LMFDB - Embedded newform 1148.2.n.c.953.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 12 x^{14} - 19 x^{13} + 49 x^{12} - 91 x^{11} + 269 x^{10} - 367 x^{9} + 1058 x^{8} + \cdots + 1 $ x^16 - 3x^15 + 12x^14 - 19x^13 + 49x^12 - 91x^11 + 269x^10 - 367x^9 + 1058x^8 - 1675x^7 + 2755x^6 - 2800x^5 + 4032x^4 - 2186x^3 + 2189x^2 + 76*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			953.3
Root			$0.321891 + 0.990677i$ of defining polynomial
Character	$\chi$	$=$	1148.953
Dual form			1148.2.n.c.365.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.04166 q^{3} +(-0.980821 - 3.01866i) q^{5} +(0.809017 - 0.587785i) q^{7} -1.91494 q^{9} +O(q^{10})$	\(q+1.04166 q^{3} +(-0.980821 - 3.01866i) q^{5} +(0.809017 - 0.587785i) q^{7} -1.91494 q^{9} +(-0.720296 + 2.21684i) q^{11} +(-4.96745 - 3.60906i) q^{13} +(-1.02168 - 3.14441i) q^{15} +(-0.584425 + 1.79867i) q^{17} +(0.874332 - 0.635240i) q^{19} +(0.842721 - 0.612272i) q^{21} +(-0.0492228 - 0.0357625i) q^{23} +(-4.10519 + 2.98260i) q^{25} -5.11970 q^{27} +(-2.10122 - 6.46688i) q^{29} +(-2.72351 + 8.38210i) q^{31} +(-0.750303 + 2.30920i) q^{33} +(-2.56782 - 1.86563i) q^{35} +(-3.72073 - 11.4512i) q^{37} +(-5.17439 - 3.75942i) q^{39} +(-0.446908 + 6.38751i) q^{41} +(5.49805 + 3.99457i) q^{43} +(1.87822 + 5.78056i) q^{45} +(1.60350 + 1.16501i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.608772 + 1.87361i) q^{51} +(-1.92119 - 5.91281i) q^{53} +7.39837 q^{55} +(0.910757 - 0.661704i) q^{57} +(3.52997 + 2.56468i) q^{59} +(-8.06096 + 5.85663i) q^{61} +(-1.54922 + 1.12558i) q^{63} +(-6.02234 + 18.5349i) q^{65} +(-2.38407 - 7.33743i) q^{67} +(-0.0512735 - 0.0372523i) q^{69} +(3.81582 - 11.7439i) q^{71} -9.13495 q^{73} +(-4.27621 + 3.10685i) q^{75} +(0.720296 + 2.21684i) q^{77} -7.10337 q^{79} +0.411848 q^{81} +2.63313 q^{83} +6.00280 q^{85} +(-2.18875 - 6.73629i) q^{87} +(4.99906 - 3.63203i) q^{89} -6.14011 q^{91} +(-2.83697 + 8.73130i) q^{93} +(-2.77513 - 2.01625i) q^{95} +(-3.62222 - 11.1481i) q^{97} +(1.37933 - 4.24513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9	$ 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - q^{17} + 15 q^{19} + 2 q^{21} + 27 q^{23} - 3 q^{25} + 28 q^{27} - q^{29} - 14 q^{31} - 13 q^{33} - 12 q^{35} - 16 q^{37} + 10 q^{39} + 26 q^{41} + 5 q^{43} - 9 q^{45} - 14 q^{47} - 4 q^{49} + 4 q^{51} - 20 q^{53} + 10 q^{55} - 13 q^{57} - 47 q^{61} + 3 q^{63} - 29 q^{65} - 27 q^{67} + 15 q^{69} - 11 q^{71} + 70 q^{73} + 14 q^{75} + q^{77} + 30 q^{79} - 72 q^{81} - 78 q^{83} + 72 q^{85} + 21 q^{87} + 17 q^{89} - 24 q^{91} - 7 q^{93} + 27 q^{95} - 17 q^{97} + 13 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - q^17 + 15 * q^19 + 2 * q^21 + 27 * q^23 - 3 * q^25 + 28 * q^27 - q^29 - 14 * q^31 - 13 * q^33 - 12 * q^35 - 16 * q^37 + 10 * q^39 + 26 * q^41 + 5 * q^43 - 9 * q^45 - 14 * q^47 - 4 * q^49 + 4 * q^51 - 20 * q^53 + 10 * q^55 - 13 * q^57 - 47 * q^61 + 3 * q^63 - 29 * q^65 - 27 * q^67 + 15 * q^69 - 11 * q^71 + 70 * q^73 + 14 * q^75 + q^77 + 30 * q^79 - 72 * q^81 - 78 * q^83 + 72 * q^85 + 21 * q^87 + 17 * q^89 - 24 * q^91 - 7 * q^93 + 27 * q^95 - 17 * q^97 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	1.04166			0.601403			0.300701	−	0.953718i	$-0.402779\pi$
$3$	1.04166			0.601403			0.300701	+	0.953718i	$0.402779\pi$
$4$		0			0
$5$	−0.980821	−	3.01866i	−0.438636	−	1.34998i	−0.889314	−	0.457297i	$-0.848818\pi$
$5$	−0.980821	−	3.01866i	−0.438636	−	1.34998i	0.450677	−	0.892687i	$-0.351182\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$		0			0
$9$	−1.91494			−0.638315
$10$		0			0
$11$	−0.720296	+	2.21684i	−0.217177	+	0.668403i	0.781815	+	0.623511i	$0.214294\pi$
$11$	−0.720296	+	2.21684i	−0.217177	+	0.668403i	−0.998992	+	0.0448920i	$0.985706\pi$
$12$		0			0
$13$	−4.96745	−	3.60906i	−1.37772	−	1.00097i	−0.997089	−	0.0762483i	$-0.975706\pi$
$13$	−4.96745	−	3.60906i	−1.37772	−	1.00097i	−0.380634	−	0.924726i	$-0.624294\pi$
$14$		0			0
$15$	−1.02168	−	3.14441i	−0.263797	−	0.811884i
$16$		0			0
$17$	−0.584425	+	1.79867i	−0.141744	+	0.436243i	−0.996578	−	0.0826588i	$-0.973659\pi$
$17$	−0.584425	+	1.79867i	−0.141744	+	0.436243i	0.854834	+	0.518901i	$0.173659\pi$
$18$		0			0
$19$	0.874332	−	0.635240i	0.200586	−	0.145734i	−0.482958	−	0.875643i	$-0.660438\pi$
$19$	0.874332	−	0.635240i	0.200586	−	0.145734i	0.683544	+	0.729909i	$0.260438\pi$
$20$		0			0
$21$	0.842721	−	0.612272i	0.183897	−	0.133609i
$22$		0			0
$23$	−0.0492228	−	0.0357625i	−0.0102637	−	0.00745699i	0.582642	−	0.812729i	$-0.302019\pi$
$23$	−0.0492228	−	0.0357625i	−0.0102637	−	0.00745699i	−0.592905	+	0.805272i	$0.702019\pi$
$24$		0			0
$25$	−4.10519	+	2.98260i	−0.821038	+	0.596519i
$26$		0			0
$27$	−5.11970			−0.985287
$28$		0			0
$29$	−2.10122	−	6.46688i	−0.390186	−	1.20087i	−0.932647	−	0.360789i	$-0.882507\pi$
$29$	−2.10122	−	6.46688i	−0.390186	−	1.20087i	0.542461	−	0.840081i	$-0.317493\pi$
$30$		0			0
$31$	−2.72351	+	8.38210i	−0.489157	+	1.50547i	0.336712	+	0.941608i	$0.390685\pi$
$31$	−2.72351	+	8.38210i	−0.489157	+	1.50547i	−0.825869	+	0.563862i	$0.809315\pi$
$32$		0			0
$33$	−0.750303	+	2.30920i	−0.130611	+	0.401979i
$34$		0			0
$35$	−2.56782	−	1.86563i	−0.434041	−	0.315349i
$36$		0			0
$37$	−3.72073	−	11.4512i	−0.611684	−	1.88257i	−0.441826	−	0.897101i	$-0.645669\pi$
$37$	−3.72073	−	11.4512i	−0.611684	−	1.88257i	−0.169858	−	0.985469i	$-0.554331\pi$
$38$		0			0
$39$	−5.17439	−	3.75942i	−0.828566	−	0.601988i
$40$		0			0
$41$	−0.446908	+	6.38751i	−0.0697953	+	0.997561i
$41$	−0.446908	+	6.38751i	−0.0697953	+	0.997561i
$42$		0			0
$43$	5.49805	+	3.99457i	0.838445	+	0.609166i	0.921936	−	0.387343i	$-0.126607\pi$
$43$	5.49805	+	3.99457i	0.838445	+	0.609166i	−0.0834909	+	0.996509i	$0.526607\pi$
$44$		0			0
$45$	1.87822	+	5.78056i	0.279988	+	0.861715i
$46$		0			0
$47$	1.60350	+	1.16501i	0.233895	+	0.169935i	0.698559	−	0.715552i	$-0.253825\pi$
$47$	1.60350	+	1.16501i	0.233895	+	0.169935i	−0.464664	+	0.885487i	$0.653825\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$		0			0
$51$	−0.608772	+	1.87361i	−0.0852451	+	0.262357i
$52$		0			0
$53$	−1.92119	−	5.91281i	−0.263895	−	0.812187i	−0.991946	−	0.126663i	$-0.959573\pi$
$53$	−1.92119	−	5.91281i	−0.263895	−	0.812187i	0.728050	−	0.685524i	$-0.240427\pi$
$54$		0			0
$55$	7.39837			0.997596
$56$		0			0
$57$	0.910757	−	0.661704i	0.120633	−	0.0876448i
$58$		0			0
$59$	3.52997	+	2.56468i	0.459563	+	0.333892i	0.793360	−	0.608753i	$-0.208330\pi$
$59$	3.52997	+	2.56468i	0.459563	+	0.333892i	−0.333797	+	0.942645i	$0.608330\pi$
$60$		0			0
$61$	−8.06096	+	5.85663i	−1.03210	+	0.749865i	−0.968728	−	0.248125i	$-0.920186\pi$
$61$	−8.06096	+	5.85663i	−1.03210	+	0.749865i	−0.0633722	+	0.997990i	$0.520186\pi$
$62$		0			0
$63$	−1.54922	+	1.12558i	−0.195184	+	0.141809i
$64$		0			0
$65$	−6.02234	+	18.5349i	−0.746980	+	2.29897i
$66$		0			0
$67$	−2.38407	−	7.33743i	−0.291261	−	0.896409i	−0.984452	−	0.175655i	$-0.943796\pi$
$67$	−2.38407	−	7.33743i	−0.291261	−	0.896409i	0.693191	−	0.720754i	$-0.256204\pi$
$68$		0			0
$69$	−0.0512735	−	0.0372523i	−0.00617260	−	0.00448466i
$70$		0			0
$71$	3.81582	−	11.7439i	0.452854	−	1.39374i	−0.420782	−	0.907162i	$-0.638244\pi$
$71$	3.81582	−	11.7439i	0.452854	−	1.39374i	0.873636	−	0.486580i	$-0.161756\pi$
$72$		0			0
$73$	−9.13495			−1.06917			−0.534583	−	0.845116i	$-0.679531\pi$
$73$	−9.13495			−1.06917			−0.534583	+	0.845116i	$0.679531\pi$
$74$		0			0
$75$	−4.27621	+	3.10685i	−0.493775	+	0.358748i
$76$		0			0
$77$	0.720296	+	2.21684i	0.0820853	+	0.252633i
$78$		0			0
$79$	−7.10337			−0.799192			−0.399596	−	0.916691i	$-0.630849\pi$
$79$	−7.10337			−0.799192			−0.399596	+	0.916691i	$0.630849\pi$
$80$		0			0
$81$	0.411848			0.0457608
$82$		0			0
$83$	2.63313			0.289023			0.144512	−	0.989503i	$-0.453839\pi$
$83$	2.63313			0.289023			0.144512	+	0.989503i	$0.453839\pi$
$84$		0			0
$85$	6.00280			0.651095
$86$		0			0
$87$	−2.18875	−	6.73629i	−0.234659	−	0.722206i
$88$		0			0
$89$	4.99906	−	3.63203i	0.529900	−	0.384995i	−0.290421	−	0.956899i	$-0.593795\pi$
$89$	4.99906	−	3.63203i	0.529900	−	0.384995i	0.820320	+	0.571904i	$0.193795\pi$
$90$		0			0
$91$	−6.14011			−0.643658
$92$		0			0
$93$	−2.83697	+	8.73130i	−0.294180	+	0.905394i
$94$		0			0
$95$	−2.77513	−	2.01625i	−0.284723	−	0.206863i
$96$		0			0
$97$	−3.62222	−	11.1481i	−0.367781	−	1.13191i	−0.948221	−	0.317611i	$-0.897119\pi$
$97$	−3.62222	−	11.1481i	−0.367781	−	1.13191i	0.580440	−	0.814303i	$-0.302881\pi$
$98$		0			0
$99$	1.37933	−	4.24513i	0.138628	−	0.426652i
$100$		0			0
$101$	6.16118	−	4.47636i	0.613060	−	0.445414i	−0.237430	−	0.971405i	$-0.576305\pi$
$101$	6.16118	−	4.47636i	0.613060	−	0.445414i	0.850491	+	0.525990i	$0.176305\pi$
$102$		0			0
$103$	1.74838	−	1.27027i	0.172273	−	0.125163i	−0.498308	−	0.867000i	$-0.666045\pi$
$103$	1.74838	−	1.27027i	0.172273	−	0.125163i	0.670580	+	0.741837i	$0.266045\pi$
$104$		0			0
$105$	−2.67480	−	1.94335i	−0.261034	−	0.189652i
$106$		0			0
$107$	3.27894	−	2.38229i	0.316987	−	0.230304i	−0.417902	−	0.908492i	$-0.637234\pi$
$107$	3.27894	−	2.38229i	0.316987	−	0.230304i	0.734889	+	0.678188i	$0.237234\pi$
$108$		0			0
$109$	8.56528			0.820405			0.410202	−	0.911995i	$-0.365458\pi$
$109$	8.56528			0.820405			0.410202	+	0.911995i	$0.365458\pi$
$110$		0			0
$111$	−3.87573	−	11.9283i	−0.367868	−	1.13218i
$112$		0			0
$113$	2.65067	−	8.15793i	0.249354	−	0.767434i	−0.745535	−	0.666466i	$-0.767806\pi$
$113$	2.65067	−	8.15793i	0.249354	−	0.767434i	0.994890	−	0.100968i	$-0.0321938\pi$
$114$		0			0
$115$	−0.0596759	+	0.183663i	−0.00556480	+	0.0171267i
$116$		0			0
$117$	9.51239	+	6.91116i	0.879421	+	0.638937i
$118$		0			0
$119$	0.584425	+	1.79867i	0.0535741	+	0.164884i
$120$		0			0
$121$	4.50362	+	3.27207i	0.409420	+	0.297461i
$122$		0			0
$123$	−0.465526	+	6.65361i	−0.0419751	+	0.599936i
$124$		0			0
$125$	0.190780	+	0.138610i	0.0170639	+	0.0123976i
$126$		0			0
$127$	−3.14222	−	9.67075i	−0.278827	−	0.858140i	−0.988181	−	0.153289i	$-0.951014\pi$
$127$	−3.14222	−	9.67075i	−0.278827	−	0.858140i	0.709355	−	0.704852i	$-0.248986\pi$
$128$		0			0
$129$	5.72710	+	4.16098i	0.504243	+	0.366354i
$130$		0			0
$131$	2.13519	−	6.57143i	0.186552	−	0.574149i	−0.813419	−	0.581678i	$-0.802397\pi$
$131$	2.13519	−	6.57143i	0.186552	−	0.574149i	0.999972	+	0.00752880i	$0.00239651\pi$
$132$		0			0
$133$	0.333965	−	1.02784i	0.0289585	−	0.0891250i
$134$		0			0
$135$	5.02151	+	15.4546i	0.432183	+	1.33012i
$136$		0			0
$137$	18.6160			1.59047			0.795235	−	0.606301i	$-0.207347\pi$
$137$	18.6160			1.59047			0.795235	+	0.606301i	$0.207347\pi$
$138$		0			0
$139$	−4.50839	+	3.27554i	−0.382397	+	0.277827i	−0.762333	−	0.647185i	$-0.775946\pi$
$139$	−4.50839	+	3.27554i	−0.382397	+	0.277827i	0.379936	+	0.925013i	$0.375946\pi$
$140$		0			0
$141$	1.67031	+	1.21355i	0.140665	+	0.102199i
$142$		0			0
$143$	11.5788	−	8.41246i	0.968264	−	0.703485i
$144$		0			0
$145$	−17.4604	+	12.6857i	−1.45001	+	1.05349i
$146$		0			0
$147$	0.321891	−	0.990677i	0.0265491	−	0.0817097i
$148$		0			0
$149$	−3.05881	−	9.41405i	−0.250588	−	0.771229i	−0.994667	−	0.103138i	$-0.967112\pi$
$149$	−3.05881	−	9.41405i	−0.250588	−	0.771229i	0.744079	−	0.668091i	$-0.232888\pi$
$150$		0			0
$151$	−13.2258	−	9.60909i	−1.07630	−	0.781977i	−0.0992651	−	0.995061i	$-0.531649\pi$
$151$	−13.2258	−	9.60909i	−1.07630	−	0.781977i	−0.977034	+	0.213084i	$0.931649\pi$
$152$		0			0
$153$	1.11914	−	3.44436i	0.0904772	−	0.278460i
$154$		0			0
$155$	27.9740			2.24692
$156$		0			0
$157$	2.36532	−	1.71850i	0.188773	−	0.137152i	−0.489385	−	0.872068i	$-0.662779\pi$
$157$	2.36532	−	1.71850i	0.188773	−	0.137152i	0.678158	+	0.734916i	$0.262779\pi$
$158$		0			0
$159$	−2.00122	−	6.15914i	−0.158707	−	0.488451i
$160$		0			0
$161$	−0.0608428			−0.00479508
$162$		0			0
$163$	−21.3657			−1.67349			−0.836747	−	0.547589i	$-0.815546\pi$
$163$	−21.3657			−1.67349			−0.836747	+	0.547589i	$0.815546\pi$
$164$		0			0
$165$	7.70658			0.599957
$166$		0			0
$167$	0.633986			0.0490593			0.0245297	−	0.999699i	$-0.492191\pi$
$167$	0.633986			0.0490593			0.0245297	+	0.999699i	$0.492191\pi$
$168$		0			0
$169$	7.63300	+	23.4919i	0.587154	+	1.80707i
$170$		0			0
$171$	−1.67430	+	1.21645i	−0.128037	+	0.0930242i
$172$		0			0
$173$	5.01695			0.381432			0.190716	−	0.981645i	$-0.438919\pi$
$173$	5.01695			0.381432			0.190716	+	0.981645i	$0.438919\pi$
$174$		0			0
$175$	−1.56804	+	4.82594i	−0.118533	+	0.364807i
$176$		0			0
$177$	3.67703	+	2.67152i	0.276383	+	0.200804i
$178$		0			0
$179$	−3.05193	−	9.39288i	−0.228112	−	0.702057i	−0.997961	−	0.0638305i	$-0.979668\pi$
$179$	−3.05193	−	9.39288i	−0.228112	−	0.702057i	0.769849	−	0.638227i	$-0.220332\pi$
$180$		0			0
$181$	−1.10943	+	3.41448i	−0.0824635	+	0.253796i	−0.983784	−	0.179356i	$-0.942599\pi$
$181$	−1.10943	+	3.41448i	−0.0824635	+	0.253796i	0.901321	+	0.433152i	$0.142599\pi$
$182$		0			0
$183$	−8.39678	+	6.10062i	−0.620708	+	0.450971i
$184$		0			0
$185$	−30.9179	+	22.4632i	−2.27313	+	1.65153i
$186$		0			0
$187$	−3.56642	−	2.59115i	−0.260802	−	0.189484i
$188$		0			0
$189$	−4.14192	+	3.00928i	−0.301281	+	0.218893i
$190$		0			0
$191$	−2.90703			−0.210346			−0.105173	−	0.994454i	$-0.533540\pi$
$191$	−2.90703			−0.210346			−0.105173	+	0.994454i	$0.533540\pi$
$192$		0			0
$193$	3.41489	+	10.5099i	0.245809	+	0.756523i	0.995502	+	0.0947371i	$0.0302010\pi$
$193$	3.41489	+	10.5099i	0.245809	+	0.756523i	−0.749693	+	0.661786i	$0.769799\pi$
$194$		0			0
$195$	−6.27323	+	19.3070i	−0.449236	+	1.38261i
$196$		0			0
$197$	−2.17181	+	6.68415i	−0.154735	+	0.476226i	−0.998134	−	0.0610622i	$-0.980551\pi$
$197$	−2.17181	+	6.68415i	−0.154735	+	0.476226i	0.843399	+	0.537288i	$0.180551\pi$
$198$		0			0
$199$	19.7807	+	14.3715i	1.40222	+	1.01877i	0.994397	+	0.105707i	$0.0337104\pi$
$199$	19.7807	+	14.3715i	1.40222	+	1.01877i	0.407819	+	0.913063i	$0.366290\pi$
$200$		0			0
$201$	−2.48339	−	7.64310i	−0.175165	−	0.539103i
$202$		0			0
$203$	−5.50106	−	3.99675i	−0.386099	−	0.280517i
$204$		0			0
$205$	19.7200	−	4.91594i	1.37731	−	0.343344i
$206$		0			0
$207$	0.0942590	+	0.0684832i	0.00655145	+	0.00475991i
$208$		0			0
$209$	0.778448	+	2.39582i	0.0538464	+	0.165722i
$210$		0			0
$211$	−3.41975	−	2.48459i	−0.235425	−	0.171047i	0.463817	−	0.885931i	$-0.346479\pi$
$211$	−3.41975	−	2.48459i	−0.235425	−	0.171047i	−0.699243	+	0.714884i	$0.746479\pi$
$212$		0			0
$213$	3.97478	−	12.2331i	0.272348	−	0.838200i
$214$		0			0
$215$	6.66562	−	20.5147i	0.454592	−	1.39909i
$216$		0			0
$217$	2.72351	+	8.38210i	0.184884	+	0.569014i
$218$		0			0
$219$	−9.51551			−0.642999
$220$		0			0
$221$	9.39463	−	6.82560i	0.631951	−	0.459139i
$222$		0			0
$223$	5.27147	+	3.82994i	0.353003	+	0.256472i	0.750128	−	0.661293i	$-0.229992\pi$
$223$	5.27147	+	3.82994i	0.353003	+	0.256472i	−0.397124	+	0.917765i	$0.629992\pi$
$224$		0			0
$225$	7.86122	−	5.71151i	0.524081	−	0.380767i
$226$		0			0
$227$	15.0767	−	10.9539i	1.00067	−	0.727033i	0.0384418	−	0.999261i	$-0.487761\pi$
$227$	15.0767	−	10.9539i	1.00067	−	0.727033i	0.962233	+	0.272228i	$0.0877606\pi$
$228$		0			0
$229$	−7.56144	+	23.2717i	−0.499674	+	1.53784i	0.309869	+	0.950779i	$0.399715\pi$
$229$	−7.56144	+	23.2717i	−0.499674	+	1.53784i	−0.809543	+	0.587060i	$0.800285\pi$
$230$		0			0
$231$	0.750303	+	2.30920i	0.0493663	+	0.151934i
$232$		0			0
$233$	−4.44360	−	3.22846i	−0.291110	−	0.211504i	0.432639	−	0.901567i	$-0.357583\pi$
$233$	−4.44360	−	3.22846i	−0.291110	−	0.211504i	−0.723749	+	0.690064i	$0.757583\pi$
$234$		0			0
$235$	1.94403	−	5.98310i	0.126814	−	0.390294i
$236$		0			0
$237$	−7.39929			−0.480636
$238$		0			0
$239$	24.5887	−	17.8648i	1.59051	−	1.15558i	0.687310	−	0.726364i	$-0.258791\pi$
$239$	24.5887	−	17.8648i	1.59051	−	1.15558i	0.903204	−	0.429212i	$-0.141209\pi$
$240$		0			0
$241$	−7.50135	−	23.0868i	−0.483204	−	1.48715i	−0.834565	−	0.550910i	$-0.814281\pi$
$241$	−7.50135	−	23.0868i	−0.483204	−	1.48715i	0.351361	−	0.936240i	$-0.385719\pi$
$242$		0			0
$243$	15.7881			1.01281
$244$		0			0
$245$	−3.17400			−0.202780
$246$		0			0
$247$	−6.63582			−0.422227
$248$		0			0
$249$	2.74282			0.173819
$250$		0			0
$251$	7.29582	+	22.4542i	0.460508	+	1.41730i	0.864545	+	0.502555i	$0.167606\pi$
$251$	7.29582	+	22.4542i	0.460508	+	1.41730i	−0.404038	+	0.914742i	$0.632394\pi$
$252$		0			0
$253$	0.114735	−	0.0833597i	0.00721331	−	0.00524078i
$254$		0			0
$255$	6.25287			0.391570
$256$		0			0
$257$	−3.71570	+	11.4357i	−0.231779	+	0.713342i	0.765754	+	0.643134i	$0.222366\pi$
$257$	−3.71570	+	11.4357i	−0.231779	+	0.713342i	−0.997532	+	0.0702078i	$0.977634\pi$
$258$		0			0
$259$	−9.74099	−	7.07724i	−0.605276	−	0.439759i
$260$		0			0
$261$	4.02371	+	12.3837i	0.249062	+	0.766533i
$262$		0			0
$263$	−9.64758	+	29.6922i	−0.594895	+	1.83090i	−0.0396492	+	0.999214i	$0.512624\pi$
$263$	−9.64758	+	29.6922i	−0.594895	+	1.83090i	−0.555246	+	0.831686i	$0.687376\pi$
$264$		0			0
$265$	−15.9644	+	11.5988i	−0.980685	+	0.712509i
$266$		0			0
$267$	5.20732	−	3.78334i	0.318683	−	0.231537i
$268$		0			0
$269$	14.3956	+	10.4590i	0.877715	+	0.637697i	0.932646	−	0.360793i	$-0.117494\pi$
$269$	14.3956	+	10.4590i	0.877715	+	0.637697i	−0.0549311	+	0.998490i	$0.517494\pi$
$270$		0			0
$271$	−5.45023	+	3.95983i	−0.331078	+	0.240542i	−0.740888	−	0.671629i	$-0.765595\pi$
$271$	−5.45023	+	3.95983i	−0.331078	+	0.240542i	0.409810	+	0.912171i	$0.365595\pi$
$272$		0			0
$273$	−6.39590			−0.387098
$274$		0			0
$275$	−3.65499	−	11.2489i	−0.220404	−	0.678335i
$276$		0			0
$277$	0.636449	−	1.95879i	0.0382405	−	0.117692i	−0.930114	−	0.367271i	$-0.880292\pi$
$277$	0.636449	−	1.95879i	0.0382405	−	0.117692i	0.968354	+	0.249579i	$0.0802922\pi$
$278$		0			0
$279$	5.21537	−	16.0513i	0.312236	−	0.960964i
$280$		0			0
$281$	20.8612	+	15.1565i	1.24447	+	0.904162i	0.997888	−	0.0649595i	$-0.0206918\pi$
$281$	20.8612	+	15.1565i	1.24447	+	0.904162i	0.246584	+	0.969121i	$0.420692\pi$
$282$		0			0
$283$	−9.83984	−	30.2839i	−0.584918	−	1.80019i	−0.599600	−	0.800300i	$-0.704673\pi$
$283$	−9.83984	−	30.2839i	−0.584918	−	1.80019i	0.0146817	−	0.999892i	$-0.495327\pi$
$284$		0			0
$285$	−2.89075	−	2.10025i	−0.171233	−	0.124408i
$286$		0			0
$287$	3.39293	+	5.43029i	0.200278	+	0.320540i
$288$		0			0
$289$	10.8596	+	7.88997i	0.638801	+	0.464116i
$290$		0			0
$291$	−3.77312	−	11.6125i	−0.221184	−	0.680736i
$292$		0			0
$293$	−12.3534	−	8.97524i	−0.721691	−	0.524339i	0.165233	−	0.986255i	$-0.447162\pi$
$293$	−12.3534	−	8.97524i	−0.721691	−	0.524339i	−0.886924	+	0.461915i	$0.847162\pi$
$294$		0			0
$295$	4.27960	−	13.1713i	0.249168	−	0.766861i
$296$		0			0
$297$	3.68770	−	11.3496i	0.213982	−	0.658569i
$298$		0			0
$299$	0.115443	+	0.355297i	0.00667624	+	0.0205473i
$300$		0			0
$301$	6.79596			0.391713
$302$		0			0
$303$	6.41785	−	4.66284i	0.368696	−	0.267873i
$304$		0			0
$305$	25.5855	+	18.5890i	1.46502	+	1.06440i
$306$		0			0
$307$	−7.49510	+	5.44551i	−0.427768	+	0.310791i	−0.780756	−	0.624836i	$-0.785166\pi$
$307$	−7.49510	+	5.44551i	−0.427768	+	0.310791i	0.352988	+	0.935628i	$0.385166\pi$
$308$		0			0
$309$	1.82121	−	1.32319i	0.103605	−	0.0752735i
$310$		0			0
$311$	−4.83294	+	14.8743i	−0.274051	+	0.843443i	0.715418	+	0.698697i	$0.246236\pi$
$311$	−4.83294	+	14.8743i	−0.274051	+	0.843443i	−0.989469	+	0.144746i	$0.953764\pi$
$312$		0			0
$313$	−0.178116	−	0.548186i	−0.0100677	−	0.0309853i	0.945896	−	0.324469i	$-0.105185\pi$
$313$	−0.178116	−	0.548186i	−0.0100677	−	0.0309853i	−0.955964	+	0.293483i	$0.905185\pi$
$314$		0			0
$315$	4.91724	+	3.57258i	0.277055	+	0.201292i
$316$		0			0
$317$	5.48671	−	16.8864i	0.308164	−	0.948432i	−0.670313	−	0.742078i	$-0.733840\pi$
$317$	5.48671	−	16.8864i	0.308164	−	0.948432i	0.978477	−	0.206354i	$-0.0661598\pi$
$318$		0			0
$319$	15.8496			0.887405
$320$		0			0
$321$	3.41554	−	2.48153i	0.190637	−	0.138506i
$322$		0			0
$323$	0.631608	+	1.94389i	0.0351436	+	0.108161i
$324$		0			0
$325$	31.1567			1.72826
$326$		0			0
$327$	8.92210			0.493393
$328$		0			0
$329$	1.98204			0.109273
$330$		0			0
$331$	8.83806			0.485783			0.242892	−	0.970053i	$-0.421904\pi$
$331$	8.83806			0.485783			0.242892	+	0.970053i	$0.421904\pi$
$332$		0			0
$333$	7.12499	+	21.9285i	0.390447	+	1.20167i
$334$		0			0
$335$	−19.8108	+	14.3934i	−1.08238	+	0.786396i
$336$		0			0
$337$	5.10399			0.278032			0.139016	−	0.990290i	$-0.455606\pi$
$337$	5.10399			0.278032			0.139016	+	0.990290i	$0.455606\pi$
$338$		0			0
$339$	2.76110	−	8.49779i	0.149962	−	0.461537i
$340$		0			0
$341$	−16.6201	−	12.0752i	−0.900027	−	0.653908i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$		0			0
$345$	−0.0621620	+	0.191315i	−0.00334669	+	0.0103000i
$346$		0			0
$347$	−16.1680	+	11.7468i	−0.867945	+	0.630599i	−0.930035	−	0.367471i	$-0.880224\pi$
$347$	−16.1680	+	11.7468i	−0.867945	+	0.630599i	0.0620895	+	0.998071i	$0.480224\pi$
$348$		0			0
$349$	14.0350	−	10.1970i	0.751274	−	0.545832i	−0.144948	−	0.989439i	$-0.546301\pi$
$349$	14.0350	−	10.1970i	0.751274	−	0.545832i	0.896221	+	0.443607i	$0.146301\pi$
$350$		0			0
$351$	25.4319	+	18.4773i	1.35745	+	0.986247i
$352$		0			0
$353$	18.3065	−	13.3005i	0.974357	−	0.707912i	0.0179164	−	0.999839i	$-0.494297\pi$
$353$	18.3065	−	13.3005i	0.974357	−	0.707912i	0.956440	+	0.291928i	$0.0942967\pi$
$354$		0			0
$355$	−39.1934			−2.08017
$356$		0			0
$357$	0.608772	+	1.87361i	0.0322196	+	0.0991618i
$358$		0			0
$359$	4.10589	−	12.6366i	0.216701	−	0.666936i	−0.782328	−	0.622867i	$-0.785968\pi$
$359$	4.10589	−	12.6366i	0.216701	−	0.666936i	0.999028	−	0.0440690i	$-0.0140321\pi$
$360$		0			0
$361$	−5.51040	+	16.9593i	−0.290021	+	0.892592i
$362$		0			0
$363$	4.69124	+	3.40839i	0.246226	+	0.178894i
$364$		0			0
$365$	8.95975	+	27.5753i	0.468975	+	1.44336i
$366$		0			0
$367$	−21.7719	−	15.8182i	−1.13648	−	0.825703i	−0.149857	−	0.988708i	$-0.547881\pi$
$367$	−21.7719	−	15.8182i	−1.13648	−	0.825703i	−0.986625	+	0.163005i	$0.947881\pi$
$368$		0			0
$369$	0.855805	−	12.2317i	0.0445514	−	0.636758i
$370$		0			0
$371$	−5.02974	−	3.65432i	−0.261131	−	0.189723i
$372$		0			0
$373$	−3.71987	−	11.4486i	−0.192607	−	0.592785i	−0.999996	−	0.00276481i	$-0.999120\pi$
$373$	−3.71987	−	11.4486i	−0.192607	−	0.592785i	0.807389	−	0.590020i	$-0.200880\pi$
$374$		0			0
$375$	0.198728	+	0.144384i	0.0102623	+	0.00745598i
$376$		0			0
$377$	−12.9017	+	39.7073i	−0.664471	+	2.04503i
$378$		0			0
$379$	9.71065	−	29.8863i	0.498803	−	1.53516i	−0.312143	−	0.950035i	$-0.601047\pi$
$379$	9.71065	−	29.8863i	0.498803	−	1.53516i	0.810945	−	0.585122i	$-0.198953\pi$
$380$		0			0
$381$	−3.27312	−	10.0736i	−0.167687	−	0.516088i
$382$		0			0
$383$	3.61022			0.184474			0.0922368	−	0.995737i	$-0.470598\pi$
$383$	3.61022			0.184474			0.0922368	+	0.995737i	$0.470598\pi$
$384$		0			0
$385$	5.98540	−	4.34865i	0.305044	−	0.221628i
$386$		0			0
$387$	−10.5285	−	7.64938i	−0.535192	−	0.388840i
$388$		0			0
$389$	−6.60912	+	4.80180i	−0.335095	+	0.243461i	−0.742590	−	0.669747i	$-0.766403\pi$
$389$	−6.60912	+	4.80180i	−0.335095	+	0.243461i	0.407494	+	0.913208i	$0.366403\pi$
$390$		0			0
$391$	0.0930921	−	0.0676354i	0.00470787	−	0.00342047i
$392$		0			0
$393$	2.22414	−	6.84520i	0.112193	−	0.345295i
$394$		0			0
$395$	6.96713	+	21.4426i	0.350555	+	1.07890i
$396$		0			0
$397$	10.0821	+	7.32507i	0.506006	+	0.367635i	0.811306	−	0.584621i	$-0.198757\pi$
$397$	10.0821	+	7.32507i	0.506006	+	0.367635i	−0.305301	+	0.952256i	$0.598757\pi$
$398$		0			0
$399$	0.347878	−	1.07066i	0.0174157	−	0.0536000i
$400$		0			0
$401$	−28.0696			−1.40173			−0.700865	−	0.713294i	$-0.747202\pi$
$401$	−28.0696			−1.40173			−0.700865	+	0.713294i	$0.747202\pi$
$402$		0			0
$403$	43.7804	−	31.8083i	2.18086	−	1.58449i
$404$		0			0
$405$	−0.403949	−	1.24323i	−0.0200724	−	0.0617764i
$406$		0			0
$407$	28.0656			1.39116
$408$		0			0
$409$	10.2692			0.507781			0.253891	−	0.967233i	$-0.418290\pi$
$409$	10.2692			0.507781			0.253891	+	0.967233i	$0.418290\pi$
$410$		0			0
$411$	19.3915			0.956513
$412$		0			0
$413$	4.36329			0.214703
$414$		0			0
$415$	−2.58263	−	7.94851i	−0.126776	−	0.390177i
$416$		0			0
$417$	−4.69621	+	3.41200i	−0.229974	+	0.167086i
$418$		0			0
$419$	33.4818			1.63569			0.817846	−	0.575437i	$-0.195168\pi$
$419$	33.4818			1.63569			0.817846	+	0.575437i	$0.195168\pi$
$420$		0			0
$421$	3.95662	−	12.1772i	0.192834	−	0.593481i	−0.807161	−	0.590331i	$-0.798997\pi$
$421$	3.95662	−	12.1772i	0.192834	−	0.593481i	0.999995	−	0.00315010i	$-0.00100271\pi$
$422$		0			0
$423$	−3.07062	−	2.23094i	−0.149299	−	0.108472i
$424$		0			0
$425$	−2.96554	−	9.12701i	−0.143850	−	0.442725i
$426$		0			0
$427$	−3.07901	+	9.47623i	−0.149004	+	0.458587i
$428$		0			0
$429$	12.0611	−	8.76292i	0.582317	−	0.423078i
$430$		0			0
$431$	−10.6730	+	7.75438i	−0.514100	+	0.373515i	−0.814377	−	0.580337i	$-0.802921\pi$
$431$	−10.6730	+	7.75438i	−0.514100	+	0.373515i	0.300277	+	0.953852i	$0.402921\pi$
$432$		0			0
$433$	−31.5036	−	22.8887i	−1.51396	−	1.09996i	−0.964380	−	0.264521i	$-0.914786\pi$
$433$	−31.5036	−	22.8887i	−1.51396	−	1.09996i	−0.549584	−	0.835438i	$-0.685214\pi$
$434$		0			0
$435$	−18.1878	+	13.2142i	−0.872037	+	0.633572i
$436$		0			0
$437$	−0.0657549			−0.00314548
$438$		0			0
$439$	−6.91700	−	21.2883i	−0.330131	−	1.01604i	−0.969071	−	0.246781i	$-0.920627\pi$
$439$	−6.91700	−	21.2883i	−0.330131	−	1.01604i	0.638941	−	0.769256i	$-0.279373\pi$
$440$		0			0
$441$	−0.591750	+	1.82122i	−0.0281786	+	0.0867248i
$442$		0			0
$443$	5.91904	−	18.2169i	0.281222	−	0.865512i	−0.706284	−	0.707929i	$-0.749630\pi$
$443$	5.91904	−	18.2169i	0.281222	−	0.865512i	0.987506	−	0.157583i	$-0.0503703\pi$
$444$		0			0
$445$	−15.8670	−	11.5281i	−0.752170	−	0.546483i
$446$		0			0
$447$	−3.18624	−	9.80624i	−0.150704	−	0.463819i
$448$		0			0
$449$	−24.4129	−	17.7370i	−1.15212	−	0.837062i	−0.163356	−	0.986567i	$-0.552232\pi$
$449$	−24.4129	−	17.7370i	−1.15212	−	0.837062i	−0.988761	+	0.149505i	$0.952232\pi$
$450$		0			0
$451$	−13.8382	−	5.59162i	−0.651615	−	0.263299i
$452$		0			0
$453$	−13.7768	−	10.0094i	−0.647289	−	0.470283i
$454$		0			0
$455$	6.02234	+	18.5349i	0.282332	+	0.868928i
$456$		0			0
$457$	5.37791	+	3.90728i	0.251568	+	0.182775i	0.706422	−	0.707791i	$-0.250308\pi$
$457$	5.37791	+	3.90728i	0.251568	+	0.182775i	−0.454853	+	0.890566i	$0.650308\pi$
$458$		0			0
$459$	2.99208	−	9.20867i	0.139658	−	0.429824i
$460$		0			0
$461$	−7.08687	+	21.8111i	−0.330068	+	1.01585i	0.639032	+	0.769180i	$0.279335\pi$
$461$	−7.08687	+	21.8111i	−0.330068	+	1.01585i	−0.969101	+	0.246666i	$0.920665\pi$
$462$		0			0
$463$	9.09753	+	27.9993i	0.422798	+	1.30124i	0.905087	+	0.425226i	$0.139806\pi$
$463$	9.09753	+	27.9993i	0.422798	+	1.30124i	−0.482289	+	0.876012i	$0.660194\pi$
$464$		0			0
$465$	29.1394			1.35131
$466$		0			0
$467$	−19.5032	+	14.1699i	−0.902500	+	0.655705i	−0.939107	−	0.343625i	$-0.888345\pi$
$467$	−19.5032	+	14.1699i	−0.902500	+	0.655705i	0.0366065	+	0.999330i	$0.488345\pi$
$468$		0			0
$469$	−6.24159	−	4.53478i	−0.288210	−	0.209397i
$470$		0			0
$471$	2.46386	−	1.79010i	0.113528	−	0.0824833i
$472$		0			0
$473$	−12.8155	+	9.31104i	−0.589260	+	0.428122i
$474$		0			0
$475$	−1.69464	+	5.21556i	−0.0777553	+	0.239306i
$476$		0			0
$477$	3.67897	+	11.3227i	0.168448	+	0.518431i
$478$		0			0
$479$	−4.80573	−	3.49156i	−0.219579	−	0.159534i	0.472558	−	0.881300i	$-0.343331\pi$
$479$	−4.80573	−	3.49156i	−0.219579	−	0.159534i	−0.692137	+	0.721766i	$0.743331\pi$
$480$		0			0
$481$	−22.8457	+	70.3117i	−1.04167	+	3.20594i
$482$		0			0
$483$	−0.0633775			−0.00288378
$484$		0			0
$485$	−30.0994	+	21.8685i	−1.36674	+	0.992997i
$486$		0			0
$487$	2.83179	+	8.71535i	0.128321	+	0.394930i	0.994491	−	0.104818i	$-0.0334259\pi$
$487$	2.83179	+	8.71535i	0.128321	+	0.394930i	−0.866171	+	0.499748i	$0.833426\pi$
$488$		0			0
$489$	−22.2558			−1.00644
$490$		0			0
$491$	−22.1094			−0.997782			−0.498891	−	0.866665i	$-0.666259\pi$
$491$	−22.1094			−0.997782			−0.498891	+	0.866665i	$0.666259\pi$
$492$		0			0
$493$	12.8598			0.579177
$494$		0			0
$495$	−14.1675			−0.636780
$496$		0			0
$497$	−3.81582	−	11.7439i	−0.171163	−	0.526785i
$498$		0			0
$499$	−19.3003	+	14.0225i	−0.863999	+	0.627732i	−0.928970	−	0.370155i	$-0.879304\pi$
$499$	−19.3003	+	14.0225i	−0.863999	+	0.627732i	0.0649711	+	0.997887i	$0.479304\pi$
$500$		0			0
$501$	0.660398			0.0295044
$502$		0			0
$503$	−7.85859	+	24.1863i	−0.350397	+	1.07841i	0.608233	+	0.793758i	$0.291879\pi$
$503$	−7.85859	+	24.1863i	−0.350397	+	1.07841i	−0.958630	+	0.284654i	$0.908121\pi$
$504$		0			0
$505$	−19.5556	−	14.2080i	−0.870213	−	0.632247i
$506$		0			0
$507$	7.95099	+	24.4706i	0.353116	+	1.08678i
$508$		0			0
$509$	−9.33947	+	28.7439i	−0.413965	+	1.27405i	0.499209	+	0.866482i	$0.333624\pi$
$509$	−9.33947	+	28.7439i	−0.413965	+	1.27405i	−0.913174	+	0.407571i	$0.866376\pi$
$510$		0			0
$511$	−7.39033	+	5.36939i	−0.326929	+	0.237528i
$512$		0			0
$513$	−4.47632	+	3.25224i	−0.197634	+	0.143590i
$514$		0			0
$515$	−5.54935	−	4.03184i	−0.244534	−	0.177664i
$516$		0			0
$517$	−3.73765	+	2.71556i	−0.164382	+	0.119430i
$518$		0			0
$519$	5.22595			0.229394
$520$		0			0
$521$	−11.1588	−	34.3433i	−0.488876	−	1.50461i	−0.826288	−	0.563248i	$-0.809551\pi$
$521$	−11.1588	−	34.3433i	−0.488876	−	1.50461i	0.337412	−	0.941357i	$-0.390449\pi$
$522$		0			0
$523$	−0.0997033	+	0.306855i	−0.00435972	+	0.0134178i	−0.953213	−	0.302300i	$-0.902245\pi$
$523$	−0.0997033	+	0.306855i	−0.00435972	+	0.0134178i	0.948853	+	0.315718i	$0.102245\pi$
$524$		0			0
$525$	−1.63337	+	5.02699i	−0.0712860	+	0.219396i
$526$		0			0
$527$	−13.4850	−	9.79741i	−0.587415	−	0.426782i
$528$		0			0
$529$	−7.10625	−	21.8708i	−0.308967	−	0.950903i
$530$		0			0
$531$	−6.75970	−	4.91121i	−0.293346	−	0.213128i
$532$		0			0
$533$	25.2729	−	30.1167i	1.09469	−	1.30450i
$534$		0			0
$535$	−10.4074	−	7.56138i	−0.449949	−	0.326907i
$536$		0			0
$537$	−3.17908	−	9.78419i	−0.137187	−	0.422219i
$538$		0			0
$539$	1.88576	+	1.37008i	0.0812254	+	0.0590137i
$540$		0			0
$541$	0.349783	−	1.07652i	0.0150383	−	0.0462832i	−0.943256	−	0.332067i	$-0.892254\pi$
$541$	0.349783	−	1.07652i	0.0150383	−	0.0462832i	0.958294	+	0.285784i	$0.0922539\pi$
$542$		0			0
$543$	−1.15565	+	3.55673i	−0.0495937	+	0.152634i
$544$		0			0
$545$	−8.40100	−	25.8556i	−0.359859	−	1.10753i
$546$		0			0
$547$	−0.886464			−0.0379025			−0.0189512	−	0.999820i	$-0.506033\pi$
$547$	−0.886464			−0.0379025			−0.0189512	+	0.999820i	$0.506033\pi$
$548$		0			0
$549$	15.4363	−	11.2151i	0.658805	−	0.478650i
$550$		0			0
$551$	−5.94518	−	4.31943i	−0.253273	−	0.184014i
$552$		0			0
$553$	−5.74675	+	4.17526i	−0.244377	+	0.177550i
$554$		0			0
$555$	−32.2060	+	23.3990i	−1.36707	+	0.993233i
$556$		0			0
$557$	−2.65247	+	8.16347i	−0.112389	+	0.345897i	−0.991393	−	0.130916i	$-0.958208\pi$
$557$	−2.65247	+	8.16347i	−0.112389	+	0.345897i	0.879005	+	0.476813i	$0.158208\pi$
$558$		0			0
$559$	−12.8946	−	39.6856i	−0.545385	−	1.67852i
$560$		0			0
$561$	−3.71500	−	2.69910i	−0.156847	−	0.113956i
$562$		0			0
$563$	3.23716	−	9.96297i	0.136430	−	0.419889i	−0.859380	−	0.511338i	$-0.829150\pi$
$563$	3.23716	−	9.96297i	0.136430	−	0.419889i	0.995810	+	0.0914492i	$0.0291499\pi$
$564$		0			0
$565$	−27.2258			−1.14540
$566$		0			0
$567$	0.333192	−	0.242078i	0.0139927	−	0.0101663i
$568$		0			0
$569$	2.16218	+	6.65450i	0.0906433	+	0.278971i	0.986094	−	0.166190i	$-0.0531464\pi$
$569$	2.16218	+	6.65450i	0.0906433	+	0.278971i	−0.895451	+	0.445161i	$0.853146\pi$
$570$		0			0
$571$	−22.8388			−0.955773			−0.477886	−	0.878422i	$-0.658597\pi$
$571$	−22.8388			−0.955773			−0.477886	+	0.878422i	$0.658597\pi$
$572$		0			0
$573$	−3.02814			−0.126502
$574$		0			0
$575$	0.308734			0.0128751
$576$		0			0
$577$	−27.9961			−1.16549			−0.582746	−	0.812654i	$-0.698022\pi$
$577$	−27.9961			−1.16549			−0.582746	+	0.812654i	$0.698022\pi$
$578$		0			0
$579$	3.55715	+	10.9478i	0.147830	+	0.454975i
$580$		0			0
$581$	2.13025	−	1.54771i	0.0883775	−	0.0642100i
$582$		0			0
$583$	14.4916			0.600180
$584$		0			0
$585$	11.5325	−	35.4933i	0.476808	−	1.46747i
$586$		0			0
$587$	20.3625	+	14.7942i	0.840449	+	0.610622i	0.922496	−	0.386006i	$-0.126146\pi$
$587$	20.3625	+	14.7942i	0.840449	+	0.610622i	−0.0820467	+	0.996628i	$0.526146\pi$
$588$		0			0
$589$	2.94339	+	9.05882i	0.121280	+	0.373262i
$590$		0			0
$591$	−2.26229	+	6.96261i	−0.0930581	+	0.286403i
$592$		0			0
$593$	−15.6948	+	11.4030i	−0.644509	+	0.468263i	−0.861396	−	0.507934i	$-0.830410\pi$
$593$	−15.6948	+	11.4030i	−0.644509	+	0.468263i	0.216887	+	0.976197i	$0.430410\pi$
$594$		0			0
$595$	4.85636	−	3.52835i	0.199092	−	0.144648i
$596$		0			0
$597$	20.6048	+	14.9702i	0.843296	+	0.612691i
$598$		0			0
$599$	38.8182	−	28.2031i	1.58607	−	1.15235i	0.676779	−	0.736186i	$-0.263375\pi$
$599$	38.8182	−	28.2031i	1.58607	−	1.15235i	0.909291	−	0.416162i	$-0.136625\pi$
$600$		0			0
$601$	−40.0787			−1.63484			−0.817421	−	0.576040i	$-0.804597\pi$
$601$	−40.0787			−1.63484			−0.817421	+	0.576040i	$0.804597\pi$
$602$		0			0
$603$	4.56537	+	14.0508i	0.185916	+	0.572191i
$604$		0			0
$605$	5.46002	−	16.8042i	0.221981	−	0.683188i
$606$		0			0
$607$	3.26027	−	10.0341i	0.132330	−	0.407270i	−0.862835	−	0.505486i	$-0.831313\pi$
$607$	3.26027	−	10.0341i	0.132330	−	0.407270i	0.995165	+	0.0982154i	$0.0313134\pi$
$608$		0			0
$609$	−5.73023	−	4.16326i	−0.232201	−	0.168704i
$610$		0			0
$611$	−3.76072	−	11.5743i	−0.152142	−	0.468246i
$612$		0			0
$613$	−11.7697	−	8.55119i	−0.475374	−	0.345379i	0.324158	−	0.946003i	$-0.394919\pi$
$613$	−11.7697	−	8.55119i	−0.475374	−	0.345379i	−0.799532	+	0.600624i	$0.794919\pi$
$614$		0			0
$615$	20.5416	−	5.12074i	0.828316	−	0.206488i
$616$		0			0
$617$	−22.9868	−	16.7009i	−0.925414	−	0.672352i	0.0194519	−	0.999811i	$-0.493808\pi$
$617$	−22.9868	−	16.7009i	−0.925414	−	0.672352i	−0.944866	+	0.327458i	$0.893808\pi$
$618$		0			0
$619$	0.604503	+	1.86047i	0.0242970	+	0.0747785i	0.962470	−	0.271389i	$-0.0874829\pi$
$619$	0.604503	+	1.86047i	0.0242970	+	0.0747785i	−0.938173	+	0.346167i	$0.887483\pi$
$620$		0			0
$621$	0.252006	+	0.183093i	0.0101127	+	0.00734728i
$622$		0			0
$623$	1.90947	−	5.87675i	0.0765014	−	0.235447i
$624$		0			0
$625$	−7.60892	+	23.4179i	−0.304357	+	0.936714i
$626$		0			0
$627$	0.810878	+	2.49563i	0.0323834	+	0.0996657i
$628$		0			0
$629$	22.7715			0.907959
$630$		0			0
$631$	10.0114	−	7.27374i	0.398549	−	0.289563i	−0.370401	−	0.928872i	$-0.620780\pi$
$631$	10.0114	−	7.27374i	0.398549	−	0.289563i	0.768950	+	0.639309i	$0.220780\pi$
$632$		0			0
$633$	−3.56222	−	2.58810i	−0.141585	−	0.102868i
$634$		0			0
$635$	−26.1107	+	18.9705i	−1.03617	+	0.752823i
$636$		0			0
$637$	−4.96745	+	3.60906i	−0.196818	+	0.142996i
$638$		0			0
$639$	−7.30708	+	22.4889i	−0.289064	+	0.889646i
$640$		0			0
$641$	−7.79154	−	23.9799i	−0.307747	−	0.947149i	−0.978638	−	0.205592i	$-0.934088\pi$
$641$	−7.79154	−	23.9799i	−0.307747	−	0.947149i	0.670890	−	0.741557i	$-0.265912\pi$
$642$		0			0
$643$	37.4059	+	27.1770i	1.47514	+	1.07176i	0.979081	+	0.203469i	$0.0652217\pi$
$643$	37.4059	+	27.1770i	1.47514	+	1.07176i	0.496064	+	0.868286i	$0.334778\pi$
$644$		0			0
$645$	6.94331	−	21.3693i	0.273393	−	0.841416i
$646$		0			0
$647$	12.1329			0.476995			0.238497	−	0.971143i	$-0.423345\pi$
$647$	12.1329			0.476995			0.238497	+	0.971143i	$0.423345\pi$
$648$		0			0
$649$	−8.22811	+	5.97807i	−0.322981	+	0.234660i
$650$		0			0
$651$	2.83697	+	8.73130i	0.111190	+	0.342207i
$652$		0			0
$653$	−4.83005			−0.189014			−0.0945072	−	0.995524i	$-0.530128\pi$
$653$	−4.83005			−0.189014			−0.0945072	+	0.995524i	$0.530128\pi$
$654$		0			0
$655$	−21.9311			−0.856921
$656$		0			0
$657$	17.4929			0.682464
$658$		0			0
$659$	−2.84677			−0.110894			−0.0554471	−	0.998462i	$-0.517658\pi$
$659$	−2.84677			−0.110894			−0.0554471	+	0.998462i	$0.517658\pi$
$660$		0			0
$661$	2.80880	+	8.64459i	0.109250	+	0.336235i	0.990704	−	0.136033i	$-0.0434353\pi$
$661$	2.80880	+	8.64459i	0.109250	+	0.336235i	−0.881455	+	0.472268i	$0.843435\pi$
$662$		0			0
$663$	9.78601	−	7.10995i	0.380057	−	0.276128i
$664$		0			0
$665$	−3.43025			−0.133020
$666$		0			0
$667$	−0.127844	+	0.393463i	−0.00495014	+	0.0152349i
$668$		0			0
$669$	5.49107	+	3.98950i	0.212297	+	0.154243i
$670$		0			0
$671$	−7.17695	−	22.0884i	−0.277063	−	0.852713i
$672$		0			0
$673$	0.428774	−	1.31963i	0.0165280	−	0.0508680i	−0.942452	−	0.334340i	$-0.891486\pi$
$673$	0.428774	−	1.31963i	0.0165280	−	0.0508680i	0.958980	+	0.283472i	$0.0914865\pi$
$674$		0			0
$675$	21.0174	−	15.2700i	0.808958	−	0.587743i
$676$		0			0
$677$	27.8696	−	20.2484i	1.07112	−	0.778211i	0.0950029	−	0.995477i	$-0.469714\pi$
$677$	27.8696	−	20.2484i	1.07112	−	0.778211i	0.976112	+	0.217266i	$0.0697139\pi$
$678$		0			0
$679$	−9.48310	−	6.88988i	−0.363928	−	0.264409i
$680$		0			0
$681$	15.7048	−	11.4102i	0.601808	−	0.437239i
$682$		0			0
$683$	26.3087			1.00668			0.503338	−	0.864090i	$-0.332105\pi$
$683$	26.3087			1.00668			0.503338	+	0.864090i	$0.332105\pi$
$684$		0			0
$685$	−18.2589	−	56.1952i	−0.697638	−	2.14711i
$686$		0			0
$687$	−7.87645	+	24.2412i	−0.300505	+	0.924860i
$688$		0			0
$689$	−11.7963	+	36.3053i	−0.449403	+	1.38312i
$690$		0			0
$691$	−10.9259	−	7.93815i	−0.415642	−	0.301981i	0.360240	−	0.932860i	$-0.382695\pi$
$691$	−10.9259	−	7.93815i	−0.415642	−	0.301981i	−0.775882	+	0.630878i	$0.782695\pi$
$692$		0			0
$693$	−1.37933	−	4.24513i	−0.0523963	−	0.161259i
$694$		0			0
$695$	14.3096	+	10.3966i	0.542796	+	0.394364i
$696$		0			0
$697$	−11.2279	−	4.53686i	−0.425286	−	0.171846i
$698$		0			0
$699$	−4.62872	−	3.36296i	−0.175074	−	0.127199i
$700$		0			0
$701$	−11.9151	−	36.6710i	−0.450029	−	1.38505i	−0.876874	−	0.480721i	$-0.840375\pi$
$701$	−11.9151	−	36.6710i	−0.450029	−	1.38505i	0.426845	−	0.904325i	$-0.359625\pi$
$702$		0			0
$703$	−10.5274	−	7.64862i	−0.397049	−	0.288473i
$704$		0			0
$705$	2.02501	−	6.23235i	0.0762664	−	0.234724i
$706$		0			0
$707$	2.35336	−	7.24290i	0.0885073	−	0.272397i
$708$		0			0
$709$	12.6310	+	38.8742i	0.474367	+	1.45995i	0.846810	+	0.531895i	$0.178520\pi$
$709$	12.6310	+	38.8742i	0.474367	+	1.45995i	−0.372444	+	0.928055i	$0.621480\pi$
$710$		0			0
$711$	13.6026			0.510136
$712$		0			0
$713$	0.433824	−	0.315191i	0.0162468	−	0.0118040i
$714$		0			0
$715$	−36.7510	−	26.7012i	−1.37441	−	0.998567i
$716$		0			0
$717$	25.6131	−	18.6090i	0.956539	−	0.694966i
$718$		0			0
$719$	−33.9164	+	24.6417i	−1.26487	+	0.918979i	−0.998986	−	0.0450267i	$-0.985663\pi$
$719$	−33.9164	+	24.6417i	−1.26487	+	0.918979i	−0.265881	+	0.964006i	$0.585663\pi$
$720$		0			0
$721$	0.667820	−	2.05534i	0.0248709	−	0.0765448i
$722$		0			0
$723$	−7.81385	−	24.0486i	−0.290600	−	0.894376i
$724$		0			0
$725$	27.9140	+	20.2807i	1.03670	+	0.753207i
$726$		0			0
$727$	10.9835	−	33.8038i	0.407357	−	1.25371i	−0.511555	−	0.859251i	$-0.670930\pi$
$727$	10.9835	−	33.8038i	0.407357	−	1.25371i	0.918911	−	0.394464i	$-0.129070\pi$
$728$		0			0
$729$	15.2103			0.563344
$730$		0			0
$731$	−10.3981	+	7.55468i	−0.384588	+	0.279420i
$732$		0			0
$733$	−1.67148	−	5.14427i	−0.0617374	−	0.190008i	0.915431	−	0.402475i	$-0.131850\pi$
$733$	−1.67148	−	5.14427i	−0.0617374	−	0.190008i	−0.977168	+	0.212467i	$0.931850\pi$
$734$		0			0
$735$	−3.30623			−0.121952
$736$		0			0
$737$	17.9832			0.662418
$738$		0			0
$739$	12.9190			0.475234			0.237617	−	0.971359i	$-0.423634\pi$
$739$	12.9190			0.475234			0.237617	+	0.971359i	$0.423634\pi$
$740$		0			0
$741$	−6.91227			−0.253929
$742$		0			0
$743$	14.2054	+	43.7197i	0.521146	+	1.60392i	0.771814	+	0.635849i	$0.219350\pi$
$743$	14.2054	+	43.7197i	0.521146	+	1.60392i	−0.250668	+	0.968073i	$0.580650\pi$
$744$		0			0
$745$	−25.4176	+	18.4670i	−0.931230	+	0.676578i
$746$		0			0
$747$	−5.04229			−0.184488
$748$		0			0
$749$	1.25244	−	3.85462i	0.0457632	−	0.140845i
$750$		0			0
$751$	−28.3359	−	20.5872i	−1.03399	−	0.751239i	−0.0648882	−	0.997893i	$-0.520669\pi$
$751$	−28.3359	−	20.5872i	−1.03399	−	0.751239i	−0.969104	+	0.246653i	$0.920669\pi$
$752$		0			0
$753$	7.59976	+	23.3896i	0.276951	+	0.852366i
$754$		0			0
$755$	−16.0344	+	49.3489i	−0.583553	+	1.79599i
$756$		0			0
$757$	12.1807	−	8.84982i	0.442716	−	0.321652i	−0.343997	−	0.938971i	$-0.611781\pi$
$757$	12.1807	−	8.84982i	0.442716	−	0.321652i	0.786713	+	0.617318i	$0.211781\pi$
$758$		0			0
$759$	0.119515	−	0.0868325i	0.00433811	−	0.00315182i
$760$		0			0
$761$	−25.7378	−	18.6996i	−0.932994	−	0.677860i	0.0137300	−	0.999906i	$-0.495629\pi$
$761$	−25.7378	−	18.6996i	−0.932994	−	0.677860i	−0.946724	+	0.322046i	$0.895629\pi$
$762$		0			0
$763$	6.92945	−	5.03454i	0.250863	−	0.182263i
$764$		0			0
$765$	−11.4950			−0.415603
$766$		0			0
$767$	−8.27889	−	25.4798i	−0.298933	−	0.920022i
$768$		0			0
$769$	5.54011	−	17.0507i	0.199782	−	0.614864i	−0.800106	−	0.599859i	$-0.795223\pi$
$769$	5.54011	−	17.0507i	0.199782	−	0.614864i	0.999887	−	0.0150055i	$-0.00477658\pi$
$770$		0			0
$771$	−3.87049	+	11.9122i	−0.139392	+	0.429006i
$772$		0			0
$773$	−17.4457	−	12.6750i	−0.627477	−	0.455889i	0.228048	−	0.973650i	$-0.426766\pi$
$773$	−17.4457	−	12.6750i	−0.627477	−	0.455889i	−0.855525	+	0.517761i	$0.826766\pi$
$774$		0			0
$775$	−13.8199	−	42.5333i	−0.496425	−	1.52784i
$776$		0			0
$777$	−10.1468	−	7.37208i	−0.364014	−	0.264472i
$778$		0			0
$779$	3.66685	+	5.86870i	0.131379	+	0.210268i
$780$		0			0
$781$	23.2858	+	16.9181i	0.833232	+	0.605378i
$782$		0			0
$783$	10.7576	+	33.1085i	0.384445	+	1.18320i
$784$		0			0
$785$	−7.50752	−	5.45454i	−0.267955	−	0.194681i
$786$		0			0
$787$	−14.3267	+	44.0930i	−0.510691	+	1.57175i	0.280297	+	0.959913i	$0.409567\pi$
$787$	−14.3267	+	44.0930i	−0.510691	+	1.57175i	−0.790988	+	0.611832i	$0.790433\pi$
$788$		0			0
$789$	−10.0495	+	30.9292i	−0.357772	+	1.10111i
$790$		0			0
$791$	−2.65067	−	8.15793i	−0.0942471	−	0.290063i
$792$		0			0
$793$	61.1794			2.17254
$794$		0			0
$795$	−16.6295	+	12.0820i	−0.589787	+	0.428505i
$796$		0			0
$797$	−7.23168	−	5.25412i	−0.256159	−	0.186111i	0.452293	−	0.891869i	$-0.350606\pi$
$797$	−7.23168	−	5.25412i	−0.256159	−	0.186111i	−0.708452	+	0.705759i	$0.750606\pi$
$798$		0			0
$799$	−3.03261	+	2.20332i	−0.107286	+	0.0779478i
$800$		0			0
$801$	−9.57293	+	6.95514i	−0.338243	+	0.245748i
$802$		0			0
$803$	6.57987	−	20.2508i	0.232198	−	0.714633i
$804$		0			0
$805$	0.0596759	+	0.183663i	0.00210330	+	0.00647329i
$806$		0			0
$807$	14.9953	+	10.8947i	0.527860	+	0.383513i
$808$		0			0
$809$	−3.91434	+	12.0471i	−0.137621	+	0.423554i	−0.995988	−	0.0894814i	$-0.971479\pi$
$809$	−3.91434	+	12.0471i	−0.137621	+	0.423554i	0.858367	+	0.513035i	$0.171479\pi$
$810$		0			0
$811$	−33.9799			−1.19320			−0.596598	−	0.802540i	$-0.703481\pi$
$811$	−33.9799			−1.19320			−0.596598	+	0.802540i	$0.703481\pi$
$812$		0			0
$813$	−5.67729	+	4.12479i	−0.199111	+	0.144663i
$814$		0			0
$815$	20.9560	+	64.4959i	0.734056	+	2.25919i
$816$		0			0
$817$	7.34463			0.256956
$818$		0			0
$819$	11.7580			0.410856
$820$		0			0
$821$	34.9895			1.22114			0.610572	−	0.791961i	$-0.290940\pi$
$821$	34.9895			1.22114			0.610572	+	0.791961i	$0.290940\pi$
$822$		0			0
$823$	−19.4044			−0.676395			−0.338197	−	0.941075i	$-0.609817\pi$
$823$	−19.4044			−0.676395			−0.338197	+	0.941075i	$0.609817\pi$
$824$		0			0
$825$	−3.80726	−	11.7175i	−0.132552	−	0.407953i
$826$		0			0
$827$	−10.9050	+	7.92298i	−0.379205	+	0.275509i	−0.761018	−	0.648731i	$-0.775300\pi$
$827$	−10.9050	+	7.92298i	−0.379205	+	0.275509i	0.381812	+	0.924240i	$0.375300\pi$
$828$		0			0
$829$	−29.5466			−1.02620			−0.513098	−	0.858330i	$-0.671502\pi$
$829$	−29.5466			−1.02620			−0.513098	+	0.858330i	$0.671502\pi$
$830$		0			0
$831$	0.662964	−	2.04039i	0.0229980	−	0.0707804i
$832$		0			0
$833$	1.53004	+	1.11164i	0.0530129	+	0.0385161i
$834$		0			0
$835$	−0.621827	−	1.91379i	−0.0215192	−	0.0662293i
$836$		0			0
$837$	13.9436	−	42.9139i	0.481960	−	1.48332i
$838$		0			0
$839$	−10.1625	+	7.38349i	−0.350849	+	0.254906i	−0.749225	−	0.662316i	$-0.769574\pi$
$839$	−10.1625	+	7.38349i	−0.350849	+	0.254906i	0.398376	+	0.917222i	$0.369574\pi$
$840$		0			0
$841$	−13.9440	+	10.1309i	−0.480826	+	0.349340i
$842$		0			0
$843$	21.7302	+	15.7879i	0.748429	+	0.543765i
$844$		0			0
$845$	63.4275	−	46.0828i	2.18197	−	1.58530i
$846$		0			0
$847$	5.56678			0.191277
$848$		0			0
$849$	−10.2498	−	31.5455i	−0.351771	−	1.08264i
$850$		0			0
$851$	−0.226379	+	0.696724i	−0.00776019	+	0.0238834i
$852$		0			0
$853$	−3.06291	+	9.42668i	−0.104872	+	0.322763i	−0.989700	−	0.143154i	$-0.954276\pi$
$853$	−3.06291	+	9.42668i	−0.104872	+	0.322763i	0.884828	+	0.465917i	$0.154276\pi$
$854$		0			0
$855$	5.31423	+	3.86101i	0.181743	+	0.132044i
$856$		0			0
$857$	15.2317	+	46.8783i	0.520305	+	1.60133i	0.773418	+	0.633897i	$0.218546\pi$
$857$	15.2317	+	46.8783i	0.520305	+	1.60133i	−0.253113	+	0.967437i	$0.581454\pi$
$858$		0			0
$859$	−22.4204	−	16.2893i	−0.764973	−	0.555785i	0.135459	−	0.990783i	$-0.456749\pi$
$859$	−22.4204	−	16.2893i	−0.764973	−	0.555785i	−0.900432	+	0.434998i	$0.856749\pi$
$860$		0			0
$861$	3.53428	+	5.65651i	0.120448	+	0.192774i
$862$		0			0
$863$	−21.6161	−	15.7050i	−0.735820	−	0.534605i	0.155579	−	0.987823i	$-0.450276\pi$
$863$	−21.6161	−	15.7050i	−0.735820	−	0.534605i	−0.891399	+	0.453219i	$0.850276\pi$
$864$		0			0
$865$	−4.92073	−	15.1444i	−0.167310	−	0.514927i
$866$		0			0
$867$	11.3120	+	8.21866i	0.384176	+	0.279120i
$868$		0			0
$869$	5.11653	−	15.7471i	0.173566	−	0.534182i
$870$		0			0
$871$	−14.6385	+	45.0526i	−0.496006	+	1.52655i
$872$		0			0
$873$	6.93636	+	21.3479i	0.234760	+	0.722517i
$874$		0			0
$875$	0.235817			0.00797208
$876$		0			0
$877$	14.1656	−	10.2919i	0.478339	−	0.347534i	−0.322343	−	0.946623i	$-0.604470\pi$
$877$	14.1656	−	10.2919i	0.478339	−	0.347534i	0.800682	+	0.599089i	$0.204470\pi$
$878$		0			0
$879$	−12.8680	−	9.34915i	−0.434027	−	0.315339i
$880$		0			0
$881$	7.99231	−	5.80675i	0.269268	−	0.195635i	−0.444955	−	0.895553i	$-0.646780\pi$
$881$	7.99231	−	5.80675i	0.269268	−	0.195635i	0.714223	+	0.699918i	$0.246780\pi$
$882$		0			0
$883$	40.5931	−	29.4926i	1.36607	−	0.992506i	0.368034	−	0.929812i	$-0.380031\pi$
$883$	40.5931	−	29.4926i	1.36607	−	0.992506i	0.998033	−	0.0626933i	$-0.0199690\pi$
$884$		0			0
$885$	4.45789	−	13.7200i	0.149850	−	0.461192i
$886$		0			0
$887$	−0.376934	−	1.16008i	−0.0126562	−	0.0389518i	0.944529	−	0.328428i	$-0.106519\pi$
$887$	−0.376934	−	1.16008i	−0.0126562	−	0.0389518i	−0.957185	+	0.289476i	$0.906519\pi$
$888$		0			0
$889$	−8.22643	−	5.97685i	−0.275906	−	0.200457i
$890$		0			0
$891$	−0.296652	+	0.913001i	−0.00993822	+	0.0305867i
$892$		0			0
$893$	2.14206			0.0716812
$894$		0			0
$895$	−25.3605	+	18.4255i	−0.847708	+	0.615896i
$896$		0			0
$897$	0.120252	+	0.370098i	0.00401511	+	0.0123572i
$898$		0			0
$899$	59.9287			1.99874
$900$		0			0
$901$	11.7580			0.391716
$902$		0			0
$903$	7.07908			0.235577
$904$		0			0
$905$	11.3953			0.378793
$906$		0			0
$907$	−12.6292	−	38.8687i	−0.419346	−	1.29061i	−0.908305	−	0.418308i	$-0.862623\pi$
$907$	−12.6292	−	38.8687i	−0.419346	−	1.29061i	0.488959	−	0.872307i	$-0.337377\pi$
$908$		0			0
$909$	−11.7983	+	8.57198i	−0.391326	+	0.284315i
$910$		0			0
$911$	−4.35416			−0.144260			−0.0721298	−	0.997395i	$-0.522980\pi$
$911$	−4.35416			−0.144260			−0.0721298	+	0.997395i	$0.522980\pi$
$912$		0			0
$913$	−1.89663	+	5.83723i	−0.0627693	+	0.193184i
$914$		0			0
$915$	26.6514	+	19.3634i	0.881068	+	0.640133i
$916$		0			0
$917$	−2.13519	−	6.57143i	−0.0705101	−	0.217008i
$918$		0			0
$919$	−13.2323	+	40.7248i	−0.436493	+	1.34339i	0.455055	+	0.890463i	$0.349620\pi$
$919$	−13.2323	+	40.7248i	−0.436493	+	1.34339i	−0.891549	+	0.452925i	$0.850380\pi$
$920$		0			0
$921$	−7.80734	+	5.67237i	−0.257261	+	0.186911i
$922$		0			0
$923$	−61.3393	+	44.5656i	−2.01901	+	1.46689i
$924$		0			0
$925$	49.4287	+	35.9120i	1.62520	+	1.18078i
$926$		0			0
$927$	−3.34804	+	2.43249i	−0.109964	+	0.0798936i
$928$		0			0
$929$	20.6327			0.676937			0.338468	−	0.940978i	$-0.390091\pi$
$929$	20.6327			0.676937			0.338468	+	0.940978i	$0.390091\pi$
$930$		0			0
$931$	−0.333965	−	1.02784i	−0.0109453	−	0.0336861i
$932$		0			0
$933$	−5.03428	+	15.4939i	−0.164815	+	0.507249i
$934$		0			0
$935$	−4.32379	+	13.3073i	−0.141403	+	0.435194i
$936$		0			0
$937$	16.5489	+	12.0235i	0.540629	+	0.392790i	0.824318	−	0.566126i	$-0.191559\pi$
$937$	16.5489	+	12.0235i	0.540629	+	0.392790i	−0.283690	+	0.958916i	$0.591559\pi$
$938$		0			0
$939$	−0.185537	−	0.571023i	−0.00605476	−	0.0186346i
$940$		0			0
$941$	−6.78926	−	4.93269i	−0.221324	−	0.160801i	0.471599	−	0.881813i	$-0.343677\pi$
$941$	−6.78926	−	4.93269i	−0.221324	−	0.160801i	−0.692922	+	0.721012i	$0.743677\pi$
$942$		0			0
$943$	0.250431	−	0.298429i	0.00815517	−	0.00971818i
$944$		0			0
$945$	13.1465	+	9.55148i	0.427655	+	0.310710i
$946$		0			0
$947$	−4.57920	−	14.0933i	−0.148804	−	0.457972i	0.848676	−	0.528912i	$-0.177400\pi$
$947$	−4.57920	−	14.0933i	−0.148804	−	0.457972i	−0.997481	+	0.0709404i	$0.977400\pi$
$948$		0			0
$949$	45.3774	+	32.9686i	1.47301	+	1.07021i
$950$		0			0
$951$	5.71529	−	17.5898i	0.185331	−	0.570390i
$952$		0			0
$953$	10.8595	−	33.4221i	0.351774	−	1.08265i	−0.606083	−	0.795401i	$-0.707260\pi$
$953$	10.8595	−	33.4221i	0.351774	−	1.08265i	0.957857	−	0.287246i	$-0.0927399\pi$
$954$		0			0
$955$	2.85128	+	8.77533i	0.0922652	+	0.283963i
$956$		0			0
$957$	16.5098			0.533688
$958$		0			0
$959$	15.0606	−	10.9422i	0.486333	−	0.353342i
$960$		0			0
$961$	−37.7626	−	27.4361i	−1.21815	−	0.885036i
$962$		0			0
$963$	−6.27898	+	4.56195i	−0.202337	+	0.147007i
$964$		0			0
$965$	28.3765	−	20.6168i	0.913473	−	0.663677i
$966$		0			0
$967$	−15.3645	+	47.2869i	−0.494088	+	1.52065i	0.324286	+	0.945959i	$0.394876\pi$
$967$	−15.3645	+	47.2869i	−0.494088	+	1.52065i	−0.818374	+	0.574686i	$0.805124\pi$
$968$		0			0
$969$	0.657920	+	2.02487i	0.0211354	+	0.0650482i
$970$		0			0
$971$	20.4798	+	14.8795i	0.657229	+	0.477505i	0.865726	−	0.500518i	$-0.166857\pi$
$971$	20.4798	+	14.8795i	0.657229	+	0.477505i	−0.208497	+	0.978023i	$0.566857\pi$
$972$		0			0
$973$	−1.72205	+	5.29993i	−0.0552064	+	0.169908i
$974$		0			0
$975$	32.4547			1.03938
$976$		0			0
$977$	33.0375	−	24.0031i	1.05696	−	0.767928i	0.0834379	−	0.996513i	$-0.473410\pi$
$977$	33.0375	−	24.0031i	1.05696	−	0.767928i	0.973524	+	0.228585i	$0.0734100\pi$
$978$		0			0
$979$	4.45084	+	13.6983i	0.142249	+	0.437799i
$980$		0			0
$981$	−16.4020			−0.523676
$982$		0			0
$983$	0.712328			0.0227197			0.0113599	−	0.999935i	$-0.496384\pi$
$983$	0.712328			0.0227197			0.0113599	+	0.999935i	$0.496384\pi$
$984$		0			0
$985$	22.3073			0.710770
$986$		0			0
$987$	2.06461			0.0657173
$988$		0			0
$989$	−0.127774	−	0.393248i	−0.00406298	−	0.0125046i
$990$		0			0
$991$	−27.4251	+	19.9255i	−0.871188	+	0.632955i	−0.930905	−	0.365260i	$-0.880980\pi$
$991$	−27.4251	+	19.9255i	−0.871188	+	0.632955i	0.0597174	+	0.998215i	$0.480980\pi$
$992$		0			0
$993$	9.20625			0.292151
$994$		0			0
$995$	23.9813	−	73.8070i	0.760260	−	2.33984i
$996$		0			0
$997$	−21.9637	−	15.9576i	−0.695597	−	0.505381i	0.182898	−	0.983132i	$-0.441452\pi$
$997$	−21.9637	−	15.9576i	−0.695597	−	0.505381i	−0.878495	+	0.477751i	$0.841452\pi$
$998$		0			0
$999$	19.0490	+	58.6268i	0.602684	+	1.85487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.c.953.3	yes	16
41.37	even	5	inner	1148.2.n.c.365.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.c.365.3	✓	16	41.37	even	5	inner
1148.2.n.c.953.3	yes	16	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.04166 q^{3} +(-0.980821 - 3.01866i) q^{5} +(0.809017 - 0.587785i) q^{7} -1.91494 q^{9} +O(q^{10})\)	\(q+1.04166 q^{3} +(-0.980821 - 3.01866i) q^{5} +(0.809017 - 0.587785i) q^{7} -1.91494 q^{9} +(-0.720296 + 2.21684i) q^{11} +(-4.96745 - 3.60906i) q^{13} +(-1.02168 - 3.14441i) q^{15} +(-0.584425 + 1.79867i) q^{17} +(0.874332 - 0.635240i) q^{19} +(0.842721 - 0.612272i) q^{21} +(-0.0492228 - 0.0357625i) q^{23} +(-4.10519 + 2.98260i) q^{25} -5.11970 q^{27} +(-2.10122 - 6.46688i) q^{29} +(-2.72351 + 8.38210i) q^{31} +(-0.750303 + 2.30920i) q^{33} +(-2.56782 - 1.86563i) q^{35} +(-3.72073 - 11.4512i) q^{37} +(-5.17439 - 3.75942i) q^{39} +(-0.446908 + 6.38751i) q^{41} +(5.49805 + 3.99457i) q^{43} +(1.87822 + 5.78056i) q^{45} +(1.60350 + 1.16501i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.608772 + 1.87361i) q^{51} +(-1.92119 - 5.91281i) q^{53} +7.39837 q^{55} +(0.910757 - 0.661704i) q^{57} +(3.52997 + 2.56468i) q^{59} +(-8.06096 + 5.85663i) q^{61} +(-1.54922 + 1.12558i) q^{63} +(-6.02234 + 18.5349i) q^{65} +(-2.38407 - 7.33743i) q^{67} +(-0.0512735 - 0.0372523i) q^{69} +(3.81582 - 11.7439i) q^{71} -9.13495 q^{73} +(-4.27621 + 3.10685i) q^{75} +(0.720296 + 2.21684i) q^{77} -7.10337 q^{79} +0.411848 q^{81} +2.63313 q^{83} +6.00280 q^{85} +(-2.18875 - 6.73629i) q^{87} +(4.99906 - 3.63203i) q^{89} -6.14011 q^{91} +(-2.83697 + 8.73130i) q^{93} +(-2.77513 - 2.01625i) q^{95} +(-3.62222 - 11.1481i) q^{97} +(1.37933 - 4.24513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - q^{17} + 15 q^{19} + 2 q^{21} + 27 q^{23} - 3 q^{25} + 28 q^{27} - q^{29} - 14 q^{31} - 13 q^{33} - 12 q^{35} - 16 q^{37} + 10 q^{39} + 26 q^{41} + 5 q^{43} - 9 q^{45} - 14 q^{47} - 4 q^{49} + 4 q^{51} - 20 q^{53} + 10 q^{55} - 13 q^{57} - 47 q^{61} + 3 q^{63} - 29 q^{65} - 27 q^{67} + 15 q^{69} - 11 q^{71} + 70 q^{73} + 14 q^{75} + q^{77} + 30 q^{79} - 72 q^{81} - 78 q^{83} + 72 q^{85} + 21 q^{87} + 17 q^{89} - 24 q^{91} - 7 q^{93} + 27 q^{95} - 17 q^{97} + 13 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - q^17 + 15 * q^19 + 2 * q^21 + 27 * q^23 - 3 * q^25 + 28 * q^27 - q^29 - 14 * q^31 - 13 * q^33 - 12 * q^35 - 16 * q^37 + 10 * q^39 + 26 * q^41 + 5 * q^43 - 9 * q^45 - 14 * q^47 - 4 * q^49 + 4 * q^51 - 20 * q^53 + 10 * q^55 - 13 * q^57 - 47 * q^61 + 3 * q^63 - 29 * q^65 - 27 * q^67 + 15 * q^69 - 11 * q^71 + 70 * q^73 + 14 * q^75 + q^77 + 30 * q^79 - 72 * q^81 - 78 * q^83 + 72 * q^85 + 21 * q^87 + 17 * q^89 - 24 * q^91 - 7 * q^93 + 27 * q^95 - 17 * q^97 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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