LMFDB - Embedded newform 966.2.f.c.461.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.16
Character	$\chi$	$=$	966.461
Dual form			966.2.f.c.461.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.55720 - 0.758370i) q^{3} -1.00000 q^{4} -2.55377 q^{5} +(0.758370 - 1.55720i) q^{6} +(0.900399 + 2.48783i) q^{7} -1.00000i q^{8} +(1.84975 + 2.36187i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.55720 - 0.758370i) q^{3} -1.00000 q^{4} -2.55377 q^{5} +(0.758370 - 1.55720i) q^{6} +(0.900399 + 2.48783i) q^{7} -1.00000i q^{8} +(1.84975 + 2.36187i) q^{9} -2.55377i q^{10} -6.10336i q^{11} +(1.55720 + 0.758370i) q^{12} -4.03112i q^{13} +(-2.48783 + 0.900399i) q^{14} +(3.97673 + 1.93670i) q^{15} +1.00000 q^{16} -1.51674 q^{17} +(-2.36187 + 1.84975i) q^{18} +4.48007i q^{19} +2.55377 q^{20} +(0.484591 - 4.55688i) q^{21} +6.10336 q^{22} +1.00000i q^{23} +(-0.758370 + 1.55720i) q^{24} +1.52174 q^{25} +4.03112 q^{26} +(-1.08926 - 5.08070i) q^{27} +(-0.900399 - 2.48783i) q^{28} +6.55121i q^{29} +(-1.93670 + 3.97673i) q^{30} +4.67703i q^{31} +1.00000i q^{32} +(-4.62860 + 9.50415i) q^{33} -1.51674i q^{34} +(-2.29941 - 6.35334i) q^{35} +(-1.84975 - 2.36187i) q^{36} +9.05297 q^{37} -4.48007 q^{38} +(-3.05708 + 6.27726i) q^{39} +2.55377i q^{40} +6.16375 q^{41} +(4.55688 + 0.484591i) q^{42} -3.13309 q^{43} +6.10336i q^{44} +(-4.72383 - 6.03167i) q^{45} -1.00000 q^{46} +0.328642 q^{47} +(-1.55720 - 0.758370i) q^{48} +(-5.37856 + 4.48007i) q^{49} +1.52174i q^{50} +(2.36187 + 1.15025i) q^{51} +4.03112i q^{52} +13.7776i q^{53} +(5.08070 - 1.08926i) q^{54} +15.5866i q^{55} +(2.48783 - 0.900399i) q^{56} +(3.39755 - 6.97637i) q^{57} -6.55121 q^{58} +13.6662 q^{59} +(-3.97673 - 1.93670i) q^{60} +3.68097i q^{61} -4.67703 q^{62} +(-4.21041 + 6.72848i) q^{63} -1.00000 q^{64} +10.2946i q^{65} +(-9.50415 - 4.62860i) q^{66} +6.92840 q^{67} +1.51674 q^{68} +(0.758370 - 1.55720i) q^{69} +(6.35334 - 2.29941i) q^{70} +11.8850i q^{71} +(2.36187 - 1.84975i) q^{72} -6.01110i q^{73} +9.05297i q^{74} +(-2.36965 - 1.15404i) q^{75} -4.48007i q^{76} +(15.1841 - 5.49546i) q^{77} +(-6.27726 - 3.05708i) q^{78} -4.13077 q^{79} -2.55377 q^{80} +(-2.15685 + 8.73773i) q^{81} +6.16375i q^{82} +13.6838 q^{83} +(-0.484591 + 4.55688i) q^{84} +3.87341 q^{85} -3.13309i q^{86} +(4.96824 - 10.2015i) q^{87} -6.10336 q^{88} -5.12440 q^{89} +(6.03167 - 4.72383i) q^{90} +(10.0287 - 3.62962i) q^{91} -1.00000i q^{92} +(3.54692 - 7.28308i) q^{93} +0.328642i q^{94} -11.4411i q^{95} +(0.758370 - 1.55720i) q^{96} +4.80614i q^{97} +(-4.48007 - 5.37856i) q^{98} +(14.4153 - 11.2897i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.55720	−	0.758370i	−0.899050	−	0.437845i
$3$	−1.55720	−	0.758370i	−0.899050	−	0.437845i
$4$	−1.00000			−0.500000
$5$	−2.55377			−1.14208			−0.571040	−	0.820922i	$-0.693460\pi$
$5$	−2.55377			−1.14208			−0.571040	+	0.820922i	$0.693460\pi$
$6$	0.758370	−	1.55720i	0.309603	−	0.635725i
$7$	0.900399	+	2.48783i	0.340319	+	0.940310i
$7$	0.900399	+	2.48783i	0.340319	+	0.940310i
$8$		−	1.00000i		−	0.353553i
$9$	1.84975	+	2.36187i	0.616583	+	0.787290i
$10$		−	2.55377i		−	0.807573i
$11$		−	6.10336i		−	1.84023i	−0.391647	−	0.920116i	$-0.628094\pi$
$11$		−	6.10336i		−	1.84023i	0.391647	−	0.920116i	$-0.371906\pi$
$12$	1.55720	+	0.758370i	0.449525	+	0.218923i
$13$		−	4.03112i		−	1.11803i	−0.829157	−	0.559016i	$-0.811179\pi$
$13$		−	4.03112i		−	1.11803i	0.829157	−	0.559016i	$-0.188821\pi$
$14$	−2.48783	+	0.900399i	−0.664900	+	0.240642i
$15$	3.97673	+	1.93670i	1.02679	+	0.500054i
$16$	1.00000			0.250000
$17$	−1.51674			−0.367864			−0.183932	−	0.982939i	$-0.558883\pi$
$17$	−1.51674			−0.367864			−0.183932	+	0.982939i	$0.558883\pi$
$18$	−2.36187	+	1.84975i	−0.556698	+	0.435990i
$19$			4.48007i			1.02780i	0.857850	+	0.513900i	$0.171800\pi$
$19$			4.48007i			1.02780i	−0.857850	+	0.513900i	$0.828200\pi$
$20$	2.55377			0.571040
$21$	0.484591	−	4.55688i	0.105747	−	0.994393i
$22$	6.10336			1.30124
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−0.758370	+	1.55720i	−0.154802	+	0.317862i
$25$	1.52174			0.304348
$26$	4.03112			0.790568
$27$	−1.08926	−	5.08070i	−0.209628	−	0.977781i
$28$	−0.900399	−	2.48783i	−0.170159	−	0.470155i
$29$			6.55121i			1.21653i	0.793735	+	0.608264i	$0.208134\pi$
$29$			6.55121i			1.21653i	−0.793735	+	0.608264i	$0.791866\pi$
$30$	−1.93670	+	3.97673i	−0.353592	+	0.726049i
$31$			4.67703i			0.840020i	0.907520	+	0.420010i	$0.137973\pi$
$31$			4.67703i			0.840020i	−0.907520	+	0.420010i	$0.862027\pi$
$32$			1.00000i			0.176777i
$33$	−4.62860	+	9.50415i	−0.805737	+	1.65446i
$34$		−	1.51674i		−	0.260119i
$35$	−2.29941	−	6.35334i	−0.388671	−	1.07391i
$36$	−1.84975	−	2.36187i	−0.308292	−	0.393645i
$37$	9.05297			1.48830			0.744149	−	0.668013i	$-0.232855\pi$
$37$	9.05297			1.48830			0.744149	+	0.668013i	$0.232855\pi$
$38$	−4.48007			−0.726764
$39$	−3.05708	+	6.27726i	−0.489525	+	1.00517i
$40$			2.55377i			0.403786i
$41$	6.16375			0.962616			0.481308	−	0.876551i	$-0.340162\pi$
$41$	6.16375			0.962616			0.481308	+	0.876551i	$0.340162\pi$
$42$	4.55688	+	0.484591i	0.703142	+	0.0747741i
$43$	−3.13309			−0.477791			−0.238896	−	0.971045i	$-0.576785\pi$
$43$	−3.13309			−0.477791			−0.238896	+	0.971045i	$0.576785\pi$
$44$			6.10336i			0.920116i
$45$	−4.72383	−	6.03167i	−0.704188	−	0.899148i
$46$	−1.00000			−0.147442
$47$	0.328642			0.0479374			0.0239687	−	0.999713i	$-0.492370\pi$
$47$	0.328642			0.0479374			0.0239687	+	0.999713i	$0.492370\pi$
$48$	−1.55720	−	0.758370i	−0.224763	−	0.109461i
$49$	−5.37856	+	4.48007i	−0.768366	+	0.640010i
$50$			1.52174i			0.215206i
$51$	2.36187	+	1.15025i	0.330728	+	0.161067i
$52$			4.03112i			0.559016i
$53$			13.7776i			1.89249i	0.323446	+	0.946247i	$0.395159\pi$
$53$			13.7776i			1.89249i	−0.323446	+	0.946247i	$0.604841\pi$
$54$	5.08070	−	1.08926i	0.691396	−	0.148229i
$55$			15.5866i			2.10169i
$56$	2.48783	−	0.900399i	0.332450	−	0.120321i
$57$	3.39755	−	6.97637i	0.450017	−	0.924043i
$58$	−6.55121			−0.860216
$59$	13.6662			1.77919			0.889594	−	0.456752i	$-0.150987\pi$
$59$	13.6662			1.77919			0.889594	+	0.456752i	$0.150987\pi$
$60$	−3.97673	−	1.93670i	−0.513394	−	0.250027i
$61$			3.68097i			0.471300i	0.971838	+	0.235650i	$0.0757219\pi$
$61$			3.68097i			0.471300i	−0.971838	+	0.235650i	$0.924278\pi$
$62$	−4.67703			−0.593983
$63$	−4.21041	+	6.72848i	−0.530462	+	0.847709i
$64$	−1.00000			−0.125000
$65$			10.2946i			1.27688i
$66$	−9.50415	−	4.62860i	−1.16988	−	0.569742i
$67$	6.92840			0.846438			0.423219	−	0.906027i	$-0.360900\pi$
$67$	6.92840			0.846438			0.423219	+	0.906027i	$0.360900\pi$
$68$	1.51674			0.183932
$69$	0.758370	−	1.55720i	0.0912970	−	0.187465i
$70$	6.35334	−	2.29941i	0.759369	−	0.274832i
$71$			11.8850i			1.41049i	0.708962	+	0.705247i	$0.249164\pi$
$71$			11.8850i			1.41049i	−0.708962	+	0.705247i	$0.750836\pi$
$72$	2.36187	−	1.84975i	0.278349	−	0.217995i
$73$		−	6.01110i		−	0.703546i	−0.936085	−	0.351773i	$-0.885579\pi$
$73$		−	6.01110i		−	0.703546i	0.936085	−	0.351773i	$-0.114421\pi$
$74$			9.05297i			1.05239i
$75$	−2.36965	−	1.15404i	−0.273624	−	0.133257i
$76$		−	4.48007i		−	0.513900i
$77$	15.1841	−	5.49546i	1.73039	−	0.626265i
$78$	−6.27726	−	3.05708i	−0.710760	−	0.346146i
$79$	−4.13077			−0.464748			−0.232374	−	0.972627i	$-0.574649\pi$
$79$	−4.13077			−0.464748			−0.232374	+	0.972627i	$0.574649\pi$
$80$	−2.55377			−0.285520
$81$	−2.15685	+	8.73773i	−0.239651	+	0.970859i
$82$			6.16375i			0.680672i
$83$	13.6838			1.50199			0.750995	−	0.660308i	$-0.229574\pi$
$83$	13.6838			1.50199			0.750995	+	0.660308i	$0.229574\pi$
$84$	−0.484591	+	4.55688i	−0.0528733	+	0.497197i
$85$	3.87341			0.420130
$86$		−	3.13309i		−	0.337849i
$87$	4.96824	−	10.2015i	0.532651	−	1.09372i
$88$	−6.10336			−0.650620
$89$	−5.12440			−0.543186			−0.271593	−	0.962412i	$-0.587550\pi$
$89$	−5.12440			−0.543186			−0.271593	+	0.962412i	$0.587550\pi$
$90$	6.03167	−	4.72383i	0.635794	−	0.497936i
$91$	10.0287	−	3.62962i	1.05130	−	0.380487i
$92$		−	1.00000i		−	0.104257i
$93$	3.54692	−	7.28308i	0.367799	−	0.755220i
$94$			0.328642i			0.0338969i
$95$		−	11.4411i		−	1.17383i
$96$	0.758370	−	1.55720i	0.0774008	−	0.158931i
$97$			4.80614i			0.487990i	0.969777	+	0.243995i	$0.0784580\pi$
$97$			4.80614i			0.487990i	−0.969777	+	0.243995i	$0.921542\pi$
$98$	−4.48007	−	5.37856i	−0.452556	−	0.543317i
$99$	14.4153	−	11.2897i	1.44880	−	1.13466i
$100$	−1.52174			−0.152174
$101$	−12.5107			−1.24486			−0.622431	−	0.782674i	$-0.713855\pi$
$101$	−12.5107			−1.24486			−0.622431	+	0.782674i	$0.713855\pi$
$102$	−1.15025	+	2.36187i	−0.113892	+	0.233860i
$103$		−	5.85890i		−	0.577295i	−0.957436	−	0.288647i	$-0.906795\pi$
$103$		−	5.85890i		−	0.577295i	0.957436	−	0.288647i	$-0.0932055\pi$
$104$	−4.03112			−0.395284
$105$	−1.23753	+	11.6372i	−0.120771	+	1.13568i
$106$	−13.7776			−1.33819
$107$			0.336140i			0.0324959i	0.999868	+	0.0162480i	$0.00517212\pi$
$107$			0.336140i			0.0324959i	−0.999868	+	0.0162480i	$0.994828\pi$
$108$	1.08926	+	5.08070i	0.104814	+	0.488891i
$109$	−16.0536			−1.53765			−0.768826	−	0.639458i	$-0.779159\pi$
$109$	−16.0536			−1.53765			−0.768826	+	0.639458i	$0.779159\pi$
$110$	−15.5866			−1.48612
$111$	−14.0973	−	6.86550i	−1.33806	−	0.651645i
$112$	0.900399	+	2.48783i	0.0850797	+	0.235078i
$113$			5.22229i			0.491272i	0.969362	+	0.245636i	$0.0789968\pi$
$113$			5.22229i			0.491272i	−0.969362	+	0.245636i	$0.921003\pi$
$114$	6.97637	+	3.39755i	0.653397	+	0.318210i
$115$		−	2.55377i		−	0.238140i
$116$		−	6.55121i		−	0.608264i
$117$	9.52098	−	7.45656i	0.880215	−	0.689359i
$118$			13.6662i			1.25808i
$119$	−1.36567	−	3.77339i	−0.125191	−	0.345906i
$120$	1.93670	−	3.97673i	0.176796	−	0.363024i
$121$	−26.2510			−2.38645
$122$	−3.68097			−0.333260
$123$	−9.59820	−	4.67441i	−0.865440	−	0.421477i
$124$		−	4.67703i		−	0.420010i
$125$	8.88268			0.794491
$126$	−6.72848	−	4.21041i	−0.599421	−	0.375093i
$127$	7.44885			0.660979			0.330489	−	0.943810i	$-0.392786\pi$
$127$	7.44885			0.660979			0.330489	+	0.943810i	$0.392786\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.87884	+	2.37604i	0.429558	+	0.209199i
$130$	−10.2946			−0.902892
$131$	0.396408			0.0346343			0.0173172	−	0.999850i	$-0.494487\pi$
$131$	0.396408			0.0346343			0.0173172	+	0.999850i	$0.494487\pi$
$132$	4.62860	−	9.50415i	0.402868	−	0.827230i
$133$	−11.1456	+	4.03385i	−0.966450	+	0.349779i
$134$			6.92840i			0.598522i
$135$	2.78172	+	12.9749i	0.239412	+	1.11670i
$136$			1.51674i			0.130059i
$137$			2.98319i			0.254871i	0.991847	+	0.127436i	$0.0406746\pi$
$137$			2.98319i			0.254871i	−0.991847	+	0.127436i	$0.959325\pi$
$138$	1.55720	+	0.758370i	0.132558	+	0.0645568i
$139$		−	17.7006i		−	1.50135i	−0.660674	−	0.750673i	$-0.729729\pi$
$139$		−	17.7006i		−	1.50135i	0.660674	−	0.750673i	$-0.270271\pi$
$140$	2.29941	+	6.35334i	0.194336	+	0.536955i
$141$	−0.511762	−	0.249233i	−0.0430982	−	0.0209892i
$142$	−11.8850			−0.997370
$143$	−24.6034			−2.05744
$144$	1.84975	+	2.36187i	0.154146	+	0.196822i
$145$		−	16.7303i		−	1.38937i
$146$	6.01110			0.497482
$147$	11.7731	−	2.89743i	0.971025	−	0.238976i
$148$	−9.05297			−0.744149
$149$		−	23.5703i		−	1.93096i	−0.260484	−	0.965478i	$-0.583882\pi$
$149$		−	23.5703i		−	1.93096i	0.260484	−	0.965478i	$-0.416118\pi$
$150$	1.15404	−	2.36965i	0.0942271	−	0.193481i
$151$	15.5335			1.26410			0.632051	−	0.774927i	$-0.282213\pi$
$151$	15.5335			1.26410			0.632051	+	0.774927i	$0.282213\pi$
$152$	4.48007			0.363382
$153$	−2.80559	−	3.58234i	−0.226818	−	0.289615i
$154$	5.49546	+	15.1841i	0.442837	+	1.22357i
$155$		−	11.9441i		−	0.959370i
$156$	3.05708	−	6.27726i	0.244762	−	0.502583i
$157$			5.79301i			0.462332i	0.972914	+	0.231166i	$0.0742541\pi$
$157$			5.79301i			0.462332i	−0.972914	+	0.231166i	$0.925746\pi$
$158$		−	4.13077i		−	0.328626i
$159$	10.4485	−	21.4544i	0.828619	−	1.70145i
$160$		−	2.55377i		−	0.201893i
$161$	−2.48783	+	0.900399i	−0.196068	+	0.0709614i
$162$	−8.73773	−	2.15685i	−0.686501	−	0.169459i
$163$	13.9101			1.08953			0.544763	−	0.838590i	$-0.316620\pi$
$163$	13.9101			1.08953			0.544763	+	0.838590i	$0.316620\pi$
$164$	−6.16375			−0.481308
$165$	11.8204	−	24.2714i	0.920216	−	1.88953i
$166$			13.6838i			1.06207i
$167$	21.5753			1.66955			0.834774	−	0.550592i	$-0.185598\pi$
$167$	21.5753			1.66955			0.834774	+	0.550592i	$0.185598\pi$
$168$	−4.55688	−	0.484591i	−0.351571	−	0.0373870i
$169$	−3.24993			−0.249995
$170$			3.87341i			0.297077i
$171$	−10.5813	+	8.28701i	−0.809176	+	0.633724i
$172$	3.13309			0.238896
$173$	6.39359			0.486096			0.243048	−	0.970014i	$-0.421853\pi$
$173$	6.39359			0.486096			0.243048	+	0.970014i	$0.421853\pi$
$174$	10.2015	+	4.96824i	0.773377	+	0.376641i
$175$	1.37017	+	3.78582i	0.103575	+	0.286181i
$176$		−	6.10336i		−	0.460058i
$177$	−21.2810	−	10.3640i	−1.59958	−	0.779009i
$178$		−	5.12440i		−	0.384090i
$179$			14.2081i			1.06196i	0.847384	+	0.530981i	$0.178177\pi$
$179$			14.2081i			1.06196i	−0.847384	+	0.530981i	$0.821823\pi$
$180$	4.72383	+	6.03167i	0.352094	+	0.449574i
$181$			9.97801i			0.741660i	0.928701	+	0.370830i	$0.120927\pi$
$181$			9.97801i			0.741660i	−0.928701	+	0.370830i	$0.879073\pi$
$182$	3.62962	+	10.0287i	0.269045	+	0.743379i
$183$	2.79154	−	5.73201i	0.206357	−	0.423723i
$184$	1.00000			0.0737210
$185$	−23.1192			−1.69976
$186$	7.28308	+	3.54692i	0.534021	+	0.260073i
$187$			9.25721i			0.676954i
$188$	−0.328642			−0.0239687
$189$	11.6591	−	7.28455i	0.848077	−	0.529873i
$190$	11.4411			0.830023
$191$		−	2.81898i		−	0.203974i	−0.994786	−	0.101987i	$-0.967480\pi$
$191$		−	2.81898i		−	0.203974i	0.994786	−	0.101987i	$-0.0325201\pi$
$192$	1.55720	+	0.758370i	0.112381	+	0.0547307i
$193$	19.2122			1.38292			0.691460	−	0.722414i	$-0.256968\pi$
$193$	19.2122			1.38292			0.691460	+	0.722414i	$0.256968\pi$
$194$	−4.80614			−0.345061
$195$	7.80708	−	16.0307i	0.559077	−	1.14798i
$196$	5.37856	−	4.48007i	0.384183	−	0.320005i
$197$		−	6.87361i		−	0.489724i	−0.969558	−	0.244862i	$-0.921257\pi$
$197$		−	6.87361i		−	0.489724i	0.969558	−	0.244862i	$-0.0787427\pi$
$198$	11.2897	+	14.4153i	0.802323	+	1.02445i
$199$			23.5213i			1.66738i	0.552233	+	0.833690i	$0.313776\pi$
$199$			23.5213i			1.66738i	−0.552233	+	0.833690i	$0.686224\pi$
$200$		−	1.52174i		−	0.107603i
$201$	−10.7889	−	5.25429i	−0.760991	−	0.370609i
$202$		−	12.5107i		−	0.880251i
$203$	−16.2983	+	5.89870i	−1.14391	+	0.414008i
$204$	−2.36187	−	1.15025i	−0.165364	−	0.0805337i
$205$	−15.7408			−1.09939
$206$	5.85890			0.408209
$207$	−2.36187	+	1.84975i	−0.164161	+	0.128566i
$208$		−	4.03112i		−	0.279508i
$209$	27.3435			1.89139
$210$	−11.6372	−	1.23753i	−0.803045	−	0.0853980i
$211$	−4.74492			−0.326654			−0.163327	−	0.986572i	$-0.552223\pi$
$211$	−4.74492			−0.326654			−0.163327	+	0.986572i	$0.552223\pi$
$212$		−	13.7776i		−	0.946247i
$213$	9.01325	−	18.5074i	0.617578	−	1.26810i
$214$	−0.336140			−0.0229781
$215$	8.00118			0.545676
$216$	−5.08070	+	1.08926i	−0.345698	+	0.0741147i
$217$	−11.6356	+	4.21119i	−0.789879	+	0.285874i
$218$		−	16.0536i		−	1.08728i
$219$	−4.55864	+	9.36049i	−0.308044	+	0.632524i
$220$		−	15.5866i		−	1.05085i
$221$			6.11416i			0.411283i
$222$	6.86550	−	14.0973i	0.460782	−	0.946148i
$223$			15.0543i			1.00811i	0.863671	+	0.504057i	$0.168160\pi$
$223$			15.0543i			1.00811i	−0.863671	+	0.504057i	$0.831840\pi$
$224$	−2.48783	+	0.900399i	−0.166225	+	0.0601604i
$225$	2.81484	+	3.59415i	0.187656	+	0.239610i
$226$	−5.22229			−0.347382
$227$	−1.25103			−0.0830337			−0.0415168	−	0.999138i	$-0.513219\pi$
$227$	−1.25103			−0.0830337			−0.0415168	+	0.999138i	$0.513219\pi$
$228$	−3.39755	+	6.97637i	−0.225009	+	0.462022i
$229$			18.6199i			1.23044i	0.788356	+	0.615219i	$0.210932\pi$
$229$			18.6199i			1.23044i	−0.788356	+	0.615219i	$0.789068\pi$
$230$	2.55377			0.168391
$231$	−27.8123	−	2.95763i	−1.82991	−	0.194598i
$232$	6.55121			0.430108
$233$			4.11040i			0.269281i	0.990895	+	0.134640i	$0.0429879\pi$
$233$			4.11040i			0.269281i	−0.990895	+	0.134640i	$0.957012\pi$
$234$	7.45656	+	9.52098i	0.487451	+	0.622406i
$235$	−0.839277			−0.0547484
$236$	−13.6662			−0.889594
$237$	6.43244	+	3.13265i	0.417832	+	0.203488i
$238$	3.77339	−	1.36567i	0.244592	−	0.0885233i
$239$			3.90391i			0.252523i	0.991997	+	0.126261i	$0.0402978\pi$
$239$			3.90391i			0.252523i	−0.991997	+	0.126261i	$0.959702\pi$
$240$	3.97673	+	1.93670i	0.256697	+	0.125014i
$241$			24.3584i			1.56906i	0.620091	+	0.784530i	$0.287096\pi$
$241$			24.3584i			1.56906i	−0.620091	+	0.784530i	$0.712904\pi$
$242$		−	26.2510i		−	1.68748i
$243$	9.98509	−	11.9707i	0.640544	−	0.767921i
$244$		−	3.68097i		−	0.235650i
$245$	13.7356	−	11.4411i	0.877536	−	0.730943i
$246$	4.67441	−	9.59820i	0.298029	−	0.611959i
$247$	18.0597			1.14911
$248$	4.67703			0.296992
$249$	−21.3084	−	10.3774i	−1.35037	−	0.657639i
$250$			8.88268i			0.561790i
$251$	7.94381			0.501409			0.250704	−	0.968064i	$-0.419338\pi$
$251$	7.94381			0.501409			0.250704	+	0.968064i	$0.419338\pi$
$252$	4.21041	−	6.72848i	0.265231	−	0.423854i
$253$	6.10336			0.383715
$254$			7.44885i			0.467383i
$255$	−6.03167	−	2.93748i	−0.377718	−	0.183952i
$256$	1.00000			0.0625000
$257$	−8.97365			−0.559761			−0.279880	−	0.960035i	$-0.590295\pi$
$257$	−8.97365			−0.559761			−0.279880	+	0.960035i	$0.590295\pi$
$258$	−2.37604	+	4.87884i	−0.147926	+	0.303744i
$259$	8.15128	+	22.5222i	0.506496	+	1.39946i
$260$		−	10.2946i		−	0.638441i
$261$	−15.4731	+	12.1181i	−0.957761	+	0.750091i
$262$			0.396408i			0.0244902i
$263$		−	9.60955i		−	0.592550i	−0.955103	−	0.296275i	$-0.904255\pi$
$263$		−	9.60955i		−	0.592550i	0.955103	−	0.296275i	$-0.0957445\pi$
$264$	9.50415	+	4.62860i	0.584940	+	0.284871i
$265$		−	35.1847i		−	2.16138i
$266$	−4.03385	−	11.1456i	−0.247331	−	0.683383i
$267$	7.97973	+	3.88619i	0.488351	+	0.237831i
$268$	−6.92840			−0.423219
$269$	−9.40861			−0.573653			−0.286826	−	0.957983i	$-0.592600\pi$
$269$	−9.40861			−0.573653			−0.286826	+	0.957983i	$0.592600\pi$
$270$	−12.9749	+	2.78172i	−0.789630	+	0.169290i
$271$			7.19891i			0.437303i	0.975803	+	0.218651i	$0.0701657\pi$
$271$			7.19891i			0.437303i	−0.975803	+	0.218651i	$0.929834\pi$
$272$	−1.51674			−0.0919659
$273$	−18.3693	−	1.95345i	−1.11176	−	0.118228i
$274$	−2.98319			−0.180221
$275$		−	9.28772i		−	0.560070i
$276$	−0.758370	+	1.55720i	−0.0456485	+	0.0937325i
$277$	4.56347			0.274192			0.137096	−	0.990558i	$-0.456223\pi$
$277$	4.56347			0.274192			0.137096	+	0.990558i	$0.456223\pi$
$278$	17.7006			1.06161
$279$	−11.0465	+	8.65133i	−0.661339	+	0.517942i
$280$	−6.35334	+	2.29941i	−0.379684	+	0.137416i
$281$		−	5.94503i		−	0.354651i	−0.984152	−	0.177325i	$-0.943256\pi$
$281$		−	5.94503i		−	0.354651i	0.984152	−	0.177325i	$-0.0567445\pi$
$282$	0.249233	−	0.511762i	0.0148416	−	0.0304750i
$283$		−	29.6466i		−	1.76231i	−0.472828	−	0.881155i	$-0.656767\pi$
$283$		−	29.6466i		−	1.76231i	0.472828	−	0.881155i	$-0.343233\pi$
$284$		−	11.8850i		−	0.705247i
$285$	−8.67657	+	17.8161i	−0.513956	+	1.05533i
$286$		−	24.6034i		−	1.45483i
$287$	5.54984	+	15.3343i	0.327596	+	0.905158i
$288$	−2.36187	+	1.84975i	−0.139174	+	0.108998i
$289$	−14.6995			−0.864676
$290$	16.7303			0.982436
$291$	3.64483	−	7.48413i	0.213664	−	0.438727i
$292$			6.01110i			0.351773i
$293$	−4.12604			−0.241046			−0.120523	−	0.992711i	$-0.538457\pi$
$293$	−4.12604			−0.241046			−0.120523	+	0.992711i	$0.538457\pi$
$294$	2.89743	+	11.7731i	0.168982	+	0.686619i
$295$	−34.9003			−2.03198
$296$		−	9.05297i		−	0.526193i
$297$	−31.0093	+	6.64814i	−1.79934	+	0.385764i
$298$	23.5703			1.36539
$299$	4.03112			0.233126
$300$	2.36965	+	1.15404i	0.136812	+	0.0666286i
$301$	−2.82103	−	7.79457i	−0.162601	−	0.449272i
$302$			15.5335i			0.893855i
$303$	19.4817	+	9.48775i	1.11919	+	0.545057i
$304$			4.48007i			0.256950i
$305$		−	9.40035i		−	0.538263i
$306$	3.58234	−	2.80559i	0.204789	−	0.160385i
$307$		−	0.0606050i		−	0.00345891i	−0.999999	−	0.00172946i	$-0.999449\pi$
$307$		−	0.0606050i		−	0.00345891i	0.999999	−	0.00172946i	$-0.000550503\pi$
$308$	−15.1841	+	5.49546i	−0.865194	+	0.313133i
$309$	−4.44322	+	9.12348i	−0.252766	+	0.519017i
$310$	11.9441			0.678377
$311$	28.2869			1.60400			0.802002	−	0.597321i	$-0.203768\pi$
$311$	28.2869			1.60400			0.802002	+	0.597321i	$0.203768\pi$
$312$	6.27726	+	3.05708i	0.355380	+	0.173073i
$313$			1.98027i			0.111932i	0.998433	+	0.0559658i	$0.0178238\pi$
$313$			1.98027i			0.111932i	−0.998433	+	0.0559658i	$0.982176\pi$
$314$	−5.79301			−0.326918
$315$	10.7524	−	17.1830i	0.605830	−	0.968152i
$316$	4.13077			0.232374
$317$			0.813147i			0.0456709i	0.999739	+	0.0228354i	$0.00726938\pi$
$317$			0.813147i			0.0456709i	−0.999739	+	0.0228354i	$0.992731\pi$
$318$	21.4544	+	10.4485i	1.20310	+	0.585922i
$319$	39.9844			2.23869
$320$	2.55377			0.142760
$321$	0.254919	−	0.523438i	0.0142282	−	0.0292155i
$322$	−0.900399	−	2.48783i	−0.0501773	−	0.138641i
$323$		−	6.79511i		−	0.378090i
$324$	2.15685	−	8.73773i	0.119825	−	0.485430i
$325$		−	6.13431i		−	0.340270i
$326$			13.9101i			0.770411i
$327$	24.9986	+	12.1745i	1.38243	+	0.673254i
$328$		−	6.16375i		−	0.340336i
$329$	0.295909	+	0.817605i	0.0163140	+	0.0450760i
$330$	24.2714	+	11.8204i	1.33610	+	0.650691i
$331$	4.03439			0.221750			0.110875	−	0.993834i	$-0.464635\pi$
$331$	4.03439			0.221750			0.110875	+	0.993834i	$0.464635\pi$
$332$	−13.6838			−0.750995
$333$	16.7457	+	21.3819i	0.917660	+	1.17172i
$334$			21.5753i			1.18055i
$335$	−17.6935			−0.966701
$336$	0.484591	−	4.55688i	0.0264366	−	0.248598i
$337$	6.55839			0.357258			0.178629	−	0.983916i	$-0.442834\pi$
$337$	6.55839			0.357258			0.178629	+	0.983916i	$0.442834\pi$
$338$		−	3.24993i		−	0.176773i
$339$	3.96043	−	8.13216i	0.215101	−	0.441678i
$340$	−3.87341			−0.210065
$341$	28.5456			1.54583
$342$	−8.28701	−	10.5813i	−0.448110	−	0.572174i
$343$	−15.9885	−	9.34708i	−0.863298	−	0.504695i
$344$			3.13309i			0.168925i
$345$	−1.93670	+	3.97673i	−0.104269	+	0.214100i
$346$			6.39359i			0.343721i
$347$		−	28.2405i		−	1.51603i	−0.652237	−	0.758015i	$-0.726169\pi$
$347$		−	28.2405i		−	1.51603i	0.652237	−	0.758015i	$-0.273831\pi$
$348$	−4.96824	+	10.2015i	−0.266326	+	0.546860i
$349$			10.7649i			0.576230i	0.957596	+	0.288115i	$0.0930286\pi$
$349$			10.7649i			0.576230i	−0.957596	+	0.288115i	$0.906971\pi$
$350$	−3.78582	+	1.37017i	−0.202361	+	0.0732388i
$351$	−20.4809	+	4.39094i	−1.09319	+	0.234371i
$352$	6.10336			0.325310
$353$	−28.1446			−1.49799			−0.748994	−	0.662577i	$-0.769463\pi$
$353$	−28.1446			−1.49799			−0.748994	+	0.662577i	$0.769463\pi$
$354$	10.3640	−	21.2810i	0.550843	−	1.13107i
$355$		−	30.3516i		−	1.61090i
$356$	5.12440			0.271593
$357$	−0.734999	+	6.91161i	−0.0389003	+	0.365801i
$358$	−14.2081			−0.750921
$359$		−	26.6543i		−	1.40676i	−0.710815	−	0.703379i	$-0.751674\pi$
$359$		−	26.6543i		−	1.40676i	0.710815	−	0.703379i	$-0.248326\pi$
$360$	−6.03167	+	4.72383i	−0.317897	+	0.248968i
$361$	−1.07106			−0.0563714
$362$	−9.97801			−0.524433
$363$	40.8780	+	19.9080i	2.14554	+	1.04490i
$364$	−10.0287	+	3.62962i	−0.525648	+	0.190244i
$365$			15.3510i			0.803506i
$366$	5.73201	+	2.79154i	0.299617	+	0.145916i
$367$			9.27729i			0.484270i	0.970243	+	0.242135i	$0.0778478\pi$
$367$			9.27729i			0.484270i	−0.970243	+	0.242135i	$0.922152\pi$
$368$			1.00000i			0.0521286i
$369$	11.4014	+	14.5580i	0.593533	+	0.757858i
$370$		−	23.1192i		−	1.20191i
$371$	−34.2762	+	12.4053i	−1.77953	+	0.644051i
$372$	−3.54692	+	7.28308i	−0.183899	+	0.377610i
$373$	−15.0035			−0.776853			−0.388427	−	0.921480i	$-0.626981\pi$
$373$	−15.0035			−0.776853			−0.388427	+	0.921480i	$0.626981\pi$
$374$	−9.25721			−0.478679
$375$	−13.8321	−	6.73636i	−0.714287	−	0.347864i
$376$		−	0.328642i		−	0.0169484i
$377$	26.4087			1.36012
$378$	7.28455	+	11.6591i	0.374677	+	0.599681i
$379$	−13.7777			−0.707712			−0.353856	−	0.935300i	$-0.615130\pi$
$379$	−13.7777			−0.707712			−0.353856	+	0.935300i	$0.615130\pi$
$380$			11.4411i			0.586915i
$381$	−11.5994	−	5.64899i	−0.594253	−	0.289406i
$382$	2.81898			0.144232
$383$	9.42182			0.481433			0.240716	−	0.970596i	$-0.422618\pi$
$383$	9.42182			0.481433			0.240716	+	0.970596i	$0.422618\pi$
$384$	−0.758370	+	1.55720i	−0.0387004	+	0.0794656i
$385$	−38.7767	+	14.0341i	−1.97624	+	0.715245i
$386$			19.2122i			0.977873i
$387$	−5.79542	−	7.39994i	−0.294598	−	0.376160i
$388$		−	4.80614i		−	0.243995i
$389$			28.8711i			1.46382i	0.681400	+	0.731912i	$0.261372\pi$
$389$			28.8711i			1.46382i	−0.681400	+	0.731912i	$0.738628\pi$
$390$	16.0307	+	7.80708i	0.811745	+	0.395327i
$391$		−	1.51674i		−	0.0767049i
$392$	4.48007	+	5.37856i	0.226278	+	0.271658i
$393$	−0.617287	−	0.300624i	−0.0311380	−	0.0151645i
$394$	6.87361			0.346287
$395$	10.5490			0.530779
$396$	−14.4153	+	11.2897i	−0.724398	+	0.567328i
$397$		−	33.6110i		−	1.68689i	−0.537219	−	0.843443i	$-0.680525\pi$
$397$		−	33.6110i		−	1.68689i	0.537219	−	0.843443i	$-0.319475\pi$
$398$	−23.5213			−1.17902
$399$	20.4152	+	2.17101i	1.02204	+	0.108686i
$400$	1.52174			0.0760869
$401$		−	4.42596i		−	0.221022i	−0.993875	−	0.110511i	$-0.964751\pi$
$401$		−	4.42596i		−	0.221022i	0.993875	−	0.110511i	$-0.0352487\pi$
$402$	5.25429	−	10.7889i	0.262060	−	0.538102i
$403$	18.8537			0.939168
$404$	12.5107			0.622431
$405$	5.50811	−	22.3142i	0.273700	−	1.10880i
$406$	−5.89870	−	16.2983i	−0.292748	−	0.808869i
$407$		−	55.2535i		−	2.73881i
$408$	1.15025	−	2.36187i	0.0569459	−	0.116930i
$409$			10.9919i			0.543514i	0.962366	+	0.271757i	$0.0876047\pi$
$409$			10.9919i			0.543514i	−0.962366	+	0.271757i	$0.912395\pi$
$410$		−	15.7408i		−	0.777383i
$411$	2.26236	−	4.64543i	0.111594	−	0.229142i
$412$			5.85890i			0.288647i
$413$	12.3050	+	33.9991i	0.605491	+	1.67299i
$414$	−1.84975	−	2.36187i	−0.0909102	−	0.116080i
$415$	−34.9452			−1.71539
$416$	4.03112			0.197642
$417$	−13.4236	+	27.5634i	−0.657357	+	1.34979i
$418$			27.3435i			1.33741i
$419$	−13.4110			−0.655170			−0.327585	−	0.944822i	$-0.606235\pi$
$419$	−13.4110			−0.655170			−0.327585	+	0.944822i	$0.606235\pi$
$420$	1.23753	−	11.6372i	0.0603855	−	0.567838i
$421$	8.69841			0.423935			0.211967	−	0.977277i	$-0.432013\pi$
$421$	8.69841			0.423935			0.211967	+	0.977277i	$0.432013\pi$
$422$		−	4.74492i		−	0.230979i
$423$	0.607906	+	0.776210i	0.0295574	+	0.0377406i
$424$	13.7776			0.669097
$425$	−2.30808			−0.111958
$426$	18.5074	+	9.01325i	0.896685	+	0.436694i
$427$	−9.15762	+	3.31434i	−0.443168	+	0.160392i
$428$		−	0.336140i		−	0.0162480i
$429$	38.3124	+	18.6585i	1.84974	+	0.900839i
$430$			8.00118i			0.385851i
$431$			25.2334i			1.21545i	0.794148	+	0.607725i	$0.207918\pi$
$431$			25.2334i			1.21545i	−0.794148	+	0.607725i	$0.792082\pi$
$432$	−1.08926	−	5.08070i	−0.0524070	−	0.244445i
$433$		−	12.2271i		−	0.587599i	−0.955867	−	0.293799i	$-0.905080\pi$
$433$		−	12.2271i		−	0.587599i	0.955867	−	0.293799i	$-0.0949198\pi$
$434$	−4.21119	−	11.6356i	−0.202144	−	0.558529i
$435$	−12.6877	+	26.0524i	−0.608331	+	1.24912i
$436$	16.0536			0.768826
$437$	−4.48007			−0.214311
$438$	−9.36049	−	4.55864i	−0.447262	−	0.217820i
$439$		−	10.3640i		−	0.494645i	−0.968933	−	0.247323i	$-0.920449\pi$
$439$		−	10.3640i		−	0.494645i	0.968933	−	0.247323i	$-0.0795508\pi$
$440$	15.5866			0.743060
$441$	−20.5303	−	4.41645i	−0.977635	−	0.210307i
$442$	−6.11416			−0.290821
$443$			27.0187i			1.28370i	0.766832	+	0.641848i	$0.221832\pi$
$443$			27.0187i			1.28370i	−0.766832	+	0.641848i	$0.778168\pi$
$444$	14.0973	+	6.86550i	0.669028	+	0.325822i
$445$	13.0865			0.620362
$446$	−15.0543			−0.712844
$447$	−17.8750	+	36.7037i	−0.845460	+	1.73603i
$448$	−0.900399	−	2.48783i	−0.0425399	−	0.117539i
$449$			38.0881i			1.79749i	0.438473	+	0.898745i	$0.355520\pi$
$449$			38.0881i			1.79749i	−0.438473	+	0.898745i	$0.644480\pi$
$450$	−3.59415	+	2.81484i	−0.169430	+	0.132693i
$451$		−	37.6196i		−	1.77144i
$452$		−	5.22229i		−	0.245636i
$453$	−24.1889	−	11.7802i	−1.13649	−	0.553481i
$454$		−	1.25103i		−	0.0587137i
$455$	−25.6111	+	9.26920i	−1.20067	+	0.434547i
$456$	−6.97637	−	3.39755i	−0.326699	−	0.159105i
$457$	−37.4592			−1.75227			−0.876133	−	0.482070i	$-0.839885\pi$
$457$	−37.4592			−1.75227			−0.876133	+	0.482070i	$0.839885\pi$
$458$	−18.6199			−0.870051
$459$	1.65212	+	7.70610i	0.0771146	+	0.359690i
$460$			2.55377i			0.119070i
$461$	−2.96163			−0.137937			−0.0689685	−	0.997619i	$-0.521971\pi$
$461$	−2.96163			−0.137937			−0.0689685	+	0.997619i	$0.521971\pi$
$462$	2.95763	−	27.8123i	0.137602	−	1.29394i
$463$	31.9983			1.48709			0.743544	−	0.668687i	$-0.233143\pi$
$463$	31.9983			1.48709			0.743544	+	0.668687i	$0.233143\pi$
$464$			6.55121i			0.304132i
$465$	−9.05802	+	18.5993i	−0.420056	+	0.862522i
$466$	−4.11040			−0.190410
$467$	−5.67699			−0.262700			−0.131350	−	0.991336i	$-0.541931\pi$
$467$	−5.67699			−0.262700			−0.131350	+	0.991336i	$0.541931\pi$
$468$	−9.52098	+	7.45656i	−0.440107	+	0.344680i
$469$	6.23832	+	17.2366i	0.288059	+	0.795914i
$470$		−	0.839277i		−	0.0387130i
$471$	4.39324	−	9.02087i	0.202430	−	0.415660i
$472$		−	13.6662i		−	0.629038i
$473$			19.1223i			0.879246i
$474$	−3.13265	+	6.43244i	−0.143887	+	0.295452i
$475$			6.81750i			0.312808i
$476$	1.36567	+	3.77339i	0.0625955	+	0.172953i
$477$	−32.5408	+	25.4850i	−1.48994	+	1.16688i
$478$	−3.90391			−0.178561
$479$	−24.9322			−1.13918			−0.569591	−	0.821928i	$-0.692898\pi$
$479$	−24.9322			−1.13918			−0.569591	+	0.821928i	$0.692898\pi$
$480$	−1.93670	+	3.97673i	−0.0883980	+	0.181512i
$481$		−	36.4936i		−	1.66397i
$482$	−24.3584			−1.10949
$483$	4.55688	+	0.484591i	0.207345	+	0.0220497i
$484$	26.2510			1.19323
$485$		−	12.2738i		−	0.557323i
$486$	11.9707	+	9.98509i	0.543002	+	0.452933i
$487$	−0.150114			−0.00680230			−0.00340115	−	0.999994i	$-0.501083\pi$
$487$	−0.150114			−0.00680230			−0.00340115	+	0.999994i	$0.501083\pi$
$488$	3.68097			0.166630
$489$	−21.6609	−	10.5490i	−0.979538	−	0.477044i
$490$	11.4411	+	13.7356i	0.516855	+	0.620512i
$491$			17.8076i			0.803647i	0.915717	+	0.401824i	$0.131624\pi$
$491$			17.8076i			0.803647i	−0.915717	+	0.401824i	$0.868376\pi$
$492$	9.59820	+	4.67441i	0.432720	+	0.210738i
$493$		−	9.93648i		−	0.447517i
$494$			18.0597i			0.812545i
$495$	−36.8134	+	28.8312i	−1.65464	+	1.29587i
$496$			4.67703i			0.210005i
$497$	−29.5679	+	10.7013i	−1.32630	+	0.480018i
$498$	10.3774	−	21.3084i	0.465021	−	0.954852i
$499$	17.0614			0.763774			0.381887	−	0.924209i	$-0.375274\pi$
$499$	17.0614			0.763774			0.381887	+	0.924209i	$0.375274\pi$
$500$	−8.88268			−0.397245
$501$	−33.5971	−	16.3621i	−1.50101	−	0.731004i
$502$			7.94381i			0.354550i
$503$	27.8477			1.24167			0.620835	−	0.783941i	$-0.286794\pi$
$503$	27.8477			1.24167			0.620835	+	0.783941i	$0.286794\pi$
$504$	6.72848	+	4.21041i	0.299710	+	0.187547i
$505$	31.9495			1.42173
$506$			6.10336i			0.271327i
$507$	5.06079	+	2.46465i	0.224758	+	0.109459i
$508$	−7.44885			−0.330489
$509$	−35.2070			−1.56052			−0.780262	−	0.625453i	$-0.784914\pi$
$509$	−35.2070			−1.56052			−0.780262	+	0.625453i	$0.784914\pi$
$510$	2.93748	−	6.03167i	0.130074	−	0.267087i
$511$	14.9546	−	5.41239i	0.661552	−	0.239430i
$512$			1.00000i			0.0441942i
$513$	22.7619	−	4.87996i	1.00496	−	0.215456i
$514$		−	8.97365i		−	0.395811i
$515$			14.9623i			0.659317i
$516$	−4.87884	−	2.37604i	−0.214779	−	0.104599i
$517$		−	2.00582i		−	0.0882159i
$518$	−22.5222	+	8.15128i	−0.989569	+	0.358147i
$519$	−9.95610	−	4.84871i	−0.437024	−	0.212835i
$520$	10.2946			0.451446
$521$	−0.0839391			−0.00367744			−0.00183872	−	0.999998i	$-0.500585\pi$
$521$	−0.0839391			−0.00367744			−0.00183872	+	0.999998i	$0.500585\pi$
$522$	−12.1181	−	15.4731i	−0.530394	−	0.677239i
$523$		−	6.93505i		−	0.303249i	−0.988438	−	0.151624i	$-0.951550\pi$
$523$		−	6.93505i		−	0.303249i	0.988438	−	0.151624i	$-0.0484504\pi$
$524$	−0.396408			−0.0173172
$525$	0.737422	−	6.93438i	0.0321837	−	0.302641i
$526$	9.60955			0.418996
$527$		−	7.09384i		−	0.309013i
$528$	−4.62860	+	9.50415i	−0.201434	+	0.413615i
$529$	−1.00000			−0.0434783
$530$	35.1847			1.52833
$531$	25.2790	+	32.2778i	1.09702	+	1.40074i
$532$	11.1456	−	4.03385i	0.483225	−	0.174890i
$533$		−	24.8468i		−	1.07624i
$534$	−3.88619	+	7.97973i	−0.168172	+	0.345316i
$535$		−	0.858425i		−	0.0371130i
$536$		−	6.92840i		−	0.299261i
$537$	10.7750	−	22.1248i	0.464975	−	0.954758i
$538$		−	9.40861i		−	0.405634i
$539$	27.3435	+	32.8273i	1.17777	+	1.41397i
$540$	−2.78172	−	12.9749i	−0.119706	−	0.558352i
$541$	2.74802			0.118147			0.0590733	−	0.998254i	$-0.481185\pi$
$541$	2.74802			0.118147			0.0590733	+	0.998254i	$0.481185\pi$
$542$	−7.19891			−0.309220
$543$	7.56703	−	15.5378i	0.324732	−	0.666790i
$544$		−	1.51674i		−	0.0650297i
$545$	40.9971			1.75612
$546$	1.95345	−	18.3693i	0.0835998	−	0.786135i
$547$	−25.6108			−1.09504			−0.547518	−	0.836794i	$-0.684427\pi$
$547$	−25.6108			−1.09504			−0.547518	+	0.836794i	$0.684427\pi$
$548$		−	2.98319i		−	0.127436i
$549$	−8.69398	+	6.80888i	−0.371050	+	0.290596i
$550$	9.28772			0.396030
$551$	−29.3499			−1.25035
$552$	−1.55720	−	0.758370i	−0.0662789	−	0.0322784i
$553$	−3.71934	−	10.2766i	−0.158162	−	0.437007i
$554$			4.56347i			0.193883i
$555$	36.0012	+	17.5329i	1.52817	+	0.744231i
$556$			17.7006i			0.750673i
$557$			7.71965i			0.327092i	0.986536	+	0.163546i	$0.0522932\pi$
$557$			7.71965i			0.327092i	−0.986536	+	0.163546i	$0.947707\pi$
$558$	−8.65133	−	11.0465i	−0.366240	−	0.467637i
$559$			12.6298i			0.534185i
$560$	−2.29941	−	6.35334i	−0.0971679	−	0.268477i
$561$	7.02039	−	14.4153i	0.296401	−	0.608616i
$562$	5.94503			0.250776
$563$	−18.9537			−0.798804			−0.399402	−	0.916776i	$-0.630782\pi$
$563$	−18.9537			−0.798804			−0.399402	+	0.916776i	$0.630782\pi$
$564$	0.511762	+	0.249233i	0.0215491	+	0.0104946i
$565$		−	13.3365i		−	0.561072i
$566$	29.6466			1.24614
$567$	−23.6800	+	2.50156i	−0.994466	+	0.105056i
$568$	11.8850			0.498685
$569$		−	30.1451i		−	1.26375i	−0.775071	−	0.631874i	$-0.782286\pi$
$569$		−	30.1451i		−	1.26375i	0.775071	−	0.631874i	$-0.217714\pi$
$570$	−17.8161	−	8.67657i	−0.746232	−	0.363422i
$571$	6.65018			0.278301			0.139151	−	0.990271i	$-0.455563\pi$
$571$	6.65018			0.278301			0.139151	+	0.990271i	$0.455563\pi$
$572$	24.6034			1.02872
$573$	−2.13783	+	4.38972i	−0.0893092	+	0.183383i
$574$	−15.3343	+	5.54984i	−0.640043	+	0.231646i
$575$			1.52174i			0.0634609i
$576$	−1.84975	−	2.36187i	−0.0770729	−	0.0984112i
$577$		−	11.9760i		−	0.498566i	−0.968431	−	0.249283i	$-0.919805\pi$
$577$		−	11.9760i		−	0.498566i	0.968431	−	0.249283i	$-0.0801949\pi$
$578$		−	14.6995i		−	0.611419i
$579$	−29.9172	−	14.5699i	−1.24332	−	0.605505i
$580$			16.7303i			0.694687i
$581$	12.3209	+	34.0429i	0.511156	+	1.41234i
$582$	7.48413	+	3.64483i	0.310227	+	0.151083i
$583$	84.0894			3.48263
$584$	−6.01110			−0.248741
$585$	−24.3144	+	19.0423i	−1.00528	+	0.787304i
$586$		−	4.12604i		−	0.170445i
$587$	−13.9660			−0.576440			−0.288220	−	0.957564i	$-0.593063\pi$
$587$	−13.9660			−0.576440			−0.288220	+	0.957564i	$0.593063\pi$
$588$	−11.7731	+	2.89743i	−0.485513	+	0.119488i
$589$	−20.9534			−0.863371
$590$		−	34.9003i		−	1.43682i
$591$	−5.21274	+	10.7036i	−0.214423	+	0.440287i
$592$	9.05297			0.372075
$593$	−38.2031			−1.56881			−0.784407	−	0.620247i	$-0.787032\pi$
$593$	−38.2031			−1.56881			−0.784407	+	0.620247i	$0.787032\pi$
$594$	−6.64814	−	31.0093i	−0.272777	−	1.27233i
$595$	3.48761	+	9.63636i	0.142978	+	0.395052i
$596$			23.5703i			0.965478i
$597$	17.8378	−	36.6274i	0.730054	−	1.49906i
$598$			4.03112i			0.164845i
$599$			0.507980i			0.0207555i	0.999946	+	0.0103778i	$0.00330340\pi$
$599$			0.507980i			0.0207555i	−0.999946	+	0.0103778i	$0.996697\pi$
$600$	−1.15404	+	2.36965i	−0.0471135	+	0.0967407i
$601$		−	17.6199i		−	0.718729i	−0.933197	−	0.359365i	$-0.882993\pi$
$601$		−	17.6199i		−	0.718729i	0.933197	−	0.359365i	$-0.117007\pi$
$602$	7.79457	−	2.82103i	0.317683	−	0.114976i
$603$	12.8158	+	16.3640i	0.521900	+	0.666392i
$604$	−15.5335			−0.632051
$605$	67.0389			2.72552
$606$	−9.48775	+	19.4817i	−0.385414	+	0.791390i
$607$		−	18.9944i		−	0.770958i	−0.922717	−	0.385479i	$-0.874036\pi$
$607$		−	18.9944i		−	0.770958i	0.922717	−	0.385479i	$-0.125964\pi$
$608$	−4.48007			−0.181691
$609$	29.8531	+	3.17466i	1.20971	+	0.128644i
$610$	9.40035			0.380609
$611$		−	1.32480i		−	0.0535955i
$612$	2.80559	+	3.58234i	0.113409	+	0.144808i
$613$	−26.3304			−1.06347			−0.531737	−	0.846910i	$-0.678460\pi$
$613$	−26.3304			−1.06347			−0.531737	+	0.846910i	$0.678460\pi$
$614$	0.0606050			0.00244582
$615$	24.5116	+	11.9374i	0.988403	+	0.481361i
$616$	−5.49546	−	15.1841i	−0.221418	−	0.611785i
$617$			23.4851i			0.945474i	0.881204	+	0.472737i	$0.156734\pi$
$617$			23.4851i			0.945474i	−0.881204	+	0.472737i	$0.843266\pi$
$618$	−9.12348	−	4.44322i	−0.367000	−	0.178732i
$619$			24.0896i			0.968241i	0.875001	+	0.484121i	$0.160860\pi$
$619$			24.0896i			0.968241i	−0.875001	+	0.484121i	$0.839140\pi$
$620$			11.9441i			0.479685i
$621$	5.08070	−	1.08926i	0.203881	−	0.0437105i
$622$			28.2869i			1.13420i
$623$	−4.61401	−	12.7486i	−0.184856	−	0.510763i
$624$	−3.05708	+	6.27726i	−0.122381	+	0.251292i
$625$	−30.2930			−1.21172
$626$	−1.98027			−0.0791476
$627$	−42.5793	−	20.7365i	−1.70045	−	0.828135i
$628$		−	5.79301i		−	0.231166i
$629$	−13.7310			−0.547491
$630$	17.1830	+	10.7524i	0.684587	+	0.428386i
$631$	−45.0611			−1.79385			−0.896927	−	0.442178i	$-0.854206\pi$
$631$	−45.0611			−1.79385			−0.896927	+	0.442178i	$0.854206\pi$
$632$			4.13077i			0.164313i
$633$	7.38880	+	3.59841i	0.293678	+	0.143024i
$634$	−0.813147			−0.0322942
$635$	−19.0227			−0.754891
$636$	−10.4485	+	21.4544i	−0.414310	+	0.850723i
$637$	18.0597	+	21.6816i	0.715552	+	0.859058i
$638$			39.9844i			1.58300i
$639$	−28.0709	+	21.9843i	−1.11047	+	0.869687i
$640$			2.55377i			0.100947i
$641$			18.4798i			0.729908i	0.931026	+	0.364954i	$0.118915\pi$
$641$			18.4798i			0.729908i	−0.931026	+	0.364954i	$0.881085\pi$
$642$	0.523438	+	0.254919i	0.0206585	+	0.0100608i
$643$			14.0680i			0.554789i	0.960756	+	0.277395i	$0.0894709\pi$
$643$			14.0680i			0.554789i	−0.960756	+	0.277395i	$0.910529\pi$
$644$	2.48783	−	0.900399i	0.0980341	−	0.0354807i
$645$	−12.4594	−	6.06786i	−0.490590	−	0.238922i
$646$	6.79511			0.267350
$647$	12.6727			0.498216			0.249108	−	0.968476i	$-0.419863\pi$
$647$	12.6727			0.498216			0.249108	+	0.968476i	$0.419863\pi$
$648$	8.73773	+	2.15685i	0.343251	+	0.0847293i
$649$		−	83.4097i		−	3.27412i
$650$	6.13431			0.240608
$651$	21.3127	+	2.26645i	0.835310	+	0.0888291i
$652$	−13.9101			−0.544763
$653$		−	21.4193i		−	0.838201i	−0.907940	−	0.419100i	$-0.862346\pi$
$653$		−	21.4193i		−	0.838201i	0.907940	−	0.419100i	$-0.137654\pi$
$654$	−12.1745	+	24.9986i	−0.476062	+	0.977523i
$655$	−1.01233			−0.0395552
$656$	6.16375			0.240654
$657$	14.1974	−	11.1190i	0.553895	−	0.433795i
$658$	−0.817605	+	0.295909i	−0.0318736	+	0.0115357i
$659$			34.9455i			1.36128i	0.732616	+	0.680642i	$0.238299\pi$
$659$			34.9455i			1.36128i	−0.732616	+	0.680642i	$0.761701\pi$
$660$	−11.8204	+	24.2714i	−0.460108	+	0.944764i
$661$		−	0.398155i		−	0.0154864i	−0.999970	−	0.00774322i	$-0.997535\pi$
$661$		−	0.398155i		−	0.0154864i	0.999970	−	0.00774322i	$-0.00246477\pi$
$662$			4.03439i			0.156801i
$663$	4.63680	−	9.52098i	0.180078	−	0.369764i
$664$		−	13.6838i		−	0.531034i
$665$	28.4634	−	10.3015i	1.10376	−	0.399476i
$666$	−21.3819	+	16.7457i	−0.828533	+	0.648884i
$667$	−6.55121			−0.253664
$668$	−21.5753			−0.834774
$669$	11.4168	−	23.4426i	0.441398	−	0.906345i
$670$		−	17.6935i		−	0.683561i
$671$	22.4663			0.867301
$672$	4.55688	+	0.484591i	0.175786	+	0.0186935i
$673$	8.44358			0.325476			0.162738	−	0.986669i	$-0.447967\pi$
$673$	8.44358			0.325476			0.162738	+	0.986669i	$0.447967\pi$
$674$			6.55839i			0.252620i
$675$	−1.65757	−	7.73150i	−0.0637999	−	0.297586i
$676$	3.24993			0.124997
$677$	36.8317			1.41556			0.707778	−	0.706435i	$-0.249698\pi$
$677$	36.8317			1.41556			0.707778	+	0.706435i	$0.249698\pi$
$678$	8.13216	+	3.96043i	0.312314	+	0.152099i
$679$	−11.9568	+	4.32744i	−0.458862	+	0.166072i
$680$		−	3.87341i		−	0.148538i
$681$	1.94810	+	0.948743i	0.0746514	+	0.0363559i
$682$			28.5456i			1.09307i
$683$		−	23.1962i		−	0.887578i	−0.896131	−	0.443789i	$-0.853634\pi$
$683$		−	23.1962i		−	0.887578i	0.896131	−	0.443789i	$-0.146366\pi$
$684$	10.5813	−	8.28701i	0.404588	−	0.316862i
$685$		−	7.61839i		−	0.291084i
$686$	9.34708	−	15.9885i	0.356873	−	0.610444i
$687$	14.1208	−	28.9949i	0.538741	−	1.10623i
$688$	−3.13309			−0.119448
$689$	55.5390			2.11587
$690$	−3.97673	−	1.93670i	−0.151392	−	0.0737290i
$691$			5.05478i			0.192293i	0.995367	+	0.0961465i	$0.0306517\pi$
$691$			5.05478i			0.192293i	−0.995367	+	0.0961465i	$0.969348\pi$
$692$	−6.39359			−0.243048
$693$	41.0663	+	25.6976i	1.55998	+	0.976172i
$694$	28.2405			1.07199
$695$			45.2033i			1.71466i
$696$	−10.2015	−	4.96824i	−0.386689	−	0.188321i
$697$	−9.34881			−0.354111
$698$	−10.7649			−0.407456
$699$	3.11720	−	6.40071i	0.117903	−	0.242097i
$700$	−1.37017	−	3.78582i	−0.0517876	−	0.143091i
$701$			0.834992i			0.0315372i	0.999876	+	0.0157686i	$0.00501951\pi$
$701$			0.834992i			0.0315372i	−0.999876	+	0.0157686i	$0.994980\pi$
$702$	−4.39094	−	20.4809i	−0.165725	−	0.773002i
$703$			40.5580i			1.52967i
$704$			6.10336i			0.230029i
$705$	1.30692	+	0.636483i	0.0492216	+	0.0239713i
$706$		−	28.1446i		−	1.05924i
$707$	−11.2646	−	31.1245i	−0.423650	−	1.17056i
$708$	21.2810	+	10.3640i	0.799790	+	0.389504i
$709$	37.9270			1.42438			0.712189	−	0.701988i	$-0.247704\pi$
$709$	37.9270			1.42438			0.712189	+	0.701988i	$0.247704\pi$
$710$	30.3516			1.13908
$711$	−7.64089	−	9.75633i	−0.286556	−	0.365891i
$712$			5.12440i			0.192045i
$713$	−4.67703			−0.175156
$714$	−6.91161	−	0.734999i	−0.258660	−	0.0275067i
$715$	62.8313			2.34976
$716$		−	14.2081i		−	0.530981i
$717$	2.96061	−	6.07917i	0.110566	−	0.227031i
$718$	26.6543			0.994728
$719$	20.1660			0.752063			0.376032	−	0.926607i	$-0.377288\pi$
$719$	20.1660			0.752063			0.376032	+	0.926607i	$0.377288\pi$
$720$	−4.72383	−	6.03167i	−0.176047	−	0.224787i
$721$	14.5759	−	5.27535i	0.542836	−	0.196464i
$722$		−	1.07106i		−	0.0398606i
$723$	18.4727	−	37.9309i	0.687006	−	1.41066i
$724$		−	9.97801i		−	0.370830i
$725$			9.96923i			0.370248i
$726$	−19.9080	+	40.8780i	−0.738853	+	1.51713i
$727$			8.42726i			0.312550i	0.987714	+	0.156275i	$0.0499485\pi$
$727$			8.42726i			0.312550i	−0.987714	+	0.156275i	$0.950051\pi$
$728$	−3.62962	−	10.0287i	−0.134523	−	0.371689i
$729$	−24.6270	+	11.0684i	−0.912112	+	0.409941i
$730$	−15.3510			−0.568165
$731$	4.75208			0.175762
$732$	−2.79154	+	5.73201i	−0.103178	+	0.211861i
$733$			39.3338i			1.45283i	0.687257	+	0.726414i	$0.258815\pi$
$733$			39.3338i			1.45283i	−0.687257	+	0.726414i	$0.741185\pi$
$734$	−9.27729			−0.342431
$735$	−30.0657	+	7.39937i	−1.10899	+	0.272930i
$736$	−1.00000			−0.0368605
$737$		−	42.2865i		−	1.55764i
$738$	−14.5580	+	11.4014i	−0.535887	+	0.419691i
$739$	−9.51835			−0.350138			−0.175069	−	0.984556i	$-0.556015\pi$
$739$	−9.51835			−0.350138			−0.175069	+	0.984556i	$0.556015\pi$
$740$	23.1192			0.849879
$741$	−28.1226	−	13.6959i	−1.03311	−	0.503133i
$742$	−12.4053	−	34.2762i	−0.455413	−	1.25832i
$743$			5.46649i			0.200546i	0.994960	+	0.100273i	$0.0319716\pi$
$743$			5.46649i			0.200546i	−0.994960	+	0.100273i	$0.968028\pi$
$744$	−7.28308	−	3.54692i	−0.267011	−	0.130036i
$745$			60.1932i			2.20531i
$746$		−	15.0035i		−	0.549318i
$747$	25.3116	+	32.3193i	0.926102	+	1.18250i
$748$		−	9.25721i		−	0.338477i
$749$	−0.836259	+	0.302661i	−0.0305562	+	0.0110590i
$750$	6.73636	−	13.8321i	0.245977	−	0.505077i
$751$	−30.4680			−1.11179			−0.555896	−	0.831252i	$-0.687625\pi$
$751$	−30.4680			−1.11179			−0.555896	+	0.831252i	$0.687625\pi$
$752$	0.328642			0.0119844
$753$	−12.3701	−	6.02435i	−0.450792	−	0.219540i
$754$			26.4087i			0.961748i
$755$	−39.6691			−1.44371
$756$	−11.6591	+	7.28455i	−0.424039	+	0.264936i
$757$	7.30393			0.265466			0.132733	−	0.991152i	$-0.457625\pi$
$757$	7.30393			0.265466			0.132733	+	0.991152i	$0.457625\pi$
$758$		−	13.7777i		−	0.500428i
$759$	−9.50415	−	4.62860i	−0.344979	−	0.168008i
$760$	−11.4411			−0.415011
$761$	26.2949			0.953191			0.476595	−	0.879123i	$-0.341871\pi$
$761$	26.2949			0.953191			0.476595	+	0.879123i	$0.341871\pi$
$762$	5.64899	−	11.5994i	0.204641	−	0.420201i
$763$	−14.4546	−	39.9385i	−0.523292	−	1.44587i
$764$			2.81898i			0.101987i
$765$	7.16483	+	9.14848i	0.259045	+	0.330764i
$766$			9.42182i			0.340424i
$767$		−	55.0901i		−	1.98919i
$768$	−1.55720	−	0.758370i	−0.0561906	−	0.0273653i
$769$			9.18242i			0.331126i	0.986199	+	0.165563i	$0.0529442\pi$
$769$			9.18242i			0.331126i	−0.986199	+	0.165563i	$0.947056\pi$
$770$	−14.0341	−	38.7767i	−0.505755	−	1.39741i
$771$	13.9738	+	6.80535i	0.503253	+	0.245089i
$772$	−19.2122			−0.691460
$773$	19.8916			0.715453			0.357726	−	0.933826i	$-0.383552\pi$
$773$	19.8916			0.715453			0.357726	+	0.933826i	$0.383552\pi$
$774$	7.39994	−	5.79542i	0.265985	−	0.208312i
$775$			7.11722i			0.255658i
$776$	4.80614			0.172530
$777$	4.38699	−	41.2533i	0.157382	−	1.47995i
$778$	−28.8711			−1.03508
$779$			27.6141i			0.989376i
$780$	−7.80708	+	16.0307i	−0.279538	+	0.573991i
$781$	72.5386			2.59563
$782$	1.51674			0.0542385
$783$	33.2847	−	7.13597i	1.18950	−	0.255019i
$784$	−5.37856	+	4.48007i	−0.192092	+	0.160003i
$785$		−	14.7940i		−	0.528021i
$786$	0.300624	−	0.617287i	0.0107229	−	0.0220179i
$787$			35.1218i			1.25196i	0.779841	+	0.625978i	$0.215300\pi$
$787$			35.1218i			1.25196i	−0.779841	+	0.625978i	$0.784700\pi$
$788$			6.87361i			0.244862i
$789$	−7.28760	+	14.9640i	−0.259445	+	0.532733i
$790$			10.5490i			0.375318i
$791$	−12.9922	+	4.70215i	−0.461948	+	0.167189i
$792$	−11.2897	−	14.4153i	−0.401161	−	0.512227i
$793$	14.8384			0.526928
$794$	33.6110			1.19281
$795$	−26.6830	+	54.7897i	−0.946350	+	1.94319i
$796$		−	23.5213i		−	0.833690i
$797$	−25.2633			−0.894872			−0.447436	−	0.894316i	$-0.647663\pi$
$797$	−25.2633			−0.894872			−0.447436	+	0.894316i	$0.647663\pi$
$798$	−2.17101	+	20.4152i	−0.0768528	+	0.722689i
$799$	−0.498465			−0.0176344
$800$			1.52174i			0.0538016i
$801$	−9.47886	−	12.1032i	−0.334919	−	0.427645i
$802$	4.42596			0.156286
$803$	−36.6879			−1.29469
$804$	10.7889	+	5.25429i	0.380495	+	0.185304i
$805$	6.35334	−	2.29941i	0.223926	−	0.0810436i
$806$			18.8537i			0.664092i
$807$	14.6511	+	7.13521i	0.515743	+	0.251171i
$808$			12.5107i			0.440125i
$809$		−	21.9126i		−	0.770407i	−0.922832	−	0.385203i	$-0.874131\pi$
$809$		−	21.9126i		−	0.770407i	0.922832	−	0.385203i	$-0.125869\pi$
$810$	22.3142	+	5.50811i	0.784040	+	0.193535i
$811$		−	2.40433i		−	0.0844274i	−0.999109	−	0.0422137i	$-0.986559\pi$
$811$		−	2.40433i		−	0.0844274i	0.999109	−	0.0422137i	$-0.0134410\pi$
$812$	16.2983	−	5.89870i	0.571957	−	0.207004i
$813$	5.45944	−	11.2101i	0.191471	−	0.393157i
$814$	55.2535			1.93663
$815$	−35.5233			−1.24433
$816$	2.36187	+	1.15025i	0.0826820	+	0.0402668i
$817$		−	14.0365i		−	0.491073i
$818$	−10.9919			−0.384322
$819$	27.1233	+	16.9727i	0.947765	+	0.593073i
$820$	15.7408			0.549693
$821$		−	20.7297i		−	0.723470i	−0.932281	−	0.361735i	$-0.882184\pi$
$821$		−	20.7297i		−	0.723470i	0.932281	−	0.361735i	$-0.117816\pi$
$822$	4.64543	+	2.26236i	0.162028	+	0.0789090i
$823$	−22.6751			−0.790405			−0.395203	−	0.918594i	$-0.629326\pi$
$823$	−22.6751			−0.790405			−0.395203	+	0.918594i	$0.629326\pi$
$824$	−5.85890			−0.204104
$825$	−7.04353	+	14.4628i	−0.245224	+	0.503531i
$826$	−33.9991	+	12.3050i	−1.18298	+	0.428147i
$827$		−	44.0204i		−	1.53074i	−0.643590	−	0.765370i	$-0.722556\pi$
$827$		−	44.0204i		−	1.53074i	0.643590	−	0.765370i	$-0.277444\pi$
$828$	2.36187	−	1.84975i	0.0820806	−	0.0642832i
$829$		−	4.94610i		−	0.171785i	−0.996304	−	0.0858927i	$-0.972626\pi$
$829$		−	4.94610i		−	0.171785i	0.996304	−	0.0858927i	$-0.0273742\pi$
$830$		−	34.9452i		−	1.21297i
$831$	−7.10624	−	3.46080i	−0.246513	−	0.120054i
$832$			4.03112i			0.139754i
$833$	8.15788	−	6.79511i	0.282654	−	0.235437i
$834$	−27.5634	−	13.4236i	−0.954443	−	0.464822i
$835$	−55.0984			−1.90676
$836$	−27.3435			−0.945694
$837$	23.7626	−	5.09450i	0.821355	−	0.176092i
$838$		−	13.4110i		−	0.463275i
$839$	10.0316			0.346331			0.173166	−	0.984893i	$-0.444600\pi$
$839$	10.0316			0.346331			0.173166	+	0.984893i	$0.444600\pi$
$840$	11.6372	+	1.23753i	0.401522	+	0.0426990i
$841$	−13.9183			−0.479942
$842$			8.69841i			0.299767i
$843$	−4.50853	+	9.25760i	−0.155282	+	0.318849i
$844$	4.74492			0.163327
$845$	8.29957			0.285514
$846$	−0.776210	+	0.607906i	−0.0266867	+	0.0209002i
$847$	−23.6363	−	65.3079i	−0.812154	−	2.24400i
$848$			13.7776i			0.473123i
$849$	−22.4831	+	46.1658i	−0.771619	+	1.58441i
$850$		−	2.30808i		−	0.0791666i
$851$			9.05297i			0.310332i
$852$	−9.01325	+	18.5074i	−0.308789	+	0.634052i
$853$			46.3969i			1.58860i	0.607526	+	0.794300i	$0.292162\pi$
$853$			46.3969i			1.58860i	−0.607526	+	0.794300i	$0.707838\pi$
$854$	−3.31434	−	9.15762i	−0.113414	−	0.313367i
$855$	27.0223	−	21.1631i	0.924144	−	0.723763i
$856$	0.336140			0.0114890
$857$	27.1091			0.926028			0.463014	−	0.886351i	$-0.346768\pi$
$857$	27.1091			0.926028			0.463014	+	0.886351i	$0.346768\pi$
$858$	−18.6585	+	38.3124i	−0.636989	+	1.30796i
$859$			11.8065i			0.402833i	0.979506	+	0.201417i	$0.0645545\pi$
$859$			11.8065i			0.402833i	−0.979506	+	0.201417i	$0.935446\pi$
$860$	−8.00118			−0.272838
$861$	2.98690	−	28.0875i	0.101793	−	0.957219i
$862$	−25.2334			−0.859453
$863$		−	12.1851i		−	0.414786i	−0.978258	−	0.207393i	$-0.933502\pi$
$863$		−	12.1851i		−	0.414786i	0.978258	−	0.207393i	$-0.0664978\pi$
$864$	5.08070	−	1.08926i	0.172849	−	0.0370574i
$865$	−16.3278			−0.555160
$866$	12.2271			0.415495
$867$	22.8901	+	11.1477i	0.777388	+	0.378594i
$868$	11.6356	−	4.21119i	0.394939	−	0.142937i
$869$			25.2116i			0.855243i
$870$	−26.0524	−	12.6877i	−0.883259	−	0.430155i
$871$		−	27.9292i		−	0.946345i
$872$			16.0536i			0.543642i
$873$	−11.3515	+	8.89015i	−0.384189	+	0.300886i
$874$		−	4.48007i		−	0.151541i
$875$	7.99795	+	22.0986i	0.270380	+	0.747068i
$876$	4.55864	−	9.36049i	0.154022	−	0.316262i
$877$	13.9904			0.472423			0.236212	−	0.971702i	$-0.424094\pi$
$877$	13.9904			0.472423			0.236212	+	0.971702i	$0.424094\pi$
$878$	10.3640			0.349767
$879$	6.42507	+	3.12906i	0.216712	+	0.105541i
$880$			15.5866i			0.525423i
$881$	−20.6146			−0.694524			−0.347262	−	0.937768i	$-0.612889\pi$
$881$	−20.6146			−0.694524			−0.347262	+	0.937768i	$0.612889\pi$
$882$	4.41645	−	20.5303i	0.148710	−	0.691293i
$883$	−17.9075			−0.602636			−0.301318	−	0.953524i	$-0.597427\pi$
$883$	−17.9075			−0.602636			−0.301318	+	0.953524i	$0.597427\pi$
$884$		−	6.11416i		−	0.205642i
$885$	54.3468	+	26.4674i	1.82685	+	0.889691i
$886$	−27.0187			−0.907711
$887$	−31.9985			−1.07441			−0.537203	−	0.843453i	$-0.680519\pi$
$887$	−31.9985			−1.07441			−0.537203	+	0.843453i	$0.680519\pi$
$888$	−6.86550	+	14.0973i	−0.230391	+	0.473074i
$889$	6.70694	+	18.5315i	0.224944	+	0.621525i
$890$			13.0865i			0.438662i
$891$	53.3295	+	13.1641i	1.78661	+	0.441012i
$892$		−	15.0543i		−	0.504057i
$893$			1.47234i			0.0492700i
$894$	−36.7037	−	17.8750i	−1.22756	−	0.597831i
$895$		−	36.2842i		−	1.21285i
$896$	2.48783	−	0.900399i	0.0831125	−	0.0300802i
$897$	−6.27726	−	3.05708i	−0.209592	−	0.102073i
$898$	−38.0881			−1.27102
$899$	−30.6402			−1.02191
$900$	−2.81484	−	3.59415i	−0.0938278	−	0.119805i
$901$		−	20.8970i		−	0.696179i
$902$	37.6196			1.25259
$903$	−1.51827	+	14.2771i	−0.0505247	+	0.475112i
$904$	5.22229			0.173691
$905$		−	25.4815i		−	0.847035i
$906$	11.7802	−	24.1889i	0.391370	−	0.803621i
$907$	−4.09112			−0.135844			−0.0679218	−	0.997691i	$-0.521637\pi$
$907$	−4.09112			−0.135844			−0.0679218	+	0.997691i	$0.521637\pi$
$908$	1.25103			0.0415168
$909$	−23.1417	−	29.5487i	−0.767561	−	0.980068i
$910$	−9.26920	−	25.6111i	−0.307271	−	0.848998i
$911$		−	53.2237i		−	1.76338i	−0.471828	−	0.881691i	$-0.656406\pi$
$911$		−	53.2237i		−	1.76338i	0.471828	−	0.881691i	$-0.343594\pi$
$912$	3.39755	−	6.97637i	0.112504	−	0.231011i
$913$		−	83.5170i		−	2.76401i
$914$		−	37.4592i		−	1.23904i
$915$	−7.12895	+	14.6382i	−0.235676	+	0.483925i
$916$		−	18.6199i		−	0.615219i
$917$	0.356925	+	0.986194i	0.0117867	+	0.0325670i
$918$	−7.70610	+	1.65212i	−0.254339	+	0.0545282i
$919$	22.9205			0.756079			0.378039	−	0.925790i	$-0.376598\pi$
$919$	22.9205			0.756079			0.378039	+	0.925790i	$0.376598\pi$
$920$	−2.55377			−0.0841953
$921$	−0.0459610	+	0.0943742i	−0.00151447	+	0.00310973i
$922$		−	2.96163i		−	0.0975362i
$923$	47.9100			1.57698
$924$	27.8123	+	2.95763i	0.914957	+	0.0972990i
$925$	13.7763			0.452960
$926$			31.9983i			1.05153i
$927$	13.8380	−	10.8375i	0.454498	−	0.355950i
$928$	−6.55121			−0.215054
$929$	56.2496			1.84549			0.922746	−	0.385410i	$-0.125940\pi$
$929$	56.2496			1.84549			0.922746	+	0.385410i	$0.125940\pi$
$930$	−18.5993	−	9.05802i	−0.609895	−	0.297024i
$931$	−20.0711	−	24.0964i	−0.657802	−	0.789726i
$932$		−	4.11040i		−	0.134640i
$933$	−44.0484	−	21.4520i	−1.44208	−	0.702306i
$934$		−	5.67699i		−	0.185757i
$935$		−	23.6408i		−	0.773136i
$936$	−7.45656	−	9.52098i	−0.243725	−	0.311203i
$937$			7.77495i			0.253996i	0.991903	+	0.126998i	$0.0405342\pi$
$937$			7.77495i			0.253996i	−0.991903	+	0.126998i	$0.959466\pi$
$938$	−17.2366	+	6.23832i	−0.562796	+	0.203688i
$939$	1.50178	−	3.08368i	0.0490087	−	0.100632i
$940$	0.839277			0.0273742
$941$	3.41087			0.111191			0.0555956	−	0.998453i	$-0.482294\pi$
$941$	3.41087			0.111191			0.0555956	+	0.998453i	$0.482294\pi$
$942$	9.02087	+	4.39324i	0.293916	+	0.143140i
$943$			6.16375i			0.200719i
$944$	13.6662			0.444797
$945$	−29.7747	+	18.6031i	−0.968572	+	0.605157i
$946$	−19.1223			−0.621721
$947$		−	19.5240i		−	0.634444i	−0.948351	−	0.317222i	$-0.897250\pi$
$947$		−	19.5240i		−	0.634444i	0.948351	−	0.317222i	$-0.102750\pi$
$948$	−6.43244	−	3.13265i	−0.208916	−	0.101744i
$949$	−24.2315			−0.786587
$950$	−6.81750			−0.221189
$951$	0.616667	−	1.26623i	0.0199968	−	0.0410604i
$952$	−3.77339	+	1.36567i	−0.122296	+	0.0442617i
$953$			4.88731i			0.158316i	0.996862	+	0.0791578i	$0.0252231\pi$
$953$			4.88731i			0.158316i	−0.996862	+	0.0791578i	$0.974777\pi$
$954$	−25.4850	−	32.5408i	−0.825108	−	1.05355i
$955$			7.19903i			0.232955i
$956$		−	3.90391i		−	0.126261i
$957$	−62.2637	−	30.3229i	−2.01270	−	0.980202i
$958$		−	24.9322i		−	0.805523i
$959$	−7.42167	+	2.68606i	−0.239658	+	0.0867375i
$960$	−3.97673	−	1.93670i	−0.128348	−	0.0625068i
$961$	9.12538			0.294367
$962$	36.4936			1.17660
$963$	−0.793920	+	0.621776i	−0.0255837	+	0.0200364i
$964$		−	24.3584i		−	0.784530i
$965$	−49.0634			−1.57941
$966$	−0.484591	+	4.55688i	−0.0155915	+	0.146615i
$967$	15.9028			0.511401			0.255700	−	0.966756i	$-0.417694\pi$
$967$	15.9028			0.511401			0.255700	+	0.966756i	$0.417694\pi$
$968$			26.2510i			0.843738i
$969$	−5.15321	+	10.5813i	−0.165545	+	0.339922i
$970$	12.2738			0.394087
$971$	−4.03540			−0.129502			−0.0647510	−	0.997901i	$-0.520625\pi$
$971$	−4.03540			−0.129502			−0.0647510	+	0.997901i	$0.520625\pi$
$972$	−9.98509	+	11.9707i	−0.320272	+	0.383961i
$973$	44.0361	−	15.9376i	1.41173	−	0.510937i
$974$		−	0.150114i		−	0.00480995i
$975$	−4.65208	+	9.55236i	−0.148986	+	0.305920i
$976$			3.68097i			0.117825i
$977$			10.6741i			0.341494i	0.985315	+	0.170747i	$0.0546181\pi$
$977$			10.6741i			0.341494i	−0.985315	+	0.170747i	$0.945382\pi$
$978$	10.5490	−	21.6609i	0.337321	−	0.692638i
$979$			31.2761i			0.999587i
$980$	−13.7356	+	11.4411i	−0.438768	+	0.365472i
$981$	−29.6951	−	37.9164i	−0.948090	−	1.21058i
$982$	−17.8076			−0.568264
$983$	−11.2835			−0.359887			−0.179943	−	0.983677i	$-0.557591\pi$
$983$	−11.2835			−0.359887			−0.179943	+	0.983677i	$0.557591\pi$
$984$	−4.67441	+	9.59820i	−0.149015	+	0.305979i
$985$			17.5536i			0.559304i
$986$	9.93648			0.316442
$987$	0.159257	−	1.49758i	0.00506922	−	0.0476686i
$988$	−18.0597			−0.574556
$989$		−	3.13309i		−	0.0996263i
$990$	−28.8312	−	36.8134i	−0.916317	−	1.17001i
$991$	46.3913			1.47367			0.736834	−	0.676074i	$-0.236320\pi$
$991$	46.3913			1.47367			0.736834	+	0.676074i	$0.236320\pi$
$992$	−4.67703			−0.148496
$993$	−6.28236	−	3.05956i	−0.199365	−	0.0970923i
$994$	−10.7013	−	29.5679i	−0.339424	−	0.937837i
$995$		−	60.0680i		−	1.90428i
$996$	21.3084	+	10.3774i	0.675183	+	0.328820i
$997$			32.9819i			1.04455i	0.852778	+	0.522273i	$0.174916\pi$
$997$			32.9819i			1.04455i	−0.852778	+	0.522273i	$0.825084\pi$
$998$			17.0614i			0.540070i
$999$	−9.86104	−	45.9954i	−0.311989	−	1.45523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.c.461.16	yes	28
3.2	odd	2	inner	966.2.f.c.461.13	yes	28
7.6	odd	2	inner	966.2.f.c.461.27	yes	28
21.20	even	2	inner	966.2.f.c.461.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.c.461.2	✓	28	21.20	even	2	inner
966.2.f.c.461.13	yes	28	3.2	odd	2	inner
966.2.f.c.461.16	yes	28	1.1	even	1	trivial
966.2.f.c.461.27	yes	28	7.6	odd	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.55720 - 0.758370i) q^{3} -1.00000 q^{4} -2.55377 q^{5} +(0.758370 - 1.55720i) q^{6} +(0.900399 + 2.48783i) q^{7} -1.00000i q^{8} +(1.84975 + 2.36187i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.55720 - 0.758370i) q^{3} -1.00000 q^{4} -2.55377 q^{5} +(0.758370 - 1.55720i) q^{6} +(0.900399 + 2.48783i) q^{7} -1.00000i q^{8} +(1.84975 + 2.36187i) q^{9} -2.55377i q^{10} -6.10336i q^{11} +(1.55720 + 0.758370i) q^{12} -4.03112i q^{13} +(-2.48783 + 0.900399i) q^{14} +(3.97673 + 1.93670i) q^{15} +1.00000 q^{16} -1.51674 q^{17} +(-2.36187 + 1.84975i) q^{18} +4.48007i q^{19} +2.55377 q^{20} +(0.484591 - 4.55688i) q^{21} +6.10336 q^{22} +1.00000i q^{23} +(-0.758370 + 1.55720i) q^{24} +1.52174 q^{25} +4.03112 q^{26} +(-1.08926 - 5.08070i) q^{27} +(-0.900399 - 2.48783i) q^{28} +6.55121i q^{29} +(-1.93670 + 3.97673i) q^{30} +4.67703i q^{31} +1.00000i q^{32} +(-4.62860 + 9.50415i) q^{33} -1.51674i q^{34} +(-2.29941 - 6.35334i) q^{35} +(-1.84975 - 2.36187i) q^{36} +9.05297 q^{37} -4.48007 q^{38} +(-3.05708 + 6.27726i) q^{39} +2.55377i q^{40} +6.16375 q^{41} +(4.55688 + 0.484591i) q^{42} -3.13309 q^{43} +6.10336i q^{44} +(-4.72383 - 6.03167i) q^{45} -1.00000 q^{46} +0.328642 q^{47} +(-1.55720 - 0.758370i) q^{48} +(-5.37856 + 4.48007i) q^{49} +1.52174i q^{50} +(2.36187 + 1.15025i) q^{51} +4.03112i q^{52} +13.7776i q^{53} +(5.08070 - 1.08926i) q^{54} +15.5866i q^{55} +(2.48783 - 0.900399i) q^{56} +(3.39755 - 6.97637i) q^{57} -6.55121 q^{58} +13.6662 q^{59} +(-3.97673 - 1.93670i) q^{60} +3.68097i q^{61} -4.67703 q^{62} +(-4.21041 + 6.72848i) q^{63} -1.00000 q^{64} +10.2946i q^{65} +(-9.50415 - 4.62860i) q^{66} +6.92840 q^{67} +1.51674 q^{68} +(0.758370 - 1.55720i) q^{69} +(6.35334 - 2.29941i) q^{70} +11.8850i q^{71} +(2.36187 - 1.84975i) q^{72} -6.01110i q^{73} +9.05297i q^{74} +(-2.36965 - 1.15404i) q^{75} -4.48007i q^{76} +(15.1841 - 5.49546i) q^{77} +(-6.27726 - 3.05708i) q^{78} -4.13077 q^{79} -2.55377 q^{80} +(-2.15685 + 8.73773i) q^{81} +6.16375i q^{82} +13.6838 q^{83} +(-0.484591 + 4.55688i) q^{84} +3.87341 q^{85} -3.13309i q^{86} +(4.96824 - 10.2015i) q^{87} -6.10336 q^{88} -5.12440 q^{89} +(6.03167 - 4.72383i) q^{90} +(10.0287 - 3.62962i) q^{91} -1.00000i q^{92} +(3.54692 - 7.28308i) q^{93} +0.328642i q^{94} -11.4411i q^{95} +(0.758370 - 1.55720i) q^{96} +4.80614i q^{97} +(-4.48007 - 5.37856i) q^{98} +(14.4153 - 11.2897i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more