i
$556$		0			0
$557$	15.3293	+	26.5512i	0.649525	+	1.12501i	0.983236	+	0.182335i	$0.0583656\pi$
$557$	15.3293	+	26.5512i	0.649525	+	1.12501i	−0.333711	+	0.942675i	$0.608301\pi$
$558$		0			0
$559$	0.218941			0.00926021
$560$		0			0
$561$	−11.2909			−0.476700
$562$		0			0
$563$	−7.25237	−	12.5615i	−0.305651	−	0.529403i	0.671755	−	0.740773i	$-0.265541\pi$
$563$	−7.25237	−	12.5615i	−0.305651	−	0.529403i	−0.977406	+	0.211370i	$0.932207\pi$
$564$		0			0
$565$	3.68866	−	6.38895i	0.155183	−	0.268785i
$566$		0			0
$567$	7.71348	+	2.94447i	0.323936	+	0.123656i
$568$		0			0
$569$	−9.50253	+	16.4589i	−0.398367	+	0.689991i	−0.993525	−	0.113618i	$-0.963756\pi$
$569$	−9.50253	+	16.4589i	−0.398367	+	0.689991i	0.595158	+	0.803609i	$0.297089\pi$
$570$		0			0
$571$	−10.5005	−	18.1873i	−0.439431	−	0.761117i	0.558215	−	0.829696i	$-0.311487\pi$
$571$	−10.5005	−	18.1873i	−0.439431	−	0.761117i	−0.997646	+	0.0685799i	$0.978153\pi$
$572$		0			0
$573$	−73.0934			−3.05352
$574$		0			0
$575$	−4.25940			−0.177629
$576$		0			0
$577$	2.59374	+	4.49249i	0.107979	+	0.187025i	0.914951	−	0.403564i	$-0.132229\pi$
$577$	2.59374	+	4.49249i	0.107979	+	0.187025i	−0.806973	+	0.590589i	$0.798895\pi$
$578$		0			0
$579$	−11.1309	+	19.2793i	−0.462584	+	0.801218i
$580$		0			0
$581$	6.88800	−	5.59905i	0.285763	−	0.232288i
$582$		0			0
$583$	3.27719	−	5.67626i	0.135727	−	0.235087i
$584$		0			0
$585$	1.14749	+	1.98751i	0.0474428	+	0.0821734i
$586$		0			0
$587$	−8.33813			−0.344151			−0.172076	−	0.985084i	$-0.555047\pi$
$587$	−8.33813			−0.344151			−0.172076	+	0.985084i	$0.555047\pi$
$588$		0			0
$589$	2.05138			0.0845258
$590$		0			0
$591$	−7.73783	−	13.4023i	−0.318292	−	0.551297i
$592$		0			0
$593$	−3.05097	+	5.28444i	−0.125288	+	0.217006i	−0.921846	−	0.387557i	$-0.873319\pi$
$593$	−3.05097	+	5.28444i	−0.125288	+	0.217006i	0.796557	+	0.604563i	$0.206652\pi$
$594$		0			0
$595$	18.8969	−	15.3607i	0.774698	−	0.629729i
$596$		0			0
$597$	−12.6420	+	21.8966i	−0.517404	+	0.896169i
$598$		0			0
$599$	−6.92514	−	11.9947i	−0.282954	−	0.490090i	0.689157	−	0.724612i	$-0.257981\pi$
$599$	−6.92514	−	11.9947i	−0.282954	−	0.490090i	−0.972111	+	0.234522i	$0.924648\pi$
$600$		0			0
$601$	31.2695			1.27551			0.637755	−	0.770239i	$-0.279863\pi$
$601$	31.2695			1.27551			0.637755	+	0.770239i	$0.279863\pi$
$602$		0			0
$603$	−19.8871			−0.809866
$604$		0			0
$605$	−1.17365	−	2.03282i	−0.0477156	−	0.0826458i
$606$		0			0
$607$	18.8981	−	32.7325i	0.767051	−	1.32857i	−0.172105	−	0.985079i	$-0.555057\pi$
$607$	18.8981	−	32.7325i	0.767051	−	1.32857i	0.939156	−	0.343492i	$-0.111610\pi$
$608$		0			0
$609$	58.1494	+	22.1974i	2.35633	+	0.899484i
$610$		0			0
$611$	0.709607	−	1.22908i	0.0287076	−	0.0497231i
$612$		0			0
$613$	−10.5672	−	18.3029i	−0.426804	−	0.739246i	0.569783	−	0.821795i	$-0.307027\pi$
$613$	−10.5672	−	18.3029i	−0.426804	−	0.739246i	−0.996587	+	0.0825490i	$0.973694\pi$
$614$		0			0
$615$	−2.87939			−0.116108
$616$		0			0
$617$	23.7743			0.957115			0.478558	−	0.878056i	$-0.341160\pi$
$617$	23.7743			0.957115			0.478558	+	0.878056i	$0.341160\pi$
$618$		0			0
$619$	6.75103	+	11.6931i	0.271347	+	0.469986i	0.969207	−	0.246248i	$-0.0791976\pi$
$619$	6.75103	+	11.6931i	0.271347	+	0.469986i	−0.697860	+	0.716234i	$0.745864\pi$
$620$		0			0
$621$	−27.5560	+	47.7284i	−1.10579	+	1.91528i
$622$		0			0
$623$	1.94831	+	12.1547i	0.0780574	+	0.486969i
$624$		0			0
$625$	13.6446	−	23.6331i	0.545782	−	0.945322i
$626$		0			0
$627$	1.11334	+	1.92836i	0.0444625	+	0.0770114i
$628$		0			0
$629$	26.7547			1.06678
$630$		0			0
$631$	38.2354			1.52213			0.761063	−	0.648678i	$-0.224678\pi$
$631$	38.2354			1.52213			0.761063	+	0.648678i	$0.224678\pi$
$632$		0			0
$633$	−6.10607	−	10.5760i	−0.242694	−	0.420359i
$634$		0			0
$635$	−0.523004	+	0.905869i	−0.0207548	+	0.0359483i
$636$		0			0
$637$	−0.264233	+	1.26627i	−0.0104693	+	0.0501715i
$638$		0			0
$639$	−26.3640	+	45.6637i	−1.04294	+	1.80643i
$640$		0			0
$641$	−19.2777	−	33.3899i	−0.761422	−	1.31882i	−0.942118	−	0.335282i	$-0.891168\pi$
$641$	−19.2777	−	33.3899i	−0.761422	−	1.31882i	0.180696	−	0.983539i	$-0.442165\pi$
$642$		0			0
$643$	−19.2627			−0.759647			−0.379823	−	0.925059i	$-0.624015\pi$
$643$	−19.2627			−0.759647			−0.379823	+	0.925059i	$0.624015\pi$
$644$		0			0
$645$	8.00774			0.315304
$646$		0			0
$647$	19.8922	+	34.4543i	0.782042	+	1.35454i	0.930750	+	0.365656i	$0.119155\pi$
$647$	19.8922	+	34.4543i	0.782042	+	1.35454i	−0.148708	+	0.988881i	$0.547511\pi$
$648$		0			0
$649$	−0.102196	+	0.177009i	−0.00401156	+	0.00694823i
$650$		0			0
$651$	−3.19846	−	19.9539i	−0.125358	−	0.782057i
$652$		0			0
$653$	−2.38326	+	4.12792i	−0.0932640	+	0.161538i	−0.908883	−	0.417052i	$-0.863063\pi$
$653$	−2.38326	+	4.12792i	−0.0932640	+	0.161538i	0.815619	+	0.578590i	$0.196397\pi$
$654$		0			0
$655$	−14.1853	−	24.5696i	−0.554264	−	0.960013i
$656$		0			0
$657$	0.638156			0.0248968
$658$		0			0
$659$	38.3550			1.49410			0.747050	−	0.664768i	$-0.231470\pi$
$659$	38.3550			1.49410			0.747050	+	0.664768i	$0.231470\pi$
$660$		0			0
$661$	5.18139	+	8.97443i	0.201533	+	0.349065i	0.949022	−	0.315208i	$-0.102074\pi$
$661$	5.18139	+	8.97443i	0.201533	+	0.349065i	−0.747490	+	0.664273i	$0.768741\pi$
$662$		0			0
$663$	1.04323	−	1.80693i	0.0405158	−	0.0701755i
$664$		0			0
$665$	−4.48680	−	1.71275i	−0.173990	−	0.0664175i
$666$		0			0
$667$	−34.1313	+	59.1172i	−1.32157	+	2.28903i
$668$		0			0
$669$	25.9650	+	44.9727i	1.00386	+	1.73874i
$670$		0			0
$671$	−14.5817			−0.562921
$672$		0			0
$673$	−25.6168			−0.987455			−0.493728	−	0.869617i	$-0.664366\pi$
$673$	−25.6168			−0.987455			−0.493728	+	0.869617i	$0.664366\pi$
$674$		0			0
$675$	1.68139	+	2.91225i	0.0647167	+	0.112093i
$676$		0			0
$677$	−20.9187	+	36.2323i	−0.803973	+	1.39252i	0.113010	+	0.993594i	$0.463951\pi$
$677$	−20.9187	+	36.2323i	−0.803973	+	1.39252i	−0.916982	+	0.398928i	$0.869382\pi$
$678$		0			0
$679$	−26.9371	+	21.8963i	−1.03375	+	0.840303i
$680$		0			0
$681$	−26.2101	+	45.3972i	−1.00437	+	1.73962i
$682$		0			0
$683$	−23.0214	−	39.8743i	−0.880890	−	1.52575i	−0.850353	−	0.526212i	$-0.823612\pi$
$683$	−23.0214	−	39.8743i	−0.880890	−	1.52575i	−0.0305366	−	0.999534i	$-0.509722\pi$
$684$		0			0
$685$	−38.3741			−1.46620
$686$		0			0
$687$	−55.4029			−2.11375
$688$		0			0
$689$	0.605600	+	1.04893i	0.0230715	+	0.0399611i
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$		0			0
$693$	10.8623	−	8.82964i	0.412625	−	0.335410i
$694$		0			0
$695$	−24.3293	+	42.1397i	−0.922865	+	1.59845i
$696$		0			0
$697$	0.835275	+	1.44674i	0.0316383	+	0.0547991i
$698$		0			0
$699$	−26.8503			−1.01557
$700$		0			0
$701$	−32.8144			−1.23938			−0.619691	−	0.784846i	$-0.712742\pi$
$701$	−32.8144			−1.23938			−0.619691	+	0.784846i	$0.712742\pi$
$702$		0			0
$703$	−2.63816	−	4.56942i	−0.0994999	−	0.172339i
$704$		0			0
$705$	25.9538	−	44.9534i	0.977478	−	1.69304i
$706$		0			0
$707$	−14.5876	−	5.56855i	−0.548625	−	0.209427i
$708$		0			0
$709$	−3.70099	+	6.41030i	−0.138994	+	0.240744i	−0.927116	−	0.374775i	$-0.877720\pi$
$709$	−3.70099	+	6.41030i	−0.138994	+	0.240744i	0.788122	+	0.615519i	$0.211053\pi$
$710$		0			0
$711$	0.866897	+	1.50151i	0.0325112	+	0.0563110i
$712$		0			0
$713$	22.1634			0.830027
$714$		0			0
$715$	0.433763			0.0162218
$716$		0			0
$717$	−16.1099	−	27.9032i	−0.601637	−	1.04207i
$718$		0			0
$719$	−7.06851	+	12.2430i	−0.263611	+	0.456588i	−0.967199	−	0.254021i	$-0.918247\pi$
$719$	−7.06851	+	12.2430i	−0.263611	+	0.456588i	0.703588	+	0.710608i	$0.251580\pi$
$720$		0			0
$721$	0.385782	+	2.40674i	0.0143673	+	0.0896317i
$722$		0			0
$723$	29.0881	−	50.3821i	1.08180	−	1.87373i
$724$		0			0
$725$	2.08260	+	3.60716i	0.0773457	+	0.133967i
$726$		0			0
$727$	−15.2790			−0.566667			−0.283333	−	0.959021i	$-0.591440\pi$
$727$	−15.2790			−0.566667			−0.283333	+	0.959021i	$0.591440\pi$
$728$		0			0
$729$	−40.4688			−1.49885
$730$		0			0
$731$	−2.32295	−	4.02346i	−0.0859173	−	0.148813i
$732$		0			0
$733$	−0.672466	+	1.16475i	−0.0248381	+	0.0430209i	−0.878177	−	0.478335i	$-0.841240\pi$
$733$	−0.672466	+	1.16475i	−0.0248381	+	0.0430209i	0.853339	+	0.521356i	$0.174574\pi$
$734$		0			0
$735$	−9.66431	+	46.3138i	−0.356474	+	1.70831i
$736$		0			0
$737$	−1.87939	+	3.25519i	−0.0692280	+	0.119906i
$738$		0			0
$739$	−12.8268	−	22.2167i	−0.471842	−	0.817255i	0.527639	−	0.849469i	$-0.323077\pi$
$739$	−12.8268	−	22.2167i	−0.471842	−	0.817255i	−0.999481	+	0.0322142i	$0.989744\pi$
$740$		0			0
$741$	−0.411474			−0.0151159
$742$		0			0
$743$	6.08109			0.223094			0.111547	−	0.993759i	$-0.464420\pi$
$743$	6.08109			0.223094			0.111547	+	0.993759i	$0.464420\pi$
$744$		0			0
$745$	0.838211	+	1.45182i	0.0307097	+	0.0531907i
$746$		0			0
$747$	8.87551	−	15.3728i	0.324738	−	0.562463i
$748$		0			0
$749$	−4.33291	−	27.0313i	−0.158321	−	0.987703i
$750$		0			0
$751$	10.4054	−	18.0227i	0.379698	−	0.657656i	−0.611320	−	0.791383i	$-0.709361\pi$
$751$	10.4054	−	18.0227i	0.379698	−	0.657656i	0.991018	+	0.133727i	$0.0426946\pi$
$752$		0			0
$753$	8.48293	+	14.6929i	0.309135	+	0.535438i
$754$		0			0
$755$	22.4047			0.815389
$756$		0			0
$757$	−5.25402			−0.190961			−0.0954804	−	0.995431i	$-0.530439\pi$
$757$	−5.25402			−0.190961			−0.0954804	+	0.995431i	$0.530439\pi$
$758$		0			0
$759$	12.0287	+	20.8343i	0.436614	+	0.756237i
$760$		0			0
$761$	20.4907	−	35.4909i	0.742786	−	1.28654i	−0.208436	−	0.978036i	$-0.566837\pi$
$761$	20.4907	−	35.4909i	0.742786	−	1.28654i	0.951222	−	0.308507i	$-0.0998294\pi$
$762$		0			0
$763$	1.17571	+	0.448804i	0.0425635	+	0.0162478i
$764$		0			0
$765$	24.3496	−	42.1747i	0.880361	−	1.52483i
$766$		0			0
$767$	−0.0188851	−	0.0327100i	−0.000681903	−	0.00118109i
$768$		0			0
$769$	47.5580			1.71499			0.857493	−	0.514496i	$-0.172021\pi$
$769$	47.5580			1.71499			0.857493	+	0.514496i	$0.172021\pi$
$770$		0			0
$771$	7.87939			0.283769
$772$		0			0
$773$	−10.2464	−	17.7474i	−0.368539	−	0.638328i	0.620798	−	0.783970i	$-0.286809\pi$
$773$	−10.2464	−	17.7474i	−0.368539	−	0.638328i	−0.989337	+	0.145642i	$0.953475\pi$
$774$		0			0
$775$	0.676174	−	1.17117i	0.0242889	−	0.0420696i
$776$		0			0
$777$	−40.3337	+	32.7860i	−1.44696	+	1.17619i
$778$		0			0
$779$	0.164725	−	0.285313i	0.00590190	−	0.0102224i
$780$		0			0
$781$	4.98293	+	8.63068i	0.178303	+	0.308830i
$782$		0			0
$783$	53.8931			1.92598
$784$		0			0
$785$	21.6919			0.774217
$786$		0			0
$787$	−9.56031	−	16.5589i	−0.340788	−	0.590262i	0.643791	−	0.765201i	$-0.277361\pi$
$787$	−9.56031	−	16.5589i	−0.340788	−	0.590262i	−0.984579	+	0.174939i	$0.944027\pi$
$788$		0			0
$789$	−8.92262	+	15.4544i	−0.317654	+	0.550192i
$790$		0			0
$791$	6.45249	−	5.24503i	0.229424	−	0.186492i
$792$		0			0
$793$	1.34730	−	2.33359i	0.0478439	−	0.0828681i
$794$		0			0
$795$	22.1498	+	38.3645i	0.785571	+	1.36065i
$796$		0			0
$797$	−52.5144			−1.86015			−0.930077	−	0.367365i	$-0.880260\pi$
$797$	−52.5144			−1.86015			−0.930077	+	0.367365i	$0.880260\pi$
$798$		0			0
$799$	−30.1156			−1.06541
$800$		0			0
$801$	12.3084	+	21.3188i	0.434896	+	0.753262i
$802$		0			0
$803$	0.0603074	−	0.104455i	0.00212820	−	0.00368615i
$804$		0			0
$805$	−48.4760	−	18.5048i	−1.70855	−	0.652207i
$806$		0			0
$807$	−6.06031	+	10.4968i	−0.213333	+	0.369503i
$808$		0			0
$809$	−20.3357	−	35.2225i	−0.714967	−	1.23836i	−0.962972	−	0.269600i	$-0.913109\pi$
$809$	−20.3357	−	35.2225i	−0.714967	−	1.23836i	0.248006	−	0.968759i	$-0.420225\pi$
$810$		0			0
$811$	20.5648			0.722128			0.361064	−	0.932541i	$-0.382414\pi$
$811$	20.5648			0.722128			0.361064	+	0.932541i	$0.382414\pi$
$812$		0			0
$813$	73.6596			2.58336
$814$		0			0
$815$	−10.3320	−	17.8956i	−0.361915	−	0.626856i
$816$		0			0
$817$	−0.458111	+	0.793471i	−0.0160273	+	0.0277601i
$818$		0			0
$819$	0.409415	+	2.55418i	0.0143061	+	0.0892501i
$820$		0			0
$821$	−3.18139	+	5.51033i	−0.111031	+	0.192312i	−0.916186	−	0.400753i	$-0.868749\pi$
$821$	−3.18139	+	5.51033i	−0.111031	+	0.192312i	0.805155	+	0.593064i	$0.202082\pi$
$822$		0			0
$823$	−1.25443	−	2.17274i	−0.0437268	−	0.0757370i	0.843334	−	0.537390i	$-0.180590\pi$
$823$	−1.25443	−	2.17274i	−0.0437268	−	0.0757370i	−0.887060	+	0.461653i	$0.847256\pi$
$824$		0			0
$825$	1.46791			0.0511061
$826$		0			0
$827$	41.2645			1.43491			0.717453	−	0.696607i	$-0.245308\pi$
$827$	41.2645			1.43491			0.717453	+	0.696607i	$0.245308\pi$
$828$		0			0
$829$	23.3889	+	40.5108i	0.812331	+	1.40700i	0.911228	+	0.411902i	$0.135135\pi$
$829$	23.3889	+	40.5108i	0.812331	+	1.40700i	−0.0988970	+	0.995098i	$0.531531\pi$
$830$		0			0
$831$	−22.1104	+	38.2963i	−0.767001	+	1.32849i
$832$		0			0
$833$	26.0737	−	8.57927i	0.903401	−	0.297254i
$834$		0			0
$835$	9.83796	−	17.0399i	0.340457	−	0.589688i
$836$		0			0
$837$	−8.74897	−	15.1537i	−0.302409	−	0.523787i
$838$		0			0
$839$	−16.5439			−0.571161			−0.285580	−	0.958355i	$-0.592186\pi$
$839$	−16.5439			−0.571161			−0.285580	+	0.958355i	$0.592186\pi$
$840$		0			0
$841$	37.7529			1.30182
$842$		0			0
$843$	27.7199	+	48.0122i	0.954723	+	1.65363i
$844$		0			0
$845$	15.2173	−	26.3572i	0.523493	−	0.906716i
$846$		0			0
$847$	−0.418748	−	2.61240i	−0.0143884	−	0.0897632i
$848$		0			0
$849$	38.9654	−	67.4901i	1.33729	−	2.31626i
$850$		0			0
$851$	−28.5030	−	49.3686i	−0.977070	−	1.69233i
$852$		0			0
$853$	13.2163			0.452516			0.226258	−	0.974067i	$-0.427351\pi$
$853$	13.2163			0.452516			0.226258	+	0.974067i	$0.427351\pi$
$854$		0			0
$855$	−9.60401			−0.328450
$856$		0			0
$857$	25.3606	+	43.9258i	0.866300	+	1.50048i	0.865750	+	0.500476i	$0.166842\pi$
$857$	25.3606	+	43.9258i	0.866300	+	1.50048i	0.000549663		1.00000i	$0.499825\pi$
$858$		0			0
$859$	27.5562	−	47.7287i	0.940205	−	1.62848i	0.175126	−	0.984546i	$-0.443967\pi$
$859$	27.5562	−	47.7287i	0.940205	−	1.62848i	0.765079	−	0.643937i	$-0.222700\pi$
$860$		0			0
$861$	−3.03209	−	1.15744i	−0.103333	−	0.0394455i
$862$		0			0
$863$	5.26011	−	9.11079i	0.179056	−	0.310135i	−0.762501	−	0.646987i	$-0.776029\pi$
$863$	5.26011	−	9.11079i	0.179056	−	0.310135i	0.941558	+	0.336852i	$0.109362\pi$
$864$		0			0
$865$	−6.39124	−	11.0700i	−0.217309	−	0.376390i
$866$		0			0
$867$	4.67499			0.158771
$868$		0			0
$869$	0.327696			0.0111163
$870$		0			0
$871$	−0.347296	−	0.601535i	−0.0117677	−	0.0203822i
$872$		0			0
$873$	−34.7097	+	60.1189i	−1.17474	+	2.03472i
$874$		0			0
$875$	21.6386	−	17.5894i	0.731519	−	0.594629i
$876$		0			0
$877$	19.8268	−	34.3411i	0.669504	−	1.15962i	−0.308539	−	0.951212i	$-0.599840\pi$
$877$	19.8268	−	34.3411i	0.669504	−	1.15962i	0.978043	−	0.208403i	$-0.0668267\pi$
$878$		0			0
$879$	5.80928	+	10.0620i	0.195942	+	0.339382i
$880$		0			0
$881$	25.0077			0.842532			0.421266	−	0.906937i	$-0.361586\pi$
$881$	25.0077			0.842532			0.421266	+	0.906937i	$0.361586\pi$
$882$		0			0
$883$	−50.9341			−1.71407			−0.857034	−	0.515260i	$-0.827695\pi$
$883$	−50.9341			−1.71407			−0.857034	+	0.515260i	$0.827695\pi$
$884$		0			0
$885$	−0.690722	−	1.19637i	−0.0232184	−	0.0402154i
$886$		0			0
$887$	16.0180	−	27.7440i	0.537832	−	0.931552i	−0.461188	−	0.887302i	$-0.652577\pi$
$887$	16.0180	−	27.7440i	0.537832	−	0.931552i	0.999020	−	0.0442502i	$-0.0140899\pi$
$888$		0			0
$889$	−0.914878	+	0.743676i	−0.0306840	+	0.0249421i
$890$		0			0
$891$	1.56031	−	2.70253i	0.0522723	−	0.0905382i
$892$		0			0
$893$	2.96956	+	5.14343i	0.0993725	+	0.172118i
$894$		0			0
$895$	23.6878			0.791795
$896$		0			0
$897$	−4.44562			−0.148435
$898$		0			0
$899$	−10.8366	−	18.7696i	−0.361421	−	0.626000i
$900$		0			0
$901$	12.8508	−	22.2582i	0.428121	−	0.741527i
$902$		0			0
$903$	8.43242	+	3.21891i	0.280613	+	0.107119i
$904$		0			0
$905$	−23.3314	+	40.4112i	−0.775562	+	1.34331i
$906$		0			0
$907$	−8.23648	−	14.2660i	−0.273488	−	0.473695i	0.696265	−	0.717785i	$-0.254844\pi$
$907$	−8.23648	−	14.2660i	−0.273488	−	0.473695i	−0.969753	+	0.244090i	$0.921511\pi$
$908$		0			0
$909$	−31.2249			−1.03567
$910$		0			0
$911$	45.3979			1.50410			0.752049	−	0.659107i	$-0.229066\pi$
$911$	45.3979			1.50410			0.752049	+	0.659107i	$0.229066\pi$
$912$		0			0
$913$	−1.67752	−	2.90555i	−0.0555178	−	0.0961596i
$914$		0			0
$915$	49.2772	−	85.3507i	1.62906	−	2.82161i
$916$		0			0
$917$	−5.06118	−	31.5747i	−0.167135	−	1.04269i
$918$		0			0
$919$	−6.16044	+	10.6702i	−0.203214	+	0.351978i	−0.949562	−	0.313578i	$-0.898472\pi$
$919$	−6.16044	+	10.6702i	−0.203214	+	0.351978i	0.746348	+	0.665556i	$0.231805\pi$
$920$		0			0
$921$	−4.21688	−	7.30385i	−0.138951	−	0.240670i
$922$		0			0
$923$	−1.84161			−0.0606175
$924$		0			0
$925$	−3.47834			−0.114367
$926$		0			0
$927$	2.43717	+	4.22130i	0.0800470	+	0.138646i
$928$		0			0
$929$	−2.96657	+	5.13824i	−0.0973299	+	0.168580i	−0.910579	−	0.413336i	$-0.864364\pi$
$929$	−2.96657	+	5.13824i	−0.0973299	+	0.168580i	0.813249	+	0.581916i	$0.197697\pi$
$930$		0			0
$931$	−4.03626	−	3.60716i	−0.132283	−	0.118220i
$932$		0			0
$933$	−22.4932	+	38.9594i	−0.736394	+	1.27547i
$934$		0			0
$935$	−4.60220	−	7.97124i	−0.150508	−	0.260687i
$936$		0			0
$937$	−45.0242			−1.47088			−0.735438	−	0.677593i	$-0.763023\pi$
$937$	−45.0242			−1.47088			−0.735438	+	0.677593i	$0.763023\pi$
$938$		0			0
$939$	63.2772			2.06497
$940$		0			0
$941$	3.03121	+	5.25021i	0.0988147	+	0.171152i	0.911194	−	0.411977i	$-0.135162\pi$
$941$	3.03121	+	5.25021i	0.0988147	+	0.171152i	−0.812380	+	0.583129i	$0.801828\pi$
$942$		0			0
$943$	1.77972	−	3.08256i	0.0579555	−	0.100382i
$944$		0			0
$945$	6.48364	+	40.4489i	0.210913	+	1.31580i
$946$		0			0
$947$	−9.47131	+	16.4048i	−0.307776	+	0.533084i	−0.977876	−	0.209187i	$-0.932918\pi$
$947$	−9.47131	+	16.4048i	−0.307776	+	0.533084i	0.670099	+	0.742272i	$0.266252\pi$
$948$		0			0
$949$	0.0111444	+	0.0193026i	0.000361761	+	0.000626588i
$950$		0			0
$951$	8.67230			0.281219
$952$		0			0
$953$	−12.4970			−0.404818			−0.202409	−	0.979301i	$-0.564877\pi$
$953$	−12.4970			−0.404818			−0.202409	+	0.979301i	$0.564877\pi$
$954$		0			0
$955$	−29.7931	−	51.6032i	−0.964083	−	1.66984i
$956$		0			0
$957$	11.7626	−	20.3735i	0.380232	−	0.658581i
$958$		0			0
$959$	−40.4093	−	15.4255i	−1.30488	−	0.498114i
$960$		0			0
$961$	11.9816	−	20.7527i	0.386503	−	0.669442i
$962$		0			0
$963$	−27.3730	−	47.4115i	−0.882084	−	1.52781i
$964$		0			0
$965$	−18.1480			−0.584203
$966$		0			0
$967$	18.5294			0.595865			0.297933	−	0.954587i	$-0.403703\pi$
$967$	18.5294			0.595865			0.297933	+	0.954587i	$0.403703\pi$
$968$		0			0
$969$	4.36571	+	7.56164i	0.140247	+	0.242915i
$970$		0			0
$971$	20.7369	−	35.9174i	0.665480	−	1.15265i	−0.313674	−	0.949531i	$-0.601560\pi$
$971$	20.7369	−	35.9174i	0.665480	−	1.15265i	0.979155	−	0.203115i	$-0.0651066\pi$
$972$		0			0
$973$	−42.5587	+	34.5947i	−1.36437	+	1.10905i
$974$		0			0
$975$	−0.135630	+	0.234917i	−0.00434362	+	0.00752337i
$976$		0			0
$977$	11.1160	+	19.2535i	0.355633	+	0.615975i	0.987226	−	0.159325i	$-0.0509319\pi$
$977$	11.1160	+	19.2535i	0.355633	+	0.615975i	−0.631593	+	0.775300i	$0.717599\pi$
$978$		0			0
$979$	4.65270			0.148701
$980$		0			0
$981$	2.51661			0.0803491
$982$		0			0
$983$	17.7062	+	30.6680i	0.564740	+	0.978159i	0.997074	+	0.0764450i	$0.0243570\pi$
$983$	17.7062	+	30.6680i	0.564740	+	0.978159i	−0.432334	+	0.901714i	$0.642310\pi$
$984$		0			0
$985$	6.30793	−	10.9257i	0.200987	−	0.348121i
$986$		0			0
$987$	45.4004	−	36.9046i	1.44511	−	1.17469i
$988$		0			0
$989$	−4.94949	+	8.57277i	−0.157385	+	0.272598i
$990$		0			0
$991$	22.7863	+	39.4670i	0.723830	+	1.25371i	0.959454	+	0.281866i	$0.0909533\pi$
$991$	22.7863	+	39.4670i	0.723830	+	1.25371i	−0.235624	+	0.971844i	$0.575713\pi$
$992$		0			0
$993$	79.0934			2.50995
$994$		0			0
$995$	−20.6117			−0.653436
$996$		0			0
$997$	−11.4183	−	19.7771i	−0.361622	−	0.626348i	0.626606	−	0.779336i	$-0.284444\pi$
$997$	−11.4183	−	19.7771i	−0.361622	−	0.626348i	−0.988228	+	0.152988i	$0.951110\pi$
$998$		0			0
$999$	−22.5030	+	38.9763i	−0.711963	+	1.23316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.m.177.3		6
4.3	odd	2		77.2.e.a.23.3	✓	6
7.2	even	3		8624.2.a.ch.1.1		3
7.4	even	3	inner	1232.2.q.m.529.3		6
7.5	odd	6		8624.2.a.co.1.3		3
12.11	even	2		693.2.i.h.100.1		6
28.3	even	6		539.2.e.m.67.3		6
28.11	odd	6		77.2.e.a.67.3	yes	6
28.19	even	6		539.2.a.g.1.1		3
28.23	odd	6		539.2.a.j.1.1		3
28.27	even	2		539.2.e.m.177.3		6
44.3	odd	10		847.2.n.g.9.1		24
44.7	even	10		847.2.n.f.632.1		24
44.15	odd	10		847.2.n.g.632.3		24
44.19	even	10		847.2.n.f.9.3		24
44.27	odd	10		847.2.n.g.366.3		24
44.31	odd	10		847.2.n.g.807.1		24
44.35	even	10		847.2.n.f.807.3		24
44.39	even	10		847.2.n.f.366.1		24
44.43	even	2		847.2.e.c.485.1		6
84.11	even	6		693.2.i.h.298.1		6
84.23	even	6		4851.2.a.bj.1.3		3
84.47	odd	6		4851.2.a.bk.1.3		3
308.39	even	30		847.2.n.f.487.3		24
308.95	even	30		847.2.n.f.753.3		24
308.123	even	30		847.2.n.f.81.1		24
308.131	odd	6		5929.2.a.u.1.3		3
308.151	even	30		847.2.n.f.130.1		24
308.179	odd	30		847.2.n.g.130.3		24
308.207	odd	30		847.2.n.g.81.3		24
308.219	even	6		5929.2.a.x.1.3		3
308.235	odd	30		847.2.n.g.753.1		24
308.263	even	6		847.2.e.c.606.1		6
308.291	odd	30		847.2.n.g.487.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.3	✓	6	4.3	odd	2
77.2.e.a.67.3	yes	6	28.11	odd	6
539.2.a.g.1.1		3	28.19	even	6
539.2.a.j.1.1		3	28.23	odd	6
539.2.e.m.67.3		6	28.3	even	6
539.2.e.m.177.3		6	28.27	even	2
693.2.i.h.100.1		6	12.11	even	2
693.2.i.h.298.1		6	84.11	even	6
847.2.e.c.485.1		6	44.43	even	2
847.2.e.c.606.1		6	308.263	even	6
847.2.n.f.9.3		24	44.19	even	10
847.2.n.f.81.1		24	308.123	even	30
847.2.n.f.130.1		24	308.151	even	30
847.2.n.f.366.1		24	44.39	even	10
847.2.n.f.487.3		24	308.39	even	30
847.2.n.f.632.1		24	44.7	even	10
847.2.n.f.753.3		24	308.95	even	30
847.2.n.f.807.3		24	44.35	even	10
847.2.n.g.9.1		24	44.3	odd	10
847.2.n.g.81.3		24	308.207	odd	30
847.2.n.g.130.3		24	308.179	odd	30
847.2.n.g.366.3		24	44.27	odd	10
847.2.n.g.487.1		24	308.291	odd	30
847.2.n.g.632.3		24	44.15	odd	10
847.2.n.g.753.1		24	308.235	odd	30
847.2.n.g.807.1		24	44.31	odd	10
1232.2.q.m.177.3		6	1.1	even	1	trivial
1232.2.q.m.529.3		6	7.4	even	3	inner
4851.2.a.bj.1.3		3	84.23	even	6
4851.2.a.bk.1.3		3	84.47	odd	6
5929.2.a.u.1.3		3	308.131	odd	6
5929.2.a.x.1.3		3	308.219	even	6
8624.2.a.ch.1.1		3	7.2	even	3
8624.2.a.co.1.3		3	7.5	odd	6

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.43969 + 2.49362i) q^{3} +(-1.17365 + 2.03282i) q^{5} +(-2.05303 + 1.66885i) q^{7} +(-2.64543 + 4.58202i) q^{9} +(0.500000 + 0.866025i) q^{11} -0.184793 q^{13} -6.75877 q^{15} +(1.96064 + 3.39592i) q^{17} +(0.386659 - 0.669713i) q^{19} +(-7.11721 - 2.71686i) q^{21} +(4.17752 - 7.23567i) q^{23} +(-0.254900 - 0.441500i) q^{25} -6.59627 q^{27} -8.17024 q^{29} +(1.32635 + 2.29731i) q^{31} +(-1.43969 + 2.49362i) q^{33} +(-0.982926 - 6.13208i) q^{35} +(3.41147 - 5.90885i) q^{37} +(-0.266044 - 0.460802i) q^{39} +0.426022 q^{41} -1.18479 q^{43} +(-6.20961 - 10.7554i) q^{45} +(-3.84002 + 6.65111i) q^{47} +(1.42989 - 6.85240i) q^{49} +(-5.64543 + 9.77817i) q^{51} +(-3.27719 - 5.67626i) q^{53} -2.34730 q^{55} +2.22668 q^{57} +(0.102196 + 0.177009i) q^{59} +(-7.29086 + 12.6281i) q^{61} +(-2.21554 - 13.8219i) q^{63} +(0.216881 - 0.375650i) q^{65} +(1.87939 + 3.25519i) q^{67} +24.0574 q^{69} +9.96585 q^{71} +(-0.0603074 - 0.104455i) q^{73} +(0.733956 - 1.27125i) q^{75} +(-2.47178 - 0.943555i) q^{77} +(0.163848 - 0.283793i) q^{79} +(-1.56031 - 2.70253i) q^{81} -3.35504 q^{83} -9.20439 q^{85} +(-11.7626 - 20.3735i) q^{87} +(2.32635 - 4.02936i) q^{89} +(0.379385 - 0.308391i) q^{91} +(-3.81908 + 6.61484i) q^{93} +(0.907604 + 1.57202i) q^{95} +13.1206 q^{97} -5.29086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 6 q^{5} + 3 q^{11} + 6 q^{13} - 18 q^{15} + 3 q^{17} + 9 q^{19} - 12 q^{21} - 3 q^{25} - 12 q^{27} - 6 q^{29} + 9 q^{31} - 3 q^{33} + 15 q^{35} + 3 q^{39} + 18 q^{41} - 3 q^{45} - 3 q^{47}+ \cdots + 90 q^{97}+O(q^{100}) \) 6 * q + 3 * q^3 - 6 * q^5 + 3 * q^11 + 6 * q^13 - 18 * q^15 + 3 * q^17 + 9 * q^19 - 12 * q^21 - 3 * q^25 - 12 * q^27 - 6 * q^29 + 9 * q^31 - 3 * q^33 + 15 * q^35 + 3 * q^39 + 18 * q^41 - 3 * q^45 - 3 * q^47 - 18 * q^51 - 9 * q^53 - 12 * q^55 - 12 * q^61 - 6 * q^63 - 15 * q^65 + 42 * q^69 + 18 * q^71 - 6 * q^73 + 9 * q^75 - 3 * q^79 - 15 * q^81 + 30 * q^83 - 54 * q^85 - 24 * q^87 + 15 * q^89 - 9 * q^91 - 6 * q^93 + 9 * q^95 + 90 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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