LMFDB - Embedded newform 1155.2.l.f.1121.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.5
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45082 q^{2} +(0.877309 + 1.49343i) q^{3} +4.00650 q^{4} -1.00000i q^{5} +(-2.15012 - 3.66012i) q^{6} -1.00000i q^{7} -4.91756 q^{8} +(-1.46066 + 2.62040i) q^{9} +O(q^{10})$	\(q-2.45082 q^{2} +(0.877309 + 1.49343i) q^{3} +4.00650 q^{4} -1.00000i q^{5} +(-2.15012 - 3.66012i) q^{6} -1.00000i q^{7} -4.91756 q^{8} +(-1.46066 + 2.62040i) q^{9} +2.45082i q^{10} +(-0.828579 + 3.21146i) q^{11} +(3.51494 + 5.98342i) q^{12} +6.76117i q^{13} +2.45082i q^{14} +(1.49343 - 0.877309i) q^{15} +4.03905 q^{16} -5.22115 q^{17} +(3.57981 - 6.42211i) q^{18} -6.21697i q^{19} -4.00650i q^{20} +(1.49343 - 0.877309i) q^{21} +(2.03069 - 7.87069i) q^{22} -3.22384i q^{23} +(-4.31422 - 7.34403i) q^{24} -1.00000 q^{25} -16.5704i q^{26} +(-5.19482 + 0.117506i) q^{27} -4.00650i q^{28} +4.08004 q^{29} +(-3.66012 + 2.15012i) q^{30} +2.16563 q^{31} -0.0638312 q^{32} +(-5.52300 + 1.58002i) q^{33} +12.7961 q^{34} -1.00000 q^{35} +(-5.85213 + 10.4986i) q^{36} -8.03446 q^{37} +15.2367i q^{38} +(-10.0973 + 5.93164i) q^{39} +4.91756i q^{40} -5.40856 q^{41} +(-3.66012 + 2.15012i) q^{42} +6.96368i q^{43} +(-3.31970 + 12.8667i) q^{44} +(2.62040 + 1.46066i) q^{45} +7.90103i q^{46} -7.86819i q^{47} +(3.54349 + 6.03203i) q^{48} -1.00000 q^{49} +2.45082 q^{50} +(-4.58056 - 7.79741i) q^{51} +27.0886i q^{52} +7.52801i q^{53} +(12.7316 - 0.287987i) q^{54} +(3.21146 + 0.828579i) q^{55} +4.91756i q^{56} +(9.28461 - 5.45421i) q^{57} -9.99943 q^{58} -4.90450i q^{59} +(5.98342 - 3.51494i) q^{60} -5.13402i q^{61} -5.30756 q^{62} +(2.62040 + 1.46066i) q^{63} -7.92165 q^{64} +6.76117 q^{65} +(13.5359 - 3.87233i) q^{66} -10.7537 q^{67} -20.9185 q^{68} +(4.81457 - 2.82830i) q^{69} +2.45082 q^{70} -8.09497i q^{71} +(7.18288 - 12.8860i) q^{72} +10.2197i q^{73} +19.6910 q^{74} +(-0.877309 - 1.49343i) q^{75} -24.9083i q^{76} +(3.21146 + 0.828579i) q^{77} +(24.7467 - 14.5373i) q^{78} +10.3009i q^{79} -4.03905i q^{80} +(-4.73295 - 7.65501i) q^{81} +13.2554 q^{82} -4.27488 q^{83} +(5.98342 - 3.51494i) q^{84} +5.22115i q^{85} -17.0667i q^{86} +(3.57945 + 6.09325i) q^{87} +(4.07459 - 15.7925i) q^{88} +7.30053i q^{89} +(-6.42211 - 3.57981i) q^{90} +6.76117 q^{91} -12.9163i q^{92} +(1.89993 + 3.23421i) q^{93} +19.2835i q^{94} -6.21697 q^{95} +(-0.0559996 - 0.0953273i) q^{96} -15.4968 q^{97} +2.45082 q^{98} +(-7.20502 - 6.86205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.45082			−1.73299			−0.866494	−	0.499187i	$-0.833632\pi$
$2$	−2.45082			−1.73299			−0.866494	+	0.499187i	$0.833632\pi$
$3$	0.877309	+	1.49343i	0.506514	+	0.862231i
$3$	0.877309	+	1.49343i	0.506514	+	0.862231i
$4$	4.00650			2.00325
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.15012	−	3.66012i	−0.877784	−	1.49424i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−4.91756			−1.73862
$9$	−1.46066	+	2.62040i	−0.486886	+	0.873465i
$10$			2.45082i			0.775016i
$11$	−0.828579	+	3.21146i	−0.249826	+	0.968291i
$11$	−0.828579	+	3.21146i	−0.249826	+	0.968291i
$12$	3.51494	+	5.98342i	1.01468	+	1.72727i
$13$			6.76117i			1.87521i	0.347700	+	0.937606i	$0.386963\pi$
$13$			6.76117i			1.87521i	−0.347700	+	0.937606i	$0.613037\pi$
$14$			2.45082i			0.655008i
$15$	1.49343	−	0.877309i	0.385602	−	0.226520i
$16$	4.03905			1.00976
$17$	−5.22115			−1.26631			−0.633157	−	0.774023i	$-0.718241\pi$
$17$	−5.22115			−1.26631			−0.633157	+	0.774023i	$0.718241\pi$
$18$	3.57981	−	6.42211i	0.843768	−	1.51371i
$19$		−	6.21697i		−	1.42627i	−0.701026	−	0.713136i	$-0.747274\pi$
$19$		−	6.21697i		−	1.42627i	0.701026	−	0.713136i	$-0.252726\pi$
$20$		−	4.00650i		−	0.895881i
$21$	1.49343	−	0.877309i	0.325893	−	0.191444i
$22$	2.03069	−	7.87069i	0.432945	−	1.67804i
$23$		−	3.22384i		−	0.672216i	−0.941823	−	0.336108i	$-0.890889\pi$
$23$		−	3.22384i		−	0.672216i	0.941823	−	0.336108i	$-0.109111\pi$
$24$	−4.31422	−	7.34403i	−0.880637	−	1.49909i
$25$	−1.00000			−0.200000
$26$		−	16.5704i		−	3.24972i
$27$	−5.19482	+	0.117506i	−0.999744	+	0.0226141i
$28$		−	4.00650i		−	0.757157i
$29$	4.08004			0.757644			0.378822	−	0.925469i	$-0.376329\pi$
$29$	4.08004			0.757644			0.378822	+	0.925469i	$0.376329\pi$
$30$	−3.66012	+	2.15012i	−0.668243	+	0.392557i
$31$	2.16563			0.388959			0.194479	−	0.980907i	$-0.437698\pi$
$31$	2.16563			0.388959			0.194479	+	0.980907i	$0.437698\pi$
$32$	−0.0638312			−0.0112839
$33$	−5.52300	+	1.58002i	−0.961431	+	0.275046i
$34$	12.7961			2.19451
$35$	−1.00000			−0.169031
$36$	−5.85213	+	10.4986i	−0.975355	+	1.74977i
$37$	−8.03446			−1.32086			−0.660428	−	0.750889i	$-0.729625\pi$
$37$	−8.03446			−1.32086			−0.660428	+	0.750889i	$0.729625\pi$
$38$			15.2367i			2.47171i
$39$	−10.0973	+	5.93164i	−1.61687	+	0.949822i
$40$			4.91756i			0.777535i
$41$	−5.40856			−0.844675			−0.422338	−	0.906439i	$-0.638790\pi$
$41$	−5.40856			−0.844675			−0.422338	+	0.906439i	$0.638790\pi$
$42$	−3.66012	+	2.15012i	−0.564769	+	0.331771i
$43$			6.96368i			1.06195i	0.847387	+	0.530976i	$0.178175\pi$
$43$			6.96368i			1.06195i	−0.847387	+	0.530976i	$0.821825\pi$
$44$	−3.31970	+	12.8667i	−0.500464	+	1.93973i
$45$	2.62040	+	1.46066i	0.390626	+	0.217742i
$46$			7.90103i			1.16494i
$47$		−	7.86819i		−	1.14769i	−0.818963	−	0.573847i	$-0.805451\pi$
$47$		−	7.86819i		−	1.14769i	0.818963	−	0.573847i	$-0.194549\pi$
$48$	3.54349	+	6.03203i	0.511459	+	0.870648i
$49$	−1.00000			−0.142857
$50$	2.45082			0.346598
$51$	−4.58056	−	7.79741i	−0.641407	−	1.09186i
$52$			27.0886i			3.75652i
$53$			7.52801i			1.03405i	0.855970	+	0.517026i	$0.172961\pi$
$53$			7.52801i			1.03405i	−0.855970	+	0.517026i	$0.827039\pi$
$54$	12.7316	−	0.287987i	1.73255	−	0.0391900i
$55$	3.21146	+	0.828579i	0.433033	+	0.111726i
$56$			4.91756i			0.657137i
$57$	9.28461	−	5.45421i	1.22978	−	0.722427i
$58$	−9.99943			−1.31299
$59$		−	4.90450i		−	0.638512i	−0.947669	−	0.319256i	$-0.896567\pi$
$59$		−	4.90450i		−	0.638512i	0.947669	−	0.319256i	$-0.103433\pi$
$60$	5.98342	−	3.51494i	0.772457	−	0.453777i
$61$		−	5.13402i		−	0.657344i	−0.944444	−	0.328672i	$-0.893399\pi$
$61$		−	5.13402i		−	0.657344i	0.944444	−	0.328672i	$-0.106601\pi$
$62$	−5.30756			−0.674061
$63$	2.62040	+	1.46066i	0.330139	+	0.184026i
$64$	−7.92165			−0.990207
$65$	6.76117			0.838620
$66$	13.5359	−	3.87233i	1.66615	−	0.476651i
$67$	−10.7537			−1.31377			−0.656886	−	0.753990i	$-0.728127\pi$
$67$	−10.7537			−1.31377			−0.656886	+	0.753990i	$0.728127\pi$
$68$	−20.9185			−2.53675
$69$	4.81457	−	2.82830i	0.579606	−	0.340487i
$70$	2.45082			0.292929
$71$		−	8.09497i		−	0.960696i	−0.877078	−	0.480348i	$-0.840510\pi$
$71$		−	8.09497i		−	0.960696i	0.877078	−	0.480348i	$-0.159490\pi$
$72$	7.18288	−	12.8860i	0.846511	−	1.51863i
$73$			10.2197i			1.19613i	0.801448	+	0.598064i	$0.204063\pi$
$73$			10.2197i			1.19613i	−0.801448	+	0.598064i	$0.795937\pi$
$74$	19.6910			2.28903
$75$	−0.877309	−	1.49343i	−0.101303	−	0.172446i
$76$		−	24.9083i		−	2.85718i
$77$	3.21146	+	0.828579i	0.365980	+	0.0944253i
$78$	24.7467	−	14.5373i	2.80201	−	1.64603i
$79$			10.3009i			1.15894i	0.814992	+	0.579472i	$0.196741\pi$
$79$			10.3009i			1.15894i	−0.814992	+	0.579472i	$0.803259\pi$
$80$		−	4.03905i		−	0.451579i
$81$	−4.73295	−	7.65501i	−0.525884	−	0.850557i
$82$	13.2554			1.46381
$83$	−4.27488			−0.469229			−0.234615	−	0.972088i	$-0.575383\pi$
$83$	−4.27488			−0.469229			−0.234615	+	0.972088i	$0.575383\pi$
$84$	5.98342	−	3.51494i	0.652845	−	0.383511i
$85$			5.22115i			0.566313i
$86$		−	17.0667i		−	1.84035i
$87$	3.57945	+	6.09325i	0.383758	+	0.653265i
$88$	4.07459	−	15.7925i	0.434353	−	1.68349i
$89$			7.30053i			0.773854i	0.922110	+	0.386927i	$0.126464\pi$
$89$			7.30053i			0.773854i	−0.922110	+	0.386927i	$0.873536\pi$
$90$	−6.42211	−	3.57981i	−0.676950	−	0.377345i
$91$	6.76117			0.708763
$92$		−	12.9163i		−	1.34662i
$93$	1.89993	+	3.23421i	0.197013	+	0.335372i
$94$			19.2835i			1.98894i
$95$	−6.21697			−0.637848
$96$	−0.0559996	−	0.0953273i	−0.00571544	−	0.00972930i
$97$	−15.4968			−1.57347			−0.786733	−	0.617294i	$-0.788229\pi$
$97$	−15.4968			−1.57347			−0.786733	+	0.617294i	$0.788229\pi$
$98$	2.45082			0.247570
$99$	−7.20502	−	6.86205i	−0.724132	−	0.689662i
$100$	−4.00650			−0.400650
$101$	−3.84761			−0.382851			−0.191426	−	0.981507i	$-0.561311\pi$
$101$	−3.84761			−0.382851			−0.191426	+	0.981507i	$0.561311\pi$
$102$	11.2261	+	19.1100i	1.11155	+	1.89217i
$103$	8.87110			0.874096			0.437048	−	0.899438i	$-0.356024\pi$
$103$	8.87110			0.874096			0.437048	+	0.899438i	$0.356024\pi$
$104$		−	33.2485i		−	3.26028i
$105$	−0.877309	−	1.49343i	−0.0856166	−	0.145744i
$106$		−	18.4498i		−	1.79200i
$107$	−11.0644			−1.06964			−0.534820	−	0.844966i	$-0.679621\pi$
$107$	−11.0644			−1.06964			−0.534820	+	0.844966i	$0.679621\pi$
$108$	−20.8131	+	0.470790i	−2.00274	+	0.0453018i
$109$		−	15.3821i		−	1.47333i	−0.676256	−	0.736667i	$-0.736398\pi$
$109$		−	15.3821i		−	1.47333i	0.676256	−	0.736667i	$-0.263602\pi$
$110$	−7.87069	−	2.03069i	−0.750441	−	0.193619i
$111$	−7.04870	−	11.9989i	−0.669033	−	1.13888i
$112$		−	4.03905i		−	0.381654i
$113$		−	2.90261i		−	0.273054i	−0.990636	−	0.136527i	$-0.956406\pi$
$113$		−	2.90261i		−	0.273054i	0.990636	−	0.136527i	$-0.0435941\pi$
$114$	−22.7549	+	13.3673i	−2.13119	+	1.25196i
$115$	−3.22384			−0.300624
$116$	16.3467			1.51775
$117$	−17.7170	−	9.87577i	−1.63793	−	0.913015i
$118$			12.0200i			1.10653i
$119$			5.22115i			0.478622i
$120$	−7.34403	+	4.31422i	−0.670415	+	0.393833i
$121$	−9.62691	−	5.32189i	−0.875174	−	0.483808i
$122$			12.5825i			1.13917i
$123$	−4.74498	−	8.07730i	−0.427840	−	0.728306i
$124$	8.67660			0.779182
$125$			1.00000i			0.0894427i
$126$	−6.42211	−	3.57981i	−0.572127	−	0.318915i
$127$			8.67052i			0.769384i	0.923045	+	0.384692i	$0.125692\pi$
$127$			8.67052i			0.769384i	−0.923045	+	0.384692i	$0.874308\pi$
$128$	19.5422			1.72730
$129$	−10.3998	+	6.10930i	−0.915648	+	0.537894i
$130$	−16.5704			−1.45332
$131$	−1.26696			−0.110695			−0.0553476	−	0.998467i	$-0.517627\pi$
$131$	−1.26696			−0.110695			−0.0553476	+	0.998467i	$0.517627\pi$
$132$	−22.1279	+	6.33034i	−1.92599	+	0.550985i
$133$	−6.21697			−0.539080
$134$	26.3553			2.27675
$135$	0.117506	+	5.19482i	0.0101133	+	0.447099i
$136$	25.6753			2.20164
$137$			7.91882i			0.676550i	0.941047	+	0.338275i	$0.109843\pi$
$137$			7.91882i			0.676550i	−0.941047	+	0.338275i	$0.890157\pi$
$138$	−11.7996	+	6.93164i	−1.00445	+	0.590060i
$139$		−	8.44234i		−	0.716070i	−0.933708	−	0.358035i	$-0.883447\pi$
$139$		−	8.44234i		−	0.716070i	0.933708	−	0.358035i	$-0.116553\pi$
$140$	−4.00650			−0.338611
$141$	11.7506	−	6.90283i	0.989577	−	0.581323i
$142$			19.8393i			1.66488i
$143$	−21.7132	−	5.60216i	−1.81575	−	0.468476i
$144$	−5.89967	+	10.5839i	−0.491639	+	0.881992i
$145$		−	4.08004i		−	0.338829i
$146$		−	25.0467i		−	2.07288i
$147$	−0.877309	−	1.49343i	−0.0723592	−	0.123176i
$148$	−32.1901			−2.64601
$149$	3.70906			0.303858			0.151929	−	0.988391i	$-0.451452\pi$
$149$	3.70906			0.303858			0.151929	+	0.988391i	$0.451452\pi$
$150$	2.15012	+	3.66012i	0.175557	+	0.298848i
$151$			3.84108i			0.312583i	0.987711	+	0.156291i	$0.0499539\pi$
$151$			3.84108i			0.312583i	−0.987711	+	0.156291i	$0.950046\pi$
$152$			30.5724i			2.47975i
$153$	7.62632	−	13.6815i	0.616551	−	1.10608i
$154$	−7.87069	−	2.03069i	−0.634238	−	0.163638i
$155$		−	2.16563i		−	0.173948i
$156$	−40.4550	+	23.7651i	−3.23899	+	1.90273i
$157$	−4.25023			−0.339206			−0.169603	−	0.985513i	$-0.554248\pi$
$157$	−4.25023			−0.339206			−0.169603	+	0.985513i	$0.554248\pi$
$158$		−	25.2457i		−	2.00844i
$159$	−11.2426	+	6.60439i	−0.891592	+	0.523762i
$160$			0.0638312i			0.00504630i
$161$	−3.22384			−0.254074
$162$	11.5996	+	18.7610i	0.911350	+	1.47401i
$163$	16.3126			1.27770			0.638850	−	0.769331i	$-0.279410\pi$
$163$	16.3126			1.27770			0.638850	+	0.769331i	$0.279410\pi$
$164$	−21.6694			−1.69210
$165$	1.58002	+	5.52300i	0.123004	+	0.429965i
$166$	10.4769			0.813169
$167$	1.33486			0.103295			0.0516474	−	0.998665i	$-0.483553\pi$
$167$	1.33486			0.103295			0.0516474	+	0.998665i	$0.483553\pi$
$168$	−7.34403	+	4.31422i	−0.566604	+	0.332849i
$169$	−32.7135			−2.51642
$170$		−	12.7961i		−	0.981414i
$171$	16.2909	+	9.08088i	1.24580	+	0.694432i
$172$			27.9000i			2.12736i
$173$	−12.3959			−0.942446			−0.471223	−	0.882014i	$-0.656187\pi$
$173$	−12.3959			−0.942446			−0.471223	+	0.882014i	$0.656187\pi$
$174$	−8.77259	−	14.9334i	−0.665048	−	1.13210i
$175$			1.00000i			0.0755929i
$176$	−3.34667	+	12.9712i	−0.252265	+	0.977743i
$177$	7.32453	−	4.30276i	0.550545	−	0.323415i
$178$		−	17.8922i		−	1.34108i
$179$			21.9783i			1.64274i	0.570397	+	0.821369i	$0.306790\pi$
$179$			21.9783i			1.64274i	−0.570397	+	0.821369i	$0.693210\pi$
$180$	10.4986	+	5.85213i	0.782521	+	0.436192i
$181$	20.1572			1.49827			0.749136	−	0.662416i	$-0.230469\pi$
$181$	20.1572			1.49827			0.749136	+	0.662416i	$0.230469\pi$
$182$	−16.5704			−1.22828
$183$	7.66729	−	4.50412i	0.566783	−	0.332954i
$184$			15.8534i			1.16873i
$185$			8.03446i			0.590705i
$186$	−4.65637	−	7.92647i	−0.341422	−	0.581197i
$187$	4.32613	−	16.7675i	0.316358	−	1.22616i
$188$		−	31.5239i		−	2.29912i
$189$	0.117506	+	5.19482i	0.00854734	+	0.377868i
$190$	15.2367			1.10538
$191$			13.4860i			0.975814i	0.872896	+	0.487907i	$0.162239\pi$
$191$			13.4860i			0.975814i	−0.872896	+	0.487907i	$0.837761\pi$
$192$	−6.94974	−	11.8304i	−0.501554	−	0.853787i
$193$		−	19.5427i		−	1.40671i	−0.710837	−	0.703357i	$-0.751684\pi$
$193$		−	19.5427i		−	1.40671i	0.710837	−	0.703357i	$-0.248316\pi$
$194$	37.9799			2.72680
$195$	5.93164	+	10.0973i	0.424773	+	0.723085i
$196$	−4.00650			−0.286179
$197$	−3.89168			−0.277271			−0.138635	−	0.990343i	$-0.544272\pi$
$197$	−3.89168			−0.277271			−0.138635	+	0.990343i	$0.544272\pi$
$198$	17.6582	+	16.8176i	1.25491	+	1.19518i
$199$	−15.5753			−1.10410			−0.552051	−	0.833810i	$-0.686155\pi$
$199$	−15.5753			−1.10410			−0.552051	+	0.833810i	$0.686155\pi$
$200$	4.91756			0.347724
$201$	−9.43431	−	16.0599i	−0.665445	−	1.13278i
$202$	9.42977			0.663477
$203$		−	4.08004i		−	0.286363i
$204$	−18.3520	−	31.2403i	−1.28490	−	2.18726i
$205$			5.40856i			0.377750i
$206$	−21.7414			−1.51480
$207$	8.44772	+	4.70892i	0.587157	+	0.327293i
$208$			27.3087i			1.89352i
$209$	19.9655	+	5.15125i	1.38105	+	0.356320i
$210$	2.15012	+	3.66012i	0.148373	+	0.252572i
$211$		−	9.87355i		−	0.679723i	−0.940475	−	0.339862i	$-0.889620\pi$
$211$		−	9.87355i		−	0.679723i	0.940475	−	0.339862i	$-0.110380\pi$
$212$			30.1610i			2.07147i
$213$	12.0893	−	7.10179i	0.828343	−	0.486606i
$214$	27.1169			1.85367
$215$	6.96368			0.474919
$216$	25.5459	−	0.577846i	1.73818	−	0.0393174i
$217$		−	2.16563i		−	0.147013i
$218$			37.6986i			2.55327i
$219$	−15.2624	+	8.96585i	−1.03134	+	0.605856i
$220$	12.8667	+	3.31970i	0.867473	+	0.223814i
$221$		−	35.3011i		−	2.37461i
$222$	17.2751	+	29.4071i	1.15943	+	1.97367i
$223$	−9.08225			−0.608192			−0.304096	−	0.952641i	$-0.598354\pi$
$223$	−9.08225			−0.608192			−0.304096	+	0.952641i	$0.598354\pi$
$224$			0.0638312i			0.00426490i
$225$	1.46066	−	2.62040i	0.0973773	−	0.174693i
$226$			7.11375i			0.473200i
$227$	18.6066			1.23496			0.617480	−	0.786587i	$-0.288154\pi$
$227$	18.6066			1.23496			0.617480	+	0.786587i	$0.288154\pi$
$228$	37.1988	−	21.8523i	2.46355	−	1.44720i
$229$	−0.491124			−0.0324544			−0.0162272	−	0.999868i	$-0.505166\pi$
$229$	−0.491124			−0.0324544			−0.0162272	+	0.999868i	$0.505166\pi$
$230$	7.90103			0.520978
$231$	1.58002	+	5.52300i	0.103957	+	0.363387i
$232$	−20.0639			−1.31726
$233$	−4.03019			−0.264027			−0.132013	−	0.991248i	$-0.542144\pi$
$233$	−4.03019			−0.264027			−0.132013	+	0.991248i	$0.542144\pi$
$234$	43.4210	+	24.2037i	2.83852	+	1.58224i
$235$	−7.86819			−0.513264
$236$		−	19.6499i		−	1.27910i
$237$	−15.3837	+	9.03708i	−0.999278	+	0.587022i
$238$		−	12.7961i		−	0.829446i
$239$	−25.6196			−1.65719			−0.828596	−	0.559847i	$-0.810860\pi$
$239$	−25.6196			−1.65719			−0.828596	+	0.559847i	$0.810860\pi$
$240$	6.03203	−	3.54349i	0.389366	−	0.228731i
$241$			20.3487i			1.31077i	0.755293	+	0.655387i	$0.227494\pi$
$241$			20.3487i			1.31077i	−0.755293	+	0.655387i	$0.772506\pi$
$242$	23.5938	+	13.0430i	1.51667	+	0.838434i
$243$	7.27995	−	13.7841i	0.467009	−	0.884253i
$244$		−	20.5695i		−	1.31682i
$245$			1.00000i			0.0638877i
$246$	11.6291	+	19.7960i	0.741442	+	1.26215i
$247$	42.0340			2.67456
$248$	−10.6496			−0.676252
$249$	−3.75039	−	6.38423i	−0.237671	−	0.404584i
$250$		−	2.45082i		−	0.155003i
$251$			20.4591i			1.29137i	0.763605	+	0.645683i	$0.223427\pi$
$251$			20.4591i			1.29137i	−0.763605	+	0.645683i	$0.776573\pi$
$252$	10.4986	+	5.85213i	0.661351	+	0.368650i
$253$	10.3532	+	2.67120i	0.650901	+	0.167937i
$254$		−	21.2499i		−	1.33333i
$255$	−7.79741	+	4.58056i	−0.488293	+	0.286846i
$256$	−32.0510			−2.00319
$257$		−	5.12084i		−	0.319429i	−0.987163	−	0.159715i	$-0.948943\pi$
$257$		−	5.12084i		−	0.319429i	0.987163	−	0.159715i	$-0.0510574\pi$
$258$	25.4879	−	14.9728i	1.58681	−	0.932164i
$259$			8.03446i			0.499237i
$260$	27.0886			1.67997
$261$	−5.95955	+	10.6913i	−0.368887	+	0.661776i
$262$	3.10510			0.191834
$263$	−17.5580			−1.08267			−0.541336	−	0.840807i	$-0.682081\pi$
$263$	−17.5580			−1.08267			−0.541336	+	0.840807i	$0.682081\pi$
$264$	27.1597	−	7.76983i	1.67157	−	0.478200i
$265$	7.52801			0.462442
$266$	15.2367			0.934220
$267$	−10.9028	+	6.40482i	−0.667242	+	0.391968i
$268$	−43.0847			−2.63182
$269$		−	16.7138i		−	1.01906i	−0.860454	−	0.509528i	$-0.829820\pi$
$269$		−	16.7138i		−	1.01906i	0.860454	−	0.509528i	$-0.170180\pi$
$270$	−0.287987	−	12.7316i	−0.0175263	−	0.774818i
$271$			29.7002i			1.80416i	0.431573	+	0.902078i	$0.357959\pi$
$271$			29.7002i			1.80416i	−0.431573	+	0.902078i	$0.642041\pi$
$272$	−21.0885			−1.27868
$273$	5.93164	+	10.0973i	0.358999	+	0.611118i
$274$		−	19.4076i		−	1.17245i
$275$	0.828579	−	3.21146i	0.0499652	−	0.193658i
$276$	19.2896	−	11.3316i	1.16110	−	0.682081i
$277$		−	10.1482i		−	0.609748i	−0.952393	−	0.304874i	$-0.901386\pi$
$277$		−	10.1482i		−	0.609748i	0.952393	−	0.304874i	$-0.0986144\pi$
$278$			20.6906i			1.24094i
$279$	−3.16325	+	5.67481i	−0.189379	+	0.339742i
$280$	4.91756			0.293881
$281$	9.84817			0.587492			0.293746	−	0.955883i	$-0.405098\pi$
$281$	9.84817			0.587492			0.293746	+	0.955883i	$0.405098\pi$
$282$	−28.7985	+	16.9176i	−1.71493	+	1.00743i
$283$			10.3929i			0.617795i	0.951095	+	0.308897i	$0.0999600\pi$
$283$			10.3929i			0.617795i	−0.951095	+	0.308897i	$0.900040\pi$
$284$		−	32.4325i		−	1.92452i
$285$	−5.45421	−	9.28461i	−0.323079	−	0.549973i
$286$	53.2151	+	13.7299i	3.14668	+	0.811865i
$287$			5.40856i			0.319257i
$288$	0.0932355	−	0.167263i	0.00549396	−	0.00985606i
$289$	10.2604			0.603553
$290$			9.99943i			0.587187i
$291$	−13.5955	−	23.1434i	−0.796983	−	1.35669i
$292$			40.9453i			2.39614i
$293$	30.1418			1.76090			0.880450	−	0.474139i	$-0.157240\pi$
$293$	30.1418			1.76090			0.880450	+	0.474139i	$0.157240\pi$
$294$	2.15012	+	3.66012i	0.125398	+	0.213463i
$295$	−4.90450			−0.285551
$296$	39.5100			2.29647
$297$	3.92695	−	16.7803i	0.227865	−	0.973693i
$298$	−9.09022			−0.526582
$299$	21.7969			1.26055
$300$	−3.51494	−	5.98342i	−0.202935	−	0.345453i
$301$	6.96368			0.401380
$302$		−	9.41378i		−	0.541702i
$303$	−3.37554	−	5.74613i	−0.193920	−	0.330106i
$304$		−	25.1106i		−	1.44019i
$305$	−5.13402			−0.293973
$306$	−18.6907	+	33.5308i	−1.06848	+	1.91683i
$307$		−	4.22373i		−	0.241061i	−0.992710	−	0.120530i	$-0.961540\pi$
$307$		−	4.22373i		−	0.241061i	0.992710	−	0.120530i	$-0.0384595\pi$
$308$	12.8667	+	3.31970i	0.733149	+	0.189158i
$309$	7.78270	+	13.2484i	0.442742	+	0.753673i
$310$			5.30756i			0.301449i
$311$			9.25912i			0.525036i	0.964927	+	0.262518i	$0.0845530\pi$
$311$			9.25912i			0.525036i	−0.964927	+	0.262518i	$0.915447\pi$
$312$	49.6543	−	29.1692i	2.81112	−	1.65138i
$313$	−16.1922			−0.915237			−0.457618	−	0.889149i	$-0.651297\pi$
$313$	−16.1922			−0.915237			−0.457618	+	0.889149i	$0.651297\pi$
$314$	10.4165			0.587839
$315$	1.46066	−	2.62040i	0.0822988	−	0.147643i
$316$			41.2706i			2.32165i
$317$			13.6532i			0.766839i	0.923574	+	0.383419i	$0.125254\pi$
$317$			13.6532i			0.766839i	−0.923574	+	0.383419i	$0.874746\pi$
$318$	27.5534	−	16.1862i	1.54512	−	0.907674i
$319$	−3.38063	+	13.1029i	−0.189279	+	0.733620i
$320$			7.92165i			0.442834i
$321$	−9.70693	−	16.5240i	−0.541788	−	0.922277i
$322$	7.90103			0.440307
$323$			32.4597i			1.80611i
$324$	−18.9626	−	30.6698i	−1.05348	−	1.70388i
$325$		−	6.76117i		−	0.375042i
$326$	−39.9792			−2.21424
$327$	22.9720	−	13.4948i	1.27036	−	0.746265i
$328$	26.5970			1.46857
$329$	−7.86819			−0.433787
$330$	−3.87233	−	13.5359i	−0.213165	−	0.745125i
$331$	15.8005			0.868476			0.434238	−	0.900798i	$-0.357018\pi$
$331$	15.8005			0.868476			0.434238	+	0.900798i	$0.357018\pi$
$332$	−17.1273			−0.939983
$333$	11.7356	−	21.0535i	0.643107	−	1.15372i
$334$	−3.27151			−0.179009
$335$			10.7537i			0.587537i
$336$	6.03203	−	3.54349i	0.329074	−	0.193313i
$337$		−	15.4400i		−	0.841069i	−0.907277	−	0.420534i	$-0.861843\pi$
$337$		−	15.4400i		−	0.841069i	0.907277	−	0.420534i	$-0.138157\pi$
$338$	80.1747			4.36093
$339$	4.33484	−	2.54648i	0.235436	−	0.138306i
$340$			20.9185i			1.13447i
$341$	−1.79440	+	6.95483i	−0.0971720	+	0.376625i
$342$	−39.9261	−	22.2556i	−2.15896	−	1.20344i
$343$			1.00000i			0.0539949i
$344$		−	34.2444i		−	1.84633i
$345$	−2.82830	−	4.81457i	−0.152270	−	0.259208i
$346$	30.3802			1.63325
$347$	0.952324			0.0511234			0.0255617	−	0.999673i	$-0.491863\pi$
$347$	0.952324			0.0511234			0.0255617	+	0.999673i	$0.491863\pi$
$348$	14.3411	+	24.4126i	0.768763	+	1.30865i
$349$		−	10.9106i		−	0.584031i	−0.956414	−	0.292015i	$-0.905674\pi$
$349$		−	10.9106i		−	0.584031i	0.956414	−	0.292015i	$-0.0943258\pi$
$350$		−	2.45082i		−	0.131002i
$351$	−0.794482	−	35.1231i	−0.0424063	−	1.87473i
$352$	0.0528891	−	0.204991i	0.00281900	−	0.0109261i
$353$		−	17.4326i		−	0.927846i	−0.885876	−	0.463923i	$-0.846442\pi$
$353$		−	17.4326i		−	0.927846i	0.885876	−	0.463923i	$-0.153558\pi$
$354$	−17.9511	+	10.5453i	−0.954088	+	0.560475i
$355$	−8.09497			−0.429636
$356$			29.2496i			1.55022i
$357$	−7.79741	+	4.58056i	−0.412683	+	0.242429i
$358$		−	53.8649i		−	2.84685i
$359$	4.35980			0.230101			0.115051	−	0.993360i	$-0.463297\pi$
$359$	4.35980			0.230101			0.115051	+	0.993360i	$0.463297\pi$
$360$	−12.8860	−	7.18288i	−0.679150	−	0.378571i
$361$	−19.6508			−1.03425
$362$	−49.4016			−2.59649
$363$	−0.497912	−	19.0461i	−0.0261336	−	0.999658i
$364$	27.0886			1.41983
$365$	10.2197			0.534925
$366$	−18.7911	+	11.0388i	−0.982228	+	0.577006i
$367$	21.9215			1.14429			0.572146	−	0.820152i	$-0.306111\pi$
$367$	21.9215			1.14429			0.572146	+	0.820152i	$0.306111\pi$
$368$		−	13.0212i		−	0.678778i
$369$	7.90006	−	14.1726i	0.411261	−	0.737795i
$370$		−	19.6910i		−	1.02369i
$371$	7.52801			0.390835
$372$	7.61206	+	12.9579i	0.394667	+	0.671835i
$373$		−	5.79535i		−	0.300072i	−0.988681	−	0.150036i	$-0.952061\pi$
$373$		−	5.79535i		−	0.300072i	0.988681	−	0.150036i	$-0.0479389\pi$
$374$	−10.6026	+	41.0941i	−0.548245	+	2.12492i
$375$	−1.49343	+	0.877309i	−0.0771203	+	0.0453040i
$376$			38.6923i			1.99540i
$377$			27.5859i			1.42074i
$378$	−0.287987	−	12.7316i	−0.0148124	−	0.654841i
$379$	25.5329			1.31154			0.655768	−	0.754963i	$-0.272345\pi$
$379$	25.5329			1.31154			0.655768	+	0.754963i	$0.272345\pi$
$380$	−24.9083			−1.27777
$381$	−12.9488	+	7.60672i	−0.663387	+	0.389704i
$382$		−	33.0518i		−	1.69107i
$383$			26.6491i			1.36170i	0.732421	+	0.680852i	$0.238390\pi$
$383$			26.6491i			1.36170i	−0.732421	+	0.680852i	$0.761610\pi$
$384$	17.1445	+	29.1849i	0.874903	+	1.48933i
$385$	0.828579	−	3.21146i	0.0422283	−	0.163671i
$386$			47.8956i			2.43782i
$387$	−18.2476	−	10.1716i	−0.927578	−	0.517050i
$388$	−62.0881			−3.15204
$389$			37.2190i			1.88708i	0.331260	+	0.943540i	$0.392526\pi$
$389$			37.2190i			1.88708i	−0.331260	+	0.943540i	$0.607474\pi$
$390$	−14.5373	−	24.7467i	−0.736127	−	1.25310i
$391$			16.8321i			0.851237i
$392$	4.91756			0.248375
$393$	−1.11152	−	1.89212i	−0.0560687	−	0.0954449i
$394$	9.53779			0.480507
$395$	10.3009			0.518295
$396$	−28.8669	−	27.4928i	−1.45062	−	1.38157i
$397$	6.56168			0.329321			0.164661	−	0.986350i	$-0.447347\pi$
$397$	6.56168			0.329321			0.164661	+	0.986350i	$0.447347\pi$
$398$	38.1721			1.91340
$399$	−5.45421	−	9.28461i	−0.273052	−	0.464812i
$400$	−4.03905			−0.201952
$401$			1.69993i			0.0848902i	0.999099	+	0.0424451i	$0.0135148\pi$
$401$			1.69993i			0.0848902i	−0.999099	+	0.0424451i	$0.986485\pi$
$402$	23.1218	+	39.3598i	1.15321	+	1.96309i
$403$			14.6422i			0.729380i
$404$	−15.4154			−0.766947
$405$	−7.65501	+	4.73295i	−0.380380	+	0.235182i
$406$			9.99943i			0.496263i
$407$	6.65718	−	25.8023i	0.329984	−	1.27897i
$408$	22.5252	+	38.3443i	1.11516	+	1.89833i
$409$		−	25.7955i		−	1.27551i	−0.770240	−	0.637754i	$-0.779864\pi$
$409$		−	25.7955i		−	1.27551i	0.770240	−	0.637754i	$-0.220136\pi$
$410$		−	13.2554i		−	0.654637i
$411$	−11.8262	+	6.94725i	−0.583343	+	0.342682i
$412$	35.5421			1.75103
$413$	−4.90450			−0.241335
$414$	−20.7038	−	11.5407i	−1.01754	−	0.567195i
$415$			4.27488i			0.209846i
$416$		−	0.431573i		−	0.0211596i
$417$	12.6080	−	7.40654i	0.617418	−	0.362700i
$418$	−48.9319	−	12.6248i	−2.39334	−	0.617498i
$419$		−	14.9751i		−	0.731579i	−0.930698	−	0.365790i	$-0.880799\pi$
$419$		−	14.9751i		−	0.731579i	0.930698	−	0.365790i	$-0.119201\pi$
$420$	−3.51494	−	5.98342i	−0.171511	−	0.291961i
$421$	−33.0972			−1.61306			−0.806529	−	0.591194i	$-0.798657\pi$
$421$	−33.0972			−1.61306			−0.806529	+	0.591194i	$0.798657\pi$
$422$			24.1983i			1.17795i
$423$	20.6178	+	11.4927i	1.00247	+	0.558796i
$424$		−	37.0195i		−	1.79783i
$425$	5.22115			0.253263
$426$	−29.6286	+	17.4052i	−1.43551	+	0.843284i
$427$	−5.13402			−0.248453
$428$	−44.3297			−2.14276
$429$	−10.6828	−	37.3420i	−0.515769	−	1.80289i
$430$	−17.0667			−0.823030
$431$	20.1624			0.971191			0.485595	−	0.874184i	$-0.338603\pi$
$431$	20.1624			0.971191			0.485595	+	0.874184i	$0.338603\pi$
$432$	−20.9821	+	0.474614i	−1.00950	+	0.0228349i
$433$	33.9440			1.63124			0.815622	−	0.578585i	$-0.196395\pi$
$433$	33.9440			1.63124			0.815622	+	0.578585i	$0.196395\pi$
$434$			5.30756i			0.254771i
$435$	6.09325	−	3.57945i	0.292149	−	0.171622i
$436$		−	61.6282i		−	2.95146i
$437$	−20.0425			−0.958763
$438$	37.4054	−	21.9737i	1.78730	−	1.04994i
$439$			34.0473i			1.62499i	0.582967	+	0.812496i	$0.301892\pi$
$439$			34.0473i			1.62499i	−0.582967	+	0.812496i	$0.698108\pi$
$440$	−15.7925	−	4.07459i	−0.752880	−	0.194248i
$441$	1.46066	−	2.62040i	0.0695552	−	0.124781i
$442$			86.5165i			4.11517i
$443$		−	4.14496i		−	0.196933i	−0.995140	−	0.0984666i	$-0.968606\pi$
$443$		−	4.14496i		−	0.196933i	0.995140	−	0.0984666i	$-0.0313938\pi$
$444$	−28.2406	−	48.0736i	−1.34024	−	2.28147i
$445$	7.30053			0.346078
$446$	22.2589			1.05399
$447$	3.25399	+	5.53921i	0.153908	+	0.261996i
$448$			7.92165i			0.374263i
$449$			26.1823i			1.23562i	0.786328	+	0.617809i	$0.211980\pi$
$449$			26.1823i			1.23562i	−0.786328	+	0.617809i	$0.788020\pi$
$450$	−3.57981	+	6.42211i	−0.168754	+	0.302741i
$451$	4.48142	−	17.3694i	0.211022	−	0.817891i
$452$		−	11.6293i		−	0.546996i
$453$	−5.73638	+	3.36981i	−0.269519	+	0.158328i
$454$	−45.6012			−2.14017
$455$		−	6.76117i		−	0.316969i
$456$	−45.6577	+	26.8214i	−2.13812	+	1.25603i
$457$			12.8229i			0.599831i	0.953966	+	0.299915i	$0.0969584\pi$
$457$			12.8229i			0.599831i	−0.953966	+	0.299915i	$0.903042\pi$
$458$	1.20365			0.0562431
$459$	27.1229	−	0.613519i	1.26599	−	0.0286366i
$460$	−12.9163			−0.602225
$461$	−16.4469			−0.766009			−0.383005	−	0.923746i	$-0.625111\pi$
$461$	−16.4469			−0.766009			−0.383005	+	0.923746i	$0.625111\pi$
$462$	−3.87233	−	13.5359i	−0.180157	−	0.629745i
$463$	−17.2397			−0.801198			−0.400599	−	0.916254i	$-0.631198\pi$
$463$	−17.2397			−0.801198			−0.400599	+	0.916254i	$0.631198\pi$
$464$	16.4795			0.765040
$465$	3.23421	−	1.89993i	0.149983	−	0.0881070i
$466$	9.87726			0.457555
$467$			35.6700i			1.65061i	0.564687	+	0.825305i	$0.308997\pi$
$467$			35.6700i			1.65061i	−0.564687	+	0.825305i	$0.691003\pi$
$468$	−70.9830	−	39.5673i	−3.28119	−	1.82900i
$469$			10.7537i			0.496559i
$470$	19.2835			0.889481
$471$	−3.72877	−	6.34742i	−0.171812	−	0.292474i
$472$			24.1182i			1.11013i
$473$	−22.3636	−	5.76996i	−1.02828	−	0.265303i
$474$	37.7026	−	22.1482i	1.73174	−	1.01730i
$475$			6.21697i			0.285254i
$476$			20.9185i			0.958800i
$477$	−19.7264	−	10.9959i	−0.903209	−	0.503466i
$478$	62.7889			2.87190
$479$	14.7539			0.674123			0.337061	−	0.941483i	$-0.390567\pi$
$479$	14.7539			0.674123			0.337061	+	0.941483i	$0.390567\pi$
$480$	−0.0953273	+	0.0559996i	−0.00435108	+	0.00255602i
$481$		−	54.3224i		−	2.47689i
$482$		−	49.8709i		−	2.27156i
$483$	−2.82830	−	4.81457i	−0.128692	−	0.219070i
$484$	−38.5702	−	21.3222i	−1.75319	−	0.969189i
$485$			15.4968i			0.703675i
$486$	−17.8418	+	33.7824i	−0.809322	+	1.53240i
$487$	35.1791			1.59412			0.797058	−	0.603903i	$-0.206388\pi$
$487$	35.1791			1.59412			0.797058	+	0.603903i	$0.206388\pi$
$488$			25.2469i			1.14287i
$489$	14.3112	+	24.3617i	0.647174	+	1.10167i
$490$		−	2.45082i		−	0.110717i
$491$	−5.41086			−0.244189			−0.122094	−	0.992519i	$-0.538961\pi$
$491$	−5.41086			−0.244189			−0.122094	+	0.992519i	$0.538961\pi$
$492$	−19.0108	−	32.3617i	−0.857071	−	1.45898i
$493$	−21.3025			−0.959416
$494$	−103.018			−4.63499
$495$	−6.86205	+	7.20502i	−0.308426	+	0.323842i
$496$	8.74708			0.392756
$497$	−8.09497			−0.363109
$498$	9.19152	+	15.6466i	0.411882	+	0.701140i
$499$	−33.6639			−1.50700			−0.753501	−	0.657447i	$-0.771636\pi$
$499$	−33.6639			−1.50700			−0.753501	+	0.657447i	$0.771636\pi$
$500$			4.00650i			0.179176i
$501$	1.17109	+	1.99352i	0.0523203	+	0.0890641i
$502$		−	50.1415i		−	2.23792i
$503$	−6.76013			−0.301419			−0.150710	−	0.988578i	$-0.548156\pi$
$503$	−6.76013			−0.301419			−0.150710	+	0.988578i	$0.548156\pi$
$504$	−12.8860	−	7.18288i	−0.573987	−	0.319951i
$505$			3.84761i			0.171216i
$506$	−25.3738	−	6.54662i	−1.12800	−	0.291033i
$507$	−28.6998	−	48.8552i	−1.27460	−	2.16974i
$508$			34.7385i			1.54127i
$509$			15.9644i			0.707612i	0.935319	+	0.353806i	$0.115113\pi$
$509$			15.9644i			0.707612i	−0.935319	+	0.353806i	$0.884887\pi$
$510$	19.1100	−	11.2261i	0.846206	−	0.497101i
$511$	10.2197			0.452094
$512$	39.4667			1.74420
$513$	0.730535	+	32.2961i	0.0322539	+	1.42591i
$514$			12.5502i			0.553567i
$515$		−	8.87110i		−	0.390908i
$516$	−41.6667	+	24.4769i	−1.83427	+	1.07754i
$517$	25.2684	+	6.51941i	1.11130	+	0.286723i
$518$		−	19.6910i		−	0.865172i
$519$	−10.8751	−	18.5125i	−0.477363	−	0.812607i
$520$	−33.2485			−1.45804
$521$			8.99231i			0.393960i	0.980407	+	0.196980i	$0.0631134\pi$
$521$			8.99231i			0.393960i	−0.980407	+	0.196980i	$0.936887\pi$
$522$	14.6058	−	26.2025i	0.639277	−	1.14685i
$523$		−	16.4392i		−	0.718838i	−0.933176	−	0.359419i	$-0.882975\pi$
$523$		−	16.4392i		−	0.718838i	0.933176	−	0.359419i	$-0.117025\pi$
$524$	−5.07609			−0.221750
$525$	−1.49343	+	0.877309i	−0.0651786	+	0.0382889i
$526$	43.0314			1.87626
$527$	−11.3071			−0.492544
$528$	−22.3077	+	6.38176i	−0.970816	+	0.277730i
$529$	12.6069			0.548126
$530$	−18.4498			−0.801407
$531$	12.8517	+	7.16381i	0.557718	+	0.310883i
$532$	−24.9083			−1.07991
$533$		−	36.5682i		−	1.58395i
$534$	26.7208	−	15.6970i	1.15632	−	0.679277i
$535$			11.0644i			0.478358i
$536$	52.8820			2.28415
$537$	−32.8231	+	19.2818i	−1.41642	+	0.832071i
$538$			40.9624i			1.76601i
$539$	0.828579	−	3.21146i	0.0356894	−	0.138327i
$540$	0.470790	+	20.8131i	0.0202596	+	0.895652i
$541$			7.78365i			0.334645i	0.985902	+	0.167323i	$0.0535121\pi$
$541$			7.78365i			0.334645i	−0.985902	+	0.167323i	$0.946488\pi$
$542$		−	72.7896i		−	3.12658i
$543$	17.6841	+	30.1033i	0.758896	+	1.29186i
$544$	0.333272			0.0142889
$545$	−15.3821			−0.658895
$546$	−14.5373	−	24.7467i	−0.622141	−	1.05906i
$547$			3.68679i			0.157636i	0.996889	+	0.0788179i	$0.0251146\pi$
$547$			3.68679i			0.157636i	−0.996889	+	0.0788179i	$0.974885\pi$
$548$			31.7267i			1.35530i
$549$	13.4532	+	7.49905i	0.574167	+	0.320052i
$550$	−2.03069	+	7.87069i	−0.0865891	+	0.335607i
$551$		−	25.3655i		−	1.08061i
$552$	−23.6759	+	13.9083i	−1.00772	+	0.591978i
$553$	10.3009			0.438040
$554$			24.8715i			1.05669i
$555$	−11.9989	+	7.04870i	−0.509325	+	0.299201i
$556$		−	33.8243i		−	1.43447i
$557$	−17.6433			−0.747572			−0.373786	−	0.927515i	$-0.621941\pi$
$557$	−17.6433			−0.747572			−0.373786	+	0.927515i	$0.621941\pi$
$558$	7.75254	−	13.9079i	0.328191	−	0.588769i
$559$	−47.0827			−1.99138
$560$	−4.03905			−0.170681
$561$	28.8364	−	8.24950i	1.21747	−	0.348294i
$562$	−24.1360			−1.01812
$563$	−23.7291			−1.00006			−0.500031	−	0.866007i	$-0.666678\pi$
$563$	−23.7291			−1.00006			−0.500031	+	0.866007i	$0.666678\pi$
$564$	47.0787	−	27.6562i	1.98237	−	1.16454i
$565$	−2.90261			−0.122114
$566$		−	25.4711i		−	1.07063i
$567$	−7.65501	+	4.73295i	−0.321480	+	0.198765i
$568$			39.8075i			1.67029i
$569$	9.02479			0.378339			0.189169	−	0.981944i	$-0.439420\pi$
$569$	9.02479			0.378339			0.189169	+	0.981944i	$0.439420\pi$
$570$	13.3673	+	22.7549i	0.559893	+	0.953097i
$571$			46.3533i			1.93983i	0.243451	+	0.969913i	$0.421721\pi$
$571$			46.3533i			1.93983i	−0.243451	+	0.969913i	$0.578279\pi$
$572$	−86.9940	−	22.4451i	−3.63740	−	0.938476i
$573$	−20.1404	+	11.8314i	−0.841378	+	0.494264i
$574$		−	13.2554i		−	0.553269i
$575$			3.22384i			0.134443i
$576$	11.5708	−	20.7579i	0.482118	−	0.864911i
$577$	11.5321			0.480087			0.240044	−	0.970762i	$-0.422838\pi$
$577$	11.5321			0.480087			0.240044	+	0.970762i	$0.422838\pi$
$578$	−25.1463			−1.04595
$579$	29.1856	−	17.1450i	1.21291	−	0.712521i
$580$		−	16.3467i		−	0.678759i
$581$			4.27488i			0.177352i
$582$	33.3201	+	56.7203i	1.38116	+	2.35113i
$583$	−24.1759	−	6.23755i	−1.00126	−	0.258333i
$584$		−	50.2561i		−	2.07961i
$585$	−9.87577	+	17.7170i	−0.408313	+	0.732506i
$586$	−73.8719			−3.05162
$587$		−	37.9265i		−	1.56540i	−0.622402	−	0.782698i	$-0.713843\pi$
$587$		−	37.9265i		−	1.56540i	0.622402	−	0.782698i	$-0.286157\pi$
$588$	−3.51494	−	5.98342i	−0.144954	−	0.246752i
$589$		−	13.4637i		−	0.554761i
$590$	12.0200			0.494857
$591$	−3.41420	−	5.81195i	−0.140442	−	0.239071i
$592$	−32.4515			−1.33375
$593$	38.3152			1.57342			0.786708	−	0.617326i	$-0.211784\pi$
$593$	38.3152			1.57342			0.786708	+	0.617326i	$0.211784\pi$
$594$	−9.62424	+	41.1255i	−0.394887	+	1.68740i
$595$	5.22115			0.214046
$596$	14.8603			0.608703
$597$	−13.6643	−	23.2606i	−0.559243	−	0.951991i
$598$	−53.4202			−2.18451
$599$			30.0699i			1.22862i	0.789064	+	0.614311i	$0.210566\pi$
$599$			30.0699i			1.22862i	−0.789064	+	0.614311i	$0.789434\pi$
$600$	4.31422	+	7.34403i	0.176127	+	0.299819i
$601$			5.54057i			0.226004i	0.993595	+	0.113002i	$0.0360467\pi$
$601$			5.54057i			0.226004i	−0.993595	+	0.113002i	$0.963953\pi$
$602$	−17.0667			−0.695587
$603$	15.7075	−	28.1789i	0.639658	−	1.14753i
$604$			15.3893i			0.626181i
$605$	−5.32189	+	9.62691i	−0.216366	+	0.391390i
$606$	8.27282	+	14.0827i	0.336060	+	0.572070i
$607$		−	21.8600i		−	0.887270i	−0.896208	−	0.443635i	$-0.853689\pi$
$607$		−	21.8600i		−	0.887270i	0.896208	−	0.443635i	$-0.146311\pi$
$608$			0.396837i			0.0160939i
$609$	6.09325	−	3.57945i	0.246911	−	0.145047i
$610$	12.5825			0.509452
$611$	53.1982			2.15217
$612$	30.5548	−	54.8149i	1.23511	−	2.21576i
$613$			18.7017i			0.755353i	0.925938	+	0.377677i	$0.123277\pi$
$613$			18.7017i			0.755353i	−0.925938	+	0.377677i	$0.876723\pi$
$614$			10.3516i			0.417756i
$615$	−8.07730	+	4.74498i	−0.325708	+	0.191336i
$616$	−15.7925	−	4.07459i	−0.636300	−	0.164170i
$617$			26.5714i			1.06973i	0.844939	+	0.534863i	$0.179637\pi$
$617$			26.5714i			1.06973i	−0.844939	+	0.534863i	$0.820363\pi$
$618$	−19.0740	−	32.4693i	−0.767267	−	1.30611i
$619$	44.2269			1.77763			0.888815	−	0.458266i	$-0.151529\pi$
$619$	44.2269			1.77763			0.888815	+	0.458266i	$0.151529\pi$
$620$		−	8.67660i		−	0.348461i
$621$	0.378822	+	16.7473i	0.0152016	+	0.672044i
$622$		−	22.6924i		−	0.909882i
$623$	7.30053			0.292489
$624$	−40.7836	+	23.9582i	−1.63265	+	0.959094i
$625$	1.00000			0.0400000
$626$	39.6841			1.58609
$627$	9.82292	+	34.3364i	0.392290	+	1.37126i
$628$	−17.0286			−0.679514
$629$	41.9491			1.67262
$630$	−3.57981	+	6.42211i	−0.142623	+	0.255863i
$631$	−10.4485			−0.415947			−0.207974	−	0.978134i	$-0.566687\pi$
$631$	−10.4485			−0.415947			−0.207974	+	0.978134i	$0.566687\pi$
$632$		−	50.6554i		−	2.01496i
$633$	14.7454	−	8.66215i	0.586079	−	0.344290i
$634$		−	33.4614i		−	1.32892i
$635$	8.67052			0.344079
$636$	−45.0433	+	26.4605i	−1.78608	+	1.04923i
$637$		−	6.76117i		−	0.267887i
$638$	8.28531	−	32.1127i	0.328019	−	1.27136i
$639$	21.2120	+	11.8240i	0.839135	+	0.467750i
$640$		−	19.5422i		−	0.772473i
$641$			11.1207i			0.439241i	0.975585	+	0.219620i	$0.0704819\pi$
$641$			11.1207i			0.439241i	−0.975585	+	0.219620i	$0.929518\pi$
$642$	23.7899	+	40.4972i	0.938913	+	1.59830i
$643$	16.6563			0.656859			0.328430	−	0.944528i	$-0.393481\pi$
$643$	16.6563			0.656859			0.328430	+	0.944528i	$0.393481\pi$
$644$	−12.9163			−0.508973
$645$	6.10930	+	10.3998i	0.240553	+	0.409490i
$646$		−	79.5529i		−	3.12997i
$647$			11.5359i			0.453521i	0.973951	+	0.226761i	$0.0728135\pi$
$647$			11.5359i			0.453521i	−0.973951	+	0.226761i	$0.927186\pi$
$648$	23.2746	+	37.6440i	0.914312	+	1.47880i
$649$	15.7506	+	4.06377i	0.618265	+	0.159517i
$650$			16.5704i			0.649944i
$651$	3.23421	−	1.89993i	0.126759	−	0.0744640i
$652$	65.3564			2.55955
$653$		−	42.2616i		−	1.65383i	−0.562330	−	0.826913i	$-0.690095\pi$
$653$		−	42.2616i		−	1.65383i	0.562330	−	0.826913i	$-0.309905\pi$
$654$	−56.3002	+	33.0733i	−2.20151	+	1.29327i
$655$			1.26696i			0.0495044i
$656$	−21.8454			−0.852921
$657$	−26.7797	−	14.9275i	−1.04478	−	0.582378i
$658$	19.2835			0.751749
$659$	9.42440			0.367122			0.183561	−	0.983008i	$-0.441237\pi$
$659$	9.42440			0.367122			0.183561	+	0.983008i	$0.441237\pi$
$660$	6.33034	+	22.1279i	0.246408	+	0.861328i
$661$	41.7218			1.62279			0.811395	−	0.584498i	$-0.198709\pi$
$661$	41.7218			1.62279			0.811395	+	0.584498i	$0.198709\pi$
$662$	−38.7242			−1.50506
$663$	52.7197	−	30.9700i	2.04746	−	1.20277i
$664$	21.0220			0.815812
$665$			6.21697i			0.241084i
$666$	−28.7618	+	51.5982i	−1.11450	+	1.99939i
$667$		−	13.1534i		−	0.509301i
$668$	5.34813			0.206925
$669$	−7.96794	−	13.5637i	−0.308058	−	0.524403i
$670$		−	26.3553i		−	1.01820i
$671$	16.4877	+	4.25394i	0.636500	+	0.164222i
$672$	−0.0953273	+	0.0559996i	−0.00367733	+	0.00216023i
$673$			18.4153i			0.709858i	0.934893	+	0.354929i	$0.115495\pi$
$673$			18.4153i			0.709858i	−0.934893	+	0.354929i	$0.884505\pi$
$674$			37.8405i			1.45756i
$675$	5.19482	−	0.117506i	0.199949	−	0.00452283i
$676$	−131.066			−5.04102
$677$	7.40444			0.284576			0.142288	−	0.989825i	$-0.454554\pi$
$677$	7.40444			0.284576			0.142288	+	0.989825i	$0.454554\pi$
$678$	−10.6239	+	6.24096i	−0.408008	+	0.239683i
$679$			15.4968i			0.594714i
$680$		−	25.6753i		−	0.984604i
$681$	16.3237	+	27.7876i	0.625525	+	1.06482i
$682$	4.39773	−	17.0450i	0.168398	−	0.652687i
$683$		−	24.9152i		−	0.953352i	−0.879079	−	0.476676i	$-0.841841\pi$
$683$		−	24.9152i		−	0.953352i	0.879079	−	0.476676i	$-0.158159\pi$
$684$	65.2696	+	36.3825i	2.49565	+	1.39112i
$685$	7.91882			0.302562
$686$		−	2.45082i		−	0.0935726i
$687$	−0.430867	−	0.733459i	−0.0164386	−	0.0279832i
$688$			28.1266i			1.07232i
$689$	−50.8982			−1.93907
$690$	6.93164	+	11.7996i	0.263883	+	0.449204i
$691$	41.5886			1.58210			0.791052	−	0.611749i	$-0.209534\pi$
$691$	41.5886			1.58210			0.791052	+	0.611749i	$0.209534\pi$
$692$	−49.6644			−1.88796
$693$	−6.86205	+	7.20502i	−0.260668	+	0.273696i
$694$	−2.33397			−0.0885964
$695$	−8.44234			−0.320236
$696$	−17.6022	−	29.9639i	−0.667210	−	1.13578i
$697$	28.2389			1.06962
$698$			26.7399i			1.01212i
$699$	−3.53572	−	6.01880i	−0.133733	−	0.227652i
$700$			4.00650i			0.151431i
$701$	−14.5839			−0.550825			−0.275412	−	0.961326i	$-0.588814\pi$
$701$	−14.5839			−0.550825			−0.275412	+	0.961326i	$0.588814\pi$
$702$	1.94713	+	86.0803i	0.0734896	+	3.24889i
$703$			49.9500i			1.88390i
$704$	6.56371	−	25.4401i	0.247379	−	0.958808i
$705$	−6.90283	−	11.7506i	−0.259976	−	0.442552i
$706$			42.7242i			1.60795i
$707$			3.84761i			0.144704i
$708$	29.3457	−	17.2390i	1.10288	−	0.647882i
$709$	−18.9610			−0.712096			−0.356048	−	0.934468i	$-0.615876\pi$
$709$	−18.9610			−0.712096			−0.356048	+	0.934468i	$0.615876\pi$
$710$	19.8393			0.744555
$711$	−26.9925	−	15.0461i	−1.01230	−	0.564274i
$712$		−	35.9008i		−	1.34544i
$713$		−	6.98164i		−	0.261464i
$714$	19.1100	−	11.2261i	0.715175	−	0.420127i
$715$	−5.60216	+	21.7132i	−0.209509	+	0.812028i
$716$			88.0563i			3.29082i
$717$	−22.4763	−	38.2610i	−0.839392	−	1.42888i
$718$	−10.6851			−0.398763
$719$		−	14.9636i		−	0.558049i	−0.960284	−	0.279025i	$-0.909989\pi$
$719$		−	14.9636i		−	0.558049i	0.960284	−	0.279025i	$-0.0900111\pi$
$720$	10.5839	+	5.89967i	0.394439	+	0.219868i
$721$		−	8.87110i		−	0.330377i
$722$	48.1604			1.79235
$723$	−30.3893	+	17.8521i	−1.13019	+	0.663926i
$724$	80.7598			3.00141
$725$	−4.08004			−0.151529
$726$	1.22029	+	46.6784i	0.0452893	+	1.73240i
$727$	−31.8033			−1.17952			−0.589760	−	0.807579i	$-0.700778\pi$
$727$	−31.8033			−1.17952			−0.589760	+	0.807579i	$0.700778\pi$
$728$	−33.2485			−1.23227
$729$	26.9724	−	1.22085i	0.998977	−	0.0452167i
$730$	−25.0467			−0.927019
$731$		−	36.3584i		−	1.34476i
$732$	30.7190	−	18.0458i	1.13541	−	0.666991i
$733$		−	4.15219i		−	0.153364i	−0.997056	−	0.0766822i	$-0.975567\pi$
$733$		−	4.15219i		−	0.153364i	0.997056	−	0.0766822i	$-0.0244327\pi$
$734$	−53.7256			−1.98305
$735$	−1.49343	+	0.877309i	−0.0550859	+	0.0323600i
$736$			0.205781i			0.00758519i
$737$	8.91028	−	34.5350i	0.328214	−	1.27211i
$738$	−19.3616	+	34.7344i	−0.712711	+	1.27859i
$739$			18.8605i			0.693796i	0.937903	+	0.346898i	$0.112765\pi$
$739$			18.8605i			0.693796i	−0.937903	+	0.346898i	$0.887235\pi$
$740$			32.1901i			1.18333i
$741$	36.8768	+	62.7748i	1.35470	+	2.30609i
$742$	−18.4498			−0.677313
$743$	−29.8260			−1.09421			−0.547105	−	0.837064i	$-0.684270\pi$
$743$	−29.8260			−1.09421			−0.547105	+	0.837064i	$0.684270\pi$
$744$	−9.34301	−	15.9045i	−0.342531	−	0.583086i
$745$		−	3.70906i		−	0.135889i
$746$			14.2033i			0.520021i
$747$	6.24414	−	11.2019i	0.228461	−	0.409855i
$748$	17.3327	−	67.1790i	0.633745	−	2.45631i
$749$			11.0644i			0.404286i
$750$	3.66012	−	2.15012i	0.133649	−	0.0785114i
$751$	0.946690			0.0345452			0.0172726	−	0.999851i	$-0.494502\pi$
$751$	0.946690			0.0345452			0.0172726	+	0.999851i	$0.494502\pi$
$752$		−	31.7800i		−	1.15890i
$753$	−30.5542	+	17.9489i	−1.11346	+	0.654096i
$754$		−	67.6079i		−	2.46213i
$755$	3.84108			0.139791
$756$	0.470790	+	20.8131i	0.0171225	+	0.756964i
$757$	−14.6974			−0.534188			−0.267094	−	0.963671i	$-0.586063\pi$
$757$	−14.6974			−0.534188			−0.267094	+	0.963671i	$0.586063\pi$
$758$	−62.5764			−2.27288
$759$	5.09371	+	17.8052i	0.184890	+	0.646290i
$760$	30.5724			1.10898
$761$	51.7603			1.87631			0.938155	−	0.346215i	$-0.112533\pi$
$761$	51.7603			1.87631			0.938155	+	0.346215i	$0.112533\pi$
$762$	31.7351	−	18.6427i	1.14964	−	0.675353i
$763$	−15.3821			−0.556868
$764$			54.0317i			1.95480i
$765$	−13.6815	−	7.62632i	−0.494655	−	0.275730i
$766$		−	65.3120i		−	2.35982i
$767$	33.1602			1.19735
$768$	−28.1186	−	47.8659i	−1.01464	−	1.72721i
$769$		−	13.4546i		−	0.485186i	−0.970128	−	0.242593i	$-0.922002\pi$
$769$		−	13.4546i		−	0.485186i	0.970128	−	0.242593i	$-0.0779980\pi$
$770$	−2.03069	+	7.87069i	−0.0731811	+	0.283640i
$771$	7.64761	−	4.49256i	0.275422	−	0.161795i
$772$		−	78.2978i		−	2.81800i
$773$		−	11.4201i		−	0.410753i	−0.978683	−	0.205376i	$-0.934158\pi$
$773$		−	11.4201i		−	0.410753i	0.978683	−	0.205376i	$-0.0658418\pi$
$774$	44.7215	+	24.9286i	1.60748	+	0.896041i
$775$	−2.16563			−0.0777917
$776$	76.2067			2.73566
$777$	−11.9989	+	7.04870i	−0.430458	+	0.252871i
$778$		−	91.2170i		−	3.27029i
$779$			33.6249i			1.20474i
$780$	23.7651	+	40.4550i	0.850927	+	1.44852i
$781$	25.9967	+	6.70732i	0.930233	+	0.240007i
$782$		−	41.2524i		−	1.47518i
$783$	−21.1951	+	0.479431i	−0.757451	+	0.0171335i
$784$	−4.03905			−0.144252
$785$			4.25023i			0.151697i
$786$	2.72413	+	4.63724i	0.0971664	+	0.165405i
$787$		−	18.4375i		−	0.657226i	−0.944465	−	0.328613i	$-0.893419\pi$
$787$		−	18.4375i		−	0.657226i	0.944465	−	0.328613i	$-0.106581\pi$
$788$	−15.5920			−0.555443
$789$	−15.4038	−	26.2216i	−0.548389	−	0.933513i
$790$	−25.2457			−0.898200
$791$	−2.90261			−0.103205
$792$	35.4311	+	33.7446i	1.25899	+	1.19906i
$793$	34.7120			1.23266
$794$	−16.0815			−0.570710
$795$	6.60439	+	11.2426i	0.234234	+	0.398732i
$796$	−62.4023			−2.21179
$797$		−	10.8354i		−	0.383810i	−0.981414	−	0.191905i	$-0.938533\pi$
$797$		−	10.8354i		−	0.383810i	0.981414	−	0.191905i	$-0.0614666\pi$
$798$	13.3673	+	22.7549i	0.473196	+	0.805514i
$799$			41.0810i			1.45334i
$800$	0.0638312			0.00225677
$801$	−19.1303	−	10.6636i	−0.675935	−	0.376779i
$802$		−	4.16620i		−	0.147114i
$803$	−32.8202	−	8.46784i	−1.15820	−	0.298824i
$804$	−37.7986	−	64.3439i	−1.33305	−	2.26923i
$805$			3.22384i			0.113625i
$806$		−	35.8853i		−	1.26401i
$807$	24.9608	−	14.6631i	0.878662	−	0.516167i
$808$	18.9208			0.665633
$809$	5.97274			0.209990			0.104995	−	0.994473i	$-0.466517\pi$
$809$	5.97274			0.209990			0.104995	+	0.994473i	$0.466517\pi$
$810$	18.7610	−	11.5996i	0.659195	−	0.407568i
$811$		−	29.1820i		−	1.02472i	−0.858772	−	0.512359i	$-0.828772\pi$
$811$		−	29.1820i		−	1.02472i	0.858772	−	0.512359i	$-0.171228\pi$
$812$		−	16.3467i		−	0.573656i
$813$	−44.3551	+	26.0562i	−1.55560	+	0.913831i
$814$	−16.3155	+	63.2367i	−0.571859	+	2.21645i
$815$		−	16.3126i		−	0.571405i
$816$	−18.5011	−	31.4941i	−0.647668	−	1.10251i
$817$	43.2930			1.51463
$818$			63.2201i			2.21044i
$819$	−9.87577	+	17.7170i	−0.345087	+	0.619080i
$820$			21.6694i			0.756729i
$821$	6.98359			0.243729			0.121865	−	0.992547i	$-0.461113\pi$
$821$	6.98359			0.243729			0.121865	+	0.992547i	$0.461113\pi$
$822$	28.9838	−	17.0264i	1.01093	−	0.593865i
$823$	−37.2635			−1.29892			−0.649461	−	0.760395i	$-0.725006\pi$
$823$	−37.2635			−1.29892			−0.649461	+	0.760395i	$0.725006\pi$
$824$	−43.6242			−1.51972
$825$	5.52300	−	1.58002i	0.192286	−	0.0550091i
$826$	12.0200			0.418231
$827$	30.8523			1.07284			0.536421	−	0.843951i	$-0.319776\pi$
$827$	30.8523			1.07284			0.536421	+	0.843951i	$0.319776\pi$
$828$	33.8458	+	18.8663i	1.17622	+	0.655649i
$829$	−45.1467			−1.56801			−0.784005	−	0.620754i	$-0.786826\pi$
$829$	−45.1467			−1.56801			−0.784005	+	0.620754i	$0.786826\pi$
$830$		−	10.4769i		−	0.363660i
$831$	15.1557	−	8.90313i	0.525744	−	0.308846i
$832$		−	53.5597i		−	1.85685i
$833$	5.22115			0.180902
$834$	−30.9000	+	18.1521i	−1.06998	+	0.628555i
$835$		−	1.33486i		−	0.0461949i
$836$	79.9920	+	20.6385i	2.76658	+	0.713797i
$837$	−11.2501	+	0.254476i	−0.388859	+	0.00879596i
$838$			36.7011i			1.26782i
$839$		−	32.7880i		−	1.13197i	−0.824417	−	0.565983i	$-0.808497\pi$
$839$		−	32.7880i		−	1.13197i	0.824417	−	0.565983i	$-0.191503\pi$
$840$	4.31422	+	7.34403i	0.148855	+	0.253393i
$841$	−12.3533			−0.425975
$842$	81.1152			2.79541
$843$	8.63988	+	14.7075i	0.297573	+	0.506554i
$844$		−	39.5584i		−	1.36166i
$845$			32.7135i			1.12538i
$846$	−50.5304	−	28.1666i	−1.73727	−	0.968387i
$847$	−5.32189	+	9.62691i	−0.182862	+	0.330785i
$848$			30.4060i			1.04415i
$849$	−15.5211	+	9.11780i	−0.532682	+	0.312922i
$850$	−12.7961			−0.438902
$851$			25.9018i			0.887901i
$852$	48.4356	−	28.4533i	1.65938	−	0.974795i
$853$			5.83489i			0.199783i	0.994998	+	0.0998914i	$0.0318495\pi$
$853$			5.83489i			0.199783i	−0.994998	+	0.0998914i	$0.968150\pi$
$854$	12.5825			0.430566
$855$	9.08088	−	16.2909i	0.310559	−	0.557138i
$856$	54.4101			1.85970
$857$	9.05521			0.309320			0.154660	−	0.987968i	$-0.450572\pi$
$857$	9.05521			0.309320			0.154660	+	0.987968i	$0.450572\pi$
$858$	26.1815	+	91.5183i	0.893821	+	3.12438i
$859$	21.7802			0.743131			0.371566	−	0.928407i	$-0.378821\pi$
$859$	21.7802			0.743131			0.371566	+	0.928407i	$0.378821\pi$
$860$	27.9000			0.951382
$861$	−8.07730	+	4.74498i	−0.275274	+	0.161708i
$862$	−49.4145			−1.68306
$863$			18.0628i			0.614866i	0.951570	+	0.307433i	$0.0994701\pi$
$863$			18.0628i			0.614866i	−0.951570	+	0.307433i	$0.900530\pi$
$864$	0.331592	−	0.00750057i	0.0112810	−	0.000255175i
$865$			12.3959i			0.421475i
$866$	−83.1905			−2.82693
$867$	9.00154	+	15.3232i	0.305708	+	0.520402i
$868$		−	8.67660i		−	0.294503i
$869$	−33.0810	−	8.53512i	−1.12219	−	0.289534i
$870$	−14.9334	+	8.77259i	−0.506291	+	0.297419i
$871$		−	72.7076i		−	2.46360i
$872$			75.6423i			2.56157i
$873$	22.6356	−	40.6078i	0.766099	−	1.37437i
$874$	49.1205			1.66153
$875$	1.00000			0.0338062
$876$	−61.1489	+	35.9217i	−2.06603	+	1.21368i
$877$			31.8025i			1.07389i	0.843616	+	0.536947i	$0.180422\pi$
$877$			31.8025i			1.07389i	−0.843616	+	0.536947i	$0.819578\pi$
$878$		−	83.4438i		−	2.81609i
$879$	26.4436	+	45.0146i	0.891921	+	1.51830i
$880$	12.9712	+	3.34667i	0.437260	+	0.112816i
$881$			4.72317i			0.159128i	0.996830	+	0.0795639i	$0.0253528\pi$
$881$			4.72317i			0.159128i	−0.996830	+	0.0795639i	$0.974647\pi$
$882$	−3.57981	+	6.42211i	−0.120538	+	0.216244i
$883$	3.61235			0.121565			0.0607826	−	0.998151i	$-0.480640\pi$
$883$	3.61235			0.121565			0.0607826	+	0.998151i	$0.480640\pi$
$884$		−	141.434i		−	4.75693i
$885$	−4.30276	−	7.32453i	−0.144636	−	0.246211i
$886$			10.1585i			0.341283i
$887$	−21.2949			−0.715013			−0.357507	−	0.933911i	$-0.616373\pi$
$887$	−21.2949			−0.715013			−0.357507	+	0.933911i	$0.616373\pi$
$888$	34.6624	+	59.0053i	1.16320	+	1.98009i
$889$	8.67052			0.290800
$890$	−17.8922			−0.599750
$891$	28.5054	−	8.85689i	0.954965	−	0.296717i
$892$	−36.3880			−1.21836
$893$	−48.9163			−1.63692
$894$	−7.97493	−	13.5756i	−0.266721	−	0.454036i
$895$	21.9783			0.734655
$896$		−	19.5422i		−	0.652858i
$897$	19.1226	+	32.5521i	0.638486	+	1.08688i
$898$		−	64.1680i		−	2.14131i
$899$	8.83586			0.294692
$900$	5.85213	−	10.4986i	0.195071	−	0.349954i
$901$		−	39.3049i		−	1.30944i
$902$	−10.9831	+	42.5691i	−0.365698	+	1.41740i
$903$	6.10930	+	10.3998i	0.203305	+	0.346082i
$904$			14.2738i			0.474738i
$905$		−	20.1572i		−	0.670048i
$906$	14.0588	−	8.25879i	0.467073	−	0.274380i
$907$	47.1038			1.56406			0.782028	−	0.623243i	$-0.214185\pi$
$907$	47.1038			1.56406			0.782028	+	0.623243i	$0.214185\pi$
$908$	74.5472			2.47393
$909$	5.62004	−	10.0823i	0.186405	−	0.334407i
$910$			16.5704i			0.549303i
$911$			11.6892i			0.387280i	0.981073	+	0.193640i	$0.0620293\pi$
$911$			11.6892i			0.387280i	−0.981073	+	0.193640i	$0.937971\pi$
$912$	37.5010	−	22.0298i	1.24178	−	0.729479i
$913$	3.54207	−	13.7286i	0.117226	−	0.454350i
$914$		−	31.4266i		−	1.03950i
$915$	−4.50412	−	7.66729i	−0.148902	−	0.253473i
$916$	−1.96769			−0.0650143
$917$			1.26696i			0.0418388i
$918$	−66.4734	+	1.50362i	−2.19395	+	0.0496269i
$919$			31.1086i			1.02618i	0.858335	+	0.513090i	$0.171499\pi$
$919$			31.1086i			1.02618i	−0.858335	+	0.513090i	$0.828501\pi$
$920$	15.8534			0.522672
$921$	6.30783	−	3.70551i	0.207850	−	0.122101i
$922$	40.3084			1.32749
$923$	54.7315			1.80151
$924$	6.33034	+	22.1279i	0.208253	+	0.727955i
$925$	8.03446			0.264171
$926$	42.2514			1.38847
$927$	−12.9577	+	23.2458i	−0.425585	+	0.763492i
$928$	−0.260434			−0.00854915
$929$		−	30.9160i		−	1.01432i	−0.861852	−	0.507160i	$-0.830695\pi$
$929$		−	30.9160i		−	1.01432i	0.861852	−	0.507160i	$-0.169305\pi$
$930$	−7.92647	+	4.65637i	−0.259919	+	0.152688i
$931$			6.21697i			0.203753i
$932$	−16.1470			−0.528911
$933$	−13.8278	+	8.12311i	−0.452703	+	0.265939i
$934$		−	87.4206i		−	2.86049i
$935$	−16.7675	−	4.32613i	−0.548356	−	0.141480i
$936$	87.1242	+	48.5647i	2.84775	+	1.58739i
$937$		−	12.3089i		−	0.402115i	−0.979579	−	0.201057i	$-0.935562\pi$
$937$		−	12.3089i		−	0.402115i	0.979579	−	0.201057i	$-0.0644378\pi$
$938$		−	26.3553i		−	0.860532i
$939$	−14.2055	−	24.1819i	−0.463580	−	0.789146i
$940$	−31.5239			−1.02820
$941$	−42.6841			−1.39146			−0.695731	−	0.718303i	$-0.744919\pi$
$941$	−42.6841			−1.39146			−0.695731	+	0.718303i	$0.744919\pi$
$942$	9.13852	+	15.5564i	0.297749	+	0.506854i
$943$			17.4363i			0.567804i
$944$		−	19.8095i		−	0.644745i
$945$	5.19482	−	0.117506i	0.168988	−	0.00382249i
$946$	54.8090	+	14.1411i	1.78199	+	0.459767i
$947$			19.7327i			0.641228i	0.947210	+	0.320614i	$0.103889\pi$
$947$			19.7327i			0.641228i	−0.947210	+	0.320614i	$0.896111\pi$
$948$	−61.6347	+	36.2071i	−2.00180	+	1.17595i
$949$	−69.0973			−2.24299
$950$		−	15.2367i		−	0.494343i
$951$	−20.3900	+	11.9780i	−0.661192	+	0.388415i
$952$		−	25.6753i		−	0.832142i
$953$	−1.70876			−0.0553521			−0.0276761	−	0.999617i	$-0.508811\pi$
$953$	−1.70876			−0.0553521			−0.0276761	+	0.999617i	$0.508811\pi$
$954$	48.3457	+	26.9488i	1.56525	+	0.872501i
$955$	13.4860			0.436397
$956$	−102.645			−3.31977
$957$	−22.5341	+	6.44653i	−0.728423	+	0.208387i
$958$	−36.1591			−1.16825
$959$	7.91882			0.255712
$960$	−11.8304	+	6.94974i	−0.381825	+	0.224302i
$961$	−26.3100			−0.848711
$962$			133.134i			4.29242i
$963$	16.1614	−	28.9932i	0.520793	−	0.934294i
$964$			81.5270i			2.62581i
$965$	−19.5427			−0.629102
$966$	6.93164	+	11.7996i	0.223022	+	0.379647i
$967$		−	26.7536i		−	0.860338i	−0.902748	−	0.430169i	$-0.858454\pi$
$967$		−	26.7536i		−	0.860338i	0.902748	−	0.430169i	$-0.141546\pi$
$968$	47.3410	+	26.1707i	1.52160	+	0.841159i
$969$	−48.4763	+	28.4772i	−1.55728	+	0.914820i
$970$		−	37.9799i		−	1.21946i
$971$		−	36.5926i		−	1.17431i	−0.809474	−	0.587156i	$-0.800247\pi$
$971$		−	36.5926i		−	1.17431i	0.809474	−	0.587156i	$-0.199753\pi$
$972$	29.1671	−	55.2261i	0.935536	−	1.77138i
$973$	−8.44234			−0.270649
$974$	−86.2174			−2.76259
$975$	10.0973	−	5.93164i	0.323373	−	0.189964i
$976$		−	20.7365i		−	0.663761i
$977$		−	17.3345i		−	0.554581i	−0.960786	−	0.277291i	$-0.910564\pi$
$977$		−	17.3345i		−	0.554581i	0.960786	−	0.277291i	$-0.0894364\pi$
$978$	−35.0741	−	59.7060i	−1.12154	−	1.90919i
$979$	−23.4453	−	6.04906i	−0.749316	−	0.193329i
$980$			4.00650i			0.127983i
$981$	40.3071	+	22.4679i	1.28691	+	0.717346i
$982$	13.2610			0.423176
$983$			24.9667i			0.796313i	0.917317	+	0.398157i	$0.130350\pi$
$983$			24.9667i			0.796313i	−0.917317	+	0.398157i	$0.869650\pi$
$984$	23.3337	+	39.7207i	0.743852	+	1.26625i
$985$			3.89168i			0.123999i
$986$	52.2085			1.66266
$987$	−6.90283	−	11.7506i	−0.219720	−	0.374025i
$988$	168.409			5.35782
$989$	22.4498			0.713861
$990$	16.8176	−	17.6582i	0.534499	−	0.561214i
$991$	−11.2435			−0.357162			−0.178581	−	0.983925i	$-0.557151\pi$
$991$	−11.2435			−0.357162			−0.178581	+	0.983925i	$0.557151\pi$
$992$	−0.138235			−0.00438896
$993$	13.8619	+	23.5970i	0.439895	+	0.748827i
$994$	19.8393			0.629264
$995$			15.5753i			0.493769i
$996$	−15.0259	−	25.5784i	−0.476115	−	0.810483i
$997$			50.2675i			1.59199i	0.605305	+	0.795994i	$0.293051\pi$
$997$			50.2675i			1.59199i	−0.605305	+	0.795994i	$0.706949\pi$
$998$	82.5040			2.61162
$999$	41.7376	−	0.944101i	1.32052	−	0.0298700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.5	yes	40
3.2	odd	2		1155.2.l.e.1121.36	yes	40
11.10	odd	2		1155.2.l.e.1121.35	✓	40
33.32	even	2	inner	1155.2.l.f.1121.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.35	✓	40	11.10	odd	2
1155.2.l.e.1121.36	yes	40	3.2	odd	2
1155.2.l.f.1121.5	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.6	yes	40	33.32	even	2	inner

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.45082 q^{2} +(0.877309 + 1.49343i) q^{3} +4.00650 q^{4} -1.00000i q^{5} +(-2.15012 - 3.66012i) q^{6} -1.00000i q^{7} -4.91756 q^{8} +(-1.46066 + 2.62040i) q^{9} +O(q^{10})\)	\(q-2.45082 q^{2} +(0.877309 + 1.49343i) q^{3} +4.00650 q^{4} -1.00000i q^{5} +(-2.15012 - 3.66012i) q^{6} -1.00000i q^{7} -4.91756 q^{8} +(-1.46066 + 2.62040i) q^{9} +2.45082i q^{10} +(-0.828579 + 3.21146i) q^{11} +(3.51494 + 5.98342i) q^{12} +6.76117i q^{13} +2.45082i q^{14} +(1.49343 - 0.877309i) q^{15} +4.03905 q^{16} -5.22115 q^{17} +(3.57981 - 6.42211i) q^{18} -6.21697i q^{19} -4.00650i q^{20} +(1.49343 - 0.877309i) q^{21} +(2.03069 - 7.87069i) q^{22} -3.22384i q^{23} +(-4.31422 - 7.34403i) q^{24} -1.00000 q^{25} -16.5704i q^{26} +(-5.19482 + 0.117506i) q^{27} -4.00650i q^{28} +4.08004 q^{29} +(-3.66012 + 2.15012i) q^{30} +2.16563 q^{31} -0.0638312 q^{32} +(-5.52300 + 1.58002i) q^{33} +12.7961 q^{34} -1.00000 q^{35} +(-5.85213 + 10.4986i) q^{36} -8.03446 q^{37} +15.2367i q^{38} +(-10.0973 + 5.93164i) q^{39} +4.91756i q^{40} -5.40856 q^{41} +(-3.66012 + 2.15012i) q^{42} +6.96368i q^{43} +(-3.31970 + 12.8667i) q^{44} +(2.62040 + 1.46066i) q^{45} +7.90103i q^{46} -7.86819i q^{47} +(3.54349 + 6.03203i) q^{48} -1.00000 q^{49} +2.45082 q^{50} +(-4.58056 - 7.79741i) q^{51} +27.0886i q^{52} +7.52801i q^{53} +(12.7316 - 0.287987i) q^{54} +(3.21146 + 0.828579i) q^{55} +4.91756i q^{56} +(9.28461 - 5.45421i) q^{57} -9.99943 q^{58} -4.90450i q^{59} +(5.98342 - 3.51494i) q^{60} -5.13402i q^{61} -5.30756 q^{62} +(2.62040 + 1.46066i) q^{63} -7.92165 q^{64} +6.76117 q^{65} +(13.5359 - 3.87233i) q^{66} -10.7537 q^{67} -20.9185 q^{68} +(4.81457 - 2.82830i) q^{69} +2.45082 q^{70} -8.09497i q^{71} +(7.18288 - 12.8860i) q^{72} +10.2197i q^{73} +19.6910 q^{74} +(-0.877309 - 1.49343i) q^{75} -24.9083i q^{76} +(3.21146 + 0.828579i) q^{77} +(24.7467 - 14.5373i) q^{78} +10.3009i q^{79} -4.03905i q^{80} +(-4.73295 - 7.65501i) q^{81} +13.2554 q^{82} -4.27488 q^{83} +(5.98342 - 3.51494i) q^{84} +5.22115i q^{85} -17.0667i q^{86} +(3.57945 + 6.09325i) q^{87} +(4.07459 - 15.7925i) q^{88} +7.30053i q^{89} +(-6.42211 - 3.57981i) q^{90} +6.76117 q^{91} -12.9163i q^{92} +(1.89993 + 3.23421i) q^{93} +19.2835i q^{94} -6.21697 q^{95} +(-0.0559996 - 0.0953273i) q^{96} -15.4968 q^{97} +2.45082 q^{98} +(-7.20502 - 6.86205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

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