LMFDB - Embedded newform 368.2.m.e.289.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [368,2,Mod(49,368)] 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("368.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(368, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30,0,-2] 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			289.3
Character	$\chi$	$=$	368.289
Dual form			368.2.m.e.177.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.78999 + 1.15036i) q^{3} +(-0.356751 + 0.781176i) q^{5} +(3.61448 + 1.06131i) q^{7} +(0.634502 + 1.38936i) q^{9} +(1.12476 - 1.29805i) q^{11} +(-5.14713 + 1.51133i) q^{13} +(-1.53721 + 0.987907i) q^{15} +(-0.432786 - 3.01009i) q^{17} +(-0.0142503 + 0.0991134i) q^{19} +(5.24900 + 6.05767i) q^{21} +(2.50317 + 4.09074i) q^{23} +(2.79134 + 3.22138i) q^{25} +(0.445925 - 3.10147i) q^{27} +(-0.849184 - 5.90620i) q^{29} +(-6.18176 + 3.97277i) q^{31} +(3.50653 - 1.02961i) q^{33} +(-2.11854 + 2.44492i) q^{35} +(-0.00609366 - 0.0133433i) q^{37} +(-10.9519 - 3.21576i) q^{39} +(2.66347 - 5.83219i) q^{41} +(-5.30804 - 3.41127i) q^{43} -1.31170 q^{45} +6.93875 q^{47} +(6.04931 + 3.88766i) q^{49} +(2.68800 - 5.88590i) q^{51} +(-4.36756 - 1.28243i) q^{53} +(0.612742 + 1.34172i) q^{55} +(-0.139524 + 0.161019i) q^{57} +(9.27539 - 2.72350i) q^{59} +(-11.1378 + 7.15784i) q^{61} +(0.818850 + 5.69523i) q^{63} +(0.655626 - 4.55998i) q^{65} +(-1.87787 - 2.16718i) q^{67} +(-0.225161 + 10.2019i) q^{69} +(-8.91297 - 10.2861i) q^{71} +(1.57969 - 10.9870i) q^{73} +(1.29074 + 8.97728i) q^{75} +(5.44306 - 3.49804i) q^{77} +(9.35973 - 2.74827i) q^{79} +(7.36669 - 8.50162i) q^{81} +(4.75226 + 10.4060i) q^{83} +(2.50581 + 0.735772i) q^{85} +(5.27422 - 11.5489i) q^{87} +(-14.2554 - 9.16140i) q^{89} -20.2082 q^{91} -15.6354 q^{93} +(-0.0723412 - 0.0464908i) q^{95} +(-5.55342 + 12.1603i) q^{97} +(2.51712 + 0.739094i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41}+ \cdots + 17 q^{99}+O(q^{100}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.78999	+	1.15036i	1.03345	+	0.664159i	0.943359	−	0.331774i	$-0.107647\pi$
$3$	1.78999	+	1.15036i	1.03345	+	0.664159i	0.0900932	+	0.995933i	$0.471284\pi$
$4$		0			0
$5$	−0.356751	+	0.781176i	−0.159544	+	0.349353i	−0.972475	−	0.233007i	$-0.925143\pi$
$5$	−0.356751	+	0.781176i	−0.159544	+	0.349353i	0.812931	+	0.582360i	$0.197871\pi$
$6$		0			0
$7$	3.61448	+	1.06131i	1.36614	+	0.401136i	0.880925	−	0.473256i	$-0.156921\pi$
$7$	3.61448	+	1.06131i	1.36614	+	0.401136i	0.485220	+	0.874392i	$0.338740\pi$
$8$		0			0
$9$	0.634502	+	1.38936i	0.211501	+	0.463122i
$10$		0			0
$11$	1.12476	−	1.29805i	0.339129	−	0.391376i	−0.560411	−	0.828215i	$-0.689357\pi$
$11$	1.12476	−	1.29805i	0.339129	−	0.391376i	0.899540	+	0.436839i	$0.143902\pi$
$12$		0			0
$13$	−5.14713	+	1.51133i	−1.42756	+	0.419168i	−0.902054	−	0.431624i	$-0.857941\pi$
$13$	−5.14713	+	1.51133i	−1.42756	+	0.419168i	−0.525502	+	0.850792i	$0.676123\pi$
$14$		0			0
$15$	−1.53721	+	0.987907i	−0.396907	+	0.255077i
$16$		0			0
$17$	−0.432786	−	3.01009i	−0.104966	−	0.730055i	−0.972538	−	0.232744i	$-0.925230\pi$
$17$	−0.432786	−	3.01009i	−0.104966	−	0.730055i	0.867572	−	0.497311i	$-0.165679\pi$
$18$		0			0
$19$	−0.0142503	+	0.0991134i	−0.00326925	+	0.0227382i	−0.991391	−	0.130936i	$-0.958202\pi$
$19$	−0.0142503	+	0.0991134i	−0.00326925	+	0.0227382i	0.988122	+	0.153675i	$0.0491107\pi$
$20$		0			0
$21$	5.24900	+	6.05767i	1.14543	+	1.32189i
$22$		0			0
$23$	2.50317	+	4.09074i	0.521947	+	0.852978i
$23$	2.50317	+	4.09074i	0.521947	+	0.852978i
$24$		0			0
$25$	2.79134	+	3.22138i	0.558268	+	0.644275i
$26$		0			0
$27$	0.445925	−	3.10147i	0.0858182	−	0.596879i
$28$		0			0
$29$	−0.849184	−	5.90620i	−0.157689	−	1.09675i	−0.902877	−	0.429899i	$-0.858549\pi$
$29$	−0.849184	−	5.90620i	−0.157689	−	1.09675i	0.745187	−	0.666855i	$-0.232360\pi$
$30$		0			0
$31$	−6.18176	+	3.97277i	−1.11028	+	0.713531i	−0.961353	−	0.275318i	$-0.911217\pi$
$31$	−6.18176	+	3.97277i	−1.11028	+	0.713531i	−0.148923	+	0.988849i	$0.547581\pi$
$32$		0			0
$33$	3.50653	−	1.02961i	0.610409	−	0.179232i
$34$		0			0
$35$	−2.11854	+	2.44492i	−0.358098	+	0.413267i
$36$		0			0
$37$	−0.00609366	−	0.0133433i	−0.00100179	−	0.00219362i	0.909130	−	0.416512i	$-0.136747\pi$
$37$	−0.00609366	−	0.0133433i	−0.00100179	−	0.00219362i	−0.910132	+	0.414318i	$0.864020\pi$
$38$		0			0
$39$	−10.9519	−	3.21576i	−1.75371	−	0.514934i
$40$		0			0
$41$	2.66347	−	5.83219i	0.415965	−	0.910836i	−0.579434	−	0.815019i	$-0.696726\pi$
$41$	2.66347	−	5.83219i	0.415965	−	0.910836i	0.995399	−	0.0958167i	$-0.0305463\pi$
$42$		0			0
$43$	−5.30804	−	3.41127i	−0.809468	−	0.520214i	0.0692246	−	0.997601i	$-0.477947\pi$
$43$	−5.30804	−	3.41127i	−0.809468	−	0.520214i	−0.878693	+	0.477387i	$0.841584\pi$
$44$		0			0
$45$	−1.31170			−0.195536
$46$		0			0
$47$	6.93875			1.01212			0.506060	−	0.862498i	$-0.331101\pi$
$47$	6.93875			1.01212			0.506060	+	0.862498i	$0.331101\pi$
$48$		0			0
$49$	6.04931	+	3.88766i	0.864187	+	0.555379i
$50$		0			0
$51$	2.68800	−	5.88590i	0.376395	−	0.824191i
$52$		0			0
$53$	−4.36756	−	1.28243i	−0.599931	−	0.176156i	−0.0323547	−	0.999476i	$-0.510301\pi$
$53$	−4.36756	−	1.28243i	−0.599931	−	0.176156i	−0.567576	+	0.823321i	$0.692119\pi$
$54$		0			0
$55$	0.612742	+	1.34172i	0.0826221	+	0.180917i
$56$		0			0
$57$	−0.139524	+	0.161019i	−0.0184804	+	0.0213275i
$58$		0			0
$59$	9.27539	−	2.72350i	1.20755	−	0.354569i	0.384816	−	0.922993i	$-0.374265\pi$
$59$	9.27539	−	2.72350i	1.20755	−	0.354569i	0.822736	+	0.568424i	$0.192447\pi$
$60$		0			0
$61$	−11.1378	+	7.15784i	−1.42605	+	0.916468i	−0.426122	+	0.904666i	$0.640120\pi$
$61$	−11.1378	+	7.15784i	−1.42605	+	0.916468i	−0.999930	+	0.0118021i	$0.996243\pi$
$62$		0			0
$63$	0.818850	+	5.69523i	0.103165	+	0.717532i
$64$		0			0
$65$	0.655626	−	4.55998i	0.0813205	−	0.565596i
$66$		0			0
$67$	−1.87787	−	2.16718i	−0.229418	−	0.264763i	0.629356	−	0.777117i	$-0.283319\pi$
$67$	−1.87787	−	2.16718i	−0.229418	−	0.264763i	−0.858774	+	0.512354i	$0.828773\pi$
$68$		0			0
$69$	−0.225161	+	10.2019i	−0.0271062	+	1.22817i
$70$		0			0
$71$	−8.91297	−	10.2861i	−1.05777	−	1.22074i	−0.974541	−	0.224207i	$-0.928021\pi$
$71$	−8.91297	−	10.2861i	−1.05777	−	1.22074i	−0.0832335	−	0.996530i	$-0.526525\pi$
$72$		0			0
$73$	1.57969	−	10.9870i	0.184888	−	1.28593i	−0.660115	−	0.751165i	$-0.729492\pi$
$73$	1.57969	−	10.9870i	0.184888	−	1.28593i	0.845003	−	0.534762i	$-0.179599\pi$
$74$		0			0
$75$	1.29074	+	8.97728i	0.149042	+	1.03661i
$76$		0			0
$77$	5.44306	−	3.49804i	0.620294	−	0.398639i
$78$		0			0
$79$	9.35973	−	2.74827i	1.05305	−	0.309204i	0.291002	−	0.956722i	$-0.406011\pi$
$79$	9.35973	−	2.74827i	1.05305	−	0.309204i	0.762050	+	0.647518i	$0.224193\pi$
$80$		0			0
$81$	7.36669	−	8.50162i	0.818521	−	0.944624i
$82$		0			0
$83$	4.75226	+	10.4060i	0.521629	+	1.14221i	0.968819	+	0.247769i	$0.0796973\pi$
$83$	4.75226	+	10.4060i	0.521629	+	1.14221i	−0.447191	+	0.894439i	$0.647575\pi$
$84$		0			0
$85$	2.50581	+	0.735772i	0.271793	+	0.0798057i
$86$		0			0
$87$	5.27422	−	11.5489i	0.565455	−	1.23817i
$88$		0			0
$89$	−14.2554	−	9.16140i	−1.51107	−	0.971107i	−0.993297	−	0.115589i	$-0.963124\pi$
$89$	−14.2554	−	9.16140i	−1.51107	−	0.971107i	−0.517774	−	0.855517i	$-0.673239\pi$
$90$		0			0
$91$	−20.2082			−2.11839
$92$		0			0
$93$	−15.6354			−1.62132
$94$		0			0
$95$	−0.0723412	−	0.0464908i	−0.00742205	−	0.00476986i
$96$		0			0
$97$	−5.55342	+	12.1603i	−0.563864	+	1.23469i	0.386136	+	0.922442i	$0.373809\pi$
$97$	−5.55342	+	12.1603i	−0.563864	+	1.23469i	−0.950000	+	0.312249i	$0.898918\pi$
$98$		0			0
$99$	2.51712	+	0.739094i	0.252980	+	0.0742818i
$100$		0			0
$101$	0.251495	+	0.550697i	0.0250247	+	0.0547964i	0.921732	−	0.387828i	$-0.126775\pi$
$101$	0.251495	+	0.550697i	0.0250247	+	0.0547964i	−0.896707	+	0.442625i	$0.854047\pi$
$102$		0			0
$103$	6.60958	−	7.62786i	0.651262	−	0.751596i	−0.330062	−	0.943959i	$-0.607070\pi$
$103$	6.60958	−	7.62786i	0.651262	−	0.751596i	0.981324	+	0.192363i	$0.0616152\pi$
$104$		0			0
$105$	−6.60470	+	1.93931i	−0.644553	+	0.189258i
$106$		0			0
$107$	−9.98171	+	6.41486i	−0.964969	+	0.620148i	−0.925369	−	0.379068i	$-0.876245\pi$
$107$	−9.98171	+	6.41486i	−0.964969	+	0.620148i	−0.0395999	+	0.999216i	$0.512608\pi$
$108$		0			0
$109$	−2.10953	−	14.6721i	−0.202056	−	1.40533i	−0.798170	−	0.602433i	$-0.794198\pi$
$109$	−2.10953	−	14.6721i	−0.202056	−	1.40533i	0.596113	−	0.802900i	$-0.296711\pi$
$110$		0			0
$111$	0.00444192	−	0.0308942i	0.000421608	−	0.00293235i
$112$		0			0
$113$	3.90672	+	4.50860i	0.367514	+	0.424133i	0.909143	−	0.416484i	$-0.136738\pi$
$113$	3.90672	+	4.50860i	0.367514	+	0.424133i	−0.541629	+	0.840617i	$0.682192\pi$
$114$		0			0
$115$	−4.08860	+	0.496040i	−0.381264	+	0.0462560i
$116$		0			0
$117$	−5.36565	−	6.19229i	−0.496055	−	0.572478i
$118$		0			0
$119$	1.63034	−	11.3392i	0.149453	−	1.03947i
$120$		0			0
$121$	1.14563	+	7.96805i	0.104148	+	0.724368i
$122$		0			0
$123$	11.4767	−	7.37563i	1.03482	−	0.665038i
$124$		0			0
$125$	−7.63226	+	2.24103i	−0.682650	+	0.200444i
$126$		0			0
$127$	−0.497860	+	0.574562i	−0.0441780	+	0.0509841i	−0.777409	−	0.628996i	$-0.783466\pi$
$127$	−0.497860	+	0.574562i	−0.0441780	+	0.0509841i	0.733231	+	0.679980i	$0.238012\pi$
$128$		0			0
$129$	−5.57716	−	12.2123i	−0.491042	−	1.07523i
$130$		0			0
$131$	−7.13730	−	2.09570i	−0.623589	−	0.183102i	−0.0453518	−	0.998971i	$-0.514441\pi$
$131$	−7.13730	−	2.09570i	−0.623589	−	0.183102i	−0.578237	+	0.815869i	$0.696259\pi$
$132$		0			0
$133$	−0.156697	+	0.343119i	−0.0135874	+	0.0297522i
$134$		0			0
$135$	2.26371	+	1.45480i	0.194829	+	0.125209i
$136$		0			0
$137$	7.22485			0.617261			0.308630	−	0.951182i	$-0.400129\pi$
$137$	7.22485			0.617261			0.308630	+	0.951182i	$0.400129\pi$
$138$		0			0
$139$	−4.87522			−0.413511			−0.206755	−	0.978393i	$-0.566290\pi$
$139$	−4.87522			−0.413511			−0.206755	+	0.978393i	$0.566290\pi$
$140$		0			0
$141$	12.4203	+	7.98204i	1.04598	+	0.672209i
$142$		0			0
$143$	−3.82752	+	8.38110i	−0.320073	+	0.700863i
$144$		0			0
$145$	4.91673	+	1.44368i	0.408312	+	0.119891i
$146$		0			0
$147$	6.35602	+	13.9177i	0.524236	+	1.14792i
$148$		0			0
$149$	−1.06195	+	1.22556i	−0.0869986	+	0.100402i	−0.797580	−	0.603214i	$-0.793887\pi$
$149$	−1.06195	+	1.22556i	−0.0869986	+	0.100402i	0.710581	+	0.703615i	$0.248432\pi$
$150$		0			0
$151$	5.72901	−	1.68219i	0.466220	−	0.136895i	−0.0401812	−	0.999192i	$-0.512794\pi$
$151$	5.72901	−	1.68219i	0.466220	−	0.136895i	0.506402	+	0.862298i	$0.330975\pi$
$152$		0			0
$153$	3.90752	−	2.51121i	0.315904	−	0.203019i
$154$		0			0
$155$	−0.898087	−	6.24633i	−0.0721361	−	0.501717i
$156$		0			0
$157$	−2.59334	+	18.0370i	−0.206971	+	1.43951i	0.575998	+	0.817451i	$0.304614\pi$
$157$	−2.59334	+	18.0370i	−0.206971	+	1.43951i	−0.782968	+	0.622062i	$0.786295\pi$
$158$		0			0
$159$	−6.34265	−	7.31980i	−0.503005	−	0.580498i
$160$		0			0
$161$	4.70612	+	17.4425i	0.370895	+	1.37466i
$162$		0			0
$163$	12.6364	+	14.5832i	0.989762	+	1.14225i	0.989831	+	0.142246i	$0.0454325\pi$
$163$	12.6364	+	14.5832i	0.989762	+	1.14225i	−6.93188e−5		1.00000i	$0.500022\pi$
$164$		0			0
$165$	−0.446652	+	3.10654i	−0.0347718	+	0.241843i
$166$		0			0
$167$	1.94635	+	13.5371i	0.150613	+	1.04754i	0.915195	+	0.403010i	$0.132036\pi$
$167$	1.94635	+	13.5371i	0.150613	+	1.04754i	−0.764583	+	0.644526i	$0.777055\pi$
$168$		0			0
$169$	13.2725	−	8.52971i	1.02096	−	0.656132i
$170$		0			0
$171$	−0.146746	+	0.0430887i	−0.0112220	+	0.00329507i
$172$		0			0
$173$	10.2436	−	11.8218i	0.778808	−	0.898792i	−0.218215	−	0.975901i	$-0.570023\pi$
$173$	10.2436	−	11.8218i	0.778808	−	0.898792i	0.997023	+	0.0771084i	$0.0245687\pi$
$174$		0			0
$175$	6.67037	+	14.6061i	0.504232	+	1.10411i
$176$		0			0
$177$	19.7359	+	5.79497i	1.48344	+	0.435577i
$178$		0			0
$179$	−1.26873	+	2.77813i	−0.0948292	+	0.207647i	−0.951102	−	0.308877i	$-0.900047\pi$
$179$	−1.26873	+	2.77813i	−0.0948292	+	0.207647i	0.856273	+	0.516524i	$0.172774\pi$
$180$		0			0
$181$	17.1054	+	10.9930i	1.27143	+	0.817101i	0.989806	−	0.142422i	$-0.0454891\pi$
$181$	17.1054	+	10.9930i	1.27143	+	0.817101i	0.281628	+	0.959524i	$0.409125\pi$
$182$		0			0
$183$	−28.1707			−2.08244
$184$		0			0
$185$	0.0125974			0.000926176
$186$		0			0
$187$	−4.39402	−	2.82387i	−0.321323	−	0.206502i
$188$		0			0
$189$	4.90340	−	10.7369i	0.356670	−	0.780998i
$190$		0			0
$191$	14.7270	+	4.32424i	1.06561	+	0.312891i	0.767107	−	0.641519i	$-0.221695\pi$
$191$	14.7270	+	4.32424i	1.06561	+	0.312891i	0.298501	+	0.954409i	$0.403514\pi$
$192$		0			0
$193$	4.54833	+	9.95945i	0.327396	+	0.716897i	0.999727	−	0.0233533i	$-0.00743427\pi$
$193$	4.54833	+	9.95945i	0.327396	+	0.716897i	−0.672331	+	0.740250i	$0.734707\pi$
$194$		0			0
$195$	6.41918	−	7.40812i	0.459687	−	0.530507i
$196$		0			0
$197$	11.9663	−	3.51361i	0.852561	−	0.250334i	0.173879	−	0.984767i	$-0.444370\pi$
$197$	11.9663	−	3.51361i	0.852561	−	0.250334i	0.678682	+	0.734433i	$0.262552\pi$
$198$		0			0
$199$	−15.2519	+	9.80178i	−1.08118	+	0.694830i	−0.954829	−	0.297156i	$-0.903962\pi$
$199$	−15.2519	+	9.80178i	−1.08118	+	0.694830i	−0.126348	+	0.991986i	$0.540326\pi$
$200$		0			0
$201$	−0.868342	−	6.03945i	−0.0612481	−	0.425990i
$202$		0			0
$203$	3.19894	−	22.2491i	0.224521	−	1.56158i
$204$		0			0
$205$	3.60577	+	4.16128i	0.251838	+	0.290637i
$206$		0			0
$207$	−4.09526	+	6.07340i	−0.284640	+	0.422130i
$208$		0			0
$209$	0.112625	+	0.129977i	0.00779046	+	0.00899067i
$210$		0			0
$211$	−1.75126	+	12.1803i	−0.120561	+	0.838523i	0.836361	+	0.548179i	$0.184679\pi$
$211$	−1.75126	+	12.1803i	−0.120561	+	0.838523i	−0.956922	+	0.290344i	$0.906230\pi$
$212$		0			0
$213$	−4.12143	−	28.6652i	−0.282396	−	1.96410i
$214$		0			0
$215$	4.55845	−	2.92954i	0.310884	−	0.199793i
$216$		0			0
$217$	−26.5602	+	7.79876i	−1.80302	+	0.529415i
$218$		0			0
$219$	15.4666	−	17.8494i	1.04513	−	1.20615i
$220$		0			0
$221$	6.77686	+	14.8393i	0.455861	+	0.998196i
$222$		0			0
$223$	3.17837	+	0.933253i	0.212839	+	0.0624952i	0.386414	−	0.922325i	$-0.373714\pi$
$223$	3.17837	+	0.933253i	0.212839	+	0.0624952i	−0.173575	+	0.984821i	$0.555532\pi$
$224$		0			0
$225$	−2.70456	+	5.92216i	−0.180304	+	0.394810i
$226$		0			0
$227$	0.274954	+	0.176702i	0.0182493	+	0.0117281i	0.549734	−	0.835340i	$-0.314729\pi$
$227$	0.274954	+	0.176702i	0.0182493	+	0.0117281i	−0.531484	+	0.847068i	$0.678366\pi$
$228$		0			0
$229$	−24.0700			−1.59059			−0.795295	−	0.606223i	$-0.792684\pi$
$229$	−24.0700			−1.59059			−0.795295	+	0.606223i	$0.792684\pi$
$230$		0			0
$231$	13.7670			0.905804
$232$		0			0
$233$	−16.0197	−	10.2952i	−1.04948	−	0.674462i	−0.102169	−	0.994767i	$-0.532578\pi$
$233$	−16.0197	−	10.2952i	−1.04948	−	0.674462i	−0.947315	+	0.320305i	$0.896215\pi$
$234$		0			0
$235$	−2.47541	+	5.42038i	−0.161478	+	0.353587i
$236$		0			0
$237$	19.9153	+	5.84767i	1.29364	+	0.379847i
$238$		0			0
$239$	3.01309	+	6.59775i	0.194901	+	0.426773i	0.981700	−	0.190436i	$-0.0609903\pi$
$239$	3.01309	+	6.59775i	0.194901	+	0.426773i	−0.786799	+	0.617210i	$0.788263\pi$
$240$		0			0
$241$	−16.3044	+	18.8162i	−1.05026	+	1.21206i	−0.0735916	+	0.997288i	$0.523446\pi$
$241$	−16.3044	+	18.8162i	−1.05026	+	1.21206i	−0.976664	+	0.214771i	$0.931099\pi$
$242$		0			0
$243$	13.9469	−	4.09518i	0.894693	−	0.262706i
$244$		0			0
$245$	−5.19504	+	3.33865i	−0.331899	+	0.213299i
$246$		0			0
$247$	−0.0764449	−	0.531686i	−0.00486407	−	0.0338304i
$248$		0			0
$249$	−3.46412	+	24.0935i	−0.219529	+	1.52686i
$250$		0			0
$251$	8.51389	+	9.82555i	0.537392	+	0.620183i	0.957899	−	0.287106i	$-0.0926933\pi$
$251$	8.51389	+	9.82555i	0.537392	+	0.620183i	−0.420507	+	0.907289i	$0.638148\pi$
$252$		0			0
$253$	8.12544	+	1.35188i	0.510842	+	0.0849922i
$254$		0			0
$255$	3.63898	+	4.19960i	0.227882	+	0.262989i
$256$		0			0
$257$	3.43532	−	23.8931i	0.214289	−	1.49041i	−0.544326	−	0.838874i	$-0.683214\pi$
$257$	3.43532	−	23.8931i	0.214289	−	1.49041i	0.758615	−	0.651540i	$-0.225877\pi$
$258$		0			0
$259$	−0.00786412	−	0.0546962i	−0.000488653	−	0.00339866i
$260$		0			0
$261$	7.66706	−	4.92732i	0.474579	−	0.304994i
$262$		0			0
$263$	−11.9409	+	3.50616i	−0.736306	+	0.216199i	−0.628322	−	0.777954i	$-0.716258\pi$
$263$	−11.9409	+	3.50616i	−0.736306	+	0.216199i	−0.107984	+	0.994153i	$0.534440\pi$
$264$		0			0
$265$	2.55994	−	2.95433i	0.157256	−	0.181483i
$266$		0			0
$267$	−14.9782	−	32.7977i	−0.916650	−	2.00718i
$268$		0			0
$269$	−4.58996	−	1.34773i	−0.279855	−	0.0821727i	0.138793	−	0.990321i	$-0.455678\pi$
$269$	−4.58996	−	1.34773i	−0.279855	−	0.0821727i	−0.418648	+	0.908149i	$0.637496\pi$
$270$		0			0
$271$	−6.59832	+	14.4483i	−0.400820	+	0.877672i	0.596367	+	0.802712i	$0.296610\pi$
$271$	−6.59832	+	14.4483i	−0.400820	+	0.877672i	−0.997187	+	0.0749605i	$0.976117\pi$
$272$		0			0
$273$	−36.1724	−	23.2466i	−2.18926	−	1.40695i
$274$		0			0
$275$	7.32109			0.441478
$276$		0			0
$277$	−3.57213			−0.214629			−0.107314	−	0.994225i	$-0.534225\pi$
$277$	−3.57213			−0.214629			−0.107314	+	0.994225i	$0.534225\pi$
$278$		0			0
$279$	−9.44196	−	6.06798i	−0.565276	−	0.363281i
$280$		0			0
$281$	−10.0607	+	22.0299i	−0.600172	+	1.31419i	0.328924	+	0.944356i	$0.393314\pi$
$281$	−10.0607	+	22.0299i	−0.600172	+	1.31419i	−0.929096	+	0.369838i	$0.879413\pi$
$282$		0			0
$283$	19.1806	+	5.63194i	1.14017	+	0.334784i	0.796697	−	0.604379i	$-0.206579\pi$
$283$	19.1806	+	5.63194i	1.14017	+	0.334784i	0.343473	+	0.939163i	$0.388397\pi$
$284$		0			0
$285$	−0.0760090	−	0.166436i	−0.00450238	−	0.00985884i
$286$		0			0
$287$	15.8168	−	18.2536i	0.933637	−	1.07747i
$288$		0			0
$289$	7.43802	−	2.18400i	0.437531	−	0.128471i
$290$		0			0
$291$	−23.9293	+	15.3784i	−1.40276	+	0.901498i
$292$		0			0
$293$	0.651892	+	4.53401i	0.0380839	+	0.264879i	0.999963	−	0.00859542i	$-0.00273604\pi$
$293$	0.651892	+	4.53401i	0.0380839	+	0.264879i	−0.961879	+	0.273475i	$0.911827\pi$
$294$		0			0
$295$	−1.18147	+	8.21732i	−0.0687880	+	0.478431i
$296$		0			0
$297$	−3.52429	−	4.06725i	−0.204500	−	0.236006i
$298$		0			0
$299$	−19.0666	−	17.2724i	−1.10265	−	0.998890i
$300$		0			0
$301$	−15.5654	−	17.9634i	−0.897174	−	1.03539i
$302$		0			0
$303$	−0.183325	+	1.27505i	−0.0105317	+	0.0732498i
$304$		0			0
$305$	−1.61811	−	11.2542i	−0.0926524	−	0.644412i
$306$		0			0
$307$	−7.50755	+	4.82481i	−0.428479	+	0.275366i	−0.737055	−	0.675833i	$-0.763784\pi$
$307$	−7.50755	+	4.82481i	−0.428479	+	0.275366i	0.308576	+	0.951200i	$0.400148\pi$
$308$		0			0
$309$	20.6059	−	6.05043i	1.17223	−	0.344197i
$310$		0			0
$311$	4.44802	−	5.13329i	0.252224	−	0.291082i	−0.615491	−	0.788144i	$-0.711042\pi$
$311$	4.44802	−	5.13329i	0.252224	−	0.291082i	0.867715	+	0.497062i	$0.165588\pi$
$312$		0			0
$313$	0.145833	+	0.319329i	0.00824295	+	0.0180495i	0.913709	−	0.406370i	$-0.133206\pi$
$313$	0.145833	+	0.319329i	0.00824295	+	0.0180495i	−0.905466	+	0.424419i	$0.860478\pi$
$314$		0			0
$315$	−4.74110	−	1.39211i	−0.267131	−	0.0784367i
$316$		0			0
$317$	4.88767	−	10.7025i	0.274519	−	0.601113i	−0.721284	−	0.692640i	$-0.756448\pi$
$317$	4.88767	−	10.7025i	0.274519	−	0.601113i	0.995803	+	0.0915271i	$0.0291748\pi$
$318$		0			0
$319$	−8.62165	−	5.54080i	−0.482720	−	0.310225i
$320$		0			0
$321$	−25.2466			−1.40913
$322$		0			0
$323$	0.304508			0.0169433
$324$		0			0
$325$	−19.2359	−	12.3622i	−1.06702	−	0.685731i
$326$		0			0
$327$	13.1021	−	28.6897i	0.724549	−	1.58654i
$328$		0			0
$329$	25.0800	+	7.36414i	1.38270	+	0.405998i
$330$		0			0
$331$	7.95809	+	17.4258i	0.437416	+	0.957807i	0.992065	+	0.125723i	$0.0401251\pi$
$331$	7.95809	+	17.4258i	0.437416	+	0.957807i	−0.554649	+	0.832084i	$0.687148\pi$
$332$		0			0
$333$	0.0146722	−	0.0169326i	0.000804033	−	0.000927903i
$334$		0			0
$335$	2.36288	−	0.693804i	0.129098	−	0.0379066i
$336$		0			0
$337$	9.87742	−	6.34783i	0.538057	−	0.345788i	−0.243221	−	0.969971i	$-0.578204\pi$
$337$	9.87742	−	6.34783i	0.538057	−	0.345788i	0.781279	+	0.624182i	$0.214568\pi$
$338$		0			0
$339$	1.80650	+	12.5645i	0.0981156	+	0.682409i
$340$		0			0
$341$	−1.79617	+	12.4926i	−0.0972680	+	0.676514i
$342$		0			0
$343$	0.470755	+	0.543280i	0.0254184	+	0.0293344i
$344$		0			0
$345$	−7.88918	−	3.81544i	−0.424739	−	0.205416i
$346$		0			0
$347$	−14.3894	−	16.6062i	−0.772463	−	0.891470i	0.224078	−	0.974571i	$-0.428063\pi$
$347$	−14.3894	−	16.6062i	−0.772463	−	0.891470i	−0.996541	+	0.0831013i	$0.973517\pi$
$348$		0			0
$349$	0.425908	−	2.96226i	0.0227983	−	0.158566i	−0.975242	−	0.221141i	$-0.929022\pi$
$349$	0.425908	−	2.96226i	0.0227983	−	0.158566i	0.998040	+	0.0625746i	$0.0199311\pi$
$350$		0			0
$351$	2.39213	+	16.6376i	0.127682	+	0.888050i
$352$		0			0
$353$	−30.1182	+	19.3558i	−1.60303	+	1.03020i	−0.637311	+	0.770607i	$0.719953\pi$
$353$	−30.1182	+	19.3558i	−1.60303	+	1.03020i	−0.965717	+	0.259597i	$0.916410\pi$
$354$		0			0
$355$	11.2150	−	3.29302i	0.595229	−	0.174775i
$356$		0			0
$357$	15.9625	−	18.4217i	0.844823	−	0.974978i
$358$		0			0
$359$	−7.26538	−	15.9090i	−0.383452	−	0.839643i	−0.998683	−	0.0512965i	$-0.983665\pi$
$359$	−7.26538	−	15.9090i	−0.383452	−	0.839643i	0.615231	−	0.788347i	$-0.289063\pi$
$360$		0			0
$361$	18.2207	+	5.35009i	0.958987	+	0.281584i
$362$		0			0
$363$	−7.11543	+	15.5806i	−0.373463	+	0.817771i
$364$		0			0
$365$	8.01920	+	5.15362i	0.419744	+	0.269753i
$366$		0			0
$367$	0.118951			0.00620922			0.00310461	−	0.999995i	$-0.499012\pi$
$367$	0.118951			0.00620922			0.00310461	+	0.999995i	$0.499012\pi$
$368$		0			0
$369$	9.79302			0.509804
$370$		0			0
$371$	−14.4254	−	9.27065i	−0.748930	−	0.481308i
$372$		0			0
$373$	11.5728	−	25.3410i	0.599219	−	1.31211i	−0.330490	−	0.943810i	$-0.607214\pi$
$373$	11.5728	−	25.3410i	0.599219	−	1.31211i	0.929709	−	0.368296i	$-0.120059\pi$
$374$		0			0
$375$	−16.2397	−	4.76839i	−0.838613	−	0.246239i
$376$		0			0
$377$	13.2971	+	29.1166i	0.684835	+	1.49958i
$378$		0			0
$379$	10.9451	−	12.6313i	0.562210	−	0.648825i	−0.401474	−	0.915870i	$-0.631502\pi$
$379$	10.9451	−	12.6313i	0.562210	−	0.648825i	0.963684	+	0.267045i	$0.0860474\pi$
$380$		0			0
$381$	−1.55212	+	0.455743i	−0.0795174	+	0.0233484i
$382$		0			0
$383$	−5.16363	+	3.31846i	−0.263849	+	0.169566i	−0.665876	−	0.746062i	$-0.731942\pi$
$383$	−5.16363	+	3.31846i	−0.263849	+	0.169566i	0.402027	+	0.915628i	$0.368306\pi$
$384$		0			0
$385$	0.790769	+	5.49992i	0.0403013	+	0.280302i
$386$		0			0
$387$	1.37154	−	9.53926i	0.0697192	−	0.484908i
$388$		0			0
$389$	12.9902	+	14.9915i	0.658629	+	0.760098i	0.982553	−	0.185985i	$-0.0595476\pi$
$389$	12.9902	+	14.9915i	0.658629	+	0.760098i	−0.323924	+	0.946083i	$0.605002\pi$
$390$		0			0
$391$	11.2302	−	9.30519i	0.567934	−	0.470584i
$392$		0			0
$393$	−10.3649	−	11.9617i	−0.522840	−	0.603390i
$394$		0			0
$395$	−1.19222	+	8.29205i	−0.0599869	+	0.417218i
$396$		0			0
$397$	−0.655562	−	4.55953i	−0.0329017	−	0.228836i	0.966735	−	0.255779i	$-0.0823319\pi$
$397$	−0.655562	−	4.55953i	−0.0329017	−	0.228836i	−0.999637	+	0.0269426i	$0.991423\pi$
$398$		0			0
$399$	−0.675196	+	0.433922i	−0.0338021	+	0.0217233i
$400$		0			0
$401$	−10.9508	+	3.21544i	−0.546856	+	0.160571i	−0.543479	−	0.839423i	$-0.682893\pi$
$401$	−10.9508	+	3.21544i	−0.546856	+	0.160571i	−0.00337695	+	0.999994i	$0.501075\pi$
$402$		0			0
$403$	25.8141	−	29.7911i	1.28589	−	1.48400i
$404$		0			0
$405$	4.01318	+	8.78765i	0.199417	+	0.436662i
$406$		0			0
$407$	−0.0241741	−	0.00709816i	−0.00119827	−	0.000351842i
$408$		0			0
$409$	10.8015	−	23.6520i	0.534100	−	1.16952i	−0.429720	−	0.902962i	$-0.641388\pi$
$409$	10.8015	−	23.6520i	0.534100	−	1.16952i	0.963820	−	0.266554i	$-0.0858851\pi$
$410$		0			0
$411$	12.9324	+	8.31117i	0.637910	+	0.409960i
$412$		0			0
$413$	36.4162			1.79192
$414$		0			0
$415$	−9.82430			−0.482256
$416$		0			0
$417$	−8.72661	−	5.60825i	−0.427344	−	0.274637i
$418$		0			0
$419$	−13.9081	+	30.4544i	−0.679454	+	1.48780i	0.183766	+	0.982970i	$0.441171\pi$
$419$	−13.9081	+	30.4544i	−0.679454	+	1.48780i	−0.863221	+	0.504827i	$0.831556\pi$
$420$		0			0
$421$	−28.5573	−	8.38518i	−1.39180	−	0.408669i	−0.501938	−	0.864904i	$-0.667379\pi$
$421$	−28.5573	−	8.38518i	−1.39180	−	0.408669i	−0.889859	+	0.456235i	$0.849198\pi$
$422$		0			0
$423$	4.40265	+	9.64045i	0.214064	+	0.468735i
$424$		0			0
$425$	8.48859	−	9.79636i	0.411757	−	0.475193i
$426$		0			0
$427$	−47.8541	+	14.0512i	−2.31582	+	0.679987i
$428$		0			0
$429$	−16.4925	+	10.5991i	−0.796265	+	0.511728i
$430$		0			0
$431$	−0.894529	−	6.22159i	−0.0430880	−	0.299683i	−0.999958	−	0.00916701i	$-0.997082\pi$
$431$	−0.894529	−	6.22159i	−0.0430880	−	0.299683i	0.956870	−	0.290516i	$-0.0938271\pi$
$432$		0			0
$433$	0.375339	−	2.61054i	0.0180376	−	0.125455i	−0.978813	−	0.204756i	$-0.934360\pi$
$433$	0.375339	−	2.61054i	0.0180376	−	0.125455i	0.996851	+	0.0793015i	$0.0252690\pi$
$434$		0			0
$435$	7.14016	+	8.24018i	0.342344	+	0.395086i
$436$		0			0
$437$	−0.441118	+	0.189803i	−0.0211015	+	0.00907951i
$438$		0			0
$439$	−4.11921	−	4.75382i	−0.196599	−	0.226888i	0.648887	−	0.760885i	$-0.275235\pi$
$439$	−4.11921	−	4.75382i	−0.196599	−	0.226888i	−0.845486	+	0.533997i	$0.820689\pi$
$440$		0			0
$441$	−1.56307	+	10.8714i	−0.0744321	+	0.517687i
$442$		0			0
$443$	0.0227869	+	0.158486i	0.00108264	+	0.00752991i	0.990356	−	0.138549i	$-0.0442438\pi$
$443$	0.0227869	+	0.158486i	0.00108264	+	0.00752991i	−0.989273	+	0.146079i	$0.953335\pi$
$444$		0			0
$445$	12.2423	−	7.86765i	0.580341	−	0.372962i
$446$		0			0
$447$	−3.31072	+	0.972115i	−0.156592	+	0.0459794i
$448$		0			0
$449$	−11.0440	+	12.7454i	−0.521196	+	0.601493i	−0.953930	−	0.300029i	$-0.903004\pi$
$449$	−11.0440	+	12.7454i	−0.521196	+	0.601493i	0.432734	+	0.901522i	$0.357549\pi$
$450$		0			0
$451$	−4.57468	−	10.0171i	−0.215413	−	0.471689i
$452$		0			0
$453$	12.1900	+	3.57931i	0.572736	+	0.168171i
$454$		0			0
$455$	7.20929	−	15.7861i	0.337977	−	0.740066i
$456$		0			0
$457$	10.4171	+	6.69467i	0.487292	+	0.313163i	0.761115	−	0.648617i	$-0.224652\pi$
$457$	10.4171	+	6.69467i	0.487292	+	0.313163i	−0.273824	+	0.961780i	$0.588288\pi$
$458$		0			0
$459$	−9.52872			−0.444762
$460$		0			0
$461$	13.4581			0.626807			0.313404	−	0.949620i	$-0.398531\pi$
$461$	13.4581			0.626807			0.313404	+	0.949620i	$0.398531\pi$
$462$		0			0
$463$	−11.8163	−	7.59387i	−0.549149	−	0.352917i	0.236458	−	0.971642i	$-0.424013\pi$
$463$	−11.8163	−	7.59387i	−0.549149	−	0.352917i	−0.785608	+	0.618725i	$0.787650\pi$
$464$		0			0
$465$	5.57795	−	12.2140i	0.258671	−	0.566411i
$466$		0			0
$467$	−13.4549	−	3.95073i	−0.622621	−	0.182818i	−0.0448190	−	0.998995i	$-0.514271\pi$
$467$	−13.4549	−	3.95073i	−0.622621	−	0.182818i	−0.577802	+	0.816177i	$0.696089\pi$
$468$		0			0
$469$	−4.48748	−	9.82622i	−0.207213	−	0.453732i
$470$		0			0
$471$	−25.3911	+	29.3029i	−1.16996	+	1.35021i
$472$		0			0
$473$	−10.3983	+	3.05321i	−0.478113	+	0.140387i
$474$		0			0
$475$	−0.359059	+	0.230753i	−0.0164748	+	0.0105877i
$476$		0			0
$477$	−0.989460	−	6.88184i	−0.0453043	−	0.315098i
$478$		0			0
$479$	−3.32792	+	23.1462i	−0.152056	+	1.05758i	0.760710	+	0.649092i	$0.224851\pi$
$479$	−3.32792	+	23.1462i	−0.152056	+	1.05758i	−0.912766	+	0.408483i	$0.866058\pi$
$480$		0			0
$481$	0.0515310	+	0.0594699i	0.00234961	+	0.00271159i
$482$		0			0
$483$	−11.6412	+	36.6357i	−0.529694	+	1.66698i
$484$		0			0
$485$	−7.51814	−	8.67640i	−0.341381	−	0.393975i
$486$		0			0
$487$	1.92568	−	13.3934i	0.0872609	−	0.606913i	−0.898527	−	0.438918i	$-0.855362\pi$
$487$	1.92568	−	13.3934i	0.0872609	−	0.606913i	0.985788	−	0.167995i	$-0.0537291\pi$
$488$		0			0
$489$	5.84319	+	40.6403i	0.264238	+	1.83782i
$490$		0			0
$491$	15.9955	−	10.2797i	0.721869	−	0.463917i	−0.127418	−	0.991849i	$-0.540669\pi$
$491$	15.9955	−	10.2797i	0.721869	−	0.463917i	0.849286	+	0.527932i	$0.177033\pi$
$492$		0			0
$493$	−17.4107	+	5.11225i	−0.784139	+	0.230244i
$494$		0			0
$495$	−1.47535	+	1.70264i	−0.0663120	+	0.0765282i
$496$		0			0
$497$	−21.2990	−	46.6383i	−0.955391	−	2.09202i
$498$		0			0
$499$	14.4936	+	4.25572i	0.648824	+	0.190512i	0.589553	−	0.807730i	$-0.299304\pi$
$499$	14.4936	+	4.25572i	0.648824	+	0.190512i	0.0592716	+	0.998242i	$0.481122\pi$
$500$		0			0
$501$	−12.0886	+	26.4704i	−0.540080	+	1.18261i
$502$		0			0
$503$	−10.5648	−	6.78958i	−0.471061	−	0.302732i	0.283489	−	0.958976i	$-0.408508\pi$
$503$	−10.5648	−	6.78958i	−0.471061	−	0.302732i	−0.754549	+	0.656243i	$0.772144\pi$
$504$		0			0
$505$	−0.519913			−0.0231358
$506$		0			0
$507$	33.5699			1.49089
$508$		0			0
$509$	−21.3040	−	13.6913i	−0.944283	−	0.606854i	−0.0246771	−	0.999695i	$-0.507856\pi$
$509$	−21.3040	−	13.6913i	−0.944283	−	0.606854i	−0.919606	+	0.392841i	$0.871492\pi$
$510$		0			0
$511$	17.3703	−	38.0356i	0.768416	−	1.68260i
$512$		0			0
$513$	0.301043	+	0.0883942i	0.0132914	+	0.00390270i
$514$		0			0
$515$	3.60073	+	7.88450i	0.158667	+	0.347432i
$516$		0			0
$517$	7.80445	−	9.00681i	0.343239	−	0.396119i
$518$		0			0
$519$	31.9353	−	9.37704i	1.40180	−	0.411606i
$520$		0			0
$521$	−3.82673	+	2.45929i	−0.167652	+	0.107743i	−0.621776	−	0.783195i	$-0.713589\pi$
$521$	−3.82673	+	2.45929i	−0.167652	+	0.107743i	0.454124	+	0.890938i	$0.349952\pi$
$522$		0			0
$523$	−2.04072	−	14.1935i	−0.0892345	−	0.620640i	−0.984536	−	0.175180i	$-0.943949\pi$
$523$	−2.04072	−	14.1935i	−0.0892345	−	0.620640i	0.895302	−	0.445460i	$-0.146960\pi$
$524$		0			0
$525$	−4.86230	+	33.8180i	−0.212208	+	1.47594i
$526$		0			0
$527$	14.6338	+	16.8883i	0.637458	+	0.735666i
$528$		0			0
$529$	−10.4683	+	20.4796i	−0.455143	+	0.890418i
$530$		0			0
$531$	9.66918	+	11.1588i	0.419607	+	0.484252i
$532$		0			0
$533$	−4.89485	+	34.0444i	−0.212020	+	1.47463i
$534$		0			0
$535$	−1.45015	−	10.0860i	−0.0626953	−	0.436055i
$536$		0			0
$537$	−5.46685	+	3.51333i	−0.235912	+	0.151612i
$538$		0			0
$539$	11.8504	−	3.47959i	0.510433	−	0.149877i
$540$		0			0
$541$	13.6952	−	15.8051i	0.588804	−	0.679516i	−0.380670	−	0.924711i	$-0.624307\pi$
$541$	13.6952	−	15.8051i	0.588804	−	0.679516i	0.969474	+	0.245195i	$0.0788520\pi$
$542$		0			0
$543$	17.9727	+	39.3547i	0.771281	+	1.68887i
$544$		0			0
$545$	12.2141	+	3.58638i	0.523194	+	0.153624i
$546$		0			0
$547$	10.5235	−	23.0432i	0.449951	−	0.985256i	−0.539713	−	0.841849i	$-0.681467\pi$
$547$	10.5235	−	23.0432i	0.449951	−	0.985256i	0.989664	−	0.143406i	$-0.0458056\pi$
$548$		0			0
$549$	−17.0118	−	10.9328i	−0.726047	−	0.466602i
$550$		0			0
$551$	0.597485			0.0254537
$552$		0			0
$553$	36.7473			1.56265
$554$		0			0
$555$	0.0225492	+	0.0144915i	0.000957159	+	0.000615129i
$556$		0			0
$557$	4.60012	−	10.0729i	0.194913	−	0.426801i	−0.786789	−	0.617222i	$-0.788258\pi$
$557$	4.60012	−	10.0729i	0.194913	−	0.426801i	0.981702	+	0.190421i	$0.0609854\pi$
$558$		0			0
$559$	32.4767	+	9.53602i	1.37362	+	0.403331i
$560$		0			0
$561$	−4.61681	−	10.1094i	−0.194922	−	0.426819i
$562$		0			0
$563$	21.1939	−	24.4591i	0.893216	−	1.03083i	−0.106118	−	0.994353i	$-0.533842\pi$
$563$	21.1939	−	24.4591i	0.893216	−	1.03083i	0.999335	−	0.0364730i	$-0.0116123\pi$
$564$		0			0
$565$	−4.91574	+	1.44339i	−0.206807	+	0.0607239i
$566$		0			0
$567$	35.6496	−	22.9106i	1.49714	−	0.962154i
$568$		0			0
$569$	−0.149298	−	1.03839i	−0.00625890	−	0.0435316i	0.986453	−	0.164046i	$-0.0524546\pi$
$569$	−0.149298	−	1.03839i	−0.00625890	−	0.0435316i	−0.992712	+	0.120515i	$0.961546\pi$
$570$		0			0
$571$	−5.02468	+	34.9474i	−0.210276	+	1.46250i	0.561958	+	0.827165i	$0.310048\pi$
$571$	−5.02468	+	34.9474i	−0.210276	+	1.46250i	−0.772235	+	0.635337i	$0.780861\pi$
$572$		0			0
$573$	21.3868	+	24.6817i	0.893445	+	1.03109i
$574$		0			0
$575$	−6.19062	+	19.4823i	−0.258167	+	0.812468i
$576$		0			0
$577$	8.86921	+	10.2356i	0.369230	+	0.426114i	0.909711	−	0.415242i	$-0.136303\pi$
$577$	8.86921	+	10.2356i	0.369230	+	0.426114i	−0.540481	+	0.841356i	$0.681758\pi$
$578$		0			0
$579$	−3.31546	+	23.0595i	−0.137786	+	0.958322i
$580$		0			0
$581$	6.13299	+	42.6559i	0.254439	+	1.76966i
$582$		0			0
$583$	−6.57713	+	4.22687i	−0.272397	+	0.175059i
$584$		0			0
$585$	6.75148	−	1.98241i	0.279139	−	0.0819626i
$586$		0			0
$587$	−18.8833	+	21.7925i	−0.779399	+	0.899475i	−0.997066	−	0.0765486i	$-0.975610\pi$
$587$	−18.8833	+	21.7925i	−0.779399	+	0.899475i	0.217667	+	0.976023i	$0.430155\pi$
$588$		0			0
$589$	−0.305663	−	0.669308i	−0.0125946	−	0.0275784i
$590$		0			0
$591$	25.4614	+	7.47614i	1.04734	+	0.307527i
$592$		0			0
$593$	−2.74812	+	6.01755i	−0.112852	+	0.247111i	−0.957628	−	0.288009i	$-0.907007\pi$
$593$	−2.74812	+	6.01755i	−0.112852	+	0.247111i	0.844776	+	0.535121i	$0.179734\pi$
$594$		0			0
$595$	8.27632	+	5.31887i	0.339296	+	0.218052i
$596$		0			0
$597$	−38.5763			−1.57882
$598$		0			0
$599$	22.5893			0.922975			0.461488	−	0.887147i	$-0.347316\pi$
$599$	22.5893			0.922975			0.461488	+	0.887147i	$0.347316\pi$
$600$		0			0
$601$	16.8063	+	10.8008i	0.685544	+	0.440572i	0.836499	−	0.547968i	$-0.184599\pi$
$601$	16.8063	+	10.8008i	0.685544	+	0.440572i	−0.150955	+	0.988541i	$0.548235\pi$
$602$		0			0
$603$	1.81949	−	3.98413i	0.0740953	−	0.162246i
$604$		0			0
$605$	−6.63315	−	1.94767i	−0.269676	−	0.0791840i
$606$		0			0
$607$	−1.38016	−	3.02213i	−0.0560189	−	0.122664i	0.879553	−	0.475802i	$-0.157842\pi$
$607$	−1.38016	−	3.02213i	−0.0560189	−	0.122664i	−0.935571	+	0.353137i	$0.885115\pi$
$608$		0			0
$609$	31.3205	−	36.1458i	1.26917	−	1.46470i
$610$		0			0
$611$	−35.7146	+	10.4868i	−1.44486	+	0.424249i
$612$		0			0
$613$	12.9374	−	8.31438i	0.522538	−	0.335815i	−0.252637	−	0.967561i	$-0.581298\pi$
$613$	12.9374	−	8.31438i	0.522538	−	0.335815i	0.775175	+	0.631746i	$0.217662\pi$
$614$		0			0
$615$	1.66734	+	11.5966i	0.0672336	+	0.467620i
$616$		0			0
$617$	6.26629	−	43.5830i	0.252271	−	1.75459i	−0.332234	−	0.943197i	$-0.607802\pi$
$617$	6.26629	−	43.5830i	0.252271	−	1.75459i	0.584506	−	0.811390i	$-0.301288\pi$
$618$		0			0
$619$	12.0340	+	13.8880i	0.483688	+	0.558206i	0.944168	−	0.329464i	$-0.106868\pi$
$619$	12.0340	+	13.8880i	0.483688	+	0.558206i	−0.460480	+	0.887670i	$0.652323\pi$
$620$		0			0
$621$	13.8035	−	5.93935i	0.553917	−	0.238338i
$622$		0			0
$623$	−41.8028	−	48.2431i	−1.67480	−	1.93282i
$624$		0			0
$625$	−2.06090	+	14.3339i	−0.0824362	+	0.573356i
$626$		0			0
$627$	0.0520789	+	0.362217i	0.00207983	+	0.0144655i
$628$		0			0
$629$	−0.0375272	+	0.0241173i	−0.00149631	+	0.000961619i
$630$		0			0
$631$	−30.0359	+	8.81933i	−1.19571	+	0.351092i	−0.818211	−	0.574918i	$-0.805034\pi$
$631$	−30.0359	+	8.81933i	−1.19571	+	0.351092i	−0.377498	+	0.926010i	$0.623216\pi$
$632$		0			0
$633$	−17.1464	+	19.7880i	−0.681508	+	0.786502i
$634$		0			0
$635$	−0.271221	−	0.593892i	−0.0107631	−	0.0235679i
$636$		0			0
$637$	−37.0121	−	10.8677i	−1.46647	−	0.430595i
$638$		0			0
$639$	8.63587	−	18.9099i	0.341630	−	0.748065i
$640$		0			0
$641$	4.75281	+	3.05445i	0.187725	+	0.120643i	0.631127	−	0.775679i	$-0.282592\pi$
$641$	4.75281	+	3.05445i	0.187725	+	0.120643i	−0.443403	+	0.896322i	$0.646229\pi$
$642$		0			0
$643$	−1.03420			−0.0407849			−0.0203925	−	0.999792i	$-0.506492\pi$
$643$	−1.03420			−0.0407849			−0.0203925	+	0.999792i	$0.506492\pi$
$644$		0			0
$645$	11.5296			0.453978
$646$		0			0
$647$	−4.25240	−	2.73285i	−0.167179	−	0.107440i	0.454376	−	0.890810i	$-0.349862\pi$
$647$	−4.25240	−	2.73285i	−0.167179	−	0.107440i	−0.621555	+	0.783371i	$0.713499\pi$
$648$		0			0
$649$	6.89739	−	15.1032i	0.270746	−	0.592851i
$650$		0			0
$651$	−56.5138	−	16.5940i	−2.21495	−	0.650368i
$652$		0			0
$653$	8.71402	+	19.0810i	0.341006	+	0.746699i	0.999985	−	0.00546228i	$-0.00173871\pi$
$653$	8.71402	+	19.0810i	0.341006	+	0.746699i	−0.658979	+	0.752161i	$0.729011\pi$
$654$		0			0
$655$	4.18335	−	4.82784i	0.163457	−	0.188640i
$656$		0			0
$657$	16.2672	−	4.77648i	0.634644	−	0.186348i
$658$		0			0
$659$	27.2497	−	17.5123i	1.06150	−	0.682183i	0.111286	−	0.993788i	$-0.464503\pi$
$659$	27.2497	−	17.5123i	1.06150	−	0.682183i	0.950211	+	0.311606i	$0.100867\pi$
$660$		0			0
$661$	−1.65566	−	11.5153i	−0.0643976	−	0.447895i	−0.996353	−	0.0853230i	$-0.972808\pi$
$661$	−1.65566	−	11.5153i	−0.0643976	−	0.447895i	0.931956	−	0.362572i	$-0.118101\pi$
$662$		0			0
$663$	−4.93993	+	34.3579i	−0.191851	+	1.33435i
$664$		0			0
$665$	−0.212135	−	0.244816i	−0.00822623	−	0.00949357i
$666$		0			0
$667$	22.0351	−	18.2580i	0.853202	−	0.706953i
$668$		0			0
$669$	4.61568	+	5.32678i	0.178452	+	0.205945i
$670$		0			0
$671$	−3.23620	+	22.5083i	−0.124932	+	0.868923i
$672$		0			0
$673$	2.65664	+	18.4774i	0.102406	+	0.712250i	0.974741	+	0.223340i	$0.0716961\pi$
$673$	2.65664	+	18.4774i	0.102406	+	0.712250i	−0.872335	+	0.488910i	$0.837395\pi$
$674$		0			0
$675$	11.2357	−	7.22077i	0.432464	−	0.277928i
$676$		0			0
$677$	1.20894	−	0.354978i	0.0464635	−	0.0136429i	−0.258418	−	0.966033i	$-0.583201\pi$
$677$	1.20894	−	0.354978i	0.0464635	−	0.0136429i	0.304882	+	0.952390i	$0.401383\pi$
$678$		0			0
$679$	−32.9785	+	38.0592i	−1.26560	+	1.46058i
$680$		0			0
$681$	0.288895	+	0.632591i	0.0110705	+	0.0242409i
$682$		0			0
$683$	40.4297	+	11.8712i	1.54700	+	0.454240i	0.940203	−	0.340615i	$-0.110635\pi$
$683$	40.4297	+	11.8712i	1.54700	+	0.454240i	0.606798	+	0.794856i	$0.292454\pi$
$684$		0			0
$685$	−2.57748	+	5.64388i	−0.0984803	+	0.215642i
$686$		0			0
$687$	−43.0851	−	27.6891i	−1.64380	−	1.05640i
$688$		0			0
$689$	24.4186			0.930274
$690$		0			0
$691$	0.374561			0.0142490			0.00712449	−	0.999975i	$-0.497732\pi$
$691$	0.374561			0.0142490			0.00712449	+	0.999975i	$0.497732\pi$
$692$		0			0
$693$	8.31368	+	5.34288i	0.315811	+	0.202959i
$694$		0			0
$695$	1.73924	−	3.80841i	0.0659732	−	0.144461i
$696$		0			0
$697$	−18.7082	−	5.49321i	−0.708622	−	0.208070i
$698$		0			0
$699$	−16.8319	−	36.8567i	−0.636641	−	1.39405i
$700$		0			0
$701$	7.44842	−	8.59593i	0.281323	−	0.324664i	−0.597448	−	0.801908i	$-0.703819\pi$
$701$	7.44842	−	8.59593i	0.281323	−	0.324664i	0.878771	+	0.477244i	$0.158364\pi$
$702$		0			0
$703$	0.00140933		0.000413817i	5.31540e−5		1.56074e-5i
$704$		0			0
$705$	−10.6663	+	6.85484i	−0.401718	+	0.258168i
$706$		0			0
$707$	0.324565	+	2.25740i	0.0122065	+	0.0848981i
$708$		0			0
$709$	1.93873	−	13.4842i	0.0728107	−	0.506410i	−0.920482	−	0.390784i	$-0.872204\pi$
$709$	1.93873	−	13.4842i	0.0728107	−	0.506410i	0.993293	−	0.115625i	$-0.0368871\pi$
$710$		0			0
$711$	9.75711	+	11.2603i	0.365920	+	0.422294i
$712$		0			0
$713$	−31.7256	−	15.3434i	−1.18813	−	0.574616i
$714$		0			0
$715$	−5.18164	−	5.97993i	−0.193782	−	0.223637i
$716$		0			0
$717$	−2.19637	+	15.2761i	−0.0820248	+	0.570495i
$718$		0			0
$719$	0.219864	+	1.52919i	0.00819954	+	0.0570291i	0.993510	−	0.113741i	$-0.0362835\pi$
$719$	0.219864	+	1.52919i	0.00819954	+	0.0570291i	−0.985311	+	0.170770i	$0.945374\pi$
$720$		0			0
$721$	31.9857	−	20.5560i	1.19121	−	0.765544i
$722$		0			0
$723$	−50.8301	+	14.9251i	−1.89039	+	0.555069i
$724$		0			0
$725$	16.6557	−	19.2218i	0.618579	−	0.713878i
$726$		0			0
$727$	−6.93842	−	15.1930i	−0.257332	−	0.563478i	0.736235	−	0.676726i	$-0.236602\pi$
$727$	−6.93842	−	15.1930i	−0.257332	−	0.563478i	−0.993567	+	0.113248i	$0.963875\pi$
$728$		0			0
$729$	−2.70501	−	0.794261i	−0.100185	−	0.0294171i
$730$		0			0
$731$	−7.97100	+	17.4540i	−0.294818	+	0.645561i
$732$		0			0
$733$	18.4811	+	11.8771i	0.682614	+	0.438690i	0.835453	−	0.549562i	$-0.185205\pi$
$733$	18.4811	+	11.8771i	0.682614	+	0.438690i	−0.152839	+	0.988251i	$0.548842\pi$
$734$		0			0
$735$	−13.1397			−0.484666
$736$		0			0
$737$	−4.92526			−0.181424
$738$		0			0
$739$	−19.7879	−	12.7169i	−0.727910	−	0.467799i	0.123470	−	0.992348i	$-0.460598\pi$
$739$	−19.7879	−	12.7169i	−0.727910	−	0.467799i	−0.851380	+	0.524549i	$0.824234\pi$
$740$		0			0
$741$	0.474793	−	1.03965i	0.0174420	−	0.0381926i
$742$		0			0
$743$	4.62514	+	1.35806i	0.169680	+	0.0498225i	0.365469	−	0.930824i	$-0.380909\pi$
$743$	4.62514	+	1.35806i	0.169680	+	0.0498225i	−0.195789	+	0.980646i	$0.562727\pi$
$744$		0			0
$745$	−0.578525	−	1.26679i	−0.0211955	−	0.0464117i
$746$		0			0
$747$	−11.4424	+	13.2053i	−0.418656	+	0.483155i
$748$		0			0
$749$	−42.8868	+	12.5927i	−1.56705	+	0.460128i
$750$		0			0
$751$	40.1003	−	25.7709i	1.46328	−	0.940394i	0.464794	−	0.885419i	$-0.346128\pi$
$751$	40.1003	−	25.7709i	1.46328	−	0.940394i	0.998488	−	0.0549757i	$-0.0175081\pi$
$752$		0			0
$753$	3.93689	+	27.3817i	0.143468	+	0.997843i
$754$		0			0
$755$	−0.729745	+	5.07549i	−0.0265582	+	0.184716i
$756$		0			0
$757$	−18.9188	−	21.8334i	−0.687615	−	0.793550i	0.299409	−	0.954125i	$-0.403211\pi$
$757$	−18.9188	−	21.8334i	−0.687615	−	0.793550i	−0.987024	+	0.160575i	$0.948665\pi$
$758$		0			0
$759$	12.9893	+	11.7670i	0.471482	+	0.427116i
$760$		0			0
$761$	−6.71301	−	7.74723i	−0.243346	−	0.280837i	0.620917	−	0.783876i	$-0.286760\pi$
$761$	−6.71301	−	7.74723i	−0.243346	−	0.280837i	−0.864263	+	0.503040i	$0.832215\pi$
$762$		0			0
$763$	7.94675	−	55.2709i	0.287692	−	2.00094i
$764$		0			0
$765$	0.567685	+	3.94833i	0.0205247	+	0.142752i
$766$		0			0
$767$	−43.6255	+	28.0364i	−1.57522	+	1.01234i
$768$		0			0
$769$	−3.58807	+	1.05355i	−0.129389	+	0.0379921i	−0.345786	−	0.938313i	$-0.612388\pi$
$769$	−3.58807	+	1.05355i	−0.129389	+	0.0379921i	0.216397	+	0.976305i	$0.430569\pi$
$770$		0			0
$771$	33.6349	−	38.8167i	1.21133	−	1.39795i
$772$		0			0
$773$	2.41119	+	5.27978i	0.0867246	+	0.189900i	0.948025	−	0.318195i	$-0.103077\pi$
$773$	2.41119	+	5.27978i	0.0867246	+	0.189900i	−0.861301	+	0.508096i	$0.830350\pi$
$774$		0			0
$775$	−30.0532	−	8.82441i	−1.07954	−	0.316982i
$776$		0			0
$777$	0.0488435	−	0.106952i	0.00175225	−	0.00383689i
$778$		0			0
$779$	0.540093	+	0.347097i	0.0193508	+	0.0124360i
$780$		0			0
$781$	−23.3768			−0.836489
$782$		0			0
$783$	−18.6966			−0.668162
$784$		0			0
$785$	−13.1649	−	8.46059i	−0.469877	−	0.301971i
$786$		0			0
$787$	18.2071	−	39.8681i	0.649014	−	1.42114i	−0.243400	−	0.969926i	$-0.578263\pi$
$787$	18.2071	−	39.8681i	0.649014	−	1.42114i	0.892414	−	0.451217i	$-0.149010\pi$
$788$		0			0
$789$	−25.4074	−	7.46029i	−0.904528	−	0.265593i
$790$		0			0
$791$	9.33576	+	20.4425i	0.331941	+	0.726850i
$792$		0			0
$793$	46.5099	−	53.6753i	1.65161	−	1.90607i
$794$		0			0
$795$	7.98080	−	2.34337i	0.283050	−	0.0831109i
$796$		0			0
$797$	−18.8760	+	12.1309i	−0.668622	+	0.429697i	−0.830428	−	0.557125i	$-0.811904\pi$
$797$	−18.8760	+	12.1309i	−0.668622	+	0.429697i	0.161807	+	0.986822i	$0.448268\pi$
$798$		0			0
$799$	−3.00299	−	20.8863i	−0.106238	−	0.738904i
$800$		0			0
$801$	3.68344	−	25.6189i	0.130148	−	0.905199i
$802$		0			0
$803$	−12.4848	−	14.4082i	−0.440579	−	0.508456i
$804$		0			0
$805$	−15.3046	−	2.54633i	−0.539416	−	0.0897463i
$806$		0			0
$807$	−6.66561	−	7.69252i	−0.234641	−	0.270790i
$808$		0			0
$809$	4.93305	−	34.3101i	0.173437	−	1.20628i	−0.698119	−	0.715982i	$-0.745979\pi$
$809$	4.93305	−	34.3101i	0.173437	−	1.20628i	0.871555	−	0.490297i	$-0.163112\pi$
$810$		0			0
$811$	0.924645	+	6.43105i	0.0324687	+	0.225825i	0.999595	−	0.0284735i	$-0.00906463\pi$
$811$	0.924645	+	6.43105i	0.0324687	+	0.225825i	−0.967126	+	0.254298i	$0.918156\pi$
$812$		0			0
$813$	−28.4317	+	18.2719i	−0.997142	+	0.640824i
$814$		0			0
$815$	−15.9001	+	4.66870i	−0.556957	+	0.163537i
$816$		0			0
$817$	0.413744	−	0.477486i	0.0144751	−	0.0167051i
$818$		0			0
$819$	−12.8221	−	28.0765i	−0.448041	−	0.981073i
$820$		0			0
$821$	−53.9497	−	15.8411i	−1.88286	−	0.552857i	−0.995840	−	0.0911237i	$-0.970954\pi$
$821$	−53.9497	−	15.8411i	−1.88286	−	0.552857i	−0.887019	−	0.461733i	$-0.847228\pi$
$822$		0			0
$823$	−4.77913	+	10.4648i	−0.166590	+	0.364781i	−0.974454	−	0.224588i	$-0.927896\pi$
$823$	−4.77913	+	10.4648i	−0.166590	+	0.364781i	0.807864	+	0.589369i	$0.200624\pi$
$824$		0			0
$825$	13.1047	+	8.42187i	0.456247	+	0.293212i
$826$		0			0
$827$	34.2674			1.19159			0.595797	−	0.803135i	$-0.296836\pi$
$827$	34.2674			1.19159			0.595797	+	0.803135i	$0.296836\pi$
$828$		0			0
$829$	−10.8712			−0.377571			−0.188786	−	0.982018i	$-0.560455\pi$
$829$	−10.8712			−0.377571			−0.188786	+	0.982018i	$0.560455\pi$
$830$		0			0
$831$	−6.39409	−	4.10923i	−0.221808	−	0.142548i
$832$		0			0
$833$	9.08415	−	19.8915i	0.314747	−	0.689200i
$834$		0			0
$835$	−11.2693	−	3.30895i	−0.389989	−	0.114511i
$836$		0			0
$837$	9.56485	+	20.9441i	0.330610	+	0.723934i
$838$		0			0
$839$	−32.8032	+	37.8569i	−1.13249	+	1.30697i	−0.186619	+	0.982432i	$0.559753\pi$
$839$	−32.8032	+	37.8569i	−1.13249	+	1.30697i	−0.945874	+	0.324534i	$0.894793\pi$
$840$		0			0
$841$	−6.33684	+	1.86066i	−0.218512	+	0.0641608i
$842$		0			0
$843$	−43.3509	+	27.8599i	−1.49308	+	0.959547i
$844$		0			0
$845$	1.92823	+	13.4111i	0.0663331	+	0.461357i
$846$		0			0
$847$	−4.31568	+	30.0162i	−0.148288	+	1.03137i
$848$		0			0
$849$	27.8544	+	32.1457i	0.955961	+	1.10324i
$850$		0			0
$851$	0.0393303	−	0.0583280i	0.00134823	−	0.00199946i
$852$		0			0
$853$	22.0734	+	25.4740i	0.755778	+	0.872214i	0.995115	−	0.0987223i	$-0.0314756\pi$
$853$	22.0734	+	25.4740i	0.755778	+	0.872214i	−0.239337	+	0.970937i	$0.576930\pi$
$854$		0			0
$855$	0.0186922	−	0.130007i	0.000639258	−	0.00444614i
$856$		0			0
$857$	−4.29395	−	29.8651i	−0.146679	−	1.02017i	−0.921607	−	0.388123i	$-0.873123\pi$
$857$	−4.29395	−	29.8651i	−0.146679	−	1.02017i	0.774929	−	0.632048i	$-0.217786\pi$
$858$		0			0
$859$	−0.826408	+	0.531100i	−0.0281967	+	0.0181209i	−0.554663	−	0.832075i	$-0.687153\pi$
$859$	−0.826408	+	0.531100i	−0.0281967	+	0.0181209i	0.526467	+	0.850196i	$0.323517\pi$
$860$		0			0
$861$	49.3101	−	14.4788i	1.68048	−	0.493435i
$862$		0			0
$863$	21.3099	−	24.5929i	0.725396	−	0.837152i	−0.266549	−	0.963821i	$-0.585883\pi$
$863$	21.3099	−	24.5929i	0.725396	−	0.837152i	0.991945	+	0.126670i	$0.0404289\pi$
$864$		0			0
$865$	5.58046	+	12.2195i	0.189741	+	0.415476i
$866$		0			0
$867$	15.8264	+	4.64704i	0.537492	+	0.157822i
$868$		0			0
$869$	6.96011	−	15.2405i	0.236106	−	0.516999i
$870$		0			0
$871$	12.9410	+	8.31665i	0.438488	+	0.281799i
$872$		0			0
$873$	−20.4187			−0.691069
$874$		0			0
$875$	−29.9650			−1.01300
$876$		0			0
$877$	−30.1724	−	19.3906i	−1.01885	−	0.654775i	−0.0791804	−	0.996860i	$-0.525230\pi$
$877$	−30.1724	−	19.3906i	−1.01885	−	0.654775i	−0.939669	+	0.342086i	$0.888867\pi$
$878$		0			0
$879$	−4.04885	+	8.86574i	−0.136564	+	0.299034i
$880$		0			0
$881$	16.7282	+	4.91183i	0.563586	+	0.165484i	0.551101	−	0.834438i	$-0.314208\pi$
$881$	16.7282	+	4.91183i	0.563586	+	0.165484i	0.0124846	+	0.999922i	$0.496026\pi$
$882$		0			0
$883$	10.9384	+	23.9517i	0.368105	+	0.806038i	0.999532	+	0.0306021i	$0.00974247\pi$
$883$	10.9384	+	23.9517i	0.368105	+	0.806038i	−0.631426	+	0.775436i	$0.717530\pi$
$884$		0			0
$885$	−11.5677	+	13.3498i	−0.388843	+	0.448749i
$886$		0			0
$887$	41.9514	−	12.3180i	1.40859	−	0.413599i	0.512965	−	0.858409i	$-0.328547\pi$
$887$	41.9514	−	12.3180i	1.40859	−	0.413599i	0.895625	+	0.444810i	$0.146729\pi$
$888$		0			0
$889$	−2.40929	+	1.54836i	−0.0808051	+	0.0519303i
$890$		0			0
$891$	−2.74970	−	19.1246i	−0.0921185	−	0.640698i
$892$		0			0
$893$	−0.0988796	+	0.687723i	−0.00330888	+	0.0230138i
$894$		0			0
$895$	−1.71759	−	1.98220i	−0.0574126	−	0.0662577i
$896$		0			0
$897$	−14.2596	−	52.8509i	−0.476113	−	1.76464i
$898$		0			0
$899$	28.7135	+	33.1371i	0.957647	+	1.10518i
$900$		0			0
$901$	−1.97002	+	13.7018i	−0.0656309	+	0.456473i
$902$		0			0
$903$	−7.19756	−	50.0601i	−0.239520	−	1.66590i
$904$		0			0
$905$	−14.6898	+	9.44057i	−0.488306	+	0.313815i
$906$		0			0
$907$	25.9651	−	7.62405i	0.862158	−	0.253152i	0.179381	−	0.983780i	$-0.442590\pi$
$907$	25.9651	−	7.62405i	0.862158	−	0.253152i	0.682777	+	0.730627i	$0.260772\pi$
$908$		0			0
$909$	−0.605545	+	0.698837i	−0.0200847	+	0.0231789i
$910$		0			0
$911$	7.77186	+	17.0180i	0.257493	+	0.563832i	0.993590	−	0.113045i	$-0.0360604\pi$
$911$	7.77186	+	17.0180i	0.257493	+	0.563832i	−0.736097	+	0.676877i	$0.763333\pi$
$912$		0			0
$913$	18.8526	+	5.53563i	0.623931	+	0.183203i
$914$		0			0
$915$	10.0499	−	22.0063i	0.332240	−	0.727505i
$916$		0			0
$917$	−23.5734	−	15.1497i	−0.778463	−	0.500288i
$918$		0			0
$919$	50.5427			1.66725			0.833626	−	0.552330i	$-0.186261\pi$
$919$	50.5427			1.66725			0.833626	+	0.552330i	$0.186261\pi$
$920$		0			0
$921$	−18.9887			−0.625699
$922$		0			0
$923$	61.4219	+	39.4735i	2.02173	+	1.29929i
$924$		0			0
$925$	0.0259742	−	0.0568756i	0.000854026	−	0.00187006i
$926$		0			0
$927$	14.7917	+	4.34323i	0.485822	+	0.142650i
$928$		0			0
$929$	24.9509	+	54.6349i	0.818613	+	1.79251i	0.564728	+	0.825277i	$0.308981\pi$
$929$	24.9509	+	54.6349i	0.818613	+	1.79251i	0.253884	+	0.967235i	$0.418292\pi$
$930$		0			0
$931$	−0.471523	+	0.544167i	−0.0154536	+	0.0178344i
$932$		0			0
$933$	13.8670	−	4.07173i	0.453987	−	0.133302i
$934$		0			0
$935$	3.77351	−	2.42509i	0.123407	−	0.0793088i
$936$		0			0
$937$	4.01672	+	27.9369i	0.131220	+	0.912658i	0.943967	+	0.330041i	$0.107062\pi$
$937$	4.01672	+	27.9369i	0.131220	+	0.912658i	−0.812746	+	0.582618i	$0.802028\pi$
$938$		0			0
$939$	−0.106303	+	0.739356i	−0.00346908	+	0.0241280i
$940$		0			0
$941$	−21.0995	−	24.3501i	−0.687824	−	0.793792i	0.299229	−	0.954181i	$-0.403270\pi$
$941$	−21.0995	−	24.3501i	−0.687824	−	0.793792i	−0.987054	+	0.160389i	$0.948725\pi$
$942$		0			0
$943$	30.5251	−	3.70339i	0.994034	−	0.120599i
$944$		0			0
$945$	6.63815	+	7.66084i	0.215939	+	0.249207i
$946$		0			0
$947$	−0.0976188	+	0.678954i	−0.00317218	+	0.0220630i	−0.991346	−	0.131274i	$-0.958093\pi$
$947$	−0.0976188	+	0.678954i	−0.00317218	+	0.0220630i	0.988174	+	0.153338i	$0.0490022\pi$
$948$		0			0
$949$	8.47411	+	58.9387i	0.275081	+	1.91323i
$950$		0			0
$951$	21.0606	−	13.5348i	0.682937	−	0.438897i
$952$		0			0
$953$	−10.7140	+	3.14590i	−0.347059	+	0.101906i	−0.450616	−	0.892718i	$-0.648796\pi$
$953$	−10.7140	+	3.14590i	−0.347059	+	0.101906i	0.103557	+	0.994624i	$0.466978\pi$
$954$		0			0
$955$	−8.63186	+	9.96170i	−0.279321	+	0.322353i
$956$		0			0
$957$	−9.05879	−	19.8360i	−0.292829	−	0.641206i
$958$		0			0
$959$	26.1141	+	7.66779i	0.843268	+	0.247606i
$960$		0			0
$961$	9.55331	−	20.9188i	0.308171	−	0.674801i
$962$		0			0
$963$	−15.2460	−	9.79800i	−0.491295	−	0.315736i
$964$		0			0
$965$	−9.40271			−0.302684
$966$		0			0
$967$	12.0546			0.387650			0.193825	−	0.981036i	$-0.437911\pi$
$967$	12.0546			0.387650			0.193825	+	0.981036i	$0.437911\pi$
$968$		0			0
$969$	0.545067	+	0.350293i	0.0175101	+	0.0112530i
$970$		0			0
$971$	−17.5899	+	38.5165i	−0.564487	+	1.23605i	0.385194	+	0.922836i	$0.374135\pi$
$971$	−17.5899	+	38.5165i	−0.564487	+	1.23605i	−0.949681	+	0.313219i	$0.898593\pi$
$972$		0			0
$973$	−17.6214	−	5.17411i	−0.564916	−	0.165874i
$974$		0			0
$975$	−20.2112	−	44.2564i	−0.647278	−	1.41734i
$976$		0			0
$977$	−25.3448	+	29.2495i	−0.810852	+	0.935773i	−0.998924	−	0.0463824i	$-0.985231\pi$
$977$	−25.3448	+	29.2495i	−0.810852	+	0.935773i	0.188072	+	0.982155i	$0.439776\pi$
$978$		0			0
$979$	−27.9259	+	8.19978i	−0.892515	+	0.262066i
$980$		0			0
$981$	19.0464	−	12.2404i	0.608105	−	0.390805i
$982$		0			0
$983$	−0.418955	−	2.91390i	−0.0133626	−	0.0929389i	0.982049	−	0.188627i	$-0.0604038\pi$
$983$	−0.418955	−	2.91390i	−0.0133626	−	0.0929389i	−0.995411	+	0.0956885i	$0.969495\pi$
$984$		0			0
$985$	−1.52423	+	10.6012i	−0.0485659	+	0.337784i
$986$		0			0
$987$	36.4215	+	42.0327i	1.15931	+	1.33791i
$988$		0			0
$989$	0.667692	−	30.2528i	0.0212314	−	0.961983i
$990$		0			0
$991$	−35.5494	−	41.0262i	−1.12927	−	1.30324i	−0.947448	−	0.319909i	$-0.896348\pi$
$991$	−35.5494	−	41.0262i	−1.12927	−	1.30324i	−0.181817	−	0.983332i	$-0.558198\pi$
$992$		0			0
$993$	−5.80097	+	40.3466i	−0.184088	+	1.28036i
$994$		0			0
$995$	−2.21580	−	15.4112i	−0.0702454	−	0.488568i
$996$		0			0
$997$	12.3730	−	7.95167i	0.391858	−	0.251832i	−0.329844	−	0.944035i	$-0.606996\pi$
$997$	12.3730	−	7.95167i	0.391858	−	0.251832i	0.721702	+	0.692203i	$0.243360\pi$
$998$		0			0
$999$	−0.0441011	+	0.0129492i	−0.00139530	+	0.000409696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.289.3		30
4.3	odd	2		184.2.i.b.105.1	✓	30
23.4	even	11		8464.2.a.cg.1.13		15
23.16	even	11	inner	368.2.m.e.177.3		30
23.19	odd	22		8464.2.a.ch.1.13		15
92.19	even	22		4232.2.a.ba.1.3		15
92.27	odd	22		4232.2.a.bb.1.3		15
92.39	odd	22		184.2.i.b.177.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.105.1	✓	30	4.3	odd	2
184.2.i.b.177.1	yes	30	92.39	odd	22
368.2.m.e.177.3		30	23.16	even	11	inner
368.2.m.e.289.3		30	1.1	even	1	trivial
4232.2.a.ba.1.3		15	92.19	even	22
4232.2.a.bb.1.3		15	92.27	odd	22
8464.2.a.cg.1.13		15	23.4	even	11
8464.2.a.ch.1.13		15	23.19	odd	22

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.78999 + 1.15036i) q^{3} +(-0.356751 + 0.781176i) q^{5} +(3.61448 + 1.06131i) q^{7} +(0.634502 + 1.38936i) q^{9} +(1.12476 - 1.29805i) q^{11} +(-5.14713 + 1.51133i) q^{13} +(-1.53721 + 0.987907i) q^{15} +(-0.432786 - 3.01009i) q^{17} +(-0.0142503 + 0.0991134i) q^{19} +(5.24900 + 6.05767i) q^{21} +(2.50317 + 4.09074i) q^{23} +(2.79134 + 3.22138i) q^{25} +(0.445925 - 3.10147i) q^{27} +(-0.849184 - 5.90620i) q^{29} +(-6.18176 + 3.97277i) q^{31} +(3.50653 - 1.02961i) q^{33} +(-2.11854 + 2.44492i) q^{35} +(-0.00609366 - 0.0133433i) q^{37} +(-10.9519 - 3.21576i) q^{39} +(2.66347 - 5.83219i) q^{41} +(-5.30804 - 3.41127i) q^{43} -1.31170 q^{45} +6.93875 q^{47} +(6.04931 + 3.88766i) q^{49} +(2.68800 - 5.88590i) q^{51} +(-4.36756 - 1.28243i) q^{53} +(0.612742 + 1.34172i) q^{55} +(-0.139524 + 0.161019i) q^{57} +(9.27539 - 2.72350i) q^{59} +(-11.1378 + 7.15784i) q^{61} +(0.818850 + 5.69523i) q^{63} +(0.655626 - 4.55998i) q^{65} +(-1.87787 - 2.16718i) q^{67} +(-0.225161 + 10.2019i) q^{69} +(-8.91297 - 10.2861i) q^{71} +(1.57969 - 10.9870i) q^{73} +(1.29074 + 8.97728i) q^{75} +(5.44306 - 3.49804i) q^{77} +(9.35973 - 2.74827i) q^{79} +(7.36669 - 8.50162i) q^{81} +(4.75226 + 10.4060i) q^{83} +(2.50581 + 0.735772i) q^{85} +(5.27422 - 11.5489i) q^{87} +(-14.2554 - 9.16140i) q^{89} -20.2082 q^{91} -15.6354 q^{93} +(-0.0723412 - 0.0464908i) q^{95} +(-5.55342 + 12.1603i) q^{97} +(2.51712 + 0.739094i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41}+ \cdots + 17 q^{99}+O(q^{100}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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