LMFDB - Embedded newform 152.2.q.c.73.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(9,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.q (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 34 x^{15} + 204 x^{14} - 267 x^{13} + 1304 x^{12} - 972 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 21x^16 - 34x^15 + 204x^14 - 267x^13 + 1304x^12 - 972x^11 + 4890x^10 - 2547x^9 + 12945x^8 - 2403x^7 + 14457x^6 - 6729x^5 + 8769x^4 - 686x^3 + 132x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.3
Root			$-0.976256 + 1.69092i$ of defining polynomial
Character	$\chi$	$=$	152.73
Dual form			152.2.q.c.25.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.83476 - 0.667798i) q^{3} +(0.302047 - 1.71299i) q^{5} +(-0.962609 - 1.66729i) q^{7} +(0.622259 - 0.522138i) q^{9} +(-2.27748 + 3.94470i) q^{11} +(2.57934 + 0.938803i) q^{13} +(-0.589750 - 3.34464i) q^{15} +(3.84088 + 3.22288i) q^{17} +(-4.18751 - 1.21026i) q^{19} +(-2.87957 - 2.41625i) q^{21} +(0.198055 + 1.12322i) q^{23} +(1.85536 + 0.675294i) q^{25} +(-2.13575 + 3.69923i) q^{27} +(3.83721 - 3.21980i) q^{29} +(-0.999936 - 1.73194i) q^{31} +(-1.54436 + 8.75848i) q^{33} +(-3.14680 + 1.14534i) q^{35} -7.06608 q^{37} +5.35941 q^{39} +(-10.3600 + 3.77075i) q^{41} +(1.05998 - 6.01147i) q^{43} +(-0.706466 - 1.22363i) q^{45} +(-6.72021 + 5.63892i) q^{47} +(1.64677 - 2.85228i) q^{49} +(9.19933 + 3.34828i) q^{51} +(0.00933315 + 0.0529309i) q^{53} +(6.06934 + 5.09278i) q^{55} +(-8.49130 + 0.575879i) q^{57} +(2.83451 + 2.37844i) q^{59} +(-2.60306 - 14.7627i) q^{61} +(-1.46955 - 0.534871i) q^{63} +(2.38724 - 4.13483i) q^{65} +(9.72449 - 8.15982i) q^{67} +(1.11347 + 1.92859i) q^{69} +(-0.359347 + 2.03796i) q^{71} +(0.670002 - 0.243861i) q^{73} +3.85509 q^{75} +8.76928 q^{77} +(10.5802 - 3.85086i) q^{79} +(-1.87142 + 10.6133i) q^{81} +(-4.99262 - 8.64748i) q^{83} +(6.68089 - 5.60593i) q^{85} +(4.89018 - 8.47005i) q^{87} +(15.2229 + 5.54068i) q^{89} +(-0.917642 - 5.20421i) q^{91} +(-2.99123 - 2.50994i) q^{93} +(-3.33799 + 6.80762i) q^{95} +(0.285278 + 0.239377i) q^{97} +(0.642497 + 3.64378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41}+ \cdots + 15 q^{99}+O(q^{100}) $ 18 * q - 9 * q^7 - 6 * q^9 - 3 * q^11 + 3 * q^13 + 33 * q^15 + 9 * q^17 - 24 * q^19 - 15 * q^21 + 6 * q^23 + 6 * q^25 - 12 * q^27 - 3 * q^29 - 6 * q^31 - 45 * q^33 - 15 * q^35 + 48 * q^37 + 12 * q^39 - 18 * q^41 - 39 * q^43 - 42 * q^45 - 27 * q^47 - 18 * q^49 + 48 * q^51 + 39 * q^53 - 27 * q^55 - 6 * q^57 + 9 * q^59 - 24 * q^61 + 3 * q^63 + 27 * q^65 + 39 * q^67 - 3 * q^69 + 12 * q^73 + 90 * q^75 + 60 * q^77 + 63 * q^79 - 6 * q^81 - 27 * q^83 - 30 * q^85 + 18 * q^87 + 66 * q^89 + 108 * q^91 + 60 * q^93 - 75 * q^95 - 81 * q^97 + 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.83476	−	0.667798i	1.05930	−	0.385554i	0.247135	−	0.968981i	$-0.420511\pi$
$3$	1.83476	−	0.667798i	1.05930	−	0.385554i	0.812165	+	0.583428i	$0.198289\pi$
$4$		0			0
$5$	0.302047	−	1.71299i	0.135079	−	0.766073i	−0.839725	−	0.543012i	$-0.817284\pi$
$5$	0.302047	−	1.71299i	0.135079	−	0.766073i	0.974804	−	0.223061i	$-0.0716050\pi$
$6$		0			0
$7$	−0.962609	−	1.66729i	−0.363832	−	0.630176i	0.624756	−	0.780820i	$-0.285198\pi$
$7$	−0.962609	−	1.66729i	−0.363832	−	0.630176i	−0.988588	+	0.150644i	$0.951865\pi$
$8$		0			0
$9$	0.622259	−	0.522138i	0.207420	−	0.174046i
$10$		0			0
$11$	−2.27748	+	3.94470i	−0.686685	+	1.18937i	0.286220	+	0.958164i	$0.407601\pi$
$11$	−2.27748	+	3.94470i	−0.686685	+	1.18937i	−0.972904	+	0.231209i	$0.925732\pi$
$12$		0			0
$13$	2.57934	+	0.938803i	0.715381	+	0.260377i	0.673963	−	0.738765i	$-0.264591\pi$
$13$	2.57934	+	0.938803i	0.715381	+	0.260377i	0.0414171	+	0.999142i	$0.486813\pi$
$14$		0			0
$15$	−0.589750	−	3.34464i	−0.152273	−	0.863581i
$16$		0			0
$17$	3.84088	+	3.22288i	0.931550	+	0.781663i	0.976095	−	0.217344i	$-0.0697393\pi$
$17$	3.84088	+	3.22288i	0.931550	+	0.781663i	−0.0445449	+	0.999007i	$0.514184\pi$
$18$		0			0
$19$	−4.18751	−	1.21026i	−0.960682	−	0.277652i
$19$	−4.18751	−	1.21026i	−0.960682	−	0.277652i
$20$		0			0
$21$	−2.87957	−	2.41625i	−0.628374	−	0.527268i
$22$		0			0
$23$	0.198055	+	1.12322i	0.0412972	+	0.234208i	0.998469	−	0.0553120i	$-0.0176154\pi$
$23$	0.198055	+	1.12322i	0.0412972	+	0.234208i	−0.957172	+	0.289520i	$0.906504\pi$
$24$		0			0
$25$	1.85536	+	0.675294i	0.371071	+	0.135059i
$26$		0			0
$27$	−2.13575	+	3.69923i	−0.411026	+	0.711918i
$28$		0			0
$29$	3.83721	−	3.21980i	0.712552	−	0.597902i	−0.212762	−	0.977104i	$-0.568246\pi$
$29$	3.83721	−	3.21980i	0.712552	−	0.597902i	0.925314	+	0.379202i	$0.123801\pi$
$30$		0			0
$31$	−0.999936	−	1.73194i	−0.179594	−	0.311066i	0.762148	−	0.647403i	$-0.224145\pi$
$31$	−0.999936	−	1.73194i	−0.179594	−	0.311066i	−0.941741	+	0.336338i	$0.890812\pi$
$32$		0			0
$33$	−1.54436	+	8.75848i	−0.268838	+	1.52466i
$34$		0			0
$35$	−3.14680	+	1.14534i	−0.531907	+	0.193598i
$36$		0			0
$37$	−7.06608			−1.16166			−0.580828	−	0.814026i	$-0.697271\pi$
$37$	−7.06608			−1.16166			−0.580828	+	0.814026i	$0.697271\pi$
$38$		0			0
$39$	5.35941			0.858192
$40$		0			0
$41$	−10.3600	+	3.77075i	−1.61797	+	0.588892i	−0.982993	−	0.183642i	$-0.941211\pi$
$41$	−10.3600	+	3.77075i	−1.61797	+	0.588892i	−0.634974	+	0.772534i	$0.718989\pi$
$42$		0			0
$43$	1.05998	−	6.01147i	0.161646	−	0.916741i	−0.790809	−	0.612063i	$-0.790340\pi$
$43$	1.05998	−	6.01147i	0.161646	−	0.916741i	0.952455	−	0.304678i	$-0.0985489\pi$
$44$		0			0
$45$	−0.706466	−	1.22363i	−0.105314	−	0.182409i
$46$		0			0
$47$	−6.72021	+	5.63892i	−0.980243	+	0.822522i	−0.984126	−	0.177471i	$-0.943208\pi$
$47$	−6.72021	+	5.63892i	−0.980243	+	0.822522i	0.00388290	+	0.999992i	$0.498764\pi$
$48$		0			0
$49$	1.64677	−	2.85228i	0.235252	−	0.407469i
$50$		0			0
$51$	9.19933	+	3.34828i	1.28816	+	0.468853i
$52$		0			0
$53$	0.00933315	+	0.0529309i	0.00128201	+	0.00727062i	0.985442	−	0.170012i	$-0.0543805\pi$
$53$	0.00933315	+	0.0529309i	0.00128201	+	0.00727062i	−0.984160	+	0.177282i	$0.943269\pi$
$54$		0			0
$55$	6.06934	+	5.09278i	0.818389	+	0.686710i
$56$		0			0
$57$	−8.49130	+	0.575879i	−1.12470	+	0.0762770i
$58$		0			0
$59$	2.83451	+	2.37844i	0.369022	+	0.309646i	0.808375	−	0.588669i	$-0.200348\pi$
$59$	2.83451	+	2.37844i	0.369022	+	0.309646i	−0.439353	+	0.898315i	$0.644792\pi$
$60$		0			0
$61$	−2.60306	−	14.7627i	−0.333288	−	1.89017i	−0.443518	−	0.896266i	$-0.646270\pi$
$61$	−2.60306	−	14.7627i	−0.333288	−	1.89017i	0.110229	−	0.993906i	$-0.464842\pi$
$62$		0			0
$63$	−1.46955	−	0.534871i	−0.185145	−	0.0673874i
$64$		0			0
$65$	2.38724	−	4.13483i	0.296101	−	0.512862i
$66$		0			0
$67$	9.72449	−	8.15982i	1.18804	−	0.996880i	0.188144	−	0.982141i	$-0.439753\pi$
$67$	9.72449	−	8.15982i	1.18804	−	0.996880i	0.999891	−	0.0147389i	$-0.00469171\pi$
$68$		0			0
$69$	1.11347	+	1.92859i	0.134046	+	0.232174i
$70$		0			0
$71$	−0.359347	+	2.03796i	−0.0426466	+	0.241861i	−0.998678	−	0.0514034i	$-0.983631\pi$
$71$	−0.359347	+	2.03796i	−0.0426466	+	0.241861i	0.956031	+	0.293265i	$0.0947417\pi$
$72$		0			0
$73$	0.670002	−	0.243861i	0.0784178	−	0.0285418i	−0.302513	−	0.953145i	$-0.597826\pi$
$73$	0.670002	−	0.243861i	0.0784178	−	0.0285418i	0.380931	+	0.924603i	$0.375603\pi$
$74$		0			0
$75$	3.85509			0.445148
$76$		0			0
$77$	8.76928			0.999352
$78$		0			0
$79$	10.5802	−	3.85086i	1.19036	−	0.433256i	0.330511	−	0.943802i	$-0.392779\pi$
$79$	10.5802	−	3.85086i	1.19036	−	0.433256i	0.859850	+	0.510546i	$0.170557\pi$
$80$		0			0
$81$	−1.87142	+	10.6133i	−0.207935	+	1.17926i
$82$		0			0
$83$	−4.99262	−	8.64748i	−0.548012	−	0.949184i	−0.998411	−	0.0563567i	$-0.982052\pi$
$83$	−4.99262	−	8.64748i	−0.548012	−	0.949184i	0.450399	−	0.892827i	$-0.351282\pi$
$84$		0			0
$85$	6.68089	−	5.60593i	0.724645	−	0.608049i
$86$		0			0
$87$	4.89018	−	8.47005i	0.524283	−	0.908084i
$88$		0			0
$89$	15.2229	+	5.54068i	1.61362	+	0.587311i	0.982152	−	0.188088i	$-0.0602289\pi$
$89$	15.2229	+	5.54068i	1.61362	+	0.587311i	0.631472	+	0.775399i	$0.282451\pi$
$90$		0			0
$91$	−0.917642	−	5.20421i	−0.0961950	−	0.545549i
$92$		0			0
$93$	−2.99123	−	2.50994i	−0.310176	−	0.260269i
$94$		0			0
$95$	−3.33799	+	6.80762i	−0.342470	+	0.698447i
$96$		0			0
$97$	0.285278	+	0.239377i	0.0289656	+	0.0243050i	0.657156	−	0.753755i	$-0.271759\pi$
$97$	0.285278	+	0.239377i	0.0289656	+	0.0243050i	−0.628190	+	0.778060i	$0.716204\pi$
$98$		0			0
$99$	0.642497	+	3.64378i	0.0645734	+	0.366214i
$100$		0			0
$101$	−17.4750	−	6.36040i	−1.73883	−	0.632883i	−0.739637	−	0.673006i	$-0.765003\pi$
$101$	−17.4750	−	6.36040i	−1.73883	−	0.632883i	−0.999195	+	0.0401224i	$0.987225\pi$
$102$		0			0
$103$	−4.48973	+	7.77645i	−0.442387	+	0.766236i	−0.997866	−	0.0652941i	$-0.979201\pi$
$103$	−4.48973	+	7.77645i	−0.442387	+	0.766236i	0.555479	+	0.831530i	$0.312535\pi$
$104$		0			0
$105$	−5.00877	+	4.20286i	−0.488806	+	0.410157i
$106$		0			0
$107$	−3.74332	−	6.48362i	−0.361881	−	0.626796i	0.626390	−	0.779510i	$-0.284532\pi$
$107$	−3.74332	−	6.48362i	−0.361881	−	0.626796i	−0.988270	+	0.152714i	$0.951199\pi$
$108$		0			0
$109$	−2.91266	+	16.5185i	−0.278982	+	1.58219i	0.447039	+	0.894515i	$0.352479\pi$
$109$	−2.91266	+	16.5185i	−0.278982	+	1.58219i	−0.726021	+	0.687672i	$0.758633\pi$
$110$		0			0
$111$	−12.9646	+	4.71871i	−1.23054	+	0.447881i
$112$		0			0
$113$	10.6659			1.00336			0.501682	−	0.865052i	$-0.332715\pi$
$113$	10.6659			1.00336			0.501682	+	0.865052i	$0.332715\pi$
$114$		0			0
$115$	1.98389			0.184999
$116$		0			0
$117$	2.09520	−	0.762592i	0.193702	−	0.0705016i
$118$		0			0
$119$	1.67620	−	9.50623i	0.153657	−	0.871435i
$120$		0			0
$121$	−4.87379	−	8.44164i	−0.443071	−	0.767422i
$122$		0			0
$123$	−16.4901	+	13.8368i	−1.48686	+	1.24763i
$124$		0			0
$125$	6.06572	−	10.5061i	0.542534	−	0.939697i
$126$		0			0
$127$	−10.3628	−	3.77175i	−0.919550	−	0.334689i	−0.161491	−	0.986874i	$-0.551630\pi$
$127$	−10.3628	−	3.77175i	−0.919550	−	0.334689i	−0.758059	+	0.652185i	$0.773852\pi$
$128$		0			0
$129$	−2.06963	−	11.7375i	−0.182221	−	1.03343i
$130$		0			0
$131$	10.7437	+	9.01505i	0.938683	+	0.787648i	0.977356	−	0.211604i	$-0.0678686\pi$
$131$	10.7437	+	9.01505i	0.938683	+	0.787648i	−0.0386728	+	0.999252i	$0.512313\pi$
$132$		0			0
$133$	2.01309	+	8.14680i	0.174557	+	0.706417i
$134$		0			0
$135$	5.69166	+	4.77587i	0.489860	+	0.411041i
$136$		0			0
$137$	1.53142	+	8.68510i	0.130838	+	0.742019i	0.977668	+	0.210155i	$0.0673969\pi$
$137$	1.53142	+	8.68510i	0.130838	+	0.742019i	−0.846830	+	0.531863i	$0.821492\pi$
$138$		0			0
$139$	−5.75603	−	2.09502i	−0.488220	−	0.177698i	0.0861681	−	0.996281i	$-0.472538\pi$
$139$	−5.75603	−	2.09502i	−0.488220	−	0.177698i	−0.574388	+	0.818583i	$0.694760\pi$
$140$		0			0
$141$	−8.56431	+	14.8338i	−0.721245	+	1.24923i
$142$		0			0
$143$	−9.57769	+	8.03663i	−0.800926	+	0.672057i
$144$		0			0
$145$	−4.35647	−	7.54564i	−0.361786	−	0.626631i
$146$		0			0
$147$	1.11667	−	6.33297i	0.0921016	−	0.522334i
$148$		0			0
$149$	2.28488	−	0.831630i	0.187185	−	0.0681298i	−0.246727	−	0.969085i	$-0.579355\pi$
$149$	2.28488	−	0.831630i	0.187185	−	0.0681298i	0.433912	+	0.900955i	$0.357133\pi$
$150$		0			0
$151$	11.4850			0.934636			0.467318	−	0.884089i	$-0.345220\pi$
$151$	11.4850			0.934636			0.467318	+	0.884089i	$0.345220\pi$
$152$		0			0
$153$	4.07281			0.329267
$154$		0			0
$155$	−3.26882	+	1.18975i	−0.262558	+	0.0955634i
$156$		0			0
$157$	−0.462101	+	2.62071i	−0.0368797	+	0.209155i	−0.997679	−	0.0680888i	$-0.978310\pi$
$157$	−0.462101	+	2.62071i	−0.0368797	+	0.209155i	0.960800	+	0.277244i	$0.0894210\pi$
$158$		0			0
$159$	0.0524713	+	0.0908830i	0.00416124	+	0.00720749i
$160$		0			0
$161$	1.68209	−	1.41144i	0.132567	−	0.111237i
$162$		0			0
$163$	2.05611	−	3.56129i	0.161047	−	0.278942i	−0.774197	−	0.632944i	$-0.781846\pi$
$163$	2.05611	−	3.56129i	0.161047	−	0.278942i	0.935245	+	0.354002i	$0.115180\pi$
$164$		0			0
$165$	14.5367	+	5.29094i	1.13168	+	0.411899i
$166$		0			0
$167$	2.59827	+	14.7355i	0.201060	+	1.14027i	0.903521	+	0.428545i	$0.140973\pi$
$167$	2.59827	+	14.7355i	0.201060	+	1.14027i	−0.702461	+	0.711722i	$0.747915\pi$
$168$		0			0
$169$	−4.18693	−	3.51325i	−0.322071	−	0.270250i
$170$		0			0
$171$	−3.23764	+	1.43336i	−0.247589	+	0.109612i
$172$		0			0
$173$	−4.88231	−	4.09674i	−0.371195	−	0.311470i	0.438039	−	0.898956i	$-0.355673\pi$
$173$	−4.88231	−	4.09674i	−0.371195	−	0.311470i	−0.809234	+	0.587486i	$0.800118\pi$
$174$		0			0
$175$	−0.660072	−	3.74346i	−0.0498968	−	0.282979i
$176$		0			0
$177$	6.78897	+	2.47098i	0.510290	+	0.185730i
$178$		0			0
$179$	−1.59062	+	2.75504i	−0.118889	+	0.205922i	−0.919328	−	0.393493i	$-0.871267\pi$
$179$	−1.59062	+	2.75504i	−0.118889	+	0.205922i	0.800439	+	0.599415i	$0.204600\pi$
$180$		0			0
$181$	−3.48401	+	2.92343i	−0.258964	+	0.217297i	−0.763021	−	0.646374i	$-0.776285\pi$
$181$	−3.48401	+	2.92343i	−0.258964	+	0.217297i	0.504057	+	0.863671i	$0.331840\pi$
$182$		0			0
$183$	−14.6345	−	25.3477i	−1.08181	−	1.87376i
$184$		0			0
$185$	−2.13428	+	12.1041i	−0.156916	+	0.889913i
$186$		0			0
$187$	−21.4608	+	7.81110i	−1.56937	+	0.571204i
$188$		0			0
$189$	8.22358			0.598178
$190$		0			0
$191$	−0.968712			−0.0700935			−0.0350468	−	0.999386i	$-0.511158\pi$
$191$	−0.968712			−0.0700935			−0.0350468	+	0.999386i	$0.511158\pi$
$192$		0			0
$193$	−14.2895	+	5.20094i	−1.02858	+	0.374372i	−0.800540	−	0.599280i	$-0.795454\pi$
$193$	−14.2895	+	5.20094i	−1.02858	+	0.374372i	−0.228039	+	0.973652i	$0.573231\pi$
$194$		0			0
$195$	1.61879	−	9.18062i	0.115924	−	0.657438i
$196$		0			0
$197$	−8.22940	−	14.2537i	−0.586320	−	1.01554i	−0.994709	−	0.102729i	$-0.967243\pi$
$197$	−8.22940	−	14.2537i	−0.586320	−	1.01554i	0.408389	−	0.912808i	$-0.366091\pi$
$198$		0			0
$199$	16.8080	−	14.1036i	1.19149	−	0.999775i	0.191653	−	0.981463i	$-0.438615\pi$
$199$	16.8080	−	14.1036i	1.19149	−	0.999775i	0.999832	−	0.0183119i	$-0.00582920\pi$
$200$		0			0
$201$	12.3930	−	21.4653i	0.874135	−	1.51405i
$202$		0			0
$203$	−9.06207	−	3.29832i	−0.636033	−	0.231497i
$204$		0			0
$205$	3.33004	+	18.8856i	0.232580	+	1.31903i
$206$		0			0
$207$	0.709718	+	0.595524i	0.0493288	+	0.0413918i
$208$		0			0
$209$	14.3111	−	13.7622i	0.989917	−	0.951949i
$210$		0			0
$211$	14.0895	+	11.8225i	0.969962	+	0.813895i	0.982545	−	0.186026i	$-0.0595610\pi$
$211$	14.0895	+	11.8225i	0.969962	+	0.813895i	−0.0125831	+	0.999921i	$0.504005\pi$
$212$		0			0
$213$	0.701629	+	3.97914i	0.0480748	+	0.272646i
$214$		0			0
$215$	−9.97744	−	3.63149i	−0.680456	−	0.247666i
$216$		0			0
$217$	−1.92509	+	3.33436i	−0.130684	+	0.226351i
$218$		0			0
$219$	1.06644	−	0.894853i	0.0720636	−	0.0604685i
$220$		0			0
$221$	6.88129	+	11.9187i	0.462886	+	0.801741i
$222$		0			0
$223$	−3.38895	+	19.2197i	−0.226941	+	1.28705i	0.631998	+	0.774970i	$0.282235\pi$
$223$	−3.38895	+	19.2197i	−0.226941	+	1.28705i	−0.858939	+	0.512077i	$0.828876\pi$
$224$		0			0
$225$	1.50711	−	0.548543i	0.100474	−	0.0365695i
$226$		0			0
$227$	7.30867			0.485094			0.242547	−	0.970140i	$-0.422017\pi$
$227$	7.30867			0.485094			0.242547	+	0.970140i	$0.422017\pi$
$228$		0			0
$229$	21.1319			1.39644			0.698218	−	0.715885i	$-0.253977\pi$
$229$	21.1319			1.39644			0.698218	+	0.715885i	$0.253977\pi$
$230$		0			0
$231$	16.0895	−	5.85611i	1.05861	−	0.385304i
$232$		0			0
$233$	0.826691	−	4.68840i	0.0541583	−	0.307147i	−0.945681	−	0.325097i	$-0.894603\pi$
$233$	0.826691	−	4.68840i	0.0541583	−	0.307147i	0.999839	+	0.0179503i	$0.00571406\pi$
$234$		0			0
$235$	7.62961	+	13.2149i	0.497701	+	0.862044i
$236$		0			0
$237$	16.8405	−	14.1308i	1.09391	−	0.917896i
$238$		0			0
$239$	10.4370	−	18.0774i	0.675114	−	1.16933i	−0.301322	−	0.953522i	$-0.597428\pi$
$239$	10.4370	−	18.0774i	0.675114	−	1.16933i	0.976436	−	0.215809i	$-0.0692388\pi$
$240$		0			0
$241$	−6.64094	−	2.41710i	−0.427781	−	0.155699i	0.119152	−	0.992876i	$-0.461982\pi$
$241$	−6.64094	−	2.41710i	−0.427781	−	0.155699i	−0.546933	+	0.837177i	$0.684205\pi$
$242$		0			0
$243$	1.42875	+	8.10284i	0.0916543	+	0.519797i
$244$		0			0
$245$	−4.38854	−	3.68242i	−0.280373	−	0.235261i
$246$		0			0
$247$	−9.66483	−	7.05292i	−0.614959	−	0.448767i
$248$		0			0
$249$	−14.9350	−	12.5320i	−0.946470	−	0.794182i
$250$		0			0
$251$	−2.11124	−	11.9734i	−0.133260	−	0.755756i	−0.976055	−	0.217522i	$-0.930203\pi$
$251$	−2.11124	−	11.9734i	−0.133260	−	0.755756i	0.842795	−	0.538234i	$-0.180908\pi$
$252$		0			0
$253$	−4.88185	−	1.77685i	−0.306919	−	0.111709i
$254$		0			0
$255$	8.51421	−	14.7470i	0.533180	−	0.923495i
$256$		0			0
$257$	−0.252279	+	0.211687i	−0.0157367	+	0.0132047i	−0.650622	−	0.759402i	$-0.725492\pi$
$257$	−0.252279	+	0.211687i	−0.0157367	+	0.0132047i	0.634885	+	0.772606i	$0.281047\pi$
$258$		0			0
$259$	6.80187	+	11.7812i	0.422648	+	0.732047i
$260$		0			0
$261$	0.706560	−	4.00710i	0.0437350	−	0.248033i
$262$		0			0
$263$	8.33131	−	3.03235i	0.513731	−	0.186983i	−0.0721288	−	0.997395i	$-0.522979\pi$
$263$	8.33131	−	3.03235i	0.513731	−	0.186983i	0.585859	+	0.810413i	$0.300757\pi$
$264$		0			0
$265$	0.0934893			0.00574300
$266$		0			0
$267$	31.6304			1.93575
$268$		0			0
$269$	−10.8291	+	3.94146i	−0.660261	+	0.240315i	−0.650349	−	0.759636i	$-0.725377\pi$
$269$	−10.8291	+	3.94146i	−0.660261	+	0.240315i	−0.00991170	+	0.999951i	$0.503155\pi$
$270$		0			0
$271$	−0.516800	+	2.93092i	−0.0313934	+	0.178041i	−0.996473	−	0.0839170i	$-0.973257\pi$
$271$	−0.516800	+	2.93092i	−0.0313934	+	0.178041i	0.965079	+	0.261958i	$0.0843681\pi$
$272$		0			0
$273$	−5.15901	−	8.93567i	−0.312238	−	0.540812i
$274$		0			0
$275$	−6.88936	+	5.78086i	−0.415444	+	0.348599i
$276$		0			0
$277$	−15.8352	+	27.4274i	−0.951445	+	1.64795i	−0.209144	+	0.977885i	$0.567068\pi$
$277$	−15.8352	+	27.4274i	−0.951445	+	1.64795i	−0.742301	+	0.670066i	$0.766266\pi$
$278$		0			0
$279$	−1.52653	−	0.555612i	−0.0913910	−	0.0332636i
$280$		0			0
$281$	−2.59294	−	14.7053i	−0.154682	−	0.877245i	−0.959076	−	0.283149i	$-0.908621\pi$
$281$	−2.59294	−	14.7053i	−0.154682	−	0.877245i	0.804394	−	0.594096i	$-0.202490\pi$
$282$		0			0
$283$	−14.2583	−	11.9642i	−0.847571	−	0.711196i	0.111683	−	0.993744i	$-0.464376\pi$
$283$	−14.2583	−	11.9642i	−0.847571	−	0.711196i	−0.959253	+	0.282548i	$0.908820\pi$
$284$		0			0
$285$	−1.57829	+	14.7195i	−0.0934899	+	0.871906i
$286$		0			0
$287$	16.2596	+	13.6434i	0.959774	+	0.805346i
$288$		0			0
$289$	1.41338	+	8.01566i	0.0831399	+	0.471510i
$290$		0			0
$291$	0.683273	+	0.248691i	0.0400542	+	0.0145785i
$292$		0			0
$293$	−5.68375	+	9.84455i	−0.332048	+	0.575125i	−0.982913	−	0.184069i	$-0.941073\pi$
$293$	−5.68375	+	9.84455i	−0.332048	+	0.575125i	0.650865	+	0.759193i	$0.274406\pi$
$294$		0			0
$295$	4.93040	−	4.13709i	0.287059	−	0.240871i
$296$		0			0
$297$	−9.72825	−	16.8498i	−0.564490	−	0.977726i
$298$		0			0
$299$	−0.543636	+	3.08311i	−0.0314393	+	0.178301i
$300$		0			0
$301$	−11.0432	+	4.01940i	−0.636520	+	0.231674i
$302$		0			0
$303$	−36.3100			−2.08595
$304$		0			0
$305$	−26.0747			−1.49303
$306$		0			0
$307$	10.0165	−	3.64570i	0.571670	−	0.208071i	−0.0399784	−	0.999201i	$-0.512729\pi$
$307$	10.0165	−	3.64570i	0.571670	−	0.208071i	0.611649	+	0.791130i	$0.290507\pi$
$308$		0			0
$309$	−3.04449	+	17.2662i	−0.173195	+	0.982238i
$310$		0			0
$311$	12.7091	+	22.0128i	0.720668	+	1.24823i	0.960733	+	0.277476i	$0.0894980\pi$
$311$	12.7091	+	22.0128i	0.720668	+	1.24823i	−0.240065	+	0.970757i	$0.577169\pi$
$312$		0			0
$313$	−1.29381	+	1.08564i	−0.0731305	+	0.0613638i	−0.678620	−	0.734489i	$-0.737422\pi$
$313$	−1.29381	+	1.08564i	−0.0731305	+	0.0613638i	0.605490	+	0.795853i	$0.292977\pi$
$314$		0			0
$315$	−1.36010	+	2.35576i	−0.0766330	+	0.132732i
$316$		0			0
$317$	−18.4942	−	6.73135i	−1.03874	−	0.378070i	−0.234337	−	0.972155i	$-0.575292\pi$
$317$	−18.4942	−	6.73135i	−1.03874	−	0.378070i	−0.804402	+	0.594085i	$0.797514\pi$
$318$		0			0
$319$	3.96201	+	22.4697i	0.221830	+	1.25806i
$320$		0			0
$321$	−11.1979	−	9.39611i	−0.625003	−	0.524440i
$322$		0			0
$323$	−12.1832	−	18.1443i	−0.677892	−	1.00958i
$324$		0			0
$325$	4.15163	+	3.48363i	0.230291	+	0.193237i
$326$		0			0
$327$	5.68700	+	32.2526i	0.314492	+	1.78357i
$328$		0			0
$329$	15.8706	+	5.77644i	0.874977	+	0.318466i
$330$		0			0
$331$	−4.50354	+	7.80036i	−0.247537	+	0.428747i	−0.962842	−	0.270066i	$-0.912955\pi$
$331$	−4.50354	+	7.80036i	−0.247537	+	0.428747i	0.715305	+	0.698813i	$0.246288\pi$
$332$		0			0
$333$	−4.39693	+	3.68946i	−0.240950	+	0.202181i
$334$		0			0
$335$	−11.0404	−	19.1226i	−0.603204	−	1.04478i
$336$		0			0
$337$	−1.90637	+	10.8115i	−0.103846	+	0.588942i	0.887828	+	0.460174i	$0.152213\pi$
$337$	−1.90637	+	10.8115i	−0.103846	+	0.588942i	−0.991675	+	0.128767i	$0.958898\pi$
$338$		0			0
$339$	19.5694	−	7.12267i	1.06286	−	0.386850i
$340$		0			0
$341$	9.10931			0.493297
$342$		0			0
$343$	−19.8173			−1.07003
$344$		0			0
$345$	3.63997	−	1.32484i	0.195969	−	0.0713270i
$346$		0			0
$347$	0.486415	−	2.75859i	0.0261121	−	0.148089i	−0.968964	−	0.247201i	$-0.920489\pi$
$347$	0.486415	−	2.75859i	0.0261121	−	0.148089i	0.995076	+	0.0991121i	$0.0316002\pi$
$348$		0			0
$349$	−16.8890	−	29.2526i	−0.904048	−	1.56586i	−0.822190	−	0.569213i	$-0.807248\pi$
$349$	−16.8890	−	29.2526i	−0.904048	−	1.56586i	−0.0818576	−	0.996644i	$-0.526085\pi$
$350$		0			0
$351$	−8.98169	+	7.53653i	−0.479407	+	0.402270i
$352$		0			0
$353$	−1.25317	+	2.17056i	−0.0666996	+	0.115527i	−0.897447	−	0.441123i	$-0.854580\pi$
$353$	−1.25317	+	2.17056i	−0.0666996	+	0.115527i	0.830747	+	0.556650i	$0.187914\pi$
$354$		0			0
$355$	3.38246	+	1.23112i	0.179523	+	0.0653409i
$356$		0			0
$357$	−3.27281	−	18.5610i	−0.173215	−	0.982354i
$358$		0			0
$359$	16.3680	+	13.7343i	0.863868	+	0.724871i	0.962798	−	0.270223i	$-0.0870975\pi$
$359$	16.3680	+	13.7343i	0.863868	+	0.724871i	−0.0989298	+	0.995094i	$0.531542\pi$
$360$		0			0
$361$	16.0705	+	10.1360i	0.845818	+	0.533471i
$362$		0			0
$363$	−14.5795	−	12.2337i	−0.765228	−	0.642102i
$364$		0			0
$365$	−0.215360	−	1.22137i	−0.0112724	−	0.0639292i
$366$		0			0
$367$	−3.36473	−	1.22466i	−0.175638	−	0.0639268i	0.252705	−	0.967543i	$-0.418680\pi$
$367$	−3.36473	−	1.22466i	−0.175638	−	0.0639268i	−0.428342	+	0.903617i	$0.640902\pi$
$368$		0			0
$369$	−4.47779	+	7.75575i	−0.233104	+	0.403748i
$370$		0			0
$371$	0.0792670	−	0.0665129i	0.00411534	−	0.00345318i
$372$		0			0
$373$	17.7609	+	30.7627i	0.919622	+	1.59283i	0.799989	+	0.600014i	$0.204838\pi$
$373$	17.7609	+	30.7627i	0.919622	+	1.59283i	0.119633	+	0.992818i	$0.461828\pi$
$374$		0			0
$375$	4.11317	−	23.3269i	0.212403	−	1.20460i
$376$		0			0
$377$	12.9202	−	4.70258i	0.665426	−	0.242195i
$378$		0			0
$379$	−7.31674			−0.375836			−0.187918	−	0.982185i	$-0.560174\pi$
$379$	−7.31674			−0.375836			−0.187918	+	0.982185i	$0.560174\pi$
$380$		0			0
$381$	−21.5320			−1.10312
$382$		0			0
$383$	−6.92985	+	2.52226i	−0.354099	+	0.128881i	−0.512944	−	0.858422i	$-0.671445\pi$
$383$	−6.92985	+	2.52226i	−0.354099	+	0.128881i	0.158845	+	0.987304i	$0.449223\pi$
$384$		0			0
$385$	2.64873	−	15.0217i	0.134992	−	0.765576i
$386$		0			0
$387$	−2.47923	−	4.29415i	−0.126026	−	0.218284i
$388$		0			0
$389$	6.00096	−	5.03540i	0.304261	−	0.255305i	−0.477854	−	0.878439i	$-0.658585\pi$
$389$	6.00096	−	5.03540i	0.304261	−	0.255305i	0.782115	+	0.623134i	$0.214141\pi$
$390$		0			0
$391$	−2.85931	+	4.95247i	−0.144602	+	0.250457i
$392$		0			0
$393$	25.7324	+	9.36582i	1.29803	+	0.472443i
$394$		0			0
$395$	−3.40080	−	19.2869i	−0.171113	−	0.970428i
$396$		0			0
$397$	15.3729	+	12.8994i	0.771546	+	0.647404i	0.941104	−	0.338116i	$-0.109790\pi$
$397$	15.3729	+	12.8994i	0.771546	+	0.647404i	−0.169558	+	0.985520i	$0.554234\pi$
$398$		0			0
$399$	9.13396	+	13.6031i	0.457270	+	0.681006i
$400$		0			0
$401$	4.85171	+	4.07107i	0.242283	+	0.203300i	0.755841	−	0.654755i	$-0.227228\pi$
$401$	4.85171	+	4.07107i	0.242283	+	0.203300i	−0.513558	+	0.858055i	$0.671673\pi$
$402$		0			0
$403$	−0.953225	−	5.40601i	−0.0474835	−	0.269292i
$404$		0			0
$405$	17.6153	+	6.41145i	0.875312	+	0.318587i
$406$		0			0
$407$	16.0928	−	27.8736i	0.797691	−	1.38164i
$408$		0			0
$409$	14.9939	−	12.5813i	0.741398	−	0.622107i	−0.191814	−	0.981431i	$-0.561437\pi$
$409$	14.9939	−	12.5813i	0.741398	−	0.622107i	0.933213	+	0.359324i	$0.116993\pi$
$410$		0			0
$411$	8.60968	+	14.9124i	0.424684	+	0.735575i
$412$		0			0
$413$	1.23701	−	7.01545i	0.0608695	−	0.345208i
$414$		0			0
$415$	−16.3211	+	5.94038i	−0.801169	+	0.291602i
$416$		0			0
$417$	−11.9600			−0.585683
$418$		0			0
$419$	−9.06493			−0.442851			−0.221426	−	0.975177i	$-0.571071\pi$
$419$	−9.06493			−0.442851			−0.221426	+	0.975177i	$0.571071\pi$
$420$		0			0
$421$	23.5586	−	8.57464i	1.14818	−	0.417902i	0.303317	−	0.952890i	$-0.401906\pi$
$421$	23.5586	−	8.57464i	1.14818	−	0.417902i	0.844860	+	0.534987i	$0.179684\pi$
$422$		0			0
$423$	−1.23742	+	7.01775i	−0.0601653	+	0.341215i
$424$		0			0
$425$	4.94980	+	8.57331i	0.240101	+	0.415867i
$426$		0			0
$427$	−22.1080	+	18.5508i	−1.06988	+	0.897735i
$428$		0			0
$429$	−12.2059	+	21.1413i	−0.589307	+	1.02071i
$430$		0			0
$431$	−6.18508	−	2.25119i	−0.297925	−	0.108436i	0.188733	−	0.982028i	$-0.439562\pi$
$431$	−6.18508	−	2.25119i	−0.297925	−	0.108436i	−0.486658	+	0.873593i	$0.661784\pi$
$432$		0			0
$433$	−3.41428	−	19.3634i	−0.164080	−	0.930544i	−0.950008	−	0.312226i	$-0.898925\pi$
$433$	−3.41428	−	19.3634i	−0.164080	−	0.930544i	0.785928	−	0.618318i	$-0.212186\pi$
$434$		0			0
$435$	−13.0321	−	10.9352i	−0.624839	−	0.524302i
$436$		0			0
$437$	0.530035	−	4.94321i	0.0253550	−	0.236466i
$438$		0			0
$439$	−12.9204	−	10.8415i	−0.616657	−	0.517437i	0.280094	−	0.959973i	$-0.409634\pi$
$439$	−12.9204	−	10.8415i	−0.616657	−	0.517437i	−0.896751	+	0.442536i	$0.854079\pi$
$440$		0			0
$441$	−0.464568	−	2.63470i	−0.0221223	−	0.125462i
$442$		0			0
$443$	35.5201	+	12.9283i	1.68761	+	0.614240i	0.994321	−	0.106419i	$-0.0339384\pi$
$443$	35.5201	+	12.9283i	1.68761	+	0.614240i	0.693290	+	0.720659i	$0.256161\pi$
$444$		0			0
$445$	14.0892	−	24.4032i	0.667891	−	1.15682i
$446$		0			0
$447$	3.63686	−	3.05168i	0.172017	−	0.144340i
$448$		0			0
$449$	7.02262	+	12.1635i	0.331418	+	0.574033i	0.982790	−	0.184726i	$-0.0591397\pi$
$449$	7.02262	+	12.1635i	0.331418	+	0.574033i	−0.651372	+	0.758758i	$0.725806\pi$
$450$		0			0
$451$	8.72026	−	49.4551i	0.410621	−	2.32875i
$452$		0			0
$453$	21.0722	−	7.66966i	0.990059	−	0.360352i
$454$		0			0
$455$	−9.19193			−0.430924
$456$		0			0
$457$	−10.9491			−0.512177			−0.256089	−	0.966653i	$-0.582434\pi$
$457$	−10.9491			−0.512177			−0.256089	+	0.966653i	$0.582434\pi$
$458$		0			0
$459$	−20.1254	+	7.32503i	−0.939371	+	0.341903i
$460$		0			0
$461$	1.36371	−	7.73396i	0.0635141	−	0.360206i	−0.936442	−	0.350823i	$-0.885902\pi$
$461$	1.36371	−	7.73396i	0.0635141	−	0.360206i	0.999956	−	0.00938355i	$-0.00298692\pi$
$462$		0			0
$463$	9.88710	+	17.1250i	0.459492	+	0.795864i	0.998934	−	0.0461588i	$-0.0146980\pi$
$463$	9.88710	+	17.1250i	0.459492	+	0.795864i	−0.539442	+	0.842023i	$0.681365\pi$
$464$		0			0
$465$	−5.20300	+	4.36583i	−0.241283	+	0.202461i
$466$		0			0
$467$	−4.56124	+	7.90030i	−0.211069	+	0.365582i	−0.952049	−	0.305944i	$-0.901028\pi$
$467$	−4.56124	+	7.90030i	−0.211069	+	0.365582i	0.740980	+	0.671527i	$0.234361\pi$
$468$		0			0
$469$	−22.9657	−	8.35881i	−1.06046	−	0.385974i
$470$		0			0
$471$	0.902258	+	5.11696i	0.0415739	+	0.235777i
$472$		0			0
$473$	21.2994	+	17.8723i	0.979347	+	0.821769i
$474$		0			0
$475$	−6.95205	−	5.07326i	−0.318982	−	0.232777i
$476$		0			0
$477$	0.0334449	+	0.0280636i	0.00153134	+	0.00128494i
$478$		0			0
$479$	−6.06849	−	34.4161i	−0.277276	−	1.57251i	−0.731637	−	0.681694i	$-0.761243\pi$
$479$	−6.06849	−	34.4161i	−0.277276	−	1.57251i	0.454361	−	0.890818i	$-0.349868\pi$
$480$		0			0
$481$	−18.2258	−	6.63366i	−0.831026	−	0.302469i
$482$		0			0
$483$	2.14367	−	3.71295i	0.0975405	−	0.168945i
$484$		0			0
$485$	0.496218	−	0.416376i	0.0225321	−	0.0189067i
$486$		0			0
$487$	14.9182	+	25.8391i	0.676009	+	1.17088i	0.976173	+	0.216994i	$0.0696253\pi$
$487$	14.9182	+	25.8391i	0.676009	+	1.17088i	−0.300164	+	0.953888i	$0.597041\pi$
$488$		0			0
$489$	1.39425	−	7.90719i	0.0630502	−	0.357575i
$490$		0			0
$491$	6.74192	−	2.45386i	0.304259	−	0.110741i	−0.185379	−	0.982667i	$-0.559351\pi$
$491$	6.74192	−	2.45386i	0.304259	−	0.110741i	0.489638	+	0.871926i	$0.337129\pi$
$492$		0			0
$493$	25.1153			1.13114
$494$		0			0
$495$	6.43583			0.289269
$496$		0			0
$497$	3.74377	−	1.36262i	0.167931	−	0.0611220i
$498$		0			0
$499$	−2.81846	+	15.9843i	−0.126172	+	0.715556i	0.854433	+	0.519561i	$0.173905\pi$
$499$	−2.81846	+	15.9843i	−0.126172	+	0.715556i	−0.980605	+	0.195994i	$0.937207\pi$
$500$		0			0
$501$	14.6075	+	25.3010i	0.652617	+	1.13037i
$502$		0			0
$503$	14.2611	−	11.9665i	0.635869	−	0.533558i	−0.266877	−	0.963731i	$-0.585992\pi$
$503$	14.2611	−	11.9665i	0.635869	−	0.533558i	0.902747	+	0.430173i	$0.141547\pi$
$504$		0			0
$505$	−16.1736	+	28.0135i	−0.719715	+	1.24658i
$506$		0			0
$507$	−10.0282	−	3.64995i	−0.445366	−	0.162100i
$508$		0			0
$509$	−0.734939	−	4.16805i	−0.0325756	−	0.184745i	0.964178	−	0.265255i	$-0.0854562\pi$
$509$	−0.734939	−	4.16805i	−0.0325756	−	0.184745i	−0.996754	+	0.0805099i	$0.974345\pi$
$510$		0			0
$511$	−1.05154	−	0.882344i	−0.0465172	−	0.0390326i
$512$		0			0
$513$	13.4205	−	12.9058i	0.592531	−	0.569804i
$514$		0			0
$515$	11.9649	+	10.0397i	0.527236	+	0.442403i
$516$		0			0
$517$	−6.93877	−	39.3517i	−0.305167	−	1.73069i
$518$		0			0
$519$	−11.6937	−	4.25615i	−0.513295	−	0.186824i
$520$		0			0
$521$	−6.40530	+	11.0943i	−0.280621	+	0.486050i	−0.971538	−	0.236884i	$-0.923874\pi$
$521$	−6.40530	+	11.0943i	−0.280621	+	0.486050i	0.690917	+	0.722934i	$0.257207\pi$
$522$		0			0
$523$	24.7911	−	20.8022i	1.08404	−	0.909618i	0.0877905	−	0.996139i	$-0.472019\pi$
$523$	24.7911	−	20.8022i	1.08404	−	0.909618i	0.996250	+	0.0865209i	$0.0275749\pi$
$524$		0			0
$525$	−3.71095	−	6.42755i	−0.161959	−	0.280521i
$526$		0			0
$527$	1.74120	−	9.87485i	0.0758479	−	0.430155i
$528$		0			0
$529$	20.3905	−	7.42154i	0.886545	−	0.322676i
$530$		0			0
$531$	3.00567			0.130435
$532$		0			0
$533$	−30.2621			−1.31080
$534$		0			0
$535$	−12.2370	+	4.45392i	−0.529054	+	0.192560i
$536$		0			0
$537$	−1.07860	+	6.11706i	−0.0465451	+	0.263971i
$538$		0			0
$539$	7.50094	+	12.9920i	0.323088	+	0.559605i
$540$		0			0
$541$	14.1268	−	11.8538i	0.607359	−	0.509634i	−0.286443	−	0.958097i	$-0.592473\pi$
$541$	14.1268	−	11.8538i	0.607359	−	0.509634i	0.893801	+	0.448463i	$0.148028\pi$
$542$		0			0
$543$	−4.44006	+	7.69040i	−0.190541	+	0.330027i
$544$		0			0
$545$	27.4163	+	9.97872i	1.17439	+	0.427442i
$546$		0			0
$547$	5.66428	+	32.1238i	0.242187	+	1.37351i	0.826935	+	0.562297i	$0.190082\pi$
$547$	5.66428	+	32.1238i	0.242187	+	1.37351i	−0.584748	+	0.811215i	$0.698807\pi$
$548$		0			0
$549$	−9.32795	−	7.82708i	−0.398107	−	0.334052i
$550$		0			0
$551$	−19.9652	+	8.83894i	−0.850544	+	0.376552i
$552$		0			0
$553$	−16.6051	−	13.9333i	−0.706119	−	0.592504i
$554$		0			0
$555$	4.16722	+	23.6335i	0.176888	+	1.00318i
$556$		0			0
$557$	−12.2636	−	4.46359i	−0.519625	−	0.189128i	0.0688747	−	0.997625i	$-0.478059\pi$
$557$	−12.2636	−	4.46359i	−0.519625	−	0.189128i	−0.588500	+	0.808497i	$0.700281\pi$
$558$		0			0
$559$	8.37765	−	14.5105i	0.354337	−	0.613730i
$560$		0			0
$561$	−34.1592	+	28.6630i	−1.44220	+	1.21015i
$562$		0			0
$563$	9.12500	+	15.8050i	0.384573	+	0.666100i	0.991710	−	0.128498i	$-0.0410155\pi$
$563$	9.12500	+	15.8050i	0.384573	+	0.666100i	−0.607137	+	0.794597i	$0.707682\pi$
$564$		0			0
$565$	3.22160	−	18.2706i	0.135534	−	0.768649i
$566$		0			0
$567$	19.4969	−	7.09631i	0.818795	−	0.298017i
$568$		0			0
$569$	−34.4274			−1.44327			−0.721636	−	0.692273i	$-0.756610\pi$
$569$	−34.4274			−1.44327			−0.721636	+	0.692273i	$0.756610\pi$
$570$		0			0
$571$	16.6525			0.696884			0.348442	−	0.937330i	$-0.386711\pi$
$571$	16.6525			0.696884			0.348442	+	0.937330i	$0.386711\pi$
$572$		0			0
$573$	−1.77735	+	0.646904i	−0.0742500	+	0.0270248i
$574$		0			0
$575$	−0.391044	+	2.21772i	−0.0163077	+	0.0924855i
$576$		0			0
$577$	18.7394	+	32.4576i	0.780130	+	1.35123i	0.931865	+	0.362804i	$0.118181\pi$
$577$	18.7394	+	32.4576i	0.780130	+	1.35123i	−0.151735	+	0.988421i	$0.548486\pi$
$578$		0			0
$579$	−22.7446	+	19.0850i	−0.945233	+	0.793144i
$580$		0			0
$581$	−9.61189	+	16.6483i	−0.398769	+	0.690687i
$582$		0			0
$583$	−0.230053	−	0.0837324i	−0.00952781	−	0.00346784i
$584$		0			0
$585$	−0.673464	−	3.81940i	−0.0278443	−	0.157913i
$586$		0			0
$587$	−26.0297	−	21.8415i	−1.07436	−	0.901494i	−0.0789185	−	0.996881i	$-0.525147\pi$
$587$	−26.0297	−	21.8415i	−1.07436	−	0.901494i	−0.995440	+	0.0953871i	$0.969591\pi$
$588$		0			0
$589$	2.09115	+	8.46270i	0.0861643	+	0.348700i
$590$		0			0
$591$	−24.6176	−	20.6566i	−1.01263	−	0.849700i
$592$		0			0
$593$	3.29313	+	18.6762i	0.135232	+	0.766941i	0.974698	+	0.223528i	$0.0717574\pi$
$593$	3.29313	+	18.6762i	0.135232	+	0.766941i	−0.839465	+	0.543414i	$0.817132\pi$
$594$		0			0
$595$	−15.7778	−	5.74265i	−0.646827	−	0.235426i
$596$		0			0
$597$	21.4203	−	37.1010i	0.876673	−	1.51844i
$598$		0			0
$599$	−25.6598	+	21.5311i	−1.04843	+	0.879738i	−0.992928	−	0.118721i	$-0.962121\pi$
$599$	−25.6598	+	21.5311i	−1.04843	+	0.879738i	−0.0555029	+	0.998459i	$0.517676\pi$
$600$		0			0
$601$	7.50056	+	12.9914i	0.305954	+	0.529928i	0.977473	−	0.211059i	$-0.0676912\pi$
$601$	7.50056	+	12.9914i	0.305954	+	0.529928i	−0.671519	+	0.740987i	$0.734358\pi$
$602$		0			0
$603$	1.79061	−	10.1550i	0.0729192	−	0.413545i
$604$		0			0
$605$	−15.9326	+	5.79898i	−0.647751	+	0.235762i
$606$		0			0
$607$	−7.06547			−0.286779			−0.143389	−	0.989666i	$-0.545800\pi$
$607$	−7.06547			−0.286779			−0.143389	+	0.989666i	$0.545800\pi$
$608$		0			0
$609$	−18.8293			−0.763003
$610$		0			0
$611$	−22.6276	+	8.23576i	−0.915413	+	0.333183i
$612$		0			0
$613$	−4.54668	+	25.7855i	−0.183639	+	1.04147i	0.744053	+	0.668120i	$0.232901\pi$
$613$	−4.54668	+	25.7855i	−0.183639	+	1.04147i	−0.927692	+	0.373346i	$0.878210\pi$
$614$		0			0
$615$	18.7216	+	32.4268i	0.754928	+	1.30757i
$616$		0			0
$617$	−33.3641	+	27.9958i	−1.34319	+	1.12707i	−0.362395	+	0.932025i	$0.618041\pi$
$617$	−33.3641	+	27.9958i	−1.34319	+	1.12707i	−0.980794	+	0.195045i	$0.937515\pi$
$618$		0			0
$619$	−12.4919	+	21.6365i	−0.502090	+	0.869646i	0.497907	+	0.867231i	$0.334102\pi$
$619$	−12.4919	+	21.6365i	−0.502090	+	0.869646i	−0.999997	+	0.00241526i	$0.999231\pi$
$620$		0			0
$621$	−4.57806	−	1.66628i	−0.183711	−	0.0668654i
$622$		0			0
$623$	−5.41579	−	30.7145i	−0.216979	−	1.23055i
$624$		0			0
$625$	−8.60229	−	7.21818i	−0.344092	−	0.288727i
$626$		0			0
$627$	17.0670	−	34.8072i	0.681592	−	1.39007i
$628$		0			0
$629$	−27.1399	−	22.7731i	−1.08214	−	0.908024i
$630$		0			0
$631$	−8.07717	−	45.8079i	−0.321547	−	1.82358i	−0.532905	−	0.846175i	$-0.678900\pi$
$631$	−8.07717	−	45.8079i	−0.321547	−	1.82358i	0.211358	−	0.977409i	$-0.432211\pi$
$632$		0			0
$633$	33.7459	+	12.2825i	1.34128	+	0.488186i
$634$		0			0
$635$	−9.59103	+	16.6121i	−0.380608	+	0.659233i
$636$		0			0
$637$	6.92531	−	5.81102i	0.274391	−	0.230241i
$638$		0			0
$639$	0.840488	+	1.45577i	0.0332492	+	0.0575893i
$640$		0			0
$641$	1.23030	−	6.97736i	0.0485938	−	0.275589i	−0.950823	−	0.309734i	$-0.899760\pi$
$641$	1.23030	−	6.97736i	0.0485938	−	0.275589i	0.999417	+	0.0341454i	$0.0108709\pi$
$642$		0			0
$643$	−0.150167	+	0.0546563i	−0.00592200	+	0.00215543i	−0.344979	−	0.938610i	$-0.612114\pi$
$643$	−0.150167	+	0.0546563i	−0.00592200	+	0.00215543i	0.339057	+	0.940766i	$0.389892\pi$
$644$		0			0
$645$	−20.7313			−0.816295
$646$		0			0
$647$	−18.8979			−0.742955			−0.371478	−	0.928442i	$-0.621149\pi$
$647$	−18.8979			−0.742955			−0.371478	+	0.928442i	$0.621149\pi$
$648$		0			0
$649$	−15.8378	+	5.76447i	−0.621686	+	0.226275i
$650$		0			0
$651$	−1.30541	+	7.40333i	−0.0511629	+	0.290159i
$652$		0			0
$653$	5.62463	+	9.74215i	0.220109	+	0.381240i	0.954841	−	0.297118i	$-0.0960254\pi$
$653$	5.62463	+	9.74215i	0.220109	+	0.381240i	−0.734732	+	0.678358i	$0.762692\pi$
$654$		0			0
$655$	18.6878	−	15.6809i	0.730193	−	0.612705i
$656$		0			0
$657$	0.289586	−	0.501578i	0.0112978	−	0.0195684i
$658$		0			0
$659$	11.8940	+	4.32904i	0.463323	+	0.168636i	0.563125	−	0.826372i	$-0.309599\pi$
$659$	11.8940	+	4.32904i	0.463323	+	0.168636i	−0.0998025	+	0.995007i	$0.531821\pi$
$660$		0			0
$661$	−0.642263	−	3.64245i	−0.0249811	−	0.141675i	0.969766	−	0.244036i	$-0.0784715\pi$
$661$	−0.642263	−	3.64245i	−0.0249811	−	0.141675i	−0.994747	+	0.102361i	$0.967360\pi$
$662$		0			0
$663$	20.5848	+	17.2727i	0.799449	+	0.670817i
$664$		0			0
$665$	14.5634	−	0.987692i	0.564746	−	0.0383010i
$666$		0			0
$667$	4.37653	+	3.67235i	0.169460	+	0.142194i
$668$		0			0
$669$	6.61697	+	37.5267i	0.255827	+	1.45087i
$670$		0			0
$671$	64.1629	+	23.3534i	2.47698	+	0.901548i
$672$		0			0
$673$	11.1273	−	19.2730i	0.428926	−	0.742921i	−0.567852	−	0.823130i	$-0.692226\pi$
$673$	11.1273	−	19.2730i	0.428926	−	0.742921i	0.996778	+	0.0802094i	$0.0255589\pi$
$674$		0			0
$675$	−6.46065	+	5.42113i	−0.248671	+	0.208659i
$676$		0			0
$677$	−11.9484	−	20.6952i	−0.459213	−	0.795380i	0.539707	−	0.841853i	$-0.318535\pi$
$677$	−11.9484	−	20.6952i	−0.459213	−	0.795380i	−0.998920	+	0.0464733i	$0.985202\pi$
$678$		0			0
$679$	0.124499	−	0.706068i	0.00477783	−	0.0270964i
$680$		0			0
$681$	13.4097	−	4.88072i	0.513860	−	0.187030i
$682$		0			0
$683$	26.9375			1.03073			0.515367	−	0.856970i	$-0.327656\pi$
$683$	26.9375			1.03073			0.515367	+	0.856970i	$0.327656\pi$
$684$		0			0
$685$	15.3401			0.586114
$686$		0			0
$687$	38.7720	−	14.1119i	1.47924	−	0.538401i
$688$		0			0
$689$	−0.0256184	+	0.145289i	−0.000975982	+	0.00553507i
$690$		0			0
$691$	−13.6869	−	23.7063i	−0.520673	−	0.901831i	−0.999711	−	0.0240374i	$-0.992348\pi$
$691$	−13.6869	−	23.7063i	−0.520673	−	0.901831i	0.479039	−	0.877794i	$-0.340985\pi$
$692$		0			0
$693$	5.45676	−	4.57877i	0.207285	−	0.173933i
$694$		0			0
$695$	−5.32735	+	9.22724i	−0.202078	+	0.350009i
$696$		0			0
$697$	−51.9444	−	18.9062i	−1.96753	−	0.716123i
$698$		0			0
$699$	−1.61412	−	9.15415i	−0.0610517	−	0.346242i
$700$		0			0
$701$	−17.7609	−	14.9032i	−0.670821	−	0.562886i	0.242487	−	0.970155i	$-0.422037\pi$
$701$	−17.7609	−	14.9032i	−0.670821	−	0.562886i	−0.913308	+	0.407269i	$0.866481\pi$
$702$		0			0
$703$	29.5893	+	8.55178i	1.11598	+	0.322537i
$704$		0			0
$705$	22.8234	+	19.1511i	0.859579	+	0.721272i
$706$		0			0
$707$	6.21703	+	35.2585i	0.233815	+	1.32603i
$708$		0			0
$709$	0.177739	+	0.0646919i	0.00667515	+	0.00242955i	0.345356	−	0.938472i	$-0.387758\pi$
$709$	0.177739	+	0.0646919i	0.00667515	+	0.00242955i	−0.338680	+	0.940901i	$0.609981\pi$
$710$		0			0
$711$	4.57292	−	7.92054i	0.171498	−	0.297043i
$712$		0			0
$713$	1.74731	−	1.46617i	0.0654374	−	0.0549085i
$714$		0			0
$715$	10.8738	+	18.8339i	0.406656	+	0.704349i
$716$		0			0
$717$	7.07734	−	40.1376i	0.264308	−	1.49896i
$718$		0			0
$719$	10.7370	−	3.90793i	0.400421	−	0.145741i	−0.133957	−	0.990987i	$-0.542768\pi$
$719$	10.7370	−	3.90793i	0.400421	−	0.145741i	0.534377	+	0.845246i	$0.320546\pi$
$720$		0			0
$721$	17.2874			0.643818
$722$		0			0
$723$	−13.7987			−0.513178
$724$		0			0
$725$	9.29370	−	3.38263i	0.345159	−	0.125628i
$726$		0			0
$727$	5.22332	−	29.6229i	0.193722	−	1.09865i	−0.720504	−	0.693451i	$-0.756090\pi$
$727$	5.22332	−	29.6229i	0.193722	−	1.09865i	0.914226	−	0.405204i	$-0.132799\pi$
$728$		0			0
$729$	−8.13313	−	14.0870i	−0.301227	−	0.521741i
$730$		0			0
$731$	23.4455	−	19.6731i	0.867164	−	0.727637i
$732$		0			0
$733$	16.3368	−	28.2962i	0.603414	−	1.04514i	−0.388885	−	0.921286i	$-0.627140\pi$
$733$	16.3368	−	28.2962i	0.603414	−	1.04514i	0.992300	−	0.123858i	$-0.0395269\pi$
$734$		0			0
$735$	−10.5110	−	3.82570i	−0.387705	−	0.141113i
$736$		0			0
$737$	10.0408	+	56.9440i	0.369856	+	2.09756i
$738$		0			0
$739$	−19.5685	−	16.4199i	−0.719838	−	0.604016i	0.207502	−	0.978235i	$-0.433467\pi$
$739$	−19.5685	−	16.4199i	−0.719838	−	0.604016i	−0.927341	+	0.374218i	$0.877911\pi$
$740$		0			0
$741$	−22.4426	−	6.48627i	−0.824449	−	0.238279i
$742$		0			0
$743$	17.6914	+	14.8449i	0.649035	+	0.544605i	0.906778	−	0.421608i	$-0.138534\pi$
$743$	17.6914	+	14.8449i	0.649035	+	0.544605i	−0.257743	+	0.966214i	$0.582979\pi$
$744$		0			0
$745$	−0.734433	−	4.16518i	−0.0269076	−	0.152600i
$746$		0			0
$747$	−7.62188	−	2.77414i	−0.278870	−	0.101500i
$748$		0			0
$749$	−7.20671	+	12.4824i	−0.263328	+	0.456097i
$750$		0			0
$751$	−9.91762	+	8.32187i	−0.361899	+	0.303670i	−0.805547	−	0.592532i	$-0.798129\pi$
$751$	−9.91762	+	8.32187i	−0.361899	+	0.303670i	0.443648	+	0.896201i	$0.353684\pi$
$752$		0			0
$753$	−11.8694	−	20.5585i	−0.432547	−	0.749193i
$754$		0			0
$755$	3.46900	−	19.6737i	0.126250	−	0.715999i
$756$		0			0
$757$	−16.4280	+	5.97928i	−0.597084	+	0.217321i	−0.622842	−	0.782347i	$-0.714022\pi$
$757$	−16.4280	+	5.97928i	−0.597084	+	0.217321i	0.0257583	+	0.999668i	$0.491800\pi$
$758$		0			0
$759$	−10.1436			−0.368189
$760$		0			0
$761$	−4.43066			−0.160611			−0.0803057	−	0.996770i	$-0.525590\pi$
$761$	−4.43066			−0.160611			−0.0803057	+	0.996770i	$0.525590\pi$
$762$		0			0
$763$	30.3449	−	11.0446i	1.09856	−	0.399843i
$764$		0			0
$765$	1.23018	−	6.97669i	0.0444772	−	0.252243i
$766$		0			0
$767$	5.07829	+	8.79585i	0.183366	+	0.317600i
$768$		0			0
$769$	31.3561	−	26.3109i	1.13073	−	0.948794i	0.131633	−	0.991299i	$-0.457978\pi$
$769$	31.3561	−	26.3109i	1.13073	−	0.948794i	0.999096	+	0.0425043i	$0.0135336\pi$
$770$		0			0
$771$	−0.321507	+	0.556867i	−0.0115788	+	0.0200551i
$772$		0			0
$773$	−7.12589	−	2.59361i	−0.256300	−	0.0932857i	0.210675	−	0.977556i	$-0.432434\pi$
$773$	−7.12589	−	2.59361i	−0.256300	−	0.0932857i	−0.466975	+	0.884271i	$0.654656\pi$
$774$		0			0
$775$	−0.685668	−	3.88861i	−0.0246299	−	0.139683i
$776$		0			0
$777$	20.3473	+	17.0734i	0.729954	+	0.612504i
$778$		0			0
$779$	47.9464	−	3.25172i	1.71786	−	0.116505i
$780$		0			0
$781$	−7.22073	−	6.05892i	−0.258378	−	0.216805i
$782$		0			0
$783$	3.71546	+	21.0714i	0.132780	+	0.753031i
$784$		0			0
$785$	4.34967	+	1.58315i	0.155246	+	0.0565051i
$786$		0			0
$787$	−15.4525	+	26.7645i	−0.550821	+	0.954050i	0.447394	+	0.894337i	$0.352352\pi$
$787$	−15.4525	+	26.7645i	−0.550821	+	0.954050i	−0.998216	+	0.0597134i	$0.980981\pi$
$788$		0			0
$789$	13.2610	−	11.1273i	0.472103	−	0.396141i
$790$		0			0
$791$	−10.2671	−	17.7831i	−0.365056	−	0.632295i
$792$		0			0
$793$	7.14509	−	40.5218i	0.253730	−	1.43897i
$794$		0			0
$795$	0.171530	−	0.0624320i	0.00608356	−	0.00221423i
$796$		0			0
$797$	−17.9708			−0.636559			−0.318279	−	0.947997i	$-0.603105\pi$
$797$	−17.9708			−0.636559			−0.318279	+	0.947997i	$0.603105\pi$
$798$		0			0
$799$	−43.9851			−1.55608
$800$		0			0
$801$	12.3656	−	4.50071i	0.436917	−	0.159025i
$802$		0			0
$803$	−0.563955	+	3.19835i	−0.0199015	+	0.112867i
$804$		0			0
$805$	−1.90971	−	3.30772i	−0.0673086	−	0.116582i
$806$		0			0
$807$	−17.2367	+	14.4633i	−0.606759	+	0.509132i
$808$		0			0
$809$	−2.52462	+	4.37277i	−0.0887608	+	0.153738i	−0.906988	−	0.421157i	$-0.861624\pi$
$809$	−2.52462	+	4.37277i	−0.0887608	+	0.153738i	0.818227	+	0.574896i	$0.194957\pi$
$810$		0			0
$811$	−18.5490	−	6.75127i	−0.651342	−	0.237069i	−0.00484814	−	0.999988i	$-0.501543\pi$
$811$	−18.5490	−	6.75127i	−0.651342	−	0.237069i	−0.646494	+	0.762919i	$0.723765\pi$
$812$		0			0
$813$	1.00906	+	5.72265i	0.0353892	+	0.200702i
$814$		0			0
$815$	−5.47942	−	4.59778i	−0.191936	−	0.161053i
$816$		0			0
$817$	−11.7141	+	23.8903i	−0.409826	+	0.835815i
$818$		0			0
$819$	−3.28832	−	2.75923i	−0.114903	−	0.0964153i
$820$		0			0
$821$	0.349550	+	1.98240i	0.0121994	+	0.0691862i	0.990300	−	0.138948i	$-0.0443721\pi$
$821$	0.349550	+	1.98240i	0.0121994	+	0.0691862i	−0.978100	+	0.208134i	$0.933261\pi$
$822$		0			0
$823$	−40.4124	−	14.7089i	−1.40869	−	0.512721i	−0.477944	−	0.878390i	$-0.658618\pi$
$823$	−40.4124	−	14.7089i	−1.40869	−	0.512721i	−0.930745	+	0.365670i	$0.880840\pi$
$824$		0			0
$825$	−8.77988	+	15.2072i	−0.305676	+	0.529447i
$826$		0			0
$827$	25.7538	−	21.6100i	0.895547	−	0.751453i	−0.0737683	−	0.997275i	$-0.523503\pi$
$827$	25.7538	−	21.6100i	0.895547	−	0.751453i	0.969315	+	0.245823i	$0.0790581\pi$
$828$		0			0
$829$	17.3799	+	30.1028i	0.603627	+	1.04551i	0.992267	+	0.124123i	$0.0396118\pi$
$829$	17.3799	+	30.1028i	0.603627	+	1.04551i	−0.388639	+	0.921390i	$0.627055\pi$
$830$		0			0
$831$	−10.7379	+	60.8974i	−0.372492	+	2.11251i
$832$		0			0
$833$	15.5176	−	5.64794i	0.537653	−	0.195690i
$834$		0			0
$835$	26.0266			0.900687
$836$		0			0
$837$	8.54246			0.295271
$838$		0			0
$839$	−17.4556	+	6.35333i	−0.602636	+	0.219341i	−0.625278	−	0.780402i	$-0.715014\pi$
$839$	−17.4556	+	6.35333i	−0.602636	+	0.219341i	0.0226423	+	0.999744i	$0.492792\pi$
$840$		0			0
$841$	−0.678741	+	3.84933i	−0.0234049	+	0.132736i
$842$		0			0
$843$	−14.5776	−	25.2492i	−0.502080	−	0.869628i
$844$		0			0
$845$	−7.28281	+	6.11101i	−0.250536	+	0.210225i
$846$		0			0
$847$	−9.38310	+	16.2520i	−0.322407	+	0.558426i
$848$		0			0
$849$	−34.1503	−	12.4297i	−1.17204	−	0.426586i
$850$		0			0
$851$	−1.39947	−	7.93678i	−0.0479732	−	0.272069i
$852$		0			0
$853$	−1.57133	−	1.31850i	−0.0538012	−	0.0451446i	0.615491	−	0.788144i	$-0.288958\pi$
$853$	−1.57133	−	1.31850i	−0.0538012	−	0.0451446i	−0.669292	+	0.743000i	$0.733402\pi$
$854$		0			0
$855$	1.47742	+	5.97900i	0.0505267	+	0.204477i
$856$		0			0
$857$	15.4175	+	12.9368i	0.526651	+	0.441913i	0.866943	−	0.498407i	$-0.166081\pi$
$857$	15.4175	+	12.9368i	0.526651	+	0.441913i	−0.340292	+	0.940320i	$0.610526\pi$
$858$		0			0
$859$	−1.65890	−	9.40808i	−0.0566009	−	0.320999i	0.943341	−	0.331826i	$-0.107665\pi$
$859$	−1.65890	−	9.40808i	−0.0566009	−	0.320999i	−0.999941	+	0.0108268i	$0.996554\pi$
$860$		0			0
$861$	38.9435	+	14.1743i	1.32719	+	0.483058i
$862$		0			0
$863$	17.3643	−	30.0759i	0.591089	−	1.02380i	−0.402997	−	0.915201i	$-0.632031\pi$
$863$	17.3643	−	30.0759i	0.591089	−	1.02380i	0.994086	−	0.108595i	$-0.0346352\pi$
$864$		0			0
$865$	−8.49237	+	7.12594i	−0.288749	+	0.242289i
$866$		0			0
$867$	7.94606	+	13.7630i	0.269862	+	0.467415i
$868$		0			0
$869$	−8.90554	+	50.5058i	−0.302100	+	1.71329i
$870$		0			0
$871$	32.7432	−	11.9176i	1.10946	−	0.403811i
$872$		0			0
$873$	0.302505			0.0102382
$874$		0			0
$875$	−23.3557			−0.789566
$876$		0			0
$877$	25.1774	−	9.16382i	0.850180	−	0.309440i	0.120066	−	0.992766i	$-0.461689\pi$
$877$	25.1774	−	9.16382i	0.850180	−	0.309440i	0.730114	+	0.683326i	$0.239467\pi$
$878$		0			0
$879$	−3.85415	+	21.8580i	−0.129997	+	0.737252i
$880$		0			0
$881$	7.87940	+	13.6475i	0.265464	+	0.459797i	0.967685	−	0.252162i	$-0.0811416\pi$
$881$	7.87940	+	13.6475i	0.265464	+	0.459797i	−0.702221	+	0.711959i	$0.747808\pi$
$882$		0			0
$883$	31.7063	−	26.6047i	1.06700	−	0.895320i	0.0722232	−	0.997388i	$-0.476991\pi$
$883$	31.7063	−	26.6047i	1.06700	−	0.895320i	0.994777	+	0.102069i	$0.0325462\pi$
$884$		0			0
$885$	6.28336	−	10.8831i	0.211213	−	0.365831i
$886$		0			0
$887$	−43.7848	−	15.9363i	−1.47015	−	0.535090i	−0.522007	−	0.852941i	$-0.674817\pi$
$887$	−43.7848	−	15.9363i	−1.47015	−	0.535090i	−0.948141	+	0.317851i	$0.897039\pi$
$888$		0			0
$889$	3.68673	+	20.9085i	0.123649	+	0.701249i
$890$		0			0
$891$	−37.6044	−	31.5538i	−1.25979	−	1.05709i
$892$		0			0
$893$	34.9655	−	15.4799i	1.17008	−	0.518015i
$894$		0			0
$895$	4.23892	+	3.55688i	0.141692	+	0.118893i
$896$		0			0
$897$	1.06145	+	6.01981i	0.0354409	+	0.200996i
$898$		0			0
$899$	−9.41346	−	3.42622i	−0.313957	−	0.114271i
$900$		0			0
$901$	−0.134743	+	0.233381i	−0.00448893	+	0.00777505i
$902$		0			0
$903$	−17.5775	+	14.7493i	−0.584943	+	0.490825i
$904$		0			0
$905$	3.95548	+	6.85108i	0.131484	+	0.227738i
$906$		0			0
$907$	0.423530	−	2.40196i	0.0140631	−	0.0797557i	−0.976968	−	0.213384i	$-0.931552\pi$
$907$	0.423530	−	2.40196i	0.0140631	−	0.0797557i	0.991032	+	0.133628i	$0.0426627\pi$
$908$		0			0
$909$	−14.1950	+	5.16656i	−0.470819	+	0.171364i
$910$		0			0
$911$	−29.8844			−0.990115			−0.495057	−	0.868860i	$-0.664853\pi$
$911$	−29.8844			−0.990115			−0.495057	+	0.868860i	$0.664853\pi$
$912$		0			0
$913$	45.4823			1.50524
$914$		0			0
$915$	−47.8407	+	17.4126i	−1.58157	+	0.575643i
$916$		0			0
$917$	4.68868	−	26.5908i	0.154834	−	0.878107i
$918$		0			0
$919$	−20.1737	−	34.9419i	−0.665469	−	1.15263i	−0.979158	−	0.203100i	$-0.934898\pi$
$919$	−20.1737	−	34.9419i	−0.665469	−	1.15263i	0.313689	−	0.949526i	$-0.398435\pi$
$920$		0			0
$921$	15.9432	−	13.3780i	0.525348	−	0.440819i
$922$		0			0
$923$	−2.84012	+	4.91923i	−0.0934837	+	0.161919i
$924$		0			0
$925$	−13.1101	−	4.77168i	−0.431057	−	0.156892i
$926$		0			0
$927$	1.26660	+	7.18323i	0.0416005	+	0.235928i
$928$		0			0
$929$	−40.3558	−	33.8625i	−1.32403	−	1.11099i	−0.985433	−	0.170062i	$-0.945603\pi$
$929$	−40.3558	−	33.8625i	−1.32403	−	1.11099i	−0.338597	−	0.940932i	$-0.609952\pi$
$930$		0			0
$931$	−10.3479	+	9.95096i	−0.339137	+	0.326130i
$932$		0			0
$933$	38.0183	+	31.9012i	1.24466	+	1.04440i
$934$		0			0
$935$	6.89818	+	39.1215i	0.225595	+	1.27941i
$936$		0			0
$937$	−30.0102	−	10.9228i	−0.980391	−	0.356833i	−0.198399	−	0.980121i	$-0.563574\pi$
$937$	−30.0102	−	10.9228i	−0.980391	−	0.356833i	−0.781992	+	0.623288i	$0.785796\pi$
$938$		0			0
$939$	−1.64885	+	2.85589i	−0.0538081	+	0.0931984i
$940$		0			0
$941$	−1.29042	+	1.08279i	−0.0420666	+	0.0352981i	−0.663579	−	0.748107i	$-0.730963\pi$
$941$	−1.29042	+	1.08279i	−0.0420666	+	0.0352981i	0.621512	+	0.783405i	$0.286519\pi$
$942$		0			0
$943$	−6.28725	−	10.8898i	−0.204741	−	0.354622i
$944$		0			0
$945$	2.48391	−	14.0869i	0.0808015	−	0.458248i
$946$		0			0
$947$	−29.2449	+	10.6443i	−0.950332	+	0.345892i	−0.770238	−	0.637757i	$-0.779862\pi$
$947$	−29.2449	+	10.6443i	−0.950332	+	0.345892i	−0.180094	+	0.983649i	$0.557640\pi$
$948$		0			0
$949$	1.95710			0.0635302
$950$		0			0
$951$	−38.4277			−1.24610
$952$		0			0
$953$	−21.9284	+	7.98128i	−0.710330	+	0.258539i	−0.671815	−	0.740719i	$-0.734485\pi$
$953$	−21.9284	+	7.98128i	−0.710330	+	0.258539i	−0.0385151	+	0.999258i	$0.512263\pi$
$954$		0			0
$955$	−0.292596	+	1.65940i	−0.00946819	+	0.0536968i
$956$		0			0
$957$	22.2745	+	38.5806i	0.720034	+	1.24713i
$958$		0			0
$959$	13.0064	−	10.9137i	0.419999	−	0.352421i
$960$		0			0
$961$	13.5003	−	23.3831i	0.435492	−	0.754295i
$962$		0			0
$963$	−5.71466	−	2.07997i	−0.184152	−	0.0670260i
$964$		0			0
$965$	4.59308	+	26.0487i	0.147857	+	0.838536i
$966$		0			0
$967$	41.7482	+	35.0309i	1.34253	+	1.12652i	0.980968	+	0.194171i	$0.0622018\pi$
$967$	41.7482	+	35.0309i	1.34253	+	1.12652i	0.361565	+	0.932347i	$0.382243\pi$
$968$		0			0
$969$	−34.4700	−	25.1546i	−1.10734	−	0.808081i
$970$		0			0
$971$	22.3904	+	18.7878i	0.718543	+	0.602929i	0.926982	−	0.375107i	$-0.122394\pi$
$971$	22.3904	+	18.7878i	0.718543	+	0.602929i	−0.208439	+	0.978035i	$0.566838\pi$
$972$		0			0
$973$	2.04780	+	11.6137i	0.0656495	+	0.372317i
$974$		0			0
$975$	9.94360	+	3.61918i	0.318450	+	0.115906i
$976$		0			0
$977$	17.0031	−	29.4502i	0.543977	−	0.942196i	−0.454693	−	0.890648i	$-0.650251\pi$
$977$	17.0031	−	29.4502i	0.543977	−	0.942196i	0.998671	−	0.0515482i	$-0.0164156\pi$
$978$		0			0
$979$	−56.5261	+	47.4310i	−1.80658	+	1.51590i
$980$		0			0
$981$	6.81251	+	11.7996i	0.217507	+	0.376733i
$982$		0			0
$983$	−5.94855	+	33.7359i	−0.189729	+	1.07601i	0.729998	+	0.683450i	$0.239521\pi$
$983$	−5.94855	+	33.7359i	−0.189729	+	1.07601i	−0.919727	+	0.392559i	$0.871590\pi$
$984$		0			0
$985$	−26.9022	+	9.79159i	−0.857175	+	0.311986i
$986$		0			0
$987$	32.9763			1.04965
$988$		0			0
$989$	6.96216			0.221384
$990$		0			0
$991$	41.2569	−	15.0163i	1.31057	−	0.477008i	0.410144	−	0.912021i	$-0.365478\pi$
$991$	41.2569	−	15.0163i	1.31057	−	0.477008i	0.900424	+	0.435013i	$0.143256\pi$
$992$		0			0
$993$	−3.05385	+	17.3193i	−0.0969111	+	0.549610i
$994$		0			0
$995$	−19.0825	−	33.0518i	−0.604955	−	1.04781i
$996$		0			0
$997$	−44.1321	+	37.0312i	−1.39768	+	1.17279i	−0.435559	+	0.900160i	$0.643449\pi$
$997$	−44.1321	+	37.0312i	−1.39768	+	1.17279i	−0.962119	+	0.272631i	$0.912106\pi$
$998$		0			0
$999$	15.0914	−	26.1391i	0.477471	−	0.827003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.q.c.73.3	yes	18
4.3	odd	2		304.2.u.f.225.1		18
19.5	even	9		2888.2.a.y.1.2		9
19.6	even	9	inner	152.2.q.c.25.3	✓	18
19.14	odd	18		2888.2.a.x.1.8		9
76.43	odd	18		5776.2.a.cd.1.8		9
76.63	odd	18		304.2.u.f.177.1		18
76.71	even	18		5776.2.a.ce.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.c.25.3	✓	18	19.6	even	9	inner
152.2.q.c.73.3	yes	18	1.1	even	1	trivial
304.2.u.f.177.1		18	76.63	odd	18
304.2.u.f.225.1		18	4.3	odd	2
2888.2.a.x.1.8		9	19.14	odd	18
2888.2.a.y.1.2		9	19.5	even	9
5776.2.a.cd.1.8		9	76.43	odd	18
5776.2.a.ce.1.2		9	76.71	even	18

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.83476 - 0.667798i) q^{3} +(0.302047 - 1.71299i) q^{5} +(-0.962609 - 1.66729i) q^{7} +(0.622259 - 0.522138i) q^{9} +(-2.27748 + 3.94470i) q^{11} +(2.57934 + 0.938803i) q^{13} +(-0.589750 - 3.34464i) q^{15} +(3.84088 + 3.22288i) q^{17} +(-4.18751 - 1.21026i) q^{19} +(-2.87957 - 2.41625i) q^{21} +(0.198055 + 1.12322i) q^{23} +(1.85536 + 0.675294i) q^{25} +(-2.13575 + 3.69923i) q^{27} +(3.83721 - 3.21980i) q^{29} +(-0.999936 - 1.73194i) q^{31} +(-1.54436 + 8.75848i) q^{33} +(-3.14680 + 1.14534i) q^{35} -7.06608 q^{37} +5.35941 q^{39} +(-10.3600 + 3.77075i) q^{41} +(1.05998 - 6.01147i) q^{43} +(-0.706466 - 1.22363i) q^{45} +(-6.72021 + 5.63892i) q^{47} +(1.64677 - 2.85228i) q^{49} +(9.19933 + 3.34828i) q^{51} +(0.00933315 + 0.0529309i) q^{53} +(6.06934 + 5.09278i) q^{55} +(-8.49130 + 0.575879i) q^{57} +(2.83451 + 2.37844i) q^{59} +(-2.60306 - 14.7627i) q^{61} +(-1.46955 - 0.534871i) q^{63} +(2.38724 - 4.13483i) q^{65} +(9.72449 - 8.15982i) q^{67} +(1.11347 + 1.92859i) q^{69} +(-0.359347 + 2.03796i) q^{71} +(0.670002 - 0.243861i) q^{73} +3.85509 q^{75} +8.76928 q^{77} +(10.5802 - 3.85086i) q^{79} +(-1.87142 + 10.6133i) q^{81} +(-4.99262 - 8.64748i) q^{83} +(6.68089 - 5.60593i) q^{85} +(4.89018 - 8.47005i) q^{87} +(15.2229 + 5.54068i) q^{89} +(-0.917642 - 5.20421i) q^{91} +(-2.99123 - 2.50994i) q^{93} +(-3.33799 + 6.80762i) q^{95} +(0.285278 + 0.239377i) q^{97} +(0.642497 + 3.64378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{7} - 6 q^{9} - 3 q^{11} + 3 q^{13} + 33 q^{15} + 9 q^{17} - 24 q^{19} - 15 q^{21} + 6 q^{23} + 6 q^{25} - 12 q^{27} - 3 q^{29} - 6 q^{31} - 45 q^{33} - 15 q^{35} + 48 q^{37} + 12 q^{39} - 18 q^{41}+ \cdots + 15 q^{99}+O(q^{100}) \) 18 * q - 9 * q^7 - 6 * q^9 - 3 * q^11 + 3 * q^13 + 33 * q^15 + 9 * q^17 - 24 * q^19 - 15 * q^21 + 6 * q^23 + 6 * q^25 - 12 * q^27 - 3 * q^29 - 6 * q^31 - 45 * q^33 - 15 * q^35 + 48 * q^37 + 12 * q^39 - 18 * q^41 - 39 * q^43 - 42 * q^45 - 27 * q^47 - 18 * q^49 + 48 * q^51 + 39 * q^53 - 27 * q^55 - 6 * q^57 + 9 * q^59 - 24 * q^61 + 3 * q^63 + 27 * q^65 + 39 * q^67 - 3 * q^69 + 12 * q^73 + 90 * q^75 + 60 * q^77 + 63 * q^79 - 6 * q^81 - 27 * q^83 - 30 * q^85 + 18 * q^87 + 66 * q^89 + 108 * q^91 + 60 * q^93 - 75 * q^95 - 81 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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