LMFDB - Embedded newform 352.2.m.f.97.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(97,352)] 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("352.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.m (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 11x^10 - 11x^9 + 39x^8 - 43x^7 + 99x^6 + 36x^5 + 431x^4 - 350x^3 + 510x^2 - 175*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			97.3
Root			$-0.674672 - 2.07643i$ of defining polynomial
Character	$\chi$	$=$	352.97
Dual form			352.2.m.f.225.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.57533 - 1.87109i) q^{3} +(-0.0283989 - 0.0874029i) q^{5} +(3.14968 + 2.28838i) q^{7} +(2.20431 - 6.78417i) q^{9} +(-3.27866 + 0.500382i) q^{11} +(-0.805542 + 2.47920i) q^{13} +(-0.236675 - 0.171954i) q^{15} +(-0.163984 - 0.504692i) q^{17} +(-4.06990 + 2.95695i) q^{19} +12.3932 q^{21} -3.05227 q^{23} +(4.03825 - 2.93396i) q^{25} +(-4.06588 - 12.5135i) q^{27} +(-5.34531 - 3.88360i) q^{29} +(-1.47274 + 4.53264i) q^{31} +(-7.50738 + 7.42331i) q^{33} +(0.110563 - 0.340278i) q^{35} +(-6.66996 - 4.84601i) q^{37} +(2.56427 + 7.89201i) q^{39} +(2.34708 - 1.70525i) q^{41} +6.01518 q^{43} -0.655556 q^{45} +(-3.53165 + 2.56589i) q^{47} +(2.52070 + 7.75792i) q^{49} +(-1.36664 - 0.992920i) q^{51} +(3.35585 - 10.3282i) q^{53} +(0.136845 + 0.272354i) q^{55} +(-4.94862 + 15.2303i) q^{57} +(9.06537 + 6.58638i) q^{59} +(3.53965 + 10.8939i) q^{61} +(22.4676 - 16.3237i) q^{63} +0.239566 q^{65} -7.33468 q^{67} +(-7.86060 + 5.71106i) q^{69} +(3.46603 + 10.6673i) q^{71} +(2.04418 + 1.48519i) q^{73} +(4.91014 - 15.1118i) q^{75} +(-11.4718 - 5.92677i) q^{77} +(2.66727 - 8.20903i) q^{79} +(-16.5720 - 12.0402i) q^{81} +(0.473934 + 1.45862i) q^{83} +(-0.0394545 + 0.0286654i) q^{85} -21.0325 q^{87} -3.93257 q^{89} +(-8.21055 + 5.96531i) q^{91} +(4.68816 + 14.4287i) q^{93} +(0.374027 + 0.271746i) q^{95} +(-1.48385 + 4.56682i) q^{97} +(-3.83251 + 23.3460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{7} - q^{9} - 11 q^{11} - 2 q^{13} + 4 q^{15} + 12 q^{17} + 5 q^{19} + 24 q^{21} - 12 q^{23} + 13 q^{25} + 3 q^{27} + 16 q^{31} - 7 q^{33} - 28 q^{35} - 4 q^{37} + 46 q^{39} - 4 q^{41} - 22 q^{43}+ \cdots - 65 q^{99}+O(q^{100}) $ 12 * q + 6 * q^7 - q^9 - 11 * q^11 - 2 * q^13 + 4 * q^15 + 12 * q^17 + 5 * q^19 + 24 * q^21 - 12 * q^23 + 13 * q^25 + 3 * q^27 + 16 * q^31 - 7 * q^33 - 28 * q^35 - 4 * q^37 + 46 * q^39 - 4 * q^41 - 22 * q^43 + 28 * q^45 - 24 * q^47 - 5 * q^49 + 17 * q^51 - 14 * q^53 - 46 * q^55 - 37 * q^57 + 31 * q^59 - 14 * q^61 + 58 * q^63 - 52 * q^65 - 62 * q^67 - 18 * q^69 + 6 * q^71 - 8 * q^73 + 53 * q^75 - 46 * q^77 - 4 * q^79 - 22 * q^81 + 41 * q^83 - 36 * q^85 - 76 * q^87 - 2 * q^89 - 22 * q^91 + 8 * q^93 + 16 * q^95 + 3 * q^97 - 65 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	2.57533	−	1.87109i	1.48687	−	1.08027i	0.511607	−	0.859220i	$-0.329051\pi$
$3$	2.57533	−	1.87109i	1.48687	−	1.08027i	0.975262	−	0.221053i	$-0.0709495\pi$
$4$		0			0
$5$	−0.0283989	−	0.0874029i	−0.0127004	−	0.0390877i	0.944505	−	0.328496i	$-0.106542\pi$
$5$	−0.0283989	−	0.0874029i	−0.0127004	−	0.0390877i	−0.957206	+	0.289408i	$0.906542\pi$
$6$		0			0
$7$	3.14968	+	2.28838i	1.19047	+	0.864925i	0.993314	−	0.115447i	$-0.0368301\pi$
$7$	3.14968	+	2.28838i	1.19047	+	0.864925i	0.197154	+	0.980373i	$0.436830\pi$
$8$		0			0
$9$	2.20431	−	6.78417i	0.734771	−	2.26139i
$10$		0			0
$11$	−3.27866	+	0.500382i	−0.988553	+	0.150871i
$11$	−3.27866	+	0.500382i	−0.988553	+	0.150871i
$12$		0			0
$13$	−0.805542	+	2.47920i	−0.223417	+	0.687607i	0.775031	+	0.631923i	$0.217734\pi$
$13$	−0.805542	+	2.47920i	−0.223417	+	0.687607i	−0.998448	+	0.0556843i	$0.982266\pi$
$14$		0			0
$15$	−0.236675	−	0.171954i	−0.0611092	−	0.0443985i
$16$		0			0
$17$	−0.163984	−	0.504692i	−0.0397721	−	0.122406i	0.929199	−	0.369579i	$-0.120498\pi$
$17$	−0.163984	−	0.504692i	−0.0397721	−	0.122406i	−0.968971	+	0.247174i	$0.920498\pi$
$18$		0			0
$19$	−4.06990	+	2.95695i	−0.933699	+	0.678372i	−0.946896	−	0.321541i	$-0.895799\pi$
$19$	−4.06990	+	2.95695i	−0.933699	+	0.678372i	0.0131968	+	0.999913i	$0.495799\pi$
$20$		0			0
$21$	12.3932			2.70442
$22$		0			0
$23$	−3.05227			−0.636442			−0.318221	−	0.948017i	$-0.603085\pi$
$23$	−3.05227			−0.636442			−0.318221	+	0.948017i	$0.603085\pi$
$24$		0			0
$25$	4.03825	−	2.93396i	0.807650	−	0.586792i
$26$		0			0
$27$	−4.06588	−	12.5135i	−0.782480	−	2.40823i
$28$		0			0
$29$	−5.34531	−	3.88360i	−0.992600	−	0.721166i	−0.0321107	−	0.999484i	$-0.510223\pi$
$29$	−5.34531	−	3.88360i	−0.992600	−	0.721166i	−0.960489	+	0.278319i	$0.910223\pi$
$30$		0			0
$31$	−1.47274	+	4.53264i	−0.264512	+	0.814086i	0.727293	+	0.686327i	$0.240778\pi$
$31$	−1.47274	+	4.53264i	−0.264512	+	0.814086i	−0.991805	+	0.127758i	$0.959222\pi$
$32$		0			0
$33$	−7.50738	+	7.42331i	−1.30687	+	1.29223i
$34$		0			0
$35$	0.110563	−	0.340278i	0.0186886	−	0.0575176i
$36$		0			0
$37$	−6.66996	−	4.84601i	−1.09654	−	0.796679i	−0.116044	−	0.993244i	$-0.537021\pi$
$37$	−6.66996	−	4.84601i	−1.09654	−	0.796679i	−0.980491	+	0.196565i	$0.937021\pi$
$38$		0			0
$39$	2.56427	+	7.89201i	0.410612	+	1.26373i
$40$		0			0
$41$	2.34708	−	1.70525i	0.366552	−	0.266316i	−0.389228	−	0.921142i	$-0.627258\pi$
$41$	2.34708	−	1.70525i	0.366552	−	0.266316i	0.755780	+	0.654826i	$0.227258\pi$
$42$		0			0
$43$	6.01518			0.917306			0.458653	−	0.888616i	$-0.348332\pi$
$43$	6.01518			0.917306			0.458653	+	0.888616i	$0.348332\pi$
$44$		0			0
$45$	−0.655556			−0.0977245
$46$		0			0
$47$	−3.53165	+	2.56589i	−0.515144	+	0.374274i	−0.814771	−	0.579782i	$-0.803138\pi$
$47$	−3.53165	+	2.56589i	−0.515144	+	0.374274i	0.299628	+	0.954056i	$0.403138\pi$
$48$		0			0
$49$	2.52070	+	7.75792i	0.360100	+	1.10827i
$50$		0			0
$51$	−1.36664	−	0.992920i	−0.191368	−	0.139037i
$52$		0			0
$53$	3.35585	−	10.3282i	0.460962	−	1.41869i	−0.403030	−	0.915187i	$-0.632043\pi$
$53$	3.35585	−	10.3282i	0.460962	−	1.41869i	0.863991	−	0.503507i	$-0.167957\pi$
$54$		0			0
$55$	0.136845	+	0.272354i	0.0184522	+	0.0367242i
$56$		0			0
$57$	−4.94862	+	15.2303i	−0.655460	+	2.01730i
$58$		0			0
$59$	9.06537	+	6.58638i	1.18021	+	0.857473i	0.992195	−	0.124693i	$-0.0397946\pi$
$59$	9.06537	+	6.58638i	1.18021	+	0.857473i	0.188015	+	0.982166i	$0.439795\pi$
$60$		0			0
$61$	3.53965	+	10.8939i	0.453206	+	1.39482i	0.873228	+	0.487311i	$0.162022\pi$
$61$	3.53965	+	10.8939i	0.453206	+	1.39482i	−0.420022	+	0.907514i	$0.637978\pi$
$62$		0			0
$63$	22.4676	−	16.3237i	2.83065	−	2.05659i
$64$		0			0
$65$	0.239566			0.0297145
$66$		0			0
$67$	−7.33468			−0.896074			−0.448037	−	0.894015i	$-0.647877\pi$
$67$	−7.33468			−0.896074			−0.448037	+	0.894015i	$0.647877\pi$
$68$		0			0
$69$	−7.86060	+	5.71106i	−0.946305	+	0.687531i
$70$		0			0
$71$	3.46603	+	10.6673i	0.411342	+	1.26598i	0.915482	+	0.402358i	$0.131809\pi$
$71$	3.46603	+	10.6673i	0.411342	+	1.26598i	−0.504140	+	0.863622i	$0.668191\pi$
$72$		0			0
$73$	2.04418	+	1.48519i	0.239254	+	0.173828i	0.700951	−	0.713210i	$-0.252759\pi$
$73$	2.04418	+	1.48519i	0.239254	+	0.173828i	−0.461697	+	0.887038i	$0.652759\pi$
$74$		0			0
$75$	4.91014	−	15.1118i	0.566974	−	1.74497i
$76$		0			0
$77$	−11.4718	−	5.92677i	−1.30733	−	0.675418i
$78$		0			0
$79$	2.66727	−	8.20903i	0.300092	−	0.923588i	−0.681372	−	0.731938i	$-0.738616\pi$
$79$	2.66727	−	8.20903i	0.300092	−	0.923588i	0.981463	−	0.191650i	$-0.0613838\pi$
$80$		0			0
$81$	−16.5720	−	12.0402i	−1.84133	−	1.33781i
$82$		0			0
$83$	0.473934	+	1.45862i	0.0520211	+	0.160104i	0.973692	−	0.227868i	$-0.0731755\pi$
$83$	0.473934	+	1.45862i	0.0520211	+	0.160104i	−0.921671	+	0.387973i	$0.873176\pi$
$84$		0			0
$85$	−0.0394545	+	0.0286654i	−0.00427945	+	0.00310920i
$86$		0			0
$87$	−21.0325			−2.25492
$88$		0			0
$89$	−3.93257			−0.416852			−0.208426	−	0.978038i	$-0.566834\pi$
$89$	−3.93257			−0.416852			−0.208426	+	0.978038i	$0.566834\pi$
$90$		0			0
$91$	−8.21055	+	5.96531i	−0.860699	+	0.625335i
$92$		0			0
$93$	4.68816	+	14.4287i	0.486140	+	1.49618i
$94$		0			0
$95$	0.374027	+	0.271746i	0.0383744	+	0.0278806i
$96$		0			0
$97$	−1.48385	+	4.56682i	−0.150662	+	0.463690i	−0.997696	−	0.0678494i	$-0.978386\pi$
$97$	−1.48385	+	4.56682i	−0.150662	+	0.463690i	0.847034	+	0.531539i	$0.178386\pi$
$98$		0			0
$99$	−3.83251	+	23.3460i	−0.385182	+	2.34636i
$100$		0			0
$101$	−1.49102	+	4.58889i	−0.148362	+	0.456611i	−0.997428	−	0.0716755i	$-0.977165\pi$
$101$	−1.49102	+	4.58889i	−0.148362	+	0.456611i	0.849066	+	0.528287i	$0.177165\pi$
$102$		0			0
$103$	−1.67951	−	1.22023i	−0.165487	−	0.120233i	0.501959	−	0.864891i	$-0.332613\pi$
$103$	−1.67951	−	1.22023i	−0.165487	−	0.120233i	−0.667446	+	0.744658i	$0.732613\pi$
$104$		0			0
$105$	−0.351954	−	1.08320i	−0.0343472	−	0.105710i
$106$		0			0
$107$	0.894840	−	0.650139i	0.0865074	−	0.0628513i	−0.543691	−	0.839286i	$-0.682974\pi$
$107$	0.894840	−	0.650139i	0.0865074	−	0.0628513i	0.630198	+	0.776434i	$0.282974\pi$
$108$		0			0
$109$	1.18772			0.113763			0.0568813	−	0.998381i	$-0.481884\pi$
$109$	1.18772			0.113763			0.0568813	+	0.998381i	$0.481884\pi$
$110$		0			0
$111$	−26.2447			−2.49103
$112$		0			0
$113$	3.41776	−	2.48315i	0.321516	−	0.233595i	−0.415306	−	0.909682i	$-0.636326\pi$
$113$	3.41776	−	2.48315i	0.321516	−	0.233595i	0.736822	+	0.676087i	$0.236326\pi$
$114$		0			0
$115$	0.0866810	+	0.266777i	0.00808305	+	0.0248771i
$116$		0			0
$117$	15.0437	+	10.9299i	1.39079	+	1.01047i
$118$		0			0
$119$	0.638427	−	1.96488i	0.0585245	−	0.180120i
$120$		0			0
$121$	10.4992	−	3.28117i	0.954476	−	0.298288i
$122$		0			0
$123$	2.85383	−	8.78318i	0.257321	−	0.791953i
$124$		0			0
$125$	−0.742865	−	0.539723i	−0.0664439	−	0.0482743i
$126$		0			0
$127$	2.85191	+	8.77727i	0.253066	+	0.778857i	0.994205	+	0.107505i	$0.0342861\pi$
$127$	2.85191	+	8.77727i	0.253066	+	0.778857i	−0.741139	+	0.671352i	$0.765714\pi$
$128$		0			0
$129$	15.4911	−	11.2549i	1.36391	−	0.990941i
$130$		0			0
$131$	2.96831			0.259343			0.129671	−	0.991557i	$-0.458608\pi$
$131$	2.96831			0.259343			0.129671	+	0.991557i	$0.458608\pi$
$132$		0			0
$133$	−19.5855			−1.69828
$134$		0			0
$135$	−0.978249	+	0.710740i	−0.0841943	+	0.0611707i
$136$		0			0
$137$	−4.97093	−	15.2989i	−0.424695	−	1.30708i	−0.903286	−	0.429039i	$-0.858852\pi$
$137$	−4.97093	−	15.2989i	−0.424695	−	1.30708i	0.478591	−	0.878038i	$-0.341148\pi$
$138$		0			0
$139$	−11.2849	−	8.19899i	−0.957177	−	0.695430i	−0.00468341	−	0.999989i	$-0.501491\pi$
$139$	−11.2849	−	8.19899i	−0.957177	−	0.695430i	−0.952493	+	0.304559i	$0.901491\pi$
$140$		0			0
$141$	−4.29415	+	13.2160i	−0.361633	+	1.11299i
$142$		0			0
$143$	1.40055	−	8.53154i	0.117120	−	0.713443i
$144$		0			0
$145$	−0.187636	+	0.577485i	−0.0155824	+	0.0479576i
$146$		0			0
$147$	21.0074	+	15.2628i	1.73266	+	1.25885i
$148$		0			0
$149$	−4.92335	−	15.1525i	−0.403336	−	1.24134i	−0.922276	−	0.386531i	$-0.873673\pi$
$149$	−4.92335	−	15.1525i	−0.403336	−	1.24134i	0.518940	−	0.854811i	$-0.326327\pi$
$150$		0			0
$151$	11.6392	−	8.45636i	0.947183	−	0.688169i	−0.00295605	−	0.999996i	$-0.500941\pi$
$151$	11.6392	−	8.45636i	0.947183	−	0.688169i	0.950139	+	0.311827i	$0.100941\pi$
$152$		0			0
$153$	−3.78539			−0.306031
$154$		0			0
$155$	0.437990			0.0351802
$156$		0			0
$157$	16.8131	−	12.2154i	1.34183	−	0.974896i	0.342455	−	0.939534i	$-0.388742\pi$
$157$	16.8131	−	12.2154i	1.34183	−	0.974896i	0.999375	−	0.0353622i	$-0.0112585\pi$
$158$		0			0
$159$	−10.6826	−	32.8778i	−0.847188	−	2.60738i
$160$		0			0
$161$	−9.61366	−	6.98474i	−0.757663	−	0.550474i
$162$		0			0
$163$	−0.602214	+	1.85342i	−0.0471690	+	0.145171i	−0.971867	−	0.235530i	$-0.924317\pi$
$163$	−0.602214	+	1.85342i	−0.0471690	+	0.145171i	0.924698	+	0.380701i	$0.124317\pi$
$164$		0			0
$165$	0.862020	+	0.445352i	0.0671082	+	0.0346706i
$166$		0			0
$167$	2.10151	−	6.46777i	0.162619	−	0.500491i	−0.836234	−	0.548373i	$-0.815247\pi$
$167$	2.10151	−	6.46777i	0.162619	−	0.500491i	0.998853	+	0.0478823i	$0.0152472\pi$
$168$		0			0
$169$	5.01967	+	3.64701i	0.386129	+	0.280539i
$170$		0			0
$171$	11.0892	+	34.1290i	0.848010	+	2.60991i
$172$		0			0
$173$	5.57858	−	4.05308i	0.424132	−	0.308150i	−0.355167	−	0.934803i	$-0.615576\pi$
$173$	5.57858	−	4.05308i	0.424132	−	0.308150i	0.779298	+	0.626653i	$0.215576\pi$
$174$		0			0
$175$	19.4332			1.46901
$176$		0			0
$177$	35.6700			2.68112
$178$		0			0
$179$	6.46116	−	4.69431i	0.482930	−	0.350869i	−0.319529	−	0.947576i	$-0.603525\pi$
$179$	6.46116	−	4.69431i	0.482930	−	0.350869i	0.802459	+	0.596707i	$0.203525\pi$
$180$		0			0
$181$	2.73553	+	8.41911i	0.203331	+	0.625787i	0.999778	+	0.0210791i	$0.00671019\pi$
$181$	2.73553	+	8.41911i	0.203331	+	0.625787i	−0.796447	+	0.604708i	$0.793290\pi$
$182$		0			0
$183$	29.4993	+	21.4325i	2.18065	+	1.58433i
$184$		0			0
$185$	−0.234136	+	0.720595i	−0.0172140	+	0.0529792i
$186$		0			0
$187$	0.790188	+	1.57266i	0.0577843	+	0.115004i
$188$		0			0
$189$	15.8294	−	48.7178i	1.15142	−	3.54370i
$190$		0			0
$191$	−15.9885	−	11.6164i	−1.15689	−	0.840530i	−0.167509	−	0.985871i	$-0.553572\pi$
$191$	−15.9885	−	11.6164i	−1.15689	−	0.840530i	−0.989382	+	0.145340i	$0.953572\pi$
$192$		0			0
$193$	7.63940	+	23.5117i	0.549896	+	1.69241i	0.709055	+	0.705153i	$0.249122\pi$
$193$	7.63940	+	23.5117i	0.549896	+	1.69241i	−0.159159	+	0.987253i	$0.550878\pi$
$194$		0			0
$195$	0.616962	−	0.448249i	0.0441815	−	0.0320998i
$196$		0			0
$197$	−9.40207			−0.669870			−0.334935	−	0.942241i	$-0.608714\pi$
$197$	−9.40207			−0.669870			−0.334935	+	0.942241i	$0.608714\pi$
$198$		0			0
$199$	−6.96116			−0.493464			−0.246732	−	0.969084i	$-0.579357\pi$
$199$	−6.96116			−0.493464			−0.246732	+	0.969084i	$0.579357\pi$
$200$		0			0
$201$	−18.8892	+	13.7238i	−1.33234	+	0.968005i
$202$		0			0
$203$	−7.94889	−	24.4642i	−0.557903	−	1.71705i
$204$		0			0
$205$	−0.215698	−	0.156714i	−0.0150650	−	0.0109454i
$206$		0			0
$207$	−6.72815	+	20.7071i	−0.467638	+	1.43924i
$208$		0			0
$209$	11.8642	−	11.7314i	0.820665	−	0.811475i
$210$		0			0
$211$	−3.30096	+	10.1593i	−0.227248	+	0.699396i	0.770808	+	0.637068i	$0.219853\pi$
$211$	−3.30096	+	10.1593i	−0.227248	+	0.699396i	−0.998056	+	0.0623289i	$0.980147\pi$
$212$		0			0
$213$	28.8857	+	20.9867i	1.97922	+	1.43798i
$214$		0			0
$215$	−0.170824	−	0.525743i	−0.0116501	−	0.0358554i
$216$		0			0
$217$	−15.0111	+	10.9062i	−1.01902	+	0.740359i
$218$		0			0
$219$	8.04337			0.543520
$220$		0			0
$221$	1.38333			0.0930528
$222$		0			0
$223$	16.9285	−	12.2993i	1.13362	−	0.823621i	0.147400	−	0.989077i	$-0.452910\pi$
$223$	16.9285	−	12.2993i	1.13362	−	0.823621i	0.986217	+	0.165456i	$0.0529096\pi$
$224$		0			0
$225$	−11.0029	−	33.8636i	−0.733529	−	2.25757i
$226$		0			0
$227$	9.86720	+	7.16894i	0.654909	+	0.475819i	0.864940	−	0.501875i	$-0.167356\pi$
$227$	9.86720	+	7.16894i	0.654909	+	0.475819i	−0.210031	+	0.977695i	$0.567356\pi$
$228$		0			0
$229$	3.53074	−	10.8665i	0.233318	−	0.718078i	−0.764022	−	0.645190i	$-0.776778\pi$
$229$	3.53074	−	10.8665i	0.233318	−	0.718078i	0.997340	−	0.0728883i	$-0.0232217\pi$
$230$		0			0
$231$	−40.6332	+	6.20135i	−2.67347	+	0.408019i
$232$		0			0
$233$	−1.98600	+	6.11229i	−0.130107	+	0.400429i	−0.994797	−	0.101877i	$-0.967515\pi$
$233$	−1.98600	+	6.11229i	−0.130107	+	0.400429i	0.864690	+	0.502307i	$0.167515\pi$
$234$		0			0
$235$	0.324561	+	0.235807i	0.0211720	+	0.0153824i
$236$		0			0
$237$	−8.49069	−	26.1317i	−0.551530	−	1.69743i
$238$		0			0
$239$	−11.1655	+	8.11219i	−0.722234	+	0.524734i	−0.887097	−	0.461582i	$-0.847282\pi$
$239$	−11.1655	+	8.11219i	−0.722234	+	0.524734i	0.164863	+	0.986316i	$0.447282\pi$
$240$		0			0
$241$	−21.0631			−1.35680			−0.678398	−	0.734694i	$-0.737326\pi$
$241$	−21.0631			−1.35680			−0.678398	+	0.734694i	$0.737326\pi$
$242$		0			0
$243$	−25.7343			−1.65085
$244$		0			0
$245$	0.606479	−	0.440633i	0.0387465	−	0.0281510i
$246$		0			0
$247$	−4.05242	−	12.4721i	−0.257849	−	0.793578i
$248$		0			0
$249$	3.94975	+	2.86966i	0.250305	+	0.181857i
$250$		0			0
$251$	3.72580	−	11.4668i	0.235171	−	0.723781i	−0.761928	−	0.647662i	$-0.775747\pi$
$251$	3.72580	−	11.4668i	0.235171	−	0.723781i	0.997099	−	0.0761191i	$-0.0242529\pi$
$252$		0			0
$253$	10.0073	−	1.52730i	0.629156	−	0.0960206i
$254$		0			0
$255$	−0.0479730	+	0.147646i	−0.00300419	+	0.00924594i
$256$		0			0
$257$	20.1351	+	14.6290i	1.25599	+	0.912534i	0.998554	−	0.0537604i	$-0.0171207\pi$
$257$	20.1351	+	14.6290i	1.25599	+	0.912534i	0.257441	+	0.966294i	$0.417121\pi$
$258$		0			0
$259$	−9.91875	−	30.5268i	−0.616321	−	1.89684i
$260$		0			0
$261$	−38.1297	+	27.7029i	−2.36017	+	1.71476i
$262$		0			0
$263$	−22.1354			−1.36492			−0.682462	−	0.730921i	$-0.739091\pi$
$263$	−22.1354			−1.36492			−0.682462	+	0.730921i	$0.739091\pi$
$264$		0			0
$265$	−0.998021			−0.0613079
$266$		0			0
$267$	−10.1277	+	7.35819i	−0.619804	+	0.450314i
$268$		0			0
$269$	0.410449	+	1.26323i	0.0250255	+	0.0770205i	0.962789	−	0.270253i	$-0.0871074\pi$
$269$	0.410449	+	1.26323i	0.0250255	+	0.0770205i	−0.937764	+	0.347274i	$0.887107\pi$
$270$		0			0
$271$	−0.544476	−	0.395585i	−0.0330746	−	0.0240301i	0.571125	−	0.820863i	$-0.306507\pi$
$271$	−0.544476	−	0.395585i	−0.0330746	−	0.0240301i	−0.604200	+	0.796833i	$0.706507\pi$
$272$		0			0
$273$	−9.98326	+	30.7253i	−0.604214	+	1.85958i
$274$		0			0
$275$	−11.7720	+	11.6401i	−0.709876	+	0.701927i
$276$		0			0
$277$	0.785318	−	2.41696i	0.0471852	−	0.145221i	−0.924688	−	0.380726i	$-0.875674\pi$
$277$	0.785318	−	2.41696i	0.0471852	−	0.145221i	0.971873	+	0.235505i	$0.0756742\pi$
$278$		0			0
$279$	27.5038	+	19.9827i	1.64661	+	1.19633i
$280$		0			0
$281$	−6.26725	−	19.2886i	−0.373873	−	1.15066i	−0.944236	−	0.329270i	$-0.893197\pi$
$281$	−6.26725	−	19.2886i	−0.373873	−	1.15066i	0.570363	−	0.821393i	$-0.306803\pi$
$282$		0			0
$283$	9.68169	−	7.03416i	0.575517	−	0.418138i	−0.261588	−	0.965180i	$-0.584246\pi$
$283$	9.68169	−	7.03416i	0.575517	−	0.418138i	0.837105	+	0.547042i	$0.184246\pi$
$284$		0			0
$285$	1.47170			0.0871763
$286$		0			0
$287$	11.2948			0.666711
$288$		0			0
$289$	13.5255	−	9.82683i	0.795616	−	0.578049i
$290$		0			0
$291$	4.72351	+	14.5375i	0.276897	+	0.852202i
$292$		0			0
$293$	−14.8975	−	10.8237i	−0.870320	−	0.632325i	0.0603525	−	0.998177i	$-0.480778\pi$
$293$	−14.8975	−	10.8237i	−0.870320	−	0.632325i	−0.930673	+	0.365852i	$0.880778\pi$
$294$		0			0
$295$	0.318221	−	0.979385i	0.0185276	−	0.0570220i
$296$		0			0
$297$	19.5922	+	38.9930i	1.13685	+	2.26261i
$298$		0			0
$299$	2.45873	−	7.56719i	0.142192	−	0.437622i
$300$		0			0
$301$	18.9459	+	13.7650i	1.09202	+	0.793401i
$302$		0			0
$303$	4.74634	+	14.6077i	0.272670	+	0.839192i
$304$		0			0
$305$	0.851638	−	0.618751i	0.0487647	−	0.0354296i
$306$		0			0
$307$	−21.3297			−1.21735			−0.608675	−	0.793420i	$-0.708298\pi$
$307$	−21.3297			−1.21735			−0.608675	+	0.793420i	$0.708298\pi$
$308$		0			0
$309$	−6.60846			−0.375942
$310$		0			0
$311$	8.29339	−	6.02550i	0.470275	−	0.341675i	−0.327273	−	0.944930i	$-0.606130\pi$
$311$	8.29339	−	6.02550i	0.470275	−	0.341675i	0.797549	+	0.603255i	$0.206130\pi$
$312$		0			0
$313$	−7.03741	−	21.6589i	−0.397778	−	1.22423i	−0.926777	−	0.375612i	$-0.877432\pi$
$313$	−7.03741	−	21.6589i	−0.397778	−	1.22423i	0.528999	−	0.848623i	$-0.322568\pi$
$314$		0			0
$315$	−2.06479	−	1.50016i	−0.116338	−	0.0845244i
$316$		0			0
$317$	−6.75541	+	20.7910i	−0.379422	+	1.16774i	0.561025	+	0.827799i	$0.310407\pi$
$317$	−6.75541	+	20.7910i	−0.379422	+	1.16774i	−0.940447	+	0.339941i	$0.889593\pi$
$318$		0			0
$319$	19.4687	+	10.0583i	1.09004	+	0.563156i
$320$		0			0
$321$	1.08804	−	3.34865i	0.0607286	−	0.186903i
$322$		0			0
$323$	2.15975	+	1.56915i	0.120172	+	0.0873099i
$324$		0			0
$325$	4.02091	+	12.3751i	0.223040	+	0.686446i
$326$		0			0
$327$	3.05876	−	2.22232i	0.169150	−	0.122895i
$328$		0			0
$329$	−16.9953			−0.936981
$330$		0			0
$331$	−3.18234			−0.174917			−0.0874587	−	0.996168i	$-0.527875\pi$
$331$	−3.18234			−0.174917			−0.0874587	+	0.996168i	$0.527875\pi$
$332$		0			0
$333$	−47.5789	+	34.5681i	−2.60731	+	1.89432i
$334$		0			0
$335$	0.208297	+	0.641072i	0.0113805	+	0.0350255i
$336$		0			0
$337$	−12.4134	−	9.01886i	−0.676201	−	0.491288i	0.195894	−	0.980625i	$-0.437239\pi$
$337$	−12.4134	−	9.01886i	−0.676201	−	0.491288i	−0.872095	+	0.489336i	$0.837239\pi$
$338$		0			0
$339$	4.15568	−	12.7899i	0.225706	−	0.694650i
$340$		0			0
$341$	2.56057	−	15.5979i	0.138663	−	0.844674i
$342$		0			0
$343$	−1.39214	+	4.28458i	−0.0751687	+	0.231346i
$344$		0			0
$345$	0.722395	+	0.524851i	0.0388925	+	0.0282570i
$346$		0			0
$347$	6.21811	+	19.1374i	0.333806	+	1.02735i	0.967307	+	0.253607i	$0.0816171\pi$
$347$	6.21811	+	19.1374i	0.333806	+	1.02735i	−0.633501	+	0.773742i	$0.718383\pi$
$348$		0			0
$349$	−21.9011	+	15.9121i	−1.17234	+	0.851753i	−0.991287	−	0.131721i	$-0.957950\pi$
$349$	−21.9011	+	15.9121i	−1.17234	+	0.851753i	−0.181050	+	0.983474i	$0.557950\pi$
$350$		0			0
$351$	34.2988			1.83073
$352$		0			0
$353$	−24.9212			−1.32642			−0.663210	−	0.748433i	$-0.730807\pi$
$353$	−24.9212			−1.32642			−0.663210	+	0.748433i	$0.730807\pi$
$354$		0			0
$355$	0.833924	−	0.605881i	0.0442601	−	0.0321568i
$356$		0			0
$357$	−2.03230	−	6.25476i	−0.107560	−	0.331037i
$358$		0			0
$359$	−8.75148	−	6.35832i	−0.461886	−	0.335580i	0.332385	−	0.943144i	$-0.392147\pi$
$359$	−8.75148	−	6.35832i	−0.461886	−	0.335580i	−0.794270	+	0.607564i	$0.792147\pi$
$360$		0			0
$361$	1.94917	−	5.99894i	0.102588	−	0.315734i
$362$		0			0
$363$	20.8997	−	28.0951i	1.09695	−	1.47461i
$364$		0			0
$365$	0.0717569	−	0.220845i	0.00375593	−	0.0115596i
$366$		0			0
$367$	10.3822	+	7.54312i	0.541947	+	0.393748i	0.824808	−	0.565413i	$-0.191283\pi$
$367$	10.3822	+	7.54312i	0.541947	+	0.393748i	−0.282860	+	0.959161i	$0.591283\pi$
$368$		0			0
$369$	−6.39504	−	19.6819i	−0.332912	−	1.02460i
$370$		0			0
$371$	34.2048	−	24.8512i	1.77582	−	1.29021i
$372$		0			0
$373$	6.70036			0.346932			0.173466	−	0.984840i	$-0.444503\pi$
$373$	6.70036			0.346932			0.173466	+	0.984840i	$0.444503\pi$
$374$		0			0
$375$	−2.92299			−0.150943
$376$		0			0
$377$	13.9341	−	10.1237i	0.717642	−	0.521398i
$378$		0			0
$379$	1.21601	+	3.74250i	0.0624624	+	0.192239i	0.977418	−	0.211315i	$-0.0677746\pi$
$379$	1.21601	+	3.74250i	0.0624624	+	0.192239i	−0.914956	+	0.403554i	$0.867775\pi$
$380$		0			0
$381$	23.7677	+	17.2682i	1.21765	+	0.884677i
$382$		0			0
$383$	3.57734	−	11.0099i	0.182794	−	0.562581i	−0.817110	−	0.576482i	$-0.804425\pi$
$383$	3.57734	−	11.0099i	0.182794	−	0.562581i	0.999903	+	0.0139014i	$0.00442509\pi$
$384$		0			0
$385$	−0.192230	+	1.17098i	−0.00979694	+	0.0596788i
$386$		0			0
$387$	13.2593	−	40.8080i	0.674009	−	2.07439i
$388$		0			0
$389$	19.0176	+	13.8171i	0.964229	+	0.700554i	0.954129	−	0.299395i	$-0.0967849\pi$
$389$	19.0176	+	13.8171i	0.964229	+	0.700554i	0.0101003	+	0.999949i	$0.496785\pi$
$390$		0			0
$391$	0.500524	+	1.54045i	0.0253126	+	0.0779041i
$392$		0			0
$393$	7.64439	−	5.55398i	0.385609	−	0.280161i
$394$		0			0
$395$	−0.793240			−0.0399122
$396$		0			0
$397$	−4.30776			−0.216200			−0.108100	−	0.994140i	$-0.534477\pi$
$397$	−4.30776			−0.216200			−0.108100	+	0.994140i	$0.534477\pi$
$398$		0			0
$399$	−50.4392	+	36.6462i	−2.52512	+	1.83461i
$400$		0			0
$401$	7.18087	+	22.1004i	0.358595	+	1.10364i	0.953895	+	0.300140i	$0.0970333\pi$
$401$	7.18087	+	22.1004i	0.358595	+	1.10364i	−0.595300	+	0.803504i	$0.702967\pi$
$402$		0			0
$403$	−10.0510	−	7.30246i	−0.500674	−	0.363761i
$404$		0			0
$405$	−0.581726	+	1.79037i	−0.0289062	+	0.0889641i
$406$		0			0
$407$	24.2934	+	12.5509i	1.20418	+	0.622125i
$408$		0			0
$409$	0.638650	−	1.96556i	0.0315792	−	0.0971908i	−0.934025	−	0.357209i	$-0.883728\pi$
$409$	0.638650	−	1.96556i	0.0315792	−	0.0971908i	0.965604	+	0.260018i	$0.0837285\pi$
$410$		0			0
$411$	−41.4274	−	30.0988i	−2.04346	−	1.48466i
$412$		0			0
$413$	13.4809	+	41.4900i	0.663352	+	2.04159i
$414$		0			0
$415$	0.114028	−	0.0828465i	0.00559743	−	0.00406677i
$416$		0			0
$417$	−44.4035			−2.17445
$418$		0			0
$419$	1.19093			0.0581809			0.0290904	−	0.999577i	$-0.490739\pi$
$419$	1.19093			0.0581809			0.0290904	+	0.999577i	$0.490739\pi$
$420$		0			0
$421$	6.88503	−	5.00227i	0.335556	−	0.243796i	−0.407228	−	0.913326i	$-0.633505\pi$
$421$	6.88503	−	5.00227i	0.335556	−	0.243796i	0.742784	+	0.669531i	$0.233505\pi$
$422$		0			0
$423$	9.62260	+	29.6153i	0.467867	+	1.43995i
$424$		0			0
$425$	−2.14296	−	1.55695i	−0.103949	−	0.0755232i
$426$		0			0
$427$	−13.7806	+	42.4125i	−0.666892	+	2.05248i
$428$		0			0
$429$	−12.3564	−	24.5921i	−0.596572	−	1.18732i
$430$		0			0
$431$	−7.71092	+	23.7318i	−0.371422	+	1.14312i	0.574439	+	0.818548i	$0.305220\pi$
$431$	−7.71092	+	23.7318i	−0.371422	+	1.14312i	−0.945861	+	0.324572i	$0.894780\pi$
$432$		0			0
$433$	−2.40165	−	1.74490i	−0.115416	−	0.0838547i	0.528580	−	0.848884i	$-0.322725\pi$
$433$	−2.40165	−	1.74490i	−0.115416	−	0.0838547i	−0.643996	+	0.765029i	$0.722725\pi$
$434$		0			0
$435$	0.597300	+	1.83830i	0.0286383	+	0.0881398i
$436$		0			0
$437$	12.4224	−	9.02541i	0.594245	−	0.431744i
$438$		0			0
$439$	−7.11680			−0.339666			−0.169833	−	0.985473i	$-0.554323\pi$
$439$	−7.11680			−0.339666			−0.169833	+	0.985473i	$0.554323\pi$
$440$		0			0
$441$	58.1875			2.77083
$442$		0			0
$443$	−27.6303	+	20.0746i	−1.31276	+	0.953774i	−0.312765	+	0.949831i	$0.601255\pi$
$443$	−27.6303	+	20.0746i	−1.31276	+	0.953774i	−0.999992	+	0.00394323i	$0.998745\pi$
$444$		0			0
$445$	0.111681	+	0.343718i	0.00529418	+	0.0162938i
$446$		0			0
$447$	−41.0309	−	29.8107i	−1.94070	−	1.41000i
$448$		0			0
$449$	0.353150	−	1.08688i	0.0166662	−	0.0512932i	−0.942378	−	0.334551i	$-0.891415\pi$
$449$	0.353150	−	1.08688i	0.0166662	−	0.0512932i	0.959044	+	0.283258i	$0.0914153\pi$
$450$		0			0
$451$	−6.84200	+	6.76538i	−0.322177	+	0.318569i
$452$		0			0
$453$	14.1522	−	43.5558i	0.664926	−	2.04643i
$454$		0			0
$455$	0.754556	+	0.548217i	0.0353741	+	0.0257008i
$456$		0			0
$457$	1.30950	+	4.03023i	0.0612560	+	0.188526i	0.977002	−	0.213232i	$-0.0683991\pi$
$457$	1.30950	+	4.03023i	0.0612560	+	0.188526i	−0.915746	+	0.401759i	$0.868399\pi$
$458$		0			0
$459$	−5.64873	+	4.10404i	−0.263660	+	0.191560i
$460$		0			0
$461$	22.1743			1.03276			0.516380	−	0.856360i	$-0.327279\pi$
$461$	22.1743			1.03276			0.516380	+	0.856360i	$0.327279\pi$
$462$		0			0
$463$	−14.1466			−0.657450			−0.328725	−	0.944426i	$-0.606619\pi$
$463$	−14.1466			−0.657450			−0.328725	+	0.944426i	$0.606619\pi$
$464$		0			0
$465$	1.12797	−	0.819517i	0.0523083	−	0.0380042i
$466$		0			0
$467$	4.08210	+	12.5634i	0.188897	+	0.581365i	0.999994	−	0.00354713i	$-0.00112909\pi$
$467$	4.08210	+	12.5634i	0.188897	+	0.581365i	−0.811097	+	0.584912i	$0.801129\pi$
$468$		0			0
$469$	−23.1019	−	16.7845i	−1.06675	−	0.775037i
$470$		0			0
$471$	20.4431	−	62.9175i	0.941970	−	2.89909i
$472$		0			0
$473$	−19.7217	+	3.00989i	−0.906806	+	0.138395i
$474$		0			0
$475$	−7.75969	+	23.8819i	−0.356039	+	1.09577i
$476$		0			0
$477$	−62.6713	−	45.5334i	−2.86952	−	2.08483i
$478$		0			0
$479$	4.58420	+	14.1087i	0.209458	+	0.644644i	0.999501	+	0.0315932i	$0.0100581\pi$
$479$	4.58420	+	14.1087i	0.209458	+	0.644644i	−0.790043	+	0.613051i	$0.789942\pi$
$480$		0			0
$481$	17.3872	−	12.6325i	0.792787	−	0.575994i
$482$		0			0
$483$	−37.8274			−1.72121
$484$		0			0
$485$	0.441293			0.0200381
$486$		0			0
$487$	30.1970	−	21.9394i	1.36836	−	0.994169i	0.370492	−	0.928836i	$-0.379189\pi$
$487$	30.1970	−	21.9394i	1.36836	−	0.994169i	0.997864	−	0.0653329i	$-0.0208109\pi$
$488$		0			0
$489$	1.91702	+	5.89998i	0.0866906	+	0.266806i
$490$		0			0
$491$	11.7361	+	8.52680i	0.529644	+	0.384809i	0.820225	−	0.572042i	$-0.193848\pi$
$491$	11.7361	+	8.52680i	0.529644	+	0.384809i	−0.290581	+	0.956851i	$0.593848\pi$
$492$		0			0
$493$	−1.08347	+	3.33459i	−0.0487972	+	0.150182i
$494$		0			0
$495$	2.14935	−	0.328029i	0.0966059	−	0.0147438i
$496$		0			0
$497$	−13.4940	+	41.5303i	−0.605289	+	1.86289i
$498$		0			0
$499$	−13.5280	−	9.82870i	−0.605599	−	0.439993i	0.242263	−	0.970211i	$-0.422110\pi$
$499$	−13.5280	−	9.82870i	−0.605599	−	0.439993i	−0.847862	+	0.530217i	$0.822110\pi$
$500$		0			0
$501$	−6.68969	−	20.5888i	−0.298873	−	0.919838i
$502$		0			0
$503$	−32.5048	+	23.6161i	−1.44932	+	1.05299i	−0.463326	+	0.886188i	$0.653344\pi$
$503$	−32.5048	+	23.6161i	−1.44932	+	1.05299i	−0.985990	+	0.166802i	$0.946656\pi$
$504$		0			0
$505$	0.443425			0.0197322
$506$		0			0
$507$	19.7512			0.877181
$508$		0			0
$509$	24.7347	−	17.9708i	1.09635	−	0.796542i	0.115887	−	0.993262i	$-0.463029\pi$
$509$	24.7347	−	17.9708i	1.09635	−	0.796542i	0.980460	+	0.196720i	$0.0630290\pi$
$510$		0			0
$511$	3.03986	+	9.35573i	0.134475	+	0.413873i
$512$		0			0
$513$	53.5496	+	38.9061i	2.36427	+	1.71774i
$514$		0			0
$515$	−0.0589558	+	0.181447i	−0.00259790	+	0.00799552i
$516$		0			0
$517$	10.2951	−	10.1799i	0.452780	−	0.447710i
$518$		0			0
$519$	6.78303	−	20.8760i	0.297742	−	0.916356i
$520$		0			0
$521$	−7.37330	−	5.35702i	−0.323030	−	0.234695i	0.414437	−	0.910078i	$-0.363978\pi$
$521$	−7.37330	−	5.35702i	−0.323030	−	0.234695i	−0.737467	+	0.675383i	$0.763978\pi$
$522$		0			0
$523$	−5.69495	−	17.5272i	−0.249023	−	0.766413i	−0.994949	−	0.100384i	$-0.967993\pi$
$523$	−5.69495	−	17.5272i	−0.249023	−	0.766413i	0.745926	−	0.666029i	$-0.232007\pi$
$524$		0			0
$525$	50.0470	−	36.3613i	2.18423	−	1.58694i
$526$		0			0
$527$	2.52909			0.110169
$528$		0			0
$529$	−13.6837			−0.594942
$530$		0			0
$531$	64.6660	−	46.9826i	2.80627	−	2.03887i
$532$		0			0
$533$	2.33700	+	7.19253i	0.101227	+	0.311543i
$534$		0			0
$535$	−0.0822365	−	0.0597483i	−0.00355539	−	0.00258315i
$536$		0			0
$537$	7.85617	−	24.1788i	0.339019	−	1.04339i
$538$		0			0
$539$	−12.1464	−	24.1743i	−0.523185	−	1.04126i
$540$		0			0
$541$	−9.62054	+	29.6090i	−0.413619	+	1.27299i	0.499861	+	0.866106i	$0.333385\pi$
$541$	−9.62054	+	29.6090i	−0.413619	+	1.27299i	−0.913480	+	0.406884i	$0.866615\pi$
$542$		0			0
$543$	22.7978	+	16.5636i	0.978347	+	0.710811i
$544$		0			0
$545$	−0.0337298	−	0.103810i	−0.00144483	−	0.00444672i
$546$		0			0
$547$	−8.18733	+	5.94844i	−0.350065	+	0.254337i	−0.748896	−	0.662687i	$-0.769416\pi$
$547$	−8.18733	+	5.94844i	−0.350065	+	0.254337i	0.398831	+	0.917024i	$0.369416\pi$
$548$		0			0
$549$	81.7088			3.48725
$550$		0			0
$551$	33.2385			1.41601
$552$		0			0
$553$	27.1864	−	19.7521i	1.15608	−	0.839944i
$554$		0			0
$555$	0.745320	+	2.29386i	0.0316371	+	0.0973689i
$556$		0			0
$557$	10.5948	+	7.69759i	0.448917	+	0.326157i	0.789168	−	0.614177i	$-0.210512\pi$
$557$	10.5948	+	7.69759i	0.448917	+	0.326157i	−0.340251	+	0.940335i	$0.610512\pi$
$558$		0			0
$559$	−4.84547	+	14.9128i	−0.204942	+	0.630746i
$560$		0			0
$561$	4.97758	+	2.57161i	0.210154	+	0.108573i
$562$		0			0
$563$	−6.73078	+	20.7152i	−0.283669	+	0.873042i	0.703126	+	0.711065i	$0.251787\pi$
$563$	−6.73078	+	20.7152i	−0.283669	+	0.873042i	−0.986795	+	0.161977i	$0.948213\pi$
$564$		0			0
$565$	−0.314095	−	0.228203i	−0.0132141	−	0.00960059i
$566$		0			0
$567$	−24.6438	−	75.8459i	−1.03494	−	3.18523i
$568$		0			0
$569$	6.68488	−	4.85685i	0.280245	−	0.203610i	−0.438779	−	0.898595i	$-0.644589\pi$
$569$	6.68488	−	4.85685i	0.280245	−	0.203610i	0.719024	+	0.694985i	$0.244589\pi$
$570$		0			0
$571$	41.2789			1.72747			0.863733	−	0.503949i	$-0.168120\pi$
$571$	41.2789			1.72747			0.863733	+	0.503949i	$0.168120\pi$
$572$		0			0
$573$	−62.9110			−2.62815
$574$		0			0
$575$	−12.3258	+	8.95523i	−0.514022	+	0.373459i
$576$		0			0
$577$	5.16327	+	15.8909i	0.214950	+	0.661547i	0.999157	+	0.0410485i	$0.0130698\pi$
$577$	5.16327	+	15.8909i	0.214950	+	0.661547i	−0.784207	+	0.620499i	$0.786930\pi$
$578$		0			0
$579$	63.6663	+	46.2563i	2.64588	+	1.92235i
$580$		0			0
$581$	−1.84513	+	5.67873i	−0.0765489	+	0.235593i
$582$		0			0
$583$	−5.83462	+	35.5420i	−0.241645	+	1.47200i
$584$		0			0
$585$	0.528078	−	1.62526i	0.0218333	−	0.0671961i
$586$		0			0
$587$	22.9814	+	16.6970i	0.948545	+	0.689158i	0.950462	−	0.310840i	$-0.100610\pi$
$587$	22.9814	+	16.6970i	0.948545	+	0.689158i	−0.00191718	+	0.999998i	$0.500610\pi$
$588$		0			0
$589$	−7.40889	−	22.8022i	−0.305278	−	0.939549i
$590$		0			0
$591$	−24.2134	+	17.5921i	−0.996008	+	0.723642i
$592$		0			0
$593$	8.51973			0.349864			0.174932	−	0.984581i	$-0.444030\pi$
$593$	8.51973			0.349864			0.174932	+	0.984581i	$0.444030\pi$
$594$		0			0
$595$	−0.189866			−0.00778377
$596$		0			0
$597$	−17.9273	+	13.0249i	−0.733716	+	0.533076i
$598$		0			0
$599$	−3.09396	−	9.52222i	−0.126416	−	0.389067i	0.867741	−	0.497017i	$-0.165571\pi$
$599$	−3.09396	−	9.52222i	−0.126416	−	0.389067i	−0.994156	+	0.107950i	$0.965571\pi$
$600$		0			0
$601$	−35.4612	−	25.7641i	−1.44649	−	1.05094i	−0.986635	−	0.162946i	$-0.947900\pi$
$601$	−35.4612	−	25.7641i	−1.44649	−	1.05094i	−0.459858	−	0.887993i	$-0.652100\pi$
$602$		0			0
$603$	−16.1679	+	49.7598i	−0.658409	+	2.02637i
$604$		0			0
$605$	−0.584950	−	0.824481i	−0.0237816	−	0.0335199i
$606$		0			0
$607$	5.54290	−	17.0593i	0.224980	−	0.692416i	−0.773314	−	0.634023i	$-0.781402\pi$
$607$	5.54290	−	17.0593i	0.224980	−	0.692416i	0.998294	−	0.0583927i	$-0.0185976\pi$
$608$		0			0
$609$	−66.2457	−	48.1303i	−2.68441	−	1.95034i
$610$		0			0
$611$	−3.51648	−	10.8226i	−0.142261	−	0.437836i
$612$		0			0
$613$	8.80854	−	6.39978i	0.355774	−	0.258485i	−0.395513	−	0.918460i	$-0.629433\pi$
$613$	8.80854	−	6.39978i	0.355774	−	0.258485i	0.751287	+	0.659975i	$0.229433\pi$
$614$		0			0
$615$	−0.848721			−0.0342237
$616$		0			0
$617$	11.9150			0.479680			0.239840	−	0.970812i	$-0.422905\pi$
$617$	11.9150			0.479680			0.239840	+	0.970812i	$0.422905\pi$
$618$		0			0
$619$	6.19836	−	4.50337i	0.249133	−	0.181006i	−0.456209	−	0.889872i	$-0.650793\pi$
$619$	6.19836	−	4.50337i	0.249133	−	0.181006i	0.705342	+	0.708867i	$0.250793\pi$
$620$		0			0
$621$	12.4102	+	38.1946i	0.498003	+	1.53269i
$622$		0			0
$623$	−12.3863	−	8.99921i	−0.496249	−	0.360546i
$624$		0			0
$625$	7.68630	−	23.6560i	0.307452	−	0.946240i
$626$		0			0
$627$	8.60387	−	52.4111i	0.343606	−	2.09310i
$628$		0			0
$629$	−1.35197	+	4.16095i	−0.0539067	+	0.165908i
$630$		0			0
$631$	−17.9488	−	13.0406i	−0.714531	−	0.519137i	0.170101	−	0.985427i	$-0.445591\pi$
$631$	−17.9488	−	13.0406i	−0.714531	−	0.519137i	−0.884632	+	0.466289i	$0.845591\pi$
$632$		0			0
$633$	10.5079	+	32.3400i	0.417652	+	1.28540i
$634$		0			0
$635$	0.686167	−	0.498530i	0.0272297	−	0.0197836i
$636$		0			0
$637$	−21.2640			−0.842510
$638$		0			0
$639$	80.0093			3.16512
$640$		0			0
$641$	−10.3987	+	7.55513i	−0.410726	+	0.298410i	−0.773896	−	0.633313i	$-0.781695\pi$
$641$	−10.3987	+	7.55513i	−0.410726	+	0.298410i	0.363170	+	0.931723i	$0.381695\pi$
$642$		0			0
$643$	0.815196	+	2.50892i	0.0321482	+	0.0989420i	0.965843	−	0.259128i	$-0.0834350\pi$
$643$	0.815196	+	2.50892i	0.0321482	+	0.0989420i	−0.933695	+	0.358070i	$0.883435\pi$
$644$		0			0
$645$	−1.42364	−	1.03434i	−0.0560558	−	0.0407269i
$646$		0			0
$647$	−1.53796	+	4.73337i	−0.0604636	+	0.186088i	−0.976726	−	0.214491i	$-0.931191\pi$
$647$	−1.53796	+	4.73337i	−0.0604636	+	0.186088i	0.916262	+	0.400579i	$0.131191\pi$
$648$		0			0
$649$	−33.0180	−	17.0583i	−1.29607	−	0.669598i
$650$		0			0
$651$	−18.2520	+	56.1740i	−0.715354	+	2.20163i
$652$		0			0
$653$	20.1411	+	14.6334i	0.788184	+	0.572649i	0.907424	−	0.420216i	$-0.138046\pi$
$653$	20.1411	+	14.6334i	0.788184	+	0.572649i	−0.119240	+	0.992865i	$0.538046\pi$
$654$		0			0
$655$	−0.0842969	−	0.259439i	−0.00329375	−	0.0101371i
$656$		0			0
$657$	14.5818	−	10.5943i	0.568889	−	0.413322i
$658$		0			0
$659$	−11.7528			−0.457823			−0.228911	−	0.973447i	$-0.573517\pi$
$659$	−11.7528			−0.457823			−0.228911	+	0.973447i	$0.573517\pi$
$660$		0			0
$661$	20.7879			0.808554			0.404277	−	0.914637i	$-0.367523\pi$
$661$	20.7879			0.808554			0.404277	+	0.914637i	$0.367523\pi$
$662$		0			0
$663$	3.56253	−	2.58833i	0.138357	−	0.100522i
$664$		0			0
$665$	0.556207	+	1.71183i	0.0215688	+	0.0663819i
$666$		0			0
$667$	16.3153	+	11.8538i	0.631732	+	0.458980i
$668$		0			0
$669$	20.5835	−	63.3495i	0.795804	−	2.44923i
$670$		0			0
$671$	−17.0565	−	33.9463i	−0.658457	−	1.31048i
$672$		0			0
$673$	−8.86044	+	27.2696i	−0.341545	+	1.05117i	0.621863	+	0.783126i	$0.286376\pi$
$673$	−8.86044	+	27.2696i	−0.341545	+	1.05117i	−0.963408	+	0.268041i	$0.913624\pi$
$674$		0			0
$675$	−53.1332	−	38.6035i	−2.04510	−	1.48585i
$676$		0			0
$677$	14.7550	+	45.4111i	0.567079	+	1.74529i	0.661692	+	0.749776i	$0.269839\pi$
$677$	14.7550	+	45.4111i	0.567079	+	1.74529i	−0.0946125	+	0.995514i	$0.530161\pi$
$678$		0			0
$679$	−15.1242	+	10.9884i	−0.580415	+	0.421696i
$680$		0			0
$681$	38.8250			1.48778
$682$		0			0
$683$	−8.67362			−0.331887			−0.165943	−	0.986135i	$-0.553067\pi$
$683$	−8.67362			−0.331887			−0.165943	+	0.986135i	$0.553067\pi$
$684$		0			0
$685$	−1.19600	+	0.868946i	−0.0456969	+	0.0332007i
$686$		0			0
$687$	−11.2393	−	34.5911i	−0.428808	−	1.31973i
$688$		0			0
$689$	22.9025	+	16.6397i	0.872517	+	0.633921i
$690$		0			0
$691$	−8.78441	+	27.0356i	−0.334175	+	1.02848i	0.632953	+	0.774190i	$0.281843\pi$
$691$	−8.78441	+	27.0356i	−0.334175	+	1.02848i	−0.967127	+	0.254293i	$0.918157\pi$
$692$		0			0
$693$	−65.4956	+	64.7622i	−2.48797	+	2.46011i
$694$		0			0
$695$	−0.396135	+	1.21918i	−0.0150263	+	0.0462461i
$696$		0			0
$697$	−1.24551	−	0.904917i	−0.0471771	−	0.0342762i
$698$		0			0
$699$	6.32201	+	19.4572i	0.239121	+	0.735937i
$700$		0			0
$701$	−33.0111	+	23.9840i	−1.24681	+	0.905863i	−0.998033	−	0.0626974i	$-0.980030\pi$
$701$	−33.0111	+	23.9840i	−1.24681	+	0.905863i	−0.248780	+	0.968560i	$0.580030\pi$
$702$		0			0
$703$	41.4755			1.56428
$704$		0			0
$705$	1.27707			0.0480972
$706$		0			0
$707$	−15.1973	+	11.0415i	−0.571555	+	0.415259i
$708$		0			0
$709$	2.23569	+	6.88073i	0.0839630	+	0.258411i	0.984221	−	0.176946i	$-0.0566219\pi$
$709$	2.23569	+	6.88073i	0.0839630	+	0.258411i	−0.900258	+	0.435358i	$0.856622\pi$
$710$		0			0
$711$	−49.8120	−	36.1905i	−1.86809	−	1.35725i
$712$		0			0
$713$	4.49520	−	13.8348i	0.168347	−	0.518118i
$714$		0			0
$715$	−0.785455	+	0.119875i	−0.0293744	+	0.00448305i
$716$		0			0
$717$	−13.5762	+	41.7832i	−0.507011	+	1.56042i
$718$		0			0
$719$	−23.1987	−	16.8548i	−0.865165	−	0.628579i	0.0641203	−	0.997942i	$-0.479576\pi$
$719$	−23.1987	−	16.8548i	−0.865165	−	0.628579i	−0.929285	+	0.369363i	$0.879576\pi$
$720$		0			0
$721$	−2.49756	−	7.68670i	−0.0930140	−	0.286268i
$722$		0			0
$723$	−54.2446	+	39.4110i	−2.01738	+	1.46571i
$724$		0			0
$725$	−32.9800			−1.22485
$726$		0			0
$727$	−44.2322			−1.64048			−0.820241	−	0.572018i	$-0.806161\pi$
$727$	−44.2322			−1.64048			−0.820241	+	0.572018i	$0.806161\pi$
$728$		0			0
$729$	−16.5583	+	12.0303i	−0.613272	+	0.445568i
$730$		0			0
$731$	−0.986395	−	3.03581i	−0.0364831	−	0.112284i
$732$		0			0
$733$	24.5117	+	17.8088i	0.905360	+	0.657782i	0.939837	−	0.341623i	$-0.110977\pi$
$733$	24.5117	+	17.8088i	0.905360	+	0.657782i	−0.0344772	+	0.999405i	$0.510977\pi$
$734$		0			0
$735$	0.737422	−	2.26955i	0.0272002	−	0.0837137i
$736$		0			0
$737$	24.0479	−	3.67015i	0.885817	−	0.135192i
$738$		0			0
$739$	5.16103	−	15.8840i	0.189852	−	0.584303i	−0.810147	−	0.586227i	$-0.800613\pi$
$739$	5.16103	−	15.8840i	0.189852	−	0.584303i	0.999998	+	0.00192435i	$0.000612541\pi$
$740$		0			0
$741$	−33.7726	−	24.5372i	−1.24067	−	0.901398i
$742$		0			0
$743$	−1.16067	−	3.57216i	−0.0425807	−	0.131050i	0.927506	−	0.373808i	$-0.121948\pi$
$743$	−1.16067	−	3.57216i	−0.0425807	−	0.131050i	−0.970087	+	0.242758i	$0.921948\pi$
$744$		0			0
$745$	−1.18455	+	0.860630i	−0.0433987	+	0.0315310i
$746$		0			0
$747$	10.9402			0.400282
$748$		0			0
$749$	4.30622			0.157346
$750$		0			0
$751$	−10.0014	+	7.26643i	−0.364955	+	0.265156i	−0.755116	−	0.655591i	$-0.772419\pi$
$751$	−10.0014	+	7.26643i	−0.364955	+	0.265156i	0.390161	+	0.920747i	$0.372419\pi$
$752$		0			0
$753$	−11.8603	−	36.5022i	−0.432213	−	1.33021i
$754$		0			0
$755$	−1.06965	−	0.777146i	−0.0389285	−	0.0282832i
$756$		0			0
$757$	4.90906	−	15.1085i	0.178423	−	0.549129i	−0.821350	−	0.570424i	$-0.806779\pi$
$757$	4.90906	−	15.1085i	0.178423	−	0.549129i	0.999773	+	0.0212951i	$0.00677896\pi$
$758$		0			0
$759$	22.9145	−	22.6579i	0.831744	−	0.822431i
$760$		0			0
$761$	−14.9367	+	45.9704i	−0.541455	+	1.66643i	0.187818	+	0.982204i	$0.439858\pi$
$761$	−14.9367	+	45.9704i	−0.541455	+	1.66643i	−0.729273	+	0.684223i	$0.760142\pi$
$762$		0			0
$763$	3.74093	+	2.71794i	0.135431	+	0.0983961i
$764$		0			0
$765$	0.107501	+	0.330854i	0.00388671	+	0.0119621i
$766$		0			0
$767$	−23.6315	+	17.1693i	−0.853284	+	0.619947i
$768$		0			0
$769$	44.3792			1.60035			0.800177	−	0.599763i	$-0.204739\pi$
$769$	44.3792			1.60035			0.800177	+	0.599763i	$0.204739\pi$
$770$		0			0
$771$	79.2268			2.85328
$772$		0			0
$773$	14.8197	−	10.7671i	0.533027	−	0.387267i	−0.288462	−	0.957491i	$-0.593144\pi$
$773$	14.8197	−	10.7671i	0.533027	−	0.387267i	0.821489	+	0.570225i	$0.193144\pi$
$774$		0			0
$775$	7.35128	+	22.6249i	0.264066	+	0.812711i
$776$		0			0
$777$	−82.6624	−	60.0577i	−2.96550	−	2.15456i
$778$		0			0
$779$	−4.51002	+	13.8804i	−0.161588	+	0.497317i
$780$		0			0
$781$	−16.7017	−	33.2402i	−0.597633	−	1.18943i
$782$		0			0
$783$	−26.8640	+	82.6788i	−0.960041	+	2.95470i
$784$		0			0
$785$	−1.54514	−	1.12261i	−0.0551482	−	0.0400675i
$786$		0			0
$787$	−12.5817	−	38.7226i	−0.448490	−	1.38031i	−0.878610	−	0.477540i	$-0.841529\pi$
$787$	−12.5817	−	38.7226i	−0.448490	−	1.38031i	0.430120	−	0.902772i	$-0.358471\pi$
$788$		0			0
$789$	−57.0059	+	41.4172i	−2.02946	+	1.47449i
$790$		0			0
$791$	16.4472			0.584797
$792$		0			0
$793$	−29.8596			−1.06035
$794$		0			0
$795$	−2.57023	+	1.86738i	−0.0911568	+	0.0662293i
$796$		0			0
$797$	12.4812	+	38.4131i	0.442106	+	1.36066i	0.885626	+	0.464399i	$0.153730\pi$
$797$	12.4812	+	38.4131i	0.442106	+	1.36066i	−0.443520	+	0.896265i	$0.646270\pi$
$798$		0			0
$799$	1.87412	+	1.36163i	0.0663016	+	0.0481709i
$800$		0			0
$801$	−8.66862	+	26.6793i	−0.306290	+	0.942665i
$802$		0			0
$803$	−7.44535	−	3.84655i	−0.262741	−	0.135742i
$804$		0			0
$805$	−0.337468	+	1.03862i	−0.0118942	+	0.0366066i
$806$		0			0
$807$	3.42066	+	2.48525i	0.120413	+	0.0874850i
$808$		0			0
$809$	11.8279	+	36.4025i	0.415847	+	1.27985i	0.911491	+	0.411320i	$0.134932\pi$
$809$	11.8279	+	36.4025i	0.415847	+	1.27985i	−0.495644	+	0.868526i	$0.665068\pi$
$810$		0			0
$811$	27.4196	−	19.9215i	0.962832	−	0.699538i	0.00902506	−	0.999959i	$-0.497127\pi$
$811$	27.4196	−	19.9215i	0.962832	−	0.699538i	0.953807	+	0.300421i	$0.0971272\pi$
$812$		0			0
$813$	−2.14238			−0.0751366
$814$		0			0
$815$	0.179097			0.00627349
$816$		0			0
$817$	−24.4812	+	17.7866i	−0.856487	+	0.622274i
$818$		0			0
$819$	22.3711	+	68.8512i	0.781710	+	2.40586i
$820$		0			0
$821$	−40.0983	−	29.1331i	−1.39944	−	1.01675i	−0.994754	−	0.102299i	$-0.967380\pi$
$821$	−40.0983	−	29.1331i	−1.39944	−	1.01675i	−0.404688	−	0.914455i	$-0.632620\pi$
$822$		0			0
$823$	6.62200	−	20.3804i	0.230829	−	0.710417i	−0.766819	−	0.641864i	$-0.778162\pi$
$823$	6.62200	−	20.3804i	0.230829	−	0.710417i	0.997647	−	0.0685537i	$-0.0218384\pi$
$824$		0			0
$825$	−8.53697	+	52.0036i	−0.297219	+	1.81053i
$826$		0			0
$827$	12.6736	−	39.0055i	0.440706	−	1.35635i	−0.446419	−	0.894824i	$-0.647301\pi$
$827$	12.6736	−	39.0055i	0.440706	−	1.35635i	0.887125	−	0.461529i	$-0.152699\pi$
$828$		0			0
$829$	10.9095	+	7.92622i	0.378903	+	0.275289i	0.760893	−	0.648877i	$-0.224761\pi$
$829$	10.9095	+	7.92622i	0.378903	+	0.275289i	−0.381990	+	0.924166i	$0.624761\pi$
$830$		0			0
$831$	−2.49989	−	7.69388i	−0.0867203	−	0.266898i
$832$		0			0
$833$	3.50200	−	2.54436i	0.121337	−	0.0881567i
$834$		0			0
$835$	−0.624982			−0.0216284
$836$		0			0
$837$	62.7072			2.16748
$838$		0			0
$839$	28.7447	−	20.8843i	0.992379	−	0.721005i	0.0319381	−	0.999490i	$-0.489832\pi$
$839$	28.7447	−	20.8843i	0.992379	−	0.721005i	0.960441	+	0.278484i	$0.0898321\pi$
$840$		0			0
$841$	4.52855	+	13.9374i	0.156157	+	0.480601i
$842$		0			0
$843$	−52.2309	−	37.9480i	−1.79893	−	1.30700i
$844$		0			0
$845$	0.176206	−	0.542305i	0.00606165	−	0.0186559i
$846$		0			0
$847$	40.5778	+	13.6916i	1.39427	+	0.470448i
$848$		0			0
$849$	11.7720	−	36.2306i	0.404015	−	1.24343i
$850$		0			0
$851$	20.3585	+	14.7913i	0.697881	+	0.507040i
$852$		0			0
$853$	−10.8967	−	33.5365i	−0.373095	−	1.14827i	−0.944755	−	0.327777i	$-0.893701\pi$
$853$	−10.8967	−	33.5365i	−0.373095	−	1.14827i	0.571661	−	0.820490i	$-0.306299\pi$
$854$		0			0
$855$	2.66805	−	1.93845i	0.0912453	−	0.0662936i
$856$		0			0
$857$	50.3640			1.72040			0.860201	−	0.509955i	$-0.170338\pi$
$857$	50.3640			1.72040			0.860201	+	0.509955i	$0.170338\pi$
$858$		0			0
$859$	−10.0493			−0.342876			−0.171438	−	0.985195i	$-0.554841\pi$
$859$	−10.0493			−0.342876			−0.171438	+	0.985195i	$0.554841\pi$
$860$		0			0
$861$	29.0879	−	21.1336i	0.991312	−	0.720230i
$862$		0			0
$863$	11.7379	+	36.1255i	0.399562	+	1.22973i	0.925351	+	0.379111i	$0.123770\pi$
$863$	11.7379	+	36.1255i	0.399562	+	1.22973i	−0.525789	+	0.850615i	$0.676230\pi$
$864$		0			0
$865$	−0.512676	−	0.372481i	−0.0174315	−	0.0126647i
$866$		0			0
$867$	16.4457	−	50.6147i	0.558525	−	1.71896i
$868$		0			0
$869$	−4.63744	+	28.2493i	−0.157314	+	0.958291i
$870$		0			0
$871$	5.90839	−	18.1842i	0.200198	−	0.616147i
$872$		0			0
$873$	27.7112	+	20.1334i	0.937883	+	0.681412i
$874$		0			0
$875$	−1.10470	−	3.39991i	−0.0373456	−	0.114938i
$876$		0			0
$877$	38.7930	−	28.1848i	1.30995	−	0.951732i	0.309947	−	0.950754i	$-0.399689\pi$
$877$	38.7930	−	28.1848i	1.30995	−	0.951732i	1.00000		0.000978349i	$-0.000311418\pi$
$878$		0			0
$879$	−58.6180			−1.97714
$880$		0			0
$881$	−26.0141			−0.876439			−0.438219	−	0.898868i	$-0.644391\pi$
$881$	−26.0141			−0.876439			−0.438219	+	0.898868i	$0.644391\pi$
$882$		0			0
$883$	4.64974	−	3.37824i	0.156476	−	0.113687i	−0.506792	−	0.862068i	$-0.669169\pi$
$883$	4.64974	−	3.37824i	0.156476	−	0.113687i	0.663268	+	0.748382i	$0.269169\pi$
$884$		0			0
$885$	−1.01299	−	3.11766i	−0.0340513	−	0.104799i
$886$		0			0
$887$	34.4423	+	25.0238i	1.15646	+	0.840218i	0.989326	−	0.145716i	$-0.0465487\pi$
$887$	34.4423	+	25.0238i	1.15646	+	0.840218i	0.167134	+	0.985934i	$0.446549\pi$
$888$		0			0
$889$	−11.1031	+	34.1718i	−0.372386	+	1.14609i
$890$		0			0
$891$	60.3586	+	31.1836i	2.02209	+	1.04469i
$892$		0			0
$893$	6.78622	−	20.8858i	0.227092	−	0.698918i
$894$		0			0
$895$	−0.593786	−	0.431411i	−0.0198481	−	0.0144205i
$896$		0			0
$897$	−7.82683	−	24.0885i	−0.261330	−	0.804292i
$898$		0			0
$899$	25.4752	−	18.5088i	0.849646	−	0.617304i
$900$		0			0
$901$	−5.76289			−0.191990
$902$		0			0
$903$	74.5474			2.48078
$904$		0			0
$905$	0.658168	−	0.478187i	0.0218782	−	0.0158955i
$906$		0			0
$907$	15.7798	+	48.5651i	0.523958	+	1.61258i	0.766366	+	0.642404i	$0.222063\pi$
$907$	15.7798	+	48.5651i	0.523958	+	1.61258i	−0.242408	+	0.970174i	$0.577937\pi$
$908$		0			0
$909$	27.8451	+	20.2307i	0.923565	+	0.671009i
$910$		0			0
$911$	15.1102	−	46.5044i	0.500623	−	1.54076i	−0.307383	−	0.951586i	$-0.599453\pi$
$911$	15.1102	−	46.5044i	0.500623	−	1.54076i	0.808006	−	0.589174i	$-0.200547\pi$
$912$		0			0
$913$	−2.28374	−	4.54517i	−0.0755807	−	0.150423i
$914$		0			0
$915$	1.03551	−	3.18698i	0.0342330	−	0.105358i
$916$		0			0
$917$	9.34924	+	6.79262i	0.308739	+	0.224312i
$918$		0			0
$919$	−18.2778	−	56.2532i	−0.602929	−	1.85562i	−0.510448	−	0.859909i	$-0.670520\pi$
$919$	−18.2778	−	56.2532i	−0.602929	−	1.85562i	−0.0924808	−	0.995714i	$-0.529480\pi$
$920$		0			0
$921$	−54.9310	+	39.9097i	−1.81004	+	1.31507i
$922$		0			0
$923$	−29.2385			−0.962398
$924$		0			0
$925$	−41.1530			−1.35310
$926$		0			0
$927$	−11.9804	+	8.70430i	−0.393490	+	0.285887i
$928$		0			0
$929$	−0.241469	−	0.743166i	−0.00792235	−	0.0243825i	0.947017	−	0.321183i	$-0.104080\pi$
$929$	−0.241469	−	0.743166i	−0.00792235	−	0.0243825i	−0.954940	+	0.296800i	$0.904080\pi$
$930$		0			0
$931$	−33.1988	−	24.1203i	−1.08805	−	0.790513i
$932$		0			0
$933$	10.0840	−	31.0353i	0.330135	−	1.01605i
$934$		0			0
$935$	0.115014	−	0.113727i	0.00376137	−	0.00371925i
$936$		0			0
$937$	−1.79210	+	5.51551i	−0.0585453	+	0.180184i	−0.976052	−	0.217535i	$-0.930198\pi$
$937$	−1.79210	+	5.51551i	−0.0585453	+	0.180184i	0.917507	+	0.397719i	$0.130198\pi$
$938$		0			0
$939$	−58.6494	−	42.6113i	−1.91395	−	1.39057i
$940$		0			0
$941$	−13.5411	−	41.6751i	−0.441426	−	1.35857i	−0.886356	−	0.463004i	$-0.846771\pi$
$941$	−13.5411	−	41.6751i	−0.441426	−	1.35857i	0.444930	−	0.895565i	$-0.353229\pi$
$942$		0			0
$943$	−7.16391	+	5.20488i	−0.233289	+	0.169494i
$944$		0			0
$945$	−4.70761			−0.153139
$946$		0			0
$947$	12.2117			0.396828			0.198414	−	0.980118i	$-0.436421\pi$
$947$	12.2117			0.396828			0.198414	+	0.980118i	$0.436421\pi$
$948$		0			0
$949$	−5.32875	+	3.87157i	−0.172979	+	0.125676i
$950$		0			0
$951$	21.5044	+	66.1838i	0.697328	+	2.14616i
$952$		0			0
$953$	11.7701	+	8.55150i	0.381272	+	0.277010i	0.761870	−	0.647731i	$-0.224282\pi$
$953$	11.7701	+	8.55150i	0.381272	+	0.277010i	−0.380598	+	0.924741i	$0.624282\pi$
$954$		0			0
$955$	−0.561246	+	1.72734i	−0.0181615	+	0.0558953i
$956$		0			0
$957$	68.9584	−	10.5243i	2.22911	−	0.340202i
$958$		0			0
$959$	19.3529	−	59.5621i	0.624938	−	1.92336i
$960$		0			0
$961$	6.70370	+	4.87052i	0.216248	+	0.157114i
$962$		0			0
$963$	−2.43815	−	7.50386i	−0.0785683	−	0.241808i
$964$		0			0
$965$	1.83803	−	1.33541i	0.0591684	−	0.0429884i
$966$		0			0
$967$	−10.3647			−0.333306			−0.166653	−	0.986016i	$-0.553296\pi$
$967$	−10.3647			−0.333306			−0.166653	+	0.986016i	$0.553296\pi$
$968$		0			0
$969$	8.49810			0.272998
$970$		0			0
$971$	−19.7811	+	14.3718i	−0.634806	+	0.461213i	−0.858062	−	0.513546i	$-0.828331\pi$
$971$	−19.7811	+	14.3718i	−0.634806	+	0.461213i	0.223256	+	0.974760i	$0.428331\pi$
$972$		0			0
$973$	−16.7816	−	51.6484i	−0.537993	−	1.65577i
$974$		0			0
$975$	33.5100	+	24.3464i	1.07318	+	0.779710i
$976$		0			0
$977$	16.1264	−	49.6319i	0.515929	−	1.58786i	−0.265657	−	0.964067i	$-0.585589\pi$
$977$	16.1264	−	49.6319i	0.515929	−	1.58786i	0.781586	−	0.623797i	$-0.214411\pi$
$978$		0			0
$979$	12.8936	−	1.96779i	0.412080	−	0.0628909i
$980$		0			0
$981$	2.61810	−	8.05767i	0.0835894	−	0.257262i
$982$		0			0
$983$	5.57537	+	4.05075i	0.177827	+	0.129199i	0.673138	−	0.739517i	$-0.264946\pi$
$983$	5.57537	+	4.05075i	0.177827	+	0.129199i	−0.495311	+	0.868716i	$0.664946\pi$
$984$		0			0
$985$	0.267008	+	0.821768i	0.00850760	+	0.0261837i
$986$		0			0
$987$	−43.7685	+	31.7997i	−1.39317	+	1.01219i
$988$		0			0
$989$	−18.3599			−0.583811
$990$		0			0
$991$	−43.2270			−1.37315			−0.686576	−	0.727058i	$-0.740887\pi$
$991$	−43.2270			−1.37315			−0.686576	+	0.727058i	$0.740887\pi$
$992$		0			0
$993$	−8.19558	+	5.95444i	−0.260079	+	0.188958i
$994$		0			0
$995$	0.197689	+	0.608426i	0.00626718	+	0.0192884i
$996$		0			0
$997$	−7.74154	−	5.62456i	−0.245177	−	0.178132i	0.458410	−	0.888741i	$-0.348419\pi$
$997$	−7.74154	−	5.62456i	−0.245177	−	0.178132i	−0.703587	+	0.710609i	$0.748419\pi$
$998$		0			0
$999$	−33.5213	+	103.168i	−1.06057	+	3.26409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.f.97.3	yes	12
4.3	odd	2		352.2.m.e.97.1	✓	12
8.3	odd	2		704.2.m.m.449.3		12
8.5	even	2		704.2.m.n.449.1		12
11.4	even	5		3872.2.a.bn.1.1		6
11.5	even	5	inner	352.2.m.f.225.3	yes	12
11.7	odd	10		3872.2.a.bo.1.1		6
44.7	even	10		3872.2.a.bp.1.6		6
44.15	odd	10		3872.2.a.bq.1.6		6
44.27	odd	10		352.2.m.e.225.1	yes	12
88.5	even	10		704.2.m.n.577.1		12
88.27	odd	10		704.2.m.m.577.3		12
88.29	odd	10		7744.2.a.dw.1.6		6
88.37	even	10		7744.2.a.dv.1.6		6
88.51	even	10		7744.2.a.dt.1.1		6
88.59	odd	10		7744.2.a.du.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.e.97.1	✓	12	4.3	odd	2
352.2.m.e.225.1	yes	12	44.27	odd	10
352.2.m.f.97.3	yes	12	1.1	even	1	trivial
352.2.m.f.225.3	yes	12	11.5	even	5	inner
704.2.m.m.449.3		12	8.3	odd	2
704.2.m.m.577.3		12	88.27	odd	10
704.2.m.n.449.1		12	8.5	even	2
704.2.m.n.577.1		12	88.5	even	10
3872.2.a.bn.1.1		6	11.4	even	5
3872.2.a.bo.1.1		6	11.7	odd	10
3872.2.a.bp.1.6		6	44.7	even	10
3872.2.a.bq.1.6		6	44.15	odd	10
7744.2.a.dt.1.1		6	88.51	even	10
7744.2.a.du.1.1		6	88.59	odd	10
7744.2.a.dv.1.6		6	88.37	even	10
7744.2.a.dw.1.6		6	88.29	odd	10

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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.57533 - 1.87109i) q^{3} +(-0.0283989 - 0.0874029i) q^{5} +(3.14968 + 2.28838i) q^{7} +(2.20431 - 6.78417i) q^{9} +(-3.27866 + 0.500382i) q^{11} +(-0.805542 + 2.47920i) q^{13} +(-0.236675 - 0.171954i) q^{15} +(-0.163984 - 0.504692i) q^{17} +(-4.06990 + 2.95695i) q^{19} +12.3932 q^{21} -3.05227 q^{23} +(4.03825 - 2.93396i) q^{25} +(-4.06588 - 12.5135i) q^{27} +(-5.34531 - 3.88360i) q^{29} +(-1.47274 + 4.53264i) q^{31} +(-7.50738 + 7.42331i) q^{33} +(0.110563 - 0.340278i) q^{35} +(-6.66996 - 4.84601i) q^{37} +(2.56427 + 7.89201i) q^{39} +(2.34708 - 1.70525i) q^{41} +6.01518 q^{43} -0.655556 q^{45} +(-3.53165 + 2.56589i) q^{47} +(2.52070 + 7.75792i) q^{49} +(-1.36664 - 0.992920i) q^{51} +(3.35585 - 10.3282i) q^{53} +(0.136845 + 0.272354i) q^{55} +(-4.94862 + 15.2303i) q^{57} +(9.06537 + 6.58638i) q^{59} +(3.53965 + 10.8939i) q^{61} +(22.4676 - 16.3237i) q^{63} +0.239566 q^{65} -7.33468 q^{67} +(-7.86060 + 5.71106i) q^{69} +(3.46603 + 10.6673i) q^{71} +(2.04418 + 1.48519i) q^{73} +(4.91014 - 15.1118i) q^{75} +(-11.4718 - 5.92677i) q^{77} +(2.66727 - 8.20903i) q^{79} +(-16.5720 - 12.0402i) q^{81} +(0.473934 + 1.45862i) q^{83} +(-0.0394545 + 0.0286654i) q^{85} -21.0325 q^{87} -3.93257 q^{89} +(-8.21055 + 5.96531i) q^{91} +(4.68816 + 14.4287i) q^{93} +(0.374027 + 0.271746i) q^{95} +(-1.48385 + 4.56682i) q^{97} +(-3.83251 + 23.3460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{7} - q^{9} - 11 q^{11} - 2 q^{13} + 4 q^{15} + 12 q^{17} + 5 q^{19} + 24 q^{21} - 12 q^{23} + 13 q^{25} + 3 q^{27} + 16 q^{31} - 7 q^{33} - 28 q^{35} - 4 q^{37} + 46 q^{39} - 4 q^{41} - 22 q^{43}+ \cdots - 65 q^{99}+O(q^{100}) \) 12 * q + 6 * q^7 - q^9 - 11 * q^11 - 2 * q^13 + 4 * q^15 + 12 * q^17 + 5 * q^19 + 24 * q^21 - 12 * q^23 + 13 * q^25 + 3 * q^27 + 16 * q^31 - 7 * q^33 - 28 * q^35 - 4 * q^37 + 46 * q^39 - 4 * q^41 - 22 * q^43 + 28 * q^45 - 24 * q^47 - 5 * q^49 + 17 * q^51 - 14 * q^53 - 46 * q^55 - 37 * q^57 + 31 * q^59 - 14 * q^61 + 58 * q^63 - 52 * q^65 - 62 * q^67 - 18 * q^69 + 6 * q^71 - 8 * q^73 + 53 * q^75 - 46 * q^77 - 4 * q^79 - 22 * q^81 + 41 * q^83 - 36 * q^85 - 76 * q^87 - 2 * q^89 - 22 * q^91 + 8 * q^93 + 16 * q^95 + 3 * q^97 - 65 * q^99

Introduction

L-functions

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