LMFDB - Embedded newform 462.2.c.b.197.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(197,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("462.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.c (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 94x^{8} + 246x^{6} + 277x^{4} + 114x^{2} + 9 $ x^12 + 16x^10 + 94x^8 + 246x^6 + 277x^4 + 114*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.10
Root			$0.319443i$ of defining polynomial
Character	$\chi$	$=$	462.197
Dual form			462.2.c.b.197.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.37401 + 1.05456i) q^{3} +1.00000 q^{4} -3.92876i q^{5} +(1.37401 + 1.05456i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(0.775791 + 2.89796i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.37401 + 1.05456i) q^{3} +1.00000 q^{4} -3.92876i q^{5} +(1.37401 + 1.05456i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(0.775791 + 2.89796i) q^{9} -3.92876i q^{10} +(-1.42857 - 2.99319i) q^{11} +(1.37401 + 1.05456i) q^{12} -0.109128i q^{13} +1.00000i q^{14} +(4.14313 - 5.39815i) q^{15} +1.00000 q^{16} +6.97666 q^{17} +(0.775791 + 2.89796i) q^{18} +5.78023i q^{19} -3.92876i q^{20} +(-1.05456 + 1.37401i) q^{21} +(-1.42857 - 2.99319i) q^{22} -0.938770i q^{23} +(1.37401 + 1.05456i) q^{24} -10.4352 q^{25} -0.109128i q^{26} +(-1.99014 + 4.79993i) q^{27} +1.00000i q^{28} -10.3479 q^{29} +(4.14313 - 5.39815i) q^{30} -2.61516 q^{31} +1.00000 q^{32} +(1.19364 - 5.61918i) q^{33} +6.97666 q^{34} +3.92876 q^{35} +(0.775791 + 2.89796i) q^{36} +7.21864 q^{37} +5.78023i q^{38} +(0.115082 - 0.149942i) q^{39} -3.92876i q^{40} -8.95059 q^{41} +(-1.05456 + 1.37401i) q^{42} +1.44880i q^{43} +(-1.42857 - 2.99319i) q^{44} +(11.3854 - 3.04790i) q^{45} -0.938770i q^{46} +11.4115i q^{47} +(1.37401 + 1.05456i) q^{48} -1.00000 q^{49} -10.4352 q^{50} +(9.58598 + 7.35733i) q^{51} -0.109128i q^{52} -5.55158i q^{53} +(-1.99014 + 4.79993i) q^{54} +(-11.7595 + 5.61252i) q^{55} +1.00000i q^{56} +(-6.09562 + 7.94207i) q^{57} -10.3479 q^{58} +7.60516i q^{59} +(4.14313 - 5.39815i) q^{60} -6.35346i q^{61} -2.61516 q^{62} +(-2.89796 + 0.775791i) q^{63} +1.00000 q^{64} -0.428736 q^{65} +(1.19364 - 5.61918i) q^{66} +5.60544 q^{67} +6.97666 q^{68} +(0.989993 - 1.28988i) q^{69} +3.92876 q^{70} -4.39287i q^{71} +(0.775791 + 2.89796i) q^{72} +3.31566i q^{73} +7.21864 q^{74} +(-14.3380 - 11.0046i) q^{75} +5.78023i q^{76} +(2.99319 - 1.42857i) q^{77} +(0.115082 - 0.149942i) q^{78} -0.361499i q^{79} -3.92876i q^{80} +(-7.79630 + 4.49641i) q^{81} -8.95059 q^{82} +1.48034 q^{83} +(-1.05456 + 1.37401i) q^{84} -27.4097i q^{85} +1.44880i q^{86} +(-14.2181 - 10.9125i) q^{87} +(-1.42857 - 2.99319i) q^{88} -0.722227i q^{89} +(11.3854 - 3.04790i) q^{90} +0.109128 q^{91} -0.938770i q^{92} +(-3.59325 - 2.75786i) q^{93} +11.4115i q^{94} +22.7092 q^{95} +(1.37401 + 1.05456i) q^{96} -3.48997 q^{97} -1.00000 q^{98} +(7.56586 - 6.46202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^2 + 4 * q^3 + 12 * q^4 + 4 * q^6 + 12 * q^8	$ 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8} + 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} + 4 q^{17} + 8 q^{22} + 4 q^{24} - 28 q^{25} - 8 q^{27} - 8 q^{29} + 4 q^{30} + 12 q^{31} + 12 q^{32} - 16 q^{33} + 4 q^{34} + 4 q^{35} + 36 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} - 28 q^{50} - 8 q^{51} - 8 q^{54} + 4 q^{55} - 28 q^{57} - 8 q^{58} + 4 q^{60} + 12 q^{62} - 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} + 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} - 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} - 44 q^{83} - 8 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} - 24 q^{93} + 4 q^{96} - 48 q^{97} - 12 q^{98} + 20 q^{99}+O(q^{100}) $ 12 * q + 12 * q^2 + 4 * q^3 + 12 * q^4 + 4 * q^6 + 12 * q^8 + 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 + 4 * q^17 + 8 * q^22 + 4 * q^24 - 28 * q^25 - 8 * q^27 - 8 * q^29 + 4 * q^30 + 12 * q^31 + 12 * q^32 - 16 * q^33 + 4 * q^34 + 4 * q^35 + 36 * q^39 - 20 * q^41 + 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 - 28 * q^50 - 8 * q^51 - 8 * q^54 + 4 * q^55 - 28 * q^57 - 8 * q^58 + 4 * q^60 + 12 * q^62 - 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 + 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 - 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 - 44 * q^83 - 8 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 - 24 * q^93 + 4 * q^96 - 48 * q^97 - 12 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.37401	+	1.05456i	0.793283	+	0.608853i
$3$	1.37401	+	1.05456i	0.793283	+	0.608853i
$4$	1.00000			0.500000
$5$		−	3.92876i		−	1.75700i	−0.477746	−	0.878498i	$-0.658546\pi$
$5$		−	3.92876i		−	1.75700i	0.477746	−	0.878498i	$-0.341454\pi$
$6$	1.37401	+	1.05456i	0.560936	+	0.430524i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.00000			0.353553
$9$	0.775791	+	2.89796i	0.258597	+	0.965985i
$10$		−	3.92876i		−	1.24238i
$11$	−1.42857	−	2.99319i	−0.430730	−	0.902481i
$11$	−1.42857	−	2.99319i	−0.430730	−	0.902481i
$12$	1.37401	+	1.05456i	0.396642	+	0.304426i
$13$		−	0.109128i		−	0.0302665i	−0.999885	−	0.0151333i	$-0.995183\pi$
$13$		−	0.109128i		−	0.0302665i	0.999885	−	0.0151333i	$-0.00481725\pi$
$14$			1.00000i			0.267261i
$15$	4.14313	−	5.39815i	1.06975	−	1.39380i
$16$	1.00000			0.250000
$17$	6.97666			1.69209			0.846045	−	0.533112i	$-0.178978\pi$
$17$	6.97666			1.69209			0.846045	+	0.533112i	$0.178978\pi$
$18$	0.775791	+	2.89796i	0.182856	+	0.683055i
$19$			5.78023i			1.32608i	0.748586	+	0.663038i	$0.230733\pi$
$19$			5.78023i			1.32608i	−0.748586	+	0.663038i	$0.769267\pi$
$20$		−	3.92876i		−	0.878498i
$21$	−1.05456	+	1.37401i	−0.230125	+	0.299833i
$22$	−1.42857	−	2.99319i	−0.304572	−	0.638150i
$23$		−	0.938770i		−	0.195747i	−0.995199	−	0.0978736i	$-0.968796\pi$
$23$		−	0.938770i		−	0.195747i	0.995199	−	0.0978736i	$-0.0312041\pi$
$24$	1.37401	+	1.05456i	0.280468	+	0.215262i
$25$	−10.4352			−2.08704
$26$		−	0.109128i		−	0.0214017i
$27$	−1.99014	+	4.79993i	−0.383002	+	0.923747i
$28$			1.00000i			0.188982i
$29$	−10.3479			−1.92155			−0.960776	−	0.277324i	$-0.910552\pi$
$29$	−10.3479			−1.92155			−0.960776	+	0.277324i	$0.910552\pi$
$30$	4.14313	−	5.39815i	0.756429	−	0.985563i
$31$	−2.61516			−0.469697			−0.234849	−	0.972032i	$-0.575459\pi$
$31$	−2.61516			−0.469697			−0.234849	+	0.972032i	$0.575459\pi$
$32$	1.00000			0.176777
$33$	1.19364	−	5.61918i	0.207787	−	0.978174i
$34$	6.97666			1.19649
$35$	3.92876			0.664082
$36$	0.775791	+	2.89796i	0.129298	+	0.482993i
$37$	7.21864			1.18674			0.593369	−	0.804931i	$-0.297798\pi$
$37$	7.21864			1.18674			0.593369	+	0.804931i	$0.297798\pi$
$38$			5.78023i			0.937677i
$39$	0.115082	−	0.149942i	0.0184279	−	0.0240099i
$40$		−	3.92876i		−	0.621192i
$41$	−8.95059			−1.39785			−0.698923	−	0.715197i	$-0.746337\pi$
$41$	−8.95059			−1.39785			−0.698923	+	0.715197i	$0.746337\pi$
$42$	−1.05456	+	1.37401i	−0.162723	+	0.212014i
$43$			1.44880i			0.220941i	0.993879	+	0.110470i	$0.0352357\pi$
$43$			1.44880i			0.220941i	−0.993879	+	0.110470i	$0.964764\pi$
$44$	−1.42857	−	2.99319i	−0.215365	−	0.451240i
$45$	11.3854	−	3.04790i	1.69723	−	0.454354i
$46$		−	0.938770i		−	0.138414i
$47$			11.4115i			1.66453i	0.554376	+	0.832266i	$0.312957\pi$
$47$			11.4115i			1.66453i	−0.554376	+	0.832266i	$0.687043\pi$
$48$	1.37401	+	1.05456i	0.198321	+	0.152213i
$49$	−1.00000			−0.142857
$50$	−10.4352			−1.47576
$51$	9.58598	+	7.35733i	1.34231	+	1.03023i
$52$		−	0.109128i		−	0.0151333i
$53$		−	5.55158i		−	0.762568i	−0.924458	−	0.381284i	$-0.875482\pi$
$53$		−	5.55158i		−	0.762568i	0.924458	−	0.381284i	$-0.124518\pi$
$54$	−1.99014	+	4.79993i	−0.270823	+	0.653188i
$55$	−11.7595	+	5.61252i	−1.58566	+	0.756792i
$56$			1.00000i			0.133631i
$57$	−6.09562	+	7.94207i	−0.807385	+	1.05195i
$58$	−10.3479			−1.35874
$59$			7.60516i			0.990107i	0.868863	+	0.495053i	$0.164852\pi$
$59$			7.60516i			0.990107i	−0.868863	+	0.495053i	$0.835148\pi$
$60$	4.14313	−	5.39815i	0.534876	−	0.696898i
$61$		−	6.35346i		−	0.813477i	−0.913545	−	0.406738i	$-0.866666\pi$
$61$		−	6.35346i		−	0.813477i	0.913545	−	0.406738i	$-0.133334\pi$
$62$	−2.61516			−0.332126
$63$	−2.89796	+	0.775791i	−0.365108	+	0.0977404i
$64$	1.00000			0.125000
$65$	−0.428736			−0.0531782
$66$	1.19364	−	5.61918i	0.146927	−	0.691674i
$67$	5.60544			0.684814			0.342407	−	0.939552i	$-0.388758\pi$
$67$	5.60544			0.684814			0.342407	+	0.939552i	$0.388758\pi$
$68$	6.97666			0.846045
$69$	0.989993	−	1.28988i	0.119181	−	0.155283i
$70$	3.92876			0.469577
$71$		−	4.39287i		−	0.521337i	−0.965428	−	0.260669i	$-0.916057\pi$
$71$		−	4.39287i		−	0.521337i	0.965428	−	0.260669i	$-0.0839430\pi$
$72$	0.775791	+	2.89796i	0.0914278	+	0.341527i
$73$			3.31566i			0.388069i	0.980995	+	0.194035i	$0.0621574\pi$
$73$			3.31566i			0.388069i	−0.980995	+	0.194035i	$0.937843\pi$
$74$	7.21864			0.839150
$75$	−14.3380	−	11.0046i	−1.65561	−	1.27070i
$76$			5.78023i			0.663038i
$77$	2.99319	−	1.42857i	0.341106	−	0.162801i
$78$	0.115082	−	0.149942i	0.0130305	−	0.0169776i
$79$		−	0.361499i		−	0.0406719i	−0.999793	−	0.0203359i	$-0.993526\pi$
$79$		−	0.361499i		−	0.0406719i	0.999793	−	0.0203359i	$-0.00647357\pi$
$80$		−	3.92876i		−	0.439249i
$81$	−7.79630	+	4.49641i	−0.866255	+	0.499602i
$82$	−8.95059			−0.988427
$83$	1.48034			0.162489			0.0812445	−	0.996694i	$-0.474111\pi$
$83$	1.48034			0.162489			0.0812445	+	0.996694i	$0.474111\pi$
$84$	−1.05456	+	1.37401i	−0.115062	+	0.149916i
$85$		−	27.4097i		−	2.97299i
$86$			1.44880i			0.156229i
$87$	−14.2181	−	10.9125i	−1.52434	−	1.16994i
$88$	−1.42857	−	2.99319i	−0.152286	−	0.319075i
$89$		−	0.722227i		−	0.0765559i	−0.999267	−	0.0382779i	$-0.987813\pi$
$89$		−	0.722227i		−	0.0765559i	0.999267	−	0.0382779i	$-0.0121872\pi$
$90$	11.3854	−	3.04790i	1.20012	−	0.321277i
$91$	0.109128			0.0114397
$92$		−	0.938770i		−	0.0978736i
$93$	−3.59325	−	2.75786i	−0.372603	−	0.285976i
$94$			11.4115i			1.17700i
$95$	22.7092			2.32991
$96$	1.37401	+	1.05456i	0.140234	+	0.107631i
$97$	−3.48997			−0.354352			−0.177176	−	0.984179i	$-0.556696\pi$
$97$	−3.48997			−0.354352			−0.177176	+	0.984179i	$0.556696\pi$
$98$	−1.00000			−0.101015
$99$	7.56586	−	6.46202i	0.760398	−	0.649458i
$100$	−10.4352			−1.04352
$101$	−10.2648			−1.02139			−0.510694	−	0.859762i	$-0.670612\pi$
$101$	−10.2648			−1.02139			−0.510694	+	0.859762i	$0.670612\pi$
$102$	9.58598	+	7.35733i	0.949154	+	0.728485i
$103$	−3.64331			−0.358986			−0.179493	−	0.983759i	$-0.557446\pi$
$103$	−3.64331			−0.358986			−0.179493	+	0.983759i	$0.557446\pi$
$104$		−	0.109128i		−	0.0107008i
$105$	5.39815	+	4.14313i	0.526805	+	0.404328i
$106$		−	5.55158i		−	0.539217i
$107$	−10.3337			−0.999000			−0.499500	−	0.866314i	$-0.666483\pi$
$107$	−10.3337			−0.999000			−0.499500	+	0.866314i	$0.666483\pi$
$108$	−1.99014	+	4.79993i	−0.191501	+	0.461874i
$109$		−	13.7090i		−	1.31308i	−0.754290	−	0.656542i	$-0.772019\pi$
$109$		−	13.7090i		−	1.31308i	0.754290	−	0.656542i	$-0.227981\pi$
$110$	−11.7595	+	5.61252i	−1.12123	+	0.535133i
$111$	9.91846	+	7.61252i	0.941419	+	0.722548i
$112$			1.00000i			0.0944911i
$113$		−	0.803856i		−	0.0756204i	−0.999285	−	0.0378102i	$-0.987962\pi$
$113$		−	0.803856i		−	0.0756204i	0.999285	−	0.0378102i	$-0.0120382\pi$
$114$	−6.09562	+	7.94207i	−0.570907	+	0.743843i
$115$	−3.68821			−0.343927
$116$	−10.3479			−0.960776
$117$	0.316247	−	0.0846601i	0.0292370	−	0.00782683i
$118$			7.60516i			0.700111i
$119$			6.97666i			0.639550i
$120$	4.14313	−	5.39815i	0.378214	−	0.492781i
$121$	−6.91837	+	8.55197i	−0.628943	+	0.777452i
$122$		−	6.35346i		−	0.575215i
$123$	−12.2982	−	9.43896i	−1.10889	−	0.851083i
$124$	−2.61516			−0.234849
$125$			21.3536i			1.90992i
$126$	−2.89796	+	0.775791i	−0.258170	+	0.0691129i
$127$		−	14.3201i		−	1.27070i	−0.772223	−	0.635351i	$-0.780855\pi$
$127$		−	14.3201i		−	1.27070i	0.772223	−	0.635351i	$-0.219145\pi$
$128$	1.00000			0.0883883
$129$	−1.52786	+	1.99067i	−0.134520	+	0.175269i
$130$	−0.428736			−0.0376026
$131$	17.8346			1.55822			0.779109	−	0.626889i	$-0.215672\pi$
$131$	17.8346			1.55822			0.779109	+	0.626889i	$0.215672\pi$
$132$	1.19364	−	5.61918i	0.103893	−	0.489087i
$133$	−5.78023			−0.501209
$134$	5.60544			0.484237
$135$	18.8578	+	7.81878i	1.62302	+	0.672933i
$136$	6.97666			0.598244
$137$			6.72300i			0.574385i	0.957873	+	0.287192i	$0.0927219\pi$
$137$			6.72300i			0.574385i	−0.957873	+	0.287192i	$0.907278\pi$
$138$	0.989993	−	1.28988i	0.0842738	−	0.109802i
$139$		−	6.05064i		−	0.513208i	−0.966517	−	0.256604i	$-0.917396\pi$
$139$		−	6.05064i		−	0.513208i	0.966517	−	0.256604i	$-0.0826036\pi$
$140$	3.92876			0.332041
$141$	−12.0341	+	15.6794i	−1.01346	+	1.32045i
$142$		−	4.39287i		−	0.368641i
$143$	−0.326639	+	0.155896i	−0.0273150	+	0.0130367i
$144$	0.775791	+	2.89796i	0.0646492	+	0.241496i
$145$			40.6544i			3.37616i
$146$			3.31566i			0.274406i
$147$	−1.37401	−	1.05456i	−0.113326	−	0.0869790i
$148$	7.21864			0.593369
$149$	6.65134			0.544899			0.272450	−	0.962170i	$-0.412166\pi$
$149$	6.65134			0.544899			0.272450	+	0.962170i	$0.412166\pi$
$150$	−14.3380	−	11.0046i	−1.17069	−	0.898519i
$151$		−	0.977889i		−	0.0795795i	−0.999208	−	0.0397897i	$-0.987331\pi$
$151$		−	0.977889i		−	0.0795795i	0.999208	−	0.0397897i	$-0.0126688\pi$
$152$			5.78023i			0.468838i
$153$	5.41243	+	20.2181i	0.437569	+	1.63453i
$154$	2.99319	−	1.42857i	0.241198	−	0.115118i
$155$			10.2744i			0.825256i
$156$	0.115082	−	0.149942i	0.00921393	−	0.0120050i
$157$	−1.12491			−0.0897774			−0.0448887	−	0.998992i	$-0.514293\pi$
$157$	−1.12491			−0.0897774			−0.0448887	+	0.998992i	$0.514293\pi$
$158$		−	0.361499i		−	0.0287593i
$159$	5.85450	−	7.62791i	0.464292	−	0.604933i
$160$		−	3.92876i		−	0.310596i
$161$	0.938770			0.0739855
$162$	−7.79630	+	4.49641i	−0.612535	+	0.353272i
$163$	−2.94048			−0.230316			−0.115158	−	0.993347i	$-0.536737\pi$
$163$	−2.94048			−0.230316			−0.115158	+	0.993347i	$0.536737\pi$
$164$	−8.95059			−0.698923
$165$	−22.0764	−	4.68954i	−1.71865	−	0.365080i
$166$	1.48034			0.114897
$167$	21.5860			1.67037			0.835186	−	0.549968i	$-0.185360\pi$
$167$	21.5860			1.67037			0.835186	+	0.549968i	$0.185360\pi$
$168$	−1.05456	+	1.37401i	−0.0813614	+	0.106007i
$169$	12.9881			0.999084
$170$		−	27.4097i		−	2.10222i
$171$	−16.7508	+	4.48425i	−1.28097	+	0.342919i
$172$			1.44880i			0.110470i
$173$	5.10422			0.388067			0.194033	−	0.980995i	$-0.437843\pi$
$173$	5.10422			0.388067			0.194033	+	0.980995i	$0.437843\pi$
$174$	−14.2181	−	10.9125i	−1.07787	−	0.827274i
$175$		−	10.4352i		−	0.788826i
$176$	−1.42857	−	2.99319i	−0.107683	−	0.225620i
$177$	−8.02012	+	10.4495i	−0.602829	+	0.785435i
$178$		−	0.722227i		−	0.0541332i
$179$		−	17.2258i		−	1.28752i	−0.765229	−	0.643759i	$-0.777374\pi$
$179$		−	17.2258i		−	1.28752i	0.765229	−	0.643759i	$-0.222626\pi$
$180$	11.3854	−	3.04790i	0.848616	−	0.227177i
$181$	11.9832			0.890701			0.445350	−	0.895356i	$-0.353079\pi$
$181$	11.9832			0.890701			0.445350	+	0.895356i	$0.353079\pi$
$182$	0.109128			0.00808907
$183$	6.70013	−	8.72970i	0.495288	−	0.645318i
$184$		−	0.938770i		−	0.0692071i
$185$		−	28.3603i		−	2.08509i
$186$	−3.59325	−	2.75786i	−0.263470	−	0.202216i
$187$	−9.96665	−	20.8825i	−0.728834	−	1.52708i
$188$			11.4115i			0.832266i
$189$	−4.79993	−	1.99014i	−0.349144	−	0.144761i
$190$	22.7092			1.64750
$191$			13.1345i			0.950381i	0.879883	+	0.475191i	$0.157621\pi$
$191$			13.1345i			0.950381i	−0.879883	+	0.475191i	$0.842379\pi$
$192$	1.37401	+	1.05456i	0.0991604	+	0.0761066i
$193$		−	7.13624i		−	0.513678i	−0.966454	−	0.256839i	$-0.917319\pi$
$193$		−	7.13624i		−	0.513678i	0.966454	−	0.256839i	$-0.0826810\pi$
$194$	−3.48997			−0.250565
$195$	−0.589087	−	0.452130i	−0.0421854	−	0.0323777i
$196$	−1.00000			−0.0714286
$197$	1.57331			0.112093			0.0560467	−	0.998428i	$-0.482150\pi$
$197$	1.57331			0.112093			0.0560467	+	0.998428i	$0.482150\pi$
$198$	7.56586	−	6.46202i	0.537682	−	0.459236i
$199$	−4.38353			−0.310740			−0.155370	−	0.987856i	$-0.549657\pi$
$199$	−4.38353			−0.310740			−0.155370	+	0.987856i	$0.549657\pi$
$200$	−10.4352			−0.737879
$201$	7.70192	+	5.91130i	0.543252	+	0.416951i
$202$	−10.2648			−0.722231
$203$		−	10.3479i		−	0.726279i
$204$	9.58598	+	7.35733i	0.671153	+	0.515116i
$205$			35.1647i			2.45601i
$206$	−3.64331			−0.253842
$207$	2.72052	−	0.728289i	0.189089	−	0.0506196i
$208$		−	0.109128i		−	0.00756663i
$209$	17.3013	−	8.25747i	1.19676	−	0.571181i
$210$	5.39815	+	4.14313i	0.372508	+	0.285903i
$211$			5.34526i			0.367983i	0.982928	+	0.183991i	$0.0589018\pi$
$211$			5.34526i			0.367983i	−0.982928	+	0.183991i	$0.941098\pi$
$212$		−	5.55158i		−	0.381284i
$213$	4.63256	−	6.03583i	0.317418	−	0.413568i
$214$	−10.3337			−0.706399
$215$	5.69201			0.388192
$216$	−1.99014	+	4.79993i	−0.135412	+	0.326594i
$217$		−	2.61516i		−	0.177529i
$218$		−	13.7090i		−	0.928490i
$219$	−3.49658	+	4.55575i	−0.236277	+	0.307849i
$220$	−11.7595	+	5.61252i	−0.792828	+	0.378396i
$221$		−	0.761346i		−	0.0512137i
$222$	9.91846	+	7.61252i	0.665684	+	0.510919i
$223$	19.0577			1.27620			0.638100	−	0.769953i	$-0.279721\pi$
$223$	19.0577			1.27620			0.638100	+	0.769953i	$0.279721\pi$
$224$			1.00000i			0.0668153i
$225$	−8.09552	−	30.2407i	−0.539701	−	2.01605i
$226$		−	0.803856i		−	0.0534717i
$227$	17.2146			1.14258			0.571288	−	0.820750i	$-0.306444\pi$
$227$	17.2146			1.14258			0.571288	+	0.820750i	$0.306444\pi$
$228$	−6.09562	+	7.94207i	−0.403692	+	0.525977i
$229$	20.4671			1.35250			0.676252	−	0.736670i	$-0.263603\pi$
$229$	20.4671			1.35250			0.676252	+	0.736670i	$0.263603\pi$
$230$	−3.68821			−0.243193
$231$	5.61918	+	1.19364i	0.369715	+	0.0785360i
$232$	−10.3479			−0.679372
$233$	−17.1712			−1.12492			−0.562460	−	0.826824i	$-0.690145\pi$
$233$	−17.1712			−1.12492			−0.562460	+	0.826824i	$0.690145\pi$
$234$	0.316247	−	0.0846601i	0.0206737	−	0.00553440i
$235$	44.8329			2.92458
$236$			7.60516i			0.495053i
$237$	0.381224	−	0.496703i	0.0247632	−	0.0322643i
$238$			6.97666i			0.452230i
$239$	−9.38967			−0.607367			−0.303684	−	0.952773i	$-0.598217\pi$
$239$	−9.38967			−0.607367			−0.303684	+	0.952773i	$0.598217\pi$
$240$	4.14313	−	5.39815i	0.267438	−	0.348449i
$241$			10.3774i			0.668470i	0.942490	+	0.334235i	$0.108478\pi$
$241$			10.3774i			0.668470i	−0.942490	+	0.334235i	$0.891522\pi$
$242$	−6.91837	+	8.55197i	−0.444730	+	0.549741i
$243$	−15.4539	−	2.04359i	−0.991370	−	0.131096i
$244$		−	6.35346i		−	0.406738i
$245$			3.92876i			0.251000i
$246$	−12.2982	−	9.43896i	−0.784103	−	0.601806i
$247$	0.630782			0.0401357
$248$	−2.61516			−0.166063
$249$	2.03400	+	1.56112i	0.128900	+	0.0989318i
$250$			21.3536i			1.35052i
$251$		−	7.75369i		−	0.489409i	−0.969598	−	0.244704i	$-0.921309\pi$
$251$		−	7.75369i		−	0.489409i	0.969598	−	0.244704i	$-0.0786909\pi$
$252$	−2.89796	+	0.775791i	−0.182554	+	0.0488702i
$253$	−2.80992	+	1.34110i	−0.176658	+	0.0843142i
$254$		−	14.3201i		−	0.898522i
$255$	28.9052	−	37.6611i	1.81012	−	2.35843i
$256$	1.00000			0.0625000
$257$			22.2224i			1.38619i	0.720844	+	0.693097i	$0.243754\pi$
$257$			22.2224i			1.38619i	−0.720844	+	0.693097i	$0.756246\pi$
$258$	−1.52786	+	1.99067i	−0.0951202	+	0.123934i
$259$			7.21864i			0.448545i
$260$	−0.428736			−0.0265891
$261$	−8.02779	−	29.9877i	−0.496908	−	1.85619i
$262$	17.8346			1.10183
$263$	−18.9287			−1.16720			−0.583598	−	0.812043i	$-0.698356\pi$
$263$	−18.9287			−1.16720			−0.583598	+	0.812043i	$0.698356\pi$
$264$	1.19364	−	5.61918i	0.0734637	−	0.345837i
$265$	−21.8109			−1.33983
$266$	−5.78023			−0.354409
$267$	0.761634	−	0.992345i	0.0466113	−	0.0607305i
$268$	5.60544			0.342407
$269$		−	17.4450i		−	1.06364i	−0.846857	−	0.531820i	$-0.821508\pi$
$269$		−	17.4450i		−	1.06364i	0.846857	−	0.531820i	$-0.178492\pi$
$270$	18.8578	+	7.81878i	1.14765	+	0.475836i
$271$		−	8.89232i		−	0.540170i	−0.962836	−	0.270085i	$-0.912948\pi$
$271$		−	8.89232i		−	0.540170i	0.962836	−	0.270085i	$-0.0870518\pi$
$272$	6.97666			0.423022
$273$	0.149942	+	0.115082i	0.00907490	+	0.00696507i
$274$			6.72300i			0.406151i
$275$	14.9074	+	31.2345i	0.898950	+	1.88351i
$276$	0.989993	−	1.28988i	0.0595906	−	0.0776415i
$277$		−	11.6381i		−	0.699266i	−0.936887	−	0.349633i	$-0.886306\pi$
$277$		−	11.6381i		−	0.699266i	0.936887	−	0.349633i	$-0.113694\pi$
$278$		−	6.05064i		−	0.362893i
$279$	−2.02882	−	7.57863i	−0.121462	−	0.453720i
$280$	3.92876			0.234789
$281$	−16.8968			−1.00798			−0.503989	−	0.863710i	$-0.668135\pi$
$281$	−16.8968			−1.00798			−0.503989	+	0.863710i	$0.668135\pi$
$282$	−12.0341	+	15.6794i	−0.716621	+	0.933696i
$283$		−	6.18032i		−	0.367382i	−0.982984	−	0.183691i	$-0.941195\pi$
$283$		−	6.18032i		−	0.367382i	0.982984	−	0.183691i	$-0.0588046\pi$
$284$		−	4.39287i		−	0.260669i
$285$	31.2025	+	23.9482i	1.84828	+	1.41857i
$286$	−0.326639	+	0.155896i	−0.0193146	+	0.00921834i
$287$		−	8.95059i		−	0.528336i
$288$	0.775791	+	2.89796i	0.0457139	+	0.170764i
$289$	31.6738			1.86317
$290$			40.6544i			2.38731i
$291$	−4.79524	−	3.68039i	−0.281102	−	0.215748i
$292$			3.31566i			0.194035i
$293$	−13.0184			−0.760544			−0.380272	−	0.924875i	$-0.624170\pi$
$293$	−13.0184			−0.760544			−0.380272	+	0.924875i	$0.624170\pi$
$294$	−1.37401	−	1.05456i	−0.0801337	−	0.0615034i
$295$	29.8789			1.73961
$296$	7.21864			0.419575
$297$	17.2102	−	0.900184i	0.998635	−	0.0522339i
$298$	6.65134			0.385302
$299$	−0.102446			−0.00592459
$300$	−14.3380	−	11.0046i	−0.827806	−	0.635349i
$301$	−1.44880			−0.0835077
$302$		−	0.977889i		−	0.0562712i
$303$	−14.1039	−	10.8249i	−0.810250	−	0.621875i
$304$			5.78023i			0.331519i
$305$	−24.9612			−1.42928
$306$	5.41243	+	20.2181i	0.309408	+	1.15579i
$307$			14.2481i			0.813182i	0.913610	+	0.406591i	$0.133283\pi$
$307$			14.2481i			0.813182i	−0.913610	+	0.406591i	$0.866717\pi$
$308$	2.99319	−	1.42857i	0.170553	−	0.0814004i
$309$	−5.00594	−	3.84211i	−0.284778	−	0.218570i
$310$			10.2744i			0.583544i
$311$			19.9015i			1.12851i	0.825601	+	0.564255i	$0.190836\pi$
$311$			19.9015i			1.12851i	−0.825601	+	0.564255i	$0.809164\pi$
$312$	0.115082	−	0.149942i	0.00651523	−	0.00848879i
$313$	−30.6797			−1.73412			−0.867059	−	0.498206i	$-0.833992\pi$
$313$	−30.6797			−1.73412			−0.867059	+	0.498206i	$0.833992\pi$
$314$	−1.12491			−0.0634822
$315$	3.04790	+	11.3854i	0.171730	+	0.641494i
$316$		−	0.361499i		−	0.0203359i
$317$		−	15.9925i		−	0.898226i	−0.893475	−	0.449113i	$-0.851740\pi$
$317$		−	15.9925i		−	0.898226i	0.893475	−	0.449113i	$-0.148260\pi$
$318$	5.85450	−	7.62791i	0.328304	−	0.427752i
$319$	14.7827	+	30.9732i	0.827671	+	1.73416i
$320$		−	3.92876i		−	0.219625i
$321$	−14.1986	−	10.8976i	−0.792490	−	0.608244i
$322$	0.938770			0.0523156
$323$			40.3267i			2.24384i
$324$	−7.79630	+	4.49641i	−0.433128	+	0.249801i
$325$			1.13877i			0.0631673i
$326$	−2.94048			−0.162858
$327$	14.4570	−	18.8363i	0.799474	−	1.04165i
$328$	−8.95059			−0.494213
$329$	−11.4115			−0.629134
$330$	−22.0764	−	4.68954i	−1.21527	−	0.258151i
$331$	−0.500933			−0.0275338			−0.0137669	−	0.999905i	$-0.504382\pi$
$331$	−0.500933			−0.0275338			−0.0137669	+	0.999905i	$0.504382\pi$
$332$	1.48034			0.0812445
$333$	5.60015	+	20.9193i	0.306887	+	1.14637i
$334$	21.5860			1.18113
$335$		−	22.0225i		−	1.20322i
$336$	−1.05456	+	1.37401i	−0.0575312	+	0.0749582i
$337$		−	11.7562i		−	0.640402i	−0.947350	−	0.320201i	$-0.896250\pi$
$337$		−	11.7562i		−	0.640402i	0.947350	−	0.320201i	$-0.103750\pi$
$338$	12.9881			0.706459
$339$	0.847717	−	1.10450i	0.0460417	−	0.0599884i
$340$		−	27.4097i		−	1.48650i
$341$	3.73594	+	7.82768i	0.202313	+	0.423892i
$342$	−16.7508	+	4.48425i	−0.905782	+	0.242480i
$343$		−	1.00000i		−	0.0539949i
$344$			1.44880i			0.0781143i
$345$	−5.06762	−	3.88945i	−0.272832	−	0.209401i
$346$	5.10422			0.274405
$347$	31.2589			1.67806			0.839032	−	0.544083i	$-0.183122\pi$
$347$	31.2589			1.67806			0.839032	+	0.544083i	$0.183122\pi$
$348$	−14.2181	−	10.9125i	−0.762168	−	0.584971i
$349$			26.8168i			1.43547i	0.696316	+	0.717736i	$0.254821\pi$
$349$			26.8168i			1.43547i	−0.696316	+	0.717736i	$0.745179\pi$
$350$		−	10.4352i		−	0.557784i
$351$	0.523805	+	0.217179i	0.0279586	+	0.0115921i
$352$	−1.42857	−	2.99319i	−0.0761431	−	0.159538i
$353$		−	30.7700i		−	1.63772i	−0.573992	−	0.818861i	$-0.694606\pi$
$353$		−	30.7700i		−	1.63772i	0.573992	−	0.818861i	$-0.305394\pi$
$354$	−8.02012	+	10.4495i	−0.426265	+	0.555387i
$355$	−17.2585			−0.915988
$356$		−	0.722227i		−	0.0382779i
$357$	−7.35733	+	9.58598i	−0.389391	+	0.507344i
$358$		−	17.2258i		−	0.910412i
$359$	14.7885			0.780510			0.390255	−	0.920707i	$-0.372387\pi$
$359$	14.7885			0.780510			0.390255	+	0.920707i	$0.372387\pi$
$360$	11.3854	−	3.04790i	0.600062	−	0.160638i
$361$	−14.4110			−0.758476
$362$	11.9832			0.629820
$363$	−18.5245	+	4.45460i	−0.972283	+	0.233806i
$364$	0.109128			0.00571984
$365$	13.0265			0.681836
$366$	6.70013	−	8.72970i	0.350221	−	0.456309i
$367$	−16.5826			−0.865606			−0.432803	−	0.901488i	$-0.642475\pi$
$367$	−16.5826			−0.865606			−0.432803	+	0.901488i	$0.642475\pi$
$368$		−	0.938770i		−	0.0489368i
$369$	−6.94378	−	25.9384i	−0.361479	−	1.35030i
$370$		−	28.3603i		−	1.47438i
$371$	5.55158			0.288224
$372$	−3.59325	−	2.75786i	−0.186301	−	0.142988i
$373$		−	18.1538i		−	0.939970i	−0.882674	−	0.469985i	$-0.844259\pi$
$373$		−	18.1538i		−	0.939970i	0.882674	−	0.469985i	$-0.155741\pi$
$374$	−9.96665	−	20.8825i	−0.515363	−	1.07981i
$375$	−22.5187	+	29.3399i	−1.16286	+	1.51511i
$376$			11.4115i			0.588501i
$377$			1.12924i			0.0581587i
$378$	−4.79993	−	1.99014i	−0.246882	−	0.102362i
$379$	−12.5603			−0.645180			−0.322590	−	0.946539i	$-0.604554\pi$
$379$	−12.5603			−0.645180			−0.322590	+	0.946539i	$0.604554\pi$
$380$	22.7092			1.16495
$381$	15.1014	−	19.6759i	0.773671	−	1.00803i
$382$			13.1345i			0.672021i
$383$		−	3.12388i		−	0.159623i	−0.996810	−	0.0798114i	$-0.974568\pi$
$383$		−	3.12388i		−	0.159623i	0.996810	−	0.0798114i	$-0.0254318\pi$
$384$	1.37401	+	1.05456i	0.0701170	+	0.0538155i
$385$	−5.61252	−	11.7595i	−0.286040	−	0.599321i
$386$		−	7.13624i		−	0.363225i
$387$	−4.19857	+	1.12397i	−0.213425	+	0.0571346i
$388$	−3.48997			−0.177176
$389$		−	25.8114i		−	1.30869i	−0.756196	−	0.654345i	$-0.772944\pi$
$389$		−	25.8114i		−	1.30869i	0.756196	−	0.654345i	$-0.227056\pi$
$390$	−0.589087	−	0.452130i	−0.0298296	−	0.0228945i
$391$		−	6.54948i		−	0.331222i
$392$	−1.00000			−0.0505076
$393$	24.5049	+	18.8077i	1.23611	+	0.948725i
$394$	1.57331			0.0792620
$395$	−1.42025			−0.0714603
$396$	7.56586	−	6.46202i	0.380199	−	0.324729i
$397$	26.4518			1.32758			0.663789	−	0.747920i	$-0.268947\pi$
$397$	26.4518			1.32758			0.663789	+	0.747920i	$0.268947\pi$
$398$	−4.38353			−0.219727
$399$	−7.94207	−	6.09562i	−0.397601	−	0.305163i
$400$	−10.4352			−0.521759
$401$			28.0552i			1.40101i	0.713649	+	0.700504i	$0.247041\pi$
$401$			28.0552i			1.40101i	−0.713649	+	0.700504i	$0.752959\pi$
$402$	7.70192	+	5.91130i	0.384137	+	0.294829i
$403$			0.285386i			0.0142161i
$404$	−10.2648			−0.510694
$405$	17.6653	+	30.6298i	0.877798	+	1.52201i
$406$		−	10.3479i		−	0.513557i
$407$	−10.3123	−	21.6068i	−0.511164	−	1.07101i
$408$	9.58598	+	7.35733i	0.474577	+	0.364242i
$409$			1.22795i			0.0607183i	0.999539	+	0.0303591i	$0.00966510\pi$
$409$			1.22795i			0.0607183i	−0.999539	+	0.0303591i	$0.990335\pi$
$410$			35.1647i			1.73666i
$411$	−7.08983	+	9.23745i	−0.349716	+	0.455650i
$412$	−3.64331			−0.179493
$413$	−7.60516			−0.374225
$414$	2.72052	−	0.728289i	0.133706	−	0.0357935i
$415$		−	5.81593i		−	0.285493i
$416$		−	0.109128i		−	0.00535042i
$417$	6.38078	−	8.31362i	0.312468	−	0.407120i
$418$	17.3013	−	8.25747i	0.846235	−	0.403886i
$419$		−	10.5048i		−	0.513192i	−0.966519	−	0.256596i	$-0.917399\pi$
$419$		−	10.5048i		−	0.513192i	0.966519	−	0.256596i	$-0.0826010\pi$
$420$	5.39815	+	4.14313i	0.263403	+	0.202164i
$421$	−14.6003			−0.711575			−0.355787	−	0.934567i	$-0.615787\pi$
$421$	−14.6003			−0.711575			−0.355787	+	0.934567i	$0.615787\pi$
$422$			5.34526i			0.260203i
$423$	−33.0699	+	8.85290i	−1.60791	+	0.430443i
$424$		−	5.55158i		−	0.269609i
$425$	−72.8028			−3.53145
$426$	4.63256	−	6.03583i	0.224448	−	0.292437i
$427$	6.35346			0.307465
$428$	−10.3337			−0.499500
$429$	−0.613207	−	0.130259i	−0.0296059	−	0.00628898i
$430$	5.69201			0.274493
$431$	−15.1801			−0.731198			−0.365599	−	0.930772i	$-0.619136\pi$
$431$	−15.1801			−0.731198			−0.365599	+	0.930772i	$0.619136\pi$
$432$	−1.99014	+	4.79993i	−0.0957505	+	0.230937i
$433$	17.1583			0.824577			0.412289	−	0.911053i	$-0.364730\pi$
$433$	17.1583			0.824577			0.412289	+	0.911053i	$0.364730\pi$
$434$		−	2.61516i		−	0.125532i
$435$	−42.8726	+	55.8594i	−2.05559	+	2.67825i
$436$		−	13.7090i		−	0.656542i
$437$	5.42631			0.259576
$438$	−3.49658	+	4.55575i	−0.167073	+	0.217682i
$439$			17.7286i			0.846141i	0.906097	+	0.423070i	$0.139048\pi$
$439$			17.7286i			0.846141i	−0.906097	+	0.423070i	$0.860952\pi$
$440$	−11.7595	+	5.61252i	−0.560614	+	0.267566i
$441$	−0.775791	−	2.89796i	−0.0369424	−	0.137998i
$442$		−	0.761346i		−	0.0362135i
$443$		−	6.70808i		−	0.318711i	−0.987221	−	0.159355i	$-0.949058\pi$
$443$		−	6.70808i		−	0.318711i	0.987221	−	0.159355i	$-0.0509415\pi$
$444$	9.91846	+	7.61252i	0.470709	+	0.361274i
$445$	−2.83746			−0.134508
$446$	19.0577			0.902410
$447$	9.13899	+	7.01426i	0.432259	+	0.331763i
$448$			1.00000i			0.0472456i
$449$			2.86960i			0.135425i	0.997705	+	0.0677123i	$0.0215700\pi$
$449$			2.86960i			0.135425i	−0.997705	+	0.0677123i	$0.978430\pi$
$450$	−8.09552	−	30.2407i	−0.381626	−	1.42556i
$451$	12.7865	+	26.7908i	0.602095	+	1.26153i
$452$		−	0.803856i		−	0.0378102i
$453$	1.03125	−	1.34363i	0.0484522	−	0.0631291i
$454$	17.2146			0.807923
$455$		−	0.428736i		−	0.0200995i
$456$	−6.09562	+	7.94207i	−0.285454	+	0.371922i
$457$			10.7141i			0.501183i	0.968093	+	0.250591i	$0.0806250\pi$
$457$			10.7141i			0.501183i	−0.968093	+	0.250591i	$0.919375\pi$
$458$	20.4671			0.956365
$459$	−13.8845	+	33.4875i	−0.648074	+	1.56306i
$460$	−3.68821			−0.171964
$461$	−5.60949			−0.261260			−0.130630	−	0.991431i	$-0.541700\pi$
$461$	−5.60949			−0.261260			−0.130630	+	0.991431i	$0.541700\pi$
$462$	5.61918	+	1.19364i	0.261428	+	0.0555333i
$463$	−3.97144			−0.184569			−0.0922843	−	0.995733i	$-0.529417\pi$
$463$	−3.97144			−0.184569			−0.0922843	+	0.995733i	$0.529417\pi$
$464$	−10.3479			−0.480388
$465$	−10.8350	+	14.1170i	−0.502459	+	0.654662i
$466$	−17.1712			−0.795439
$467$			6.98066i			0.323026i	0.986871	+	0.161513i	$0.0516374\pi$
$467$			6.98066i			0.323026i	−0.986871	+	0.161513i	$0.948363\pi$
$468$	0.316247	−	0.0846601i	0.0146185	−	0.00391341i
$469$			5.60544i			0.258835i
$470$	44.8329			2.06799
$471$	−1.54563	−	1.18629i	−0.0712189	−	0.0546612i
$472$			7.60516i			0.350056i
$473$	4.33655	−	2.06972i	0.199395	−	0.0951658i
$474$	0.381224	−	0.496703i	0.0175102	−	0.0228143i
$475$		−	60.3178i		−	2.76757i
$476$			6.97666i			0.319775i
$477$	16.0882	−	4.30686i	0.736630	−	0.197198i
$478$	−9.38967			−0.429474
$479$	−22.5631			−1.03093			−0.515467	−	0.856909i	$-0.672382\pi$
$479$	−22.5631			−1.03093			−0.515467	+	0.856909i	$0.672382\pi$
$480$	4.14313	−	5.39815i	0.189107	−	0.246391i
$481$		−	0.787752i		−	0.0359184i
$482$			10.3774i			0.472679i
$483$	1.28988	+	0.989993i	0.0586914	+	0.0450463i
$484$	−6.91837	+	8.55197i	−0.314471	+	0.388726i
$485$			13.7113i			0.622596i
$486$	−15.4539	−	2.04359i	−0.701004	−	0.0926991i
$487$	−9.83009			−0.445444			−0.222722	−	0.974882i	$-0.571494\pi$
$487$	−9.83009			−0.445444			−0.222722	+	0.974882i	$0.571494\pi$
$488$		−	6.35346i		−	0.287608i
$489$	−4.04024	−	3.10093i	−0.182706	−	0.140229i
$490$			3.92876i			0.177483i
$491$	7.60395			0.343161			0.171581	−	0.985170i	$-0.445113\pi$
$491$	7.60395			0.343161			0.171581	+	0.985170i	$0.445113\pi$
$492$	−12.2982	−	9.43896i	−0.554444	−	0.425541i
$493$	−72.1937			−3.25144
$494$	0.630782			0.0283802
$495$	−25.3878	−	29.7245i	−1.14110	−	1.33602i
$496$	−2.61516			−0.117424
$497$	4.39287			0.197047
$498$	2.03400	+	1.56112i	0.0911459	+	0.0699554i
$499$	−40.0276			−1.79188			−0.895941	−	0.444173i	$-0.853498\pi$
$499$	−40.0276			−1.79188			−0.895941	+	0.444173i	$0.853498\pi$
$500$			21.3536i			0.954960i
$501$	29.6593	+	22.7638i	1.32508	+	1.01701i
$502$		−	7.75369i		−	0.346064i
$503$	15.7056			0.700279			0.350139	−	0.936698i	$-0.386134\pi$
$503$	15.7056			0.700279			0.350139	+	0.936698i	$0.386134\pi$
$504$	−2.89796	+	0.775791i	−0.129085	+	0.0345565i
$505$			40.3281i			1.79458i
$506$	−2.80992	+	1.34110i	−0.124916	+	0.0596192i
$507$	17.8457	+	13.6968i	0.792557	+	0.608295i
$508$		−	14.3201i		−	0.635351i
$509$			3.26942i			0.144915i	0.997372	+	0.0724573i	$0.0230841\pi$
$509$			3.26942i			0.144915i	−0.997372	+	0.0724573i	$0.976916\pi$
$510$	28.9052	−	37.6611i	1.27995	−	1.66766i
$511$	−3.31566			−0.146676
$512$	1.00000			0.0441942
$513$	−27.7447	−	11.5035i	−1.22496	−	0.507890i
$514$			22.2224i			0.980187i
$515$			14.3137i			0.630738i
$516$	−1.52786	+	1.99067i	−0.0672602	+	0.0876343i
$517$	34.1567	−	16.3021i	1.50221	−	0.716965i
$518$			7.21864i			0.317169i
$519$	7.01324	+	5.38273i	0.307847	+	0.236276i
$520$	−0.428736			−0.0188013
$521$		−	31.6143i		−	1.38505i	−0.721395	−	0.692524i	$-0.756499\pi$
$521$		−	31.6143i		−	1.38505i	0.721395	−	0.692524i	$-0.243501\pi$
$522$	−8.02779	−	29.9877i	−0.351367	−	1.31253i
$523$		−	13.1081i		−	0.573177i	−0.958054	−	0.286589i	$-0.907479\pi$
$523$		−	13.1081i		−	0.573177i	0.958054	−	0.286589i	$-0.0925213\pi$
$524$	17.8346			0.779109
$525$	11.0046	−	14.3380i	0.480279	−	0.625762i
$526$	−18.9287			−0.825332
$527$	−18.2451			−0.794769
$528$	1.19364	−	5.61918i	0.0519467	−	0.244544i
$529$	22.1187			0.961683
$530$	−21.8109			−0.947403
$531$	−22.0394	+	5.90001i	−0.956429	+	0.256039i
$532$	−5.78023			−0.250605
$533$			0.976755i			0.0423080i
$534$	0.761634	−	0.992345i	0.0329591	−	0.0429430i
$535$			40.5988i			1.75524i
$536$	5.60544			0.242118
$537$	18.1657	−	23.6684i	0.783908	−	1.02137i
$538$		−	17.4450i		−	0.752107i
$539$	1.42857	+	2.99319i	0.0615329	+	0.128926i
$540$	18.8578	+	7.81878i	0.811511	+	0.336467i
$541$			22.4743i			0.966244i	0.875553	+	0.483122i	$0.160497\pi$
$541$			22.4743i			0.966244i	−0.875553	+	0.483122i	$0.839503\pi$
$542$		−	8.89232i		−	0.381958i
$543$	16.4649	+	12.6370i	0.706578	+	0.542305i
$544$	6.97666			0.299122
$545$	−53.8594			−2.30708
$546$	0.149942	+	0.115082i	0.00641692	+	0.00492505i
$547$		−	42.0607i		−	1.79839i	−0.437553	−	0.899193i	$-0.644155\pi$
$547$		−	42.0607i		−	1.79839i	0.437553	−	0.899193i	$-0.355845\pi$
$548$			6.72300i			0.287192i
$549$	18.4120	−	4.92895i	0.785807	−	0.210363i
$550$	14.9074	+	31.2345i	0.635654	+	1.33184i
$551$		−	59.8131i		−	2.54812i
$552$	0.989993	−	1.28988i	0.0421369	−	0.0549008i
$553$	0.361499			0.0153725
$554$		−	11.6381i		−	0.494456i
$555$	29.9078	−	38.9673i	1.26951	−	1.65407i
$556$		−	6.05064i		−	0.256604i
$557$	−19.4913			−0.825873			−0.412937	−	0.910760i	$-0.635497\pi$
$557$	−19.4913			−0.825873			−0.412937	+	0.910760i	$0.635497\pi$
$558$	−2.02882	−	7.57863i	−0.0858867	−	0.320829i
$559$	0.158104			0.00668711
$560$	3.92876			0.166021
$561$	8.32765	−	39.2031i	0.351593	−	1.65516i
$562$	−16.8968			−0.712749
$563$	−15.9611			−0.672679			−0.336340	−	0.941741i	$-0.609189\pi$
$563$	−15.9611			−0.672679			−0.336340	+	0.941741i	$0.609189\pi$
$564$	−12.0341	+	15.6794i	−0.506728	+	0.660223i
$565$	−3.15816			−0.132865
$566$		−	6.18032i		−	0.259778i
$567$	−4.49641	−	7.79630i	−0.188832	−	0.327414i
$568$		−	4.39287i		−	0.184321i
$569$	13.4452			0.563653			0.281827	−	0.959465i	$-0.409060\pi$
$569$	13.4452			0.563653			0.281827	+	0.959465i	$0.409060\pi$
$570$	31.2025	+	23.9482i	1.30693	+	1.00308i
$571$		−	7.63852i		−	0.319662i	−0.987144	−	0.159831i	$-0.948905\pi$
$571$		−	7.63852i		−	0.319662i	0.987144	−	0.159831i	$-0.0510950\pi$
$572$	−0.326639	+	0.155896i	−0.0136575	+	0.00651835i
$573$	−13.8512	+	18.0469i	−0.578642	+	0.753922i
$574$		−	8.95059i		−	0.373590i
$575$			9.79624i			0.408532i
$576$	0.775791	+	2.89796i	0.0323246	+	0.120748i
$577$	−34.2239			−1.42476			−0.712380	−	0.701794i	$-0.752383\pi$
$577$	−34.2239			−1.42476			−0.712380	+	0.701794i	$0.752383\pi$
$578$	31.6738			1.31746
$579$	7.52562	−	9.80524i	0.312754	−	0.407492i
$580$			40.6544i			1.68808i
$581$			1.48034i			0.0614151i
$582$	−4.79524	−	3.68039i	−0.198769	−	0.152557i
$583$	−16.6169	+	7.93083i	−0.688203	+	0.328461i
$584$			3.31566i			0.137203i
$585$	−0.332609	−	1.24246i	−0.0137517	−	0.0513693i
$586$	−13.0184			−0.537786
$587$			6.57288i			0.271292i	0.990757	+	0.135646i	$0.0433109\pi$
$587$			6.57288i			0.271292i	−0.990757	+	0.135646i	$0.956689\pi$
$588$	−1.37401	−	1.05456i	−0.0566631	−	0.0434895i
$589$		−	15.1162i		−	0.622854i
$590$	29.8789			1.23009
$591$	2.16173	+	1.65915i	0.0889218	+	0.0682484i
$592$	7.21864			0.296684
$593$	−9.78733			−0.401917			−0.200959	−	0.979600i	$-0.564406\pi$
$593$	−9.78733			−0.401917			−0.200959	+	0.979600i	$0.564406\pi$
$594$	17.2102	−	0.900184i	0.706141	−	0.0369350i
$595$	27.4097			1.12369
$596$	6.65134			0.272450
$597$	−6.02301	−	4.62272i	−0.246505	−	0.189195i
$598$	−0.102446			−0.00418932
$599$			34.2466i			1.39928i	0.714497	+	0.699639i	$0.246656\pi$
$599$			34.2466i			1.39928i	−0.714497	+	0.699639i	$0.753344\pi$
$600$	−14.3380	−	11.0046i	−0.585347	−	0.449260i
$601$		−	41.4594i		−	1.69117i	−0.533845	−	0.845583i	$-0.679253\pi$
$601$		−	41.4594i		−	1.69117i	0.533845	−	0.845583i	$-0.320747\pi$
$602$	−1.44880			−0.0590489
$603$	4.34865	+	16.2443i	0.177091	+	0.661520i
$604$		−	0.977889i		−	0.0397897i
$605$	33.5987	+	27.1806i	1.36598	+	1.10505i
$606$	−14.1039	−	10.8249i	−0.572934	−	0.439732i
$607$			2.09167i			0.0848983i	0.999099	+	0.0424491i	$0.0135160\pi$
$607$			2.09167i			0.0848983i	−0.999099	+	0.0424491i	$0.986484\pi$
$608$			5.78023i			0.234419i
$609$	10.9125	−	14.2181i	0.442197	−	0.576145i
$610$	−24.9612			−1.01065
$611$	1.24530			0.0503796
$612$	5.41243	+	20.2181i	0.218784	+	0.817267i
$613$		−	9.03532i		−	0.364933i	−0.983212	−	0.182467i	$-0.941592\pi$
$613$		−	9.03532i		−	0.364933i	0.983212	−	0.182467i	$-0.0584081\pi$
$614$			14.2481i			0.575007i
$615$	−37.0835	+	48.3166i	−1.49535	+	1.94831i
$616$	2.99319	−	1.42857i	0.120599	−	0.0575588i
$617$			2.52949i			0.101834i	0.998703	+	0.0509168i	$0.0162143\pi$
$617$			2.52949i			0.101834i	−0.998703	+	0.0509168i	$0.983786\pi$
$618$	−5.00594	−	3.84211i	−0.201368	−	0.154552i
$619$	23.8636			0.959161			0.479580	−	0.877498i	$-0.340789\pi$
$619$	23.8636			0.959161			0.479580	+	0.877498i	$0.340789\pi$
$620$			10.2744i			0.412628i
$621$	4.50603	+	1.86828i	0.180821	+	0.0749716i
$622$			19.9015i			0.797977i
$623$	0.722227			0.0289354
$624$	0.115082	−	0.149942i	0.00460696	−	0.00600248i
$625$	31.7172			1.26869
$626$	−30.6797			−1.22621
$627$	32.4802	+	6.89953i	1.29713	+	0.275541i
$628$	−1.12491			−0.0448887
$629$	50.3620			2.00807
$630$	3.04790	+	11.3854i	0.121431	+	0.453605i
$631$	5.50038			0.218967			0.109483	−	0.993989i	$-0.465080\pi$
$631$	5.50038			0.218967			0.109483	+	0.993989i	$0.465080\pi$
$632$		−	0.361499i		−	0.0143797i
$633$	−5.63691	+	7.34442i	−0.224047	+	0.291914i
$634$		−	15.9925i		−	0.635142i
$635$	−56.2603			−2.23262
$636$	5.85450	−	7.62791i	0.232146	−	0.302466i
$637$			0.109128i			0.00432379i
$638$	14.7827	+	30.9732i	0.585252	+	1.22624i
$639$	12.7303	−	3.40794i	0.503604	−	0.134816i
$640$		−	3.92876i		−	0.155298i
$641$		−	19.8911i		−	0.785652i	−0.919613	−	0.392826i	$-0.871497\pi$
$641$		−	19.8911i		−	0.785652i	0.919613	−	0.392826i	$-0.128503\pi$
$642$	−14.1986	−	10.8976i	−0.560375	−	0.430093i
$643$	−5.96699			−0.235315			−0.117657	−	0.993054i	$-0.537538\pi$
$643$	−5.96699			−0.235315			−0.117657	+	0.993054i	$0.537538\pi$
$644$	0.938770			0.0369927
$645$	7.82086	+	6.00259i	0.307946	+	0.236352i
$646$			40.3267i			1.58663i
$647$		−	2.10535i		−	0.0827700i	−0.999143	−	0.0413850i	$-0.986823\pi$
$647$		−	2.10535i		−	0.0827700i	0.999143	−	0.0413850i	$-0.0131770\pi$
$648$	−7.79630	+	4.49641i	−0.306268	+	0.176636i
$649$	22.7637	−	10.8645i	0.893552	−	0.426469i
$650$			1.13877i			0.0446661i
$651$	2.75786	−	3.59325i	0.108089	−	0.140831i
$652$	−2.94048			−0.115158
$653$			28.1561i			1.10183i	0.834561	+	0.550916i	$0.185722\pi$
$653$			28.1561i			1.10183i	−0.834561	+	0.550916i	$0.814278\pi$
$654$	14.4570	−	18.8363i	0.565314	−	0.736556i
$655$		−	70.0680i		−	2.73778i
$656$	−8.95059			−0.349462
$657$	−9.60865	+	2.57226i	−0.374869	+	0.100353i
$658$	−11.4115			−0.444865
$659$	49.3012			1.92050			0.960251	−	0.279138i	$-0.0900487\pi$
$659$	49.3012			1.92050			0.960251	+	0.279138i	$0.0900487\pi$
$660$	−22.0764	−	4.68954i	−0.859324	−	0.182540i
$661$	4.68898			0.182380			0.0911900	−	0.995834i	$-0.470933\pi$
$661$	4.68898			0.182380			0.0911900	+	0.995834i	$0.470933\pi$
$662$	−0.500933			−0.0194693
$663$	0.802888	−	1.04609i	0.0311816	−	0.0406269i
$664$	1.48034			0.0574485
$665$			22.7092i			0.880623i
$666$	5.60015	+	20.9193i	0.217002	+	0.810607i
$667$			9.71428i			0.376139i
$668$	21.5860			0.835186
$669$	26.1855	+	20.0976i	1.01239	+	0.777018i
$670$		−	22.0225i		−	0.850802i
$671$	−19.0171	+	9.07636i	−0.734147	+	0.350389i
$672$	−1.05456	+	1.37401i	−0.0406807	+	0.0530035i
$673$			40.7322i			1.57011i	0.619426	+	0.785055i	$0.287365\pi$
$673$			40.7322i			1.57011i	−0.619426	+	0.785055i	$0.712635\pi$
$674$		−	11.7562i		−	0.452833i
$675$	20.7675	−	50.0882i	0.799340	−	1.92789i
$676$	12.9881			0.499542
$677$	16.1261			0.619776			0.309888	−	0.950773i	$-0.399708\pi$
$677$	16.1261			0.619776			0.309888	+	0.950773i	$0.399708\pi$
$678$	0.847717	−	1.10450i	0.0325564	−	0.0424182i
$679$		−	3.48997i		−	0.133933i
$680$		−	27.4097i		−	1.05111i
$681$	23.6530	+	18.1539i	0.906386	+	0.695660i
$682$	3.73594	+	7.82768i	0.143057	+	0.299737i
$683$		−	35.6615i		−	1.36455i	−0.731095	−	0.682276i	$-0.760990\pi$
$683$		−	35.6615i		−	1.36455i	0.731095	−	0.682276i	$-0.239010\pi$
$684$	−16.7508	+	4.48425i	−0.640485	+	0.171459i
$685$	26.4131			1.00919
$686$		−	1.00000i		−	0.0381802i
$687$	28.1220	+	21.5839i	1.07292	+	0.823476i
$688$			1.44880i			0.0552352i
$689$	−0.605830			−0.0230803
$690$	−5.06762	−	3.88945i	−0.192921	−	0.148069i
$691$	−35.8799			−1.36494			−0.682468	−	0.730916i	$-0.739093\pi$
$691$	−35.8799			−1.36494			−0.682468	+	0.730916i	$0.739093\pi$
$692$	5.10422			0.194033
$693$	6.46202	+	7.56586i	0.245472	+	0.287403i
$694$	31.2589			1.18657
$695$	−23.7715			−0.901705
$696$	−14.2181	−	10.9125i	−0.538934	−	0.413637i
$697$	−62.4452			−2.36528
$698$			26.8168i			1.01503i
$699$	−23.5933	−	18.1081i	−0.892381	−	0.684911i
$700$		−	10.4352i		−	0.394413i
$701$	22.3303			0.843405			0.421702	−	0.906734i	$-0.361433\pi$
$701$	22.3303			0.843405			0.421702	+	0.906734i	$0.361433\pi$
$702$	0.523805	+	0.217179i	0.0197697	+	0.00819688i
$703$			41.7254i			1.57370i
$704$	−1.42857	−	2.99319i	−0.0538413	−	0.112810i
$705$	61.6008	+	47.2792i	2.32002	+	1.78064i
$706$		−	30.7700i		−	1.15804i
$707$		−	10.2648i		−	0.386049i
$708$	−8.02012	+	10.4495i	−0.301415	+	0.392718i
$709$	22.2230			0.834601			0.417300	−	0.908769i	$-0.362976\pi$
$709$	22.2230			0.834601			0.417300	+	0.908769i	$0.362976\pi$
$710$	−17.2585			−0.647701
$711$	1.04761	−	0.280448i	0.0392884	−	0.0105176i
$712$		−	0.722227i		−	0.0270666i
$713$			2.45504i			0.0919419i
$714$	−7.35733	+	9.58598i	−0.275341	+	0.358746i
$715$	0.612480	+	1.28329i	0.0229055	+	0.0479923i
$716$		−	17.2258i		−	0.643759i
$717$	−12.9015	−	9.90201i	−0.481814	−	0.369797i
$718$	14.7885			0.551904
$719$		−	14.2388i		−	0.531017i	−0.964109	−	0.265508i	$-0.914460\pi$
$719$		−	14.2388i		−	0.531017i	0.964109	−	0.265508i	$-0.0855398\pi$
$720$	11.3854	−	3.04790i	0.424308	−	0.113588i
$721$		−	3.64331i		−	0.135684i
$722$	−14.4110			−0.536324
$723$	−10.9437	+	14.2587i	−0.407000	+	0.530286i
$724$	11.9832			0.445350
$725$	107.982			4.01035
$726$	−18.5245	+	4.45460i	−0.687508	+	0.165326i
$727$	−0.772552			−0.0286524			−0.0143262	−	0.999897i	$-0.504560\pi$
$727$	−0.772552			−0.0286524			−0.0143262	+	0.999897i	$0.504560\pi$
$728$	0.109128			0.00404453
$729$	−19.0787	−	19.1051i	−0.706619	−	0.707595i
$730$	13.0265			0.482131
$731$			10.1078i			0.373851i
$732$	6.70013	−	8.72970i	0.247644	−	0.322659i
$733$		−	20.9468i		−	0.773687i	−0.922145	−	0.386844i	$-0.873565\pi$
$733$		−	20.9468i		−	0.773687i	0.922145	−	0.386844i	$-0.126435\pi$
$734$	−16.5826			−0.612076
$735$	−4.14313	+	5.39815i	−0.152822	+	0.199114i
$736$		−	0.938770i		−	0.0346035i
$737$	−8.00777	−	16.7782i	−0.294970	−	0.618031i
$738$	−6.94378	−	25.9384i	−0.255604	−	0.954806i
$739$			31.8490i			1.17159i	0.810461	+	0.585793i	$0.199217\pi$
$739$			31.8490i			1.17159i	−0.810461	+	0.585793i	$0.800783\pi$
$740$		−	28.3603i		−	1.04255i
$741$	0.866699	+	0.665200i	0.0318390	+	0.0244367i
$742$	5.55158			0.203805
$743$	2.95393			0.108369			0.0541847	−	0.998531i	$-0.482744\pi$
$743$	2.95393			0.108369			0.0541847	+	0.998531i	$0.482744\pi$
$744$	−3.59325	−	2.75786i	−0.131735	−	0.101108i
$745$		−	26.1316i		−	0.957386i
$746$		−	18.1538i		−	0.664659i
$747$	1.14844	+	4.28997i	0.0420191	+	0.156962i
$748$	−9.96665	−	20.8825i	−0.364417	−	0.763539i
$749$		−	10.3337i		−	0.377586i
$750$	−22.5187	+	29.3399i	−0.822266	+	1.07134i
$751$	−7.94197			−0.289807			−0.144903	−	0.989446i	$-0.546287\pi$
$751$	−7.94197			−0.289807			−0.144903	+	0.989446i	$0.546287\pi$
$752$			11.4115i			0.416133i
$753$	8.17676	−	10.6536i	0.297978	−	0.388240i
$754$			1.12924i			0.0411244i
$755$	−3.84190			−0.139821
$756$	−4.79993	−	1.99014i	−0.174572	−	0.0723806i
$757$	−22.0057			−0.799810			−0.399905	−	0.916557i	$-0.630957\pi$
$757$	−22.0057			−0.799810			−0.399905	+	0.916557i	$0.630957\pi$
$758$	−12.5603			−0.456211
$759$	−5.27512	−	1.12056i	−0.191475	−	0.0406736i
$760$	22.7092			0.823748
$761$	32.8592			1.19114			0.595572	−	0.803302i	$-0.296925\pi$
$761$	32.8592			1.19114			0.595572	+	0.803302i	$0.296925\pi$
$762$	15.1014	−	19.6759i	0.547068	−	0.712783i
$763$	13.7090			0.496299
$764$			13.1345i			0.475191i
$765$	79.4320	−	21.2642i	2.87187	−	0.768807i
$766$		−	3.12388i		−	0.112870i
$767$	0.829932			0.0299671
$768$	1.37401	+	1.05456i	0.0495802	+	0.0380533i
$769$		−	8.41547i		−	0.303470i	−0.988421	−	0.151735i	$-0.951514\pi$
$769$		−	8.41547i		−	0.303470i	0.988421	−	0.151735i	$-0.0484860\pi$
$770$	−5.61252	−	11.7595i	−0.202261	−	0.423784i
$771$	−23.4349	+	30.5337i	−0.843988	+	1.09964i
$772$		−	7.13624i		−	0.256839i
$773$			38.4899i			1.38438i	0.721713	+	0.692192i	$0.243355\pi$
$773$			38.4899i			1.38438i	−0.721713	+	0.692192i	$0.756645\pi$
$774$	−4.19857	+	1.12397i	−0.150915	+	0.0404002i
$775$	27.2897			0.980275
$776$	−3.48997			−0.125282
$777$	−7.61252	+	9.91846i	−0.273098	+	0.355823i
$778$		−	25.8114i		−	0.925383i
$779$		−	51.7364i		−	1.85365i
$780$	−0.589087	−	0.452130i	−0.0210927	−	0.0161888i
$781$	−13.1487	+	6.27552i	−0.470497	+	0.224556i
$782$		−	6.54948i		−	0.234209i
$783$	20.5937	−	49.6691i	0.735959	−	1.77503i
$784$	−1.00000			−0.0357143
$785$			4.41950i			0.157739i
$786$	24.5049	+	18.8077i	0.874060	+	0.670850i
$787$			23.4784i			0.836916i	0.908236	+	0.418458i	$0.137429\pi$
$787$			23.4784i			0.836916i	−0.908236	+	0.418458i	$0.862571\pi$
$788$	1.57331			0.0560467
$789$	−26.0082	−	19.9616i	−0.925917	−	0.710650i
$790$	−1.42025			−0.0505301
$791$	0.803856			0.0285818
$792$	7.56586	−	6.46202i	0.268841	−	0.229618i
$793$	−0.693337			−0.0246211
$794$	26.4518			0.938739
$795$	−29.9683	−	23.0009i	−1.06286	−	0.815759i
$796$	−4.38353			−0.155370
$797$		−	19.4036i		−	0.687311i	−0.939096	−	0.343655i	$-0.888335\pi$
$797$		−	19.4036i		−	0.687311i	0.939096	−	0.343655i	$-0.111665\pi$
$798$	−7.94207	−	6.09562i	−0.281146	−	0.215783i
$799$			79.6139i			2.81654i
$800$	−10.4352			−0.368939
$801$	2.09298	−	0.560297i	0.0739519	−	0.0197971i
$802$			28.0552i			0.990662i
$803$	9.92441	−	4.73666i	0.350225	−	0.167153i
$804$	7.70192	+	5.91130i	0.271626	+	0.208475i
$805$		−	3.68821i		−	0.129992i
$806$			0.285386i			0.0100523i
$807$	18.3969	−	23.9696i	0.647600	−	0.843768i
$808$	−10.2648			−0.361115
$809$	11.7416			0.412814			0.206407	−	0.978466i	$-0.433823\pi$
$809$	11.7416			0.412814			0.206407	+	0.978466i	$0.433823\pi$
$810$	17.6653	+	30.6298i	0.620697	+	1.07622i
$811$			12.4057i			0.435622i	0.975991	+	0.217811i	$0.0698917\pi$
$811$			12.4057i			0.435622i	−0.975991	+	0.217811i	$0.930108\pi$
$812$		−	10.3479i		−	0.363139i
$813$	9.37752	−	12.2181i	0.328884	−	0.428508i
$814$	−10.3123	−	21.6068i	−0.361447	−	0.757317i
$815$			11.5525i			0.404665i
$816$	9.58598	+	7.35733i	0.335576	+	0.257558i
$817$	−8.37442			−0.292984
$818$			1.22795i			0.0429343i
$819$	0.0846601	+	0.316247i	0.00295826	+	0.0110506i
$820$			35.1647i			1.22801i
$821$	−26.3947			−0.921182			−0.460591	−	0.887612i	$-0.652363\pi$
$821$	−26.3947			−0.921182			−0.460591	+	0.887612i	$0.652363\pi$
$822$	−7.08983	+	9.23745i	−0.247286	+	0.322193i
$823$	−28.8057			−1.00410			−0.502052	−	0.864837i	$-0.667421\pi$
$823$	−28.8057			−1.00410			−0.502052	+	0.864837i	$0.667421\pi$
$824$	−3.64331			−0.126921
$825$	−12.4559	+	58.6372i	−0.433658	+	2.04149i
$826$	−7.60516			−0.264617
$827$	−30.8632			−1.07322			−0.536609	−	0.843831i	$-0.680295\pi$
$827$	−30.8632			−1.07322			−0.536609	+	0.843831i	$0.680295\pi$
$828$	2.72052	−	0.728289i	0.0945444	−	0.0253098i
$829$	3.62488			0.125897			0.0629486	−	0.998017i	$-0.479950\pi$
$829$	3.62488			0.125897			0.0629486	+	0.998017i	$0.479950\pi$
$830$		−	5.81593i		−	0.201874i
$831$	12.2731	−	15.9908i	0.425750	−	0.554716i
$832$		−	0.109128i		−	0.00378332i
$833$	−6.97666			−0.241727
$834$	6.38078	−	8.31362i	0.220948	−	0.287877i
$835$		−	84.8061i		−	2.93484i
$836$	17.3013	−	8.25747i	0.598379	−	0.285590i
$837$	5.20453	−	12.5526i	0.179895	−	0.433881i
$838$		−	10.5048i		−	0.362882i
$839$		−	26.1251i		−	0.901939i	−0.892539	−	0.450969i	$-0.851078\pi$
$839$		−	26.1251i		−	0.901939i	0.892539	−	0.450969i	$-0.148922\pi$
$840$	5.39815	+	4.14313i	0.186254	+	0.142952i
$841$	78.0786			2.69237
$842$	−14.6003			−0.503159
$843$	−23.2163	−	17.8188i	−0.799613	−	0.613711i
$844$			5.34526i			0.183991i
$845$		−	51.0271i		−	1.75539i
$846$	−33.0699	+	8.85290i	−1.13697	+	0.304369i
$847$	−8.55197	−	6.91837i	−0.293849	−	0.237718i
$848$		−	5.55158i		−	0.190642i
$849$	6.51754	−	8.49181i	0.223682	−	0.291438i
$850$	−72.8028			−2.49711
$851$		−	6.77665i		−	0.232300i
$852$	4.63256	−	6.03583i	0.158709	−	0.206784i
$853$			31.5638i			1.08073i	0.841432	+	0.540363i	$0.181713\pi$
$853$			31.5638i			1.08073i	−0.841432	+	0.540363i	$0.818287\pi$
$854$	6.35346			0.217411
$855$	17.6175	+	65.8101i	0.602507	+	2.25066i
$856$	−10.3337			−0.353200
$857$	−20.8294			−0.711519			−0.355760	−	0.934577i	$-0.615778\pi$
$857$	−20.8294			−0.711519			−0.355760	+	0.934577i	$0.615778\pi$
$858$	−0.613207	−	0.130259i	−0.0209346	−	0.00444698i
$859$	−22.4198			−0.764952			−0.382476	−	0.923965i	$-0.624929\pi$
$859$	−22.4198			−0.764952			−0.382476	+	0.923965i	$0.624929\pi$
$860$	5.69201			0.194096
$861$	9.43896	−	12.2982i	0.321679	−	0.419120i
$862$	−15.1801			−0.517035
$863$			23.5284i			0.800915i	0.916315	+	0.400457i	$0.131149\pi$
$863$			23.5284i			0.800915i	−0.916315	+	0.400457i	$0.868851\pi$
$864$	−1.99014	+	4.79993i	−0.0677059	+	0.163297i
$865$		−	20.0533i		−	0.681832i
$866$	17.1583			0.583064
$867$	43.5200	+	33.4020i	1.47802	+	1.13439i
$868$		−	2.61516i		−	0.0887644i
$869$	−1.08204	+	0.516427i	−0.0367056	+	0.0175186i
$870$	−42.8726	+	55.8594i	−1.45352	+	1.89381i
$871$		−	0.611708i		−	0.0207269i
$872$		−	13.7090i		−	0.464245i
$873$	−2.70748	−	10.1138i	−0.0916344	−	0.342299i
$874$	5.42631			0.183548
$875$	−21.3536			−0.721882
$876$	−3.49658	+	4.55575i	−0.118138	+	0.153924i
$877$			4.71771i			0.159306i	0.996823	+	0.0796528i	$0.0253812\pi$
$877$			4.71771i			0.159306i	−0.996823	+	0.0796528i	$0.974619\pi$
$878$			17.7286i			0.598312i
$879$	−17.8874	−	13.7288i	−0.603327	−	0.463059i
$880$	−11.7595	+	5.61252i	−0.396414	+	0.189198i
$881$		−	41.4868i		−	1.39773i	−0.715256	−	0.698863i	$-0.753690\pi$
$881$		−	41.4868i		−	1.39773i	0.715256	−	0.698863i	$-0.246310\pi$
$882$	−0.775791	−	2.89796i	−0.0261222	−	0.0975793i
$883$	15.8632			0.533839			0.266920	−	0.963719i	$-0.413994\pi$
$883$	15.8632			0.533839			0.266920	+	0.963719i	$0.413994\pi$
$884$		−	0.761346i		−	0.0256068i
$885$	41.0538	+	31.5092i	1.38001	+	1.05917i
$886$		−	6.70808i		−	0.225362i
$887$	51.9855			1.74550			0.872750	−	0.488167i	$-0.162334\pi$
$887$	51.9855			1.74550			0.872750	+	0.488167i	$0.162334\pi$
$888$	9.91846	+	7.61252i	0.332842	+	0.255459i
$889$	14.3201			0.480280
$890$	−2.83746			−0.0951118
$891$	24.5962	+	16.9124i	0.824003	+	0.566585i
$892$	19.0577			0.638100
$893$	−65.9609			−2.20730
$894$	9.13899	+	7.01426i	0.305654	+	0.234592i
$895$	−67.6761			−2.26216
$896$			1.00000i			0.0334077i
$897$	−0.140761	−	0.108035i	−0.00469988	−	0.00360720i
$898$			2.86960i			0.0957597i
$899$	27.0614			0.902548
$900$	−8.09552	−	30.2407i	−0.269851	−	1.00802i
$901$		−	38.7315i		−	1.29033i
$902$	12.7865	+	26.7908i	0.425745	+	0.892036i
$903$	−1.99067	−	1.52786i	−0.0662453	−	0.0508439i
$904$		−	0.803856i		−	0.0267358i
$905$		−	47.0790i		−	1.56496i
$906$	1.03125	−	1.34363i	0.0342609	−	0.0446390i
$907$	−19.0347			−0.632038			−0.316019	−	0.948753i	$-0.602346\pi$
$907$	−19.0347			−0.632038			−0.316019	+	0.948753i	$0.602346\pi$
$908$	17.2146			0.571288
$909$	−7.96336	−	29.7470i	−0.264128	−	0.986646i
$910$		−	0.428736i		−	0.0142125i
$911$			33.2014i			1.10001i	0.835160	+	0.550006i	$0.185375\pi$
$911$			33.2014i			1.10001i	−0.835160	+	0.550006i	$0.814625\pi$
$912$	−6.09562	+	7.94207i	−0.201846	+	0.262988i
$913$	−2.11478	−	4.43095i	−0.0699889	−	0.146643i
$914$			10.7141i			0.354390i
$915$	−34.2969	−	26.3232i	−1.13382	−	0.870219i
$916$	20.4671			0.676252
$917$			17.8346i			0.588951i
$918$	−13.8845	+	33.4875i	−0.458257	+	1.10525i
$919$			16.5613i			0.546306i	0.961971	+	0.273153i	$0.0880666\pi$
$919$			16.5613i			0.546306i	−0.961971	+	0.273153i	$0.911933\pi$
$920$	−3.68821			−0.121597
$921$	−15.0255	+	19.5770i	−0.495108	+	0.645084i
$922$	−5.60949			−0.184739
$923$	−0.479382			−0.0157791
$924$	5.61918	+	1.19364i	0.184858	+	0.0392680i
$925$	−75.3278			−2.47676
$926$	−3.97144			−0.130510
$927$	−2.82645	−	10.5582i	−0.0928328	−	0.346776i
$928$	−10.3479			−0.339686
$929$		−	4.32333i		−	0.141844i	−0.997482	−	0.0709219i	$-0.977406\pi$
$929$		−	4.32333i		−	0.141844i	0.997482	−	0.0709219i	$-0.0225941\pi$
$930$	−10.8350	+	14.1170i	−0.355292	+	0.462916i
$931$		−	5.78023i		−	0.189439i
$932$	−17.1712			−0.562460
$933$	−20.9874	+	27.3448i	−0.687096	+	0.895228i
$934$			6.98066i			0.228414i
$935$	−82.0423	+	39.1566i	−2.68307	+	1.28056i
$936$	0.316247	−	0.0846601i	0.0103368	−	0.00276720i
$937$		−	0.667158i		−	0.0217951i	−0.999941	−	0.0108975i	$-0.996531\pi$
$937$		−	0.667158i		−	0.0217951i	0.999941	−	0.0108975i	$-0.00346887\pi$
$938$			5.60544i			0.183024i
$939$	−42.1541	−	32.3537i	−1.37565	−	1.05582i
$940$	44.8329			1.46229
$941$	−33.6358			−1.09650			−0.548248	−	0.836316i	$-0.684705\pi$
$941$	−33.6358			−1.09650			−0.548248	+	0.836316i	$0.684705\pi$
$942$	−1.54563	−	1.18629i	−0.0503594	−	0.0386513i
$943$			8.40255i			0.273625i
$944$			7.60516i			0.247527i
$945$	−7.81878	+	18.8578i	−0.254345	+	0.613444i
$946$	4.33655	−	2.06972i	0.140993	−	0.0672924i
$947$			54.3038i			1.76464i	0.470652	+	0.882319i	$0.344019\pi$
$947$			54.3038i			1.76464i	−0.470652	+	0.882319i	$0.655981\pi$
$948$	0.381224	−	0.496703i	0.0123816	−	0.0161322i
$949$	0.361830			0.0117455
$950$		−	60.3178i		−	1.95697i
$951$	16.8651	−	21.9738i	0.546887	−	0.712548i
$952$			6.97666i			0.226115i
$953$	−8.99829			−0.291483			−0.145742	−	0.989323i	$-0.546557\pi$
$953$	−8.99829			−0.291483			−0.145742	+	0.989323i	$0.546557\pi$
$954$	16.0882	−	4.30686i	0.520876	−	0.139440i
$955$	51.6025			1.66982
$956$	−9.38967			−0.303684
$957$	−12.3517	+	58.1466i	−0.399273	+	1.87961i
$958$	−22.5631			−0.728981
$959$	−6.72300			−0.217097
$960$	4.14313	−	5.39815i	0.133719	−	0.174225i
$961$	−24.1609			−0.779385
$962$		−	0.787752i		−	0.0253982i
$963$	−8.01681	−	29.9467i	−0.258338	−	0.965019i
$964$			10.3774i			0.334235i
$965$	−28.0366			−0.902530
$966$	1.28988	+	0.989993i	0.0415011	+	0.0318525i
$967$			29.1744i			0.938187i	0.883149	+	0.469093i	$0.155419\pi$
$967$			29.1744i			0.938187i	−0.883149	+	0.469093i	$0.844581\pi$
$968$	−6.91837	+	8.55197i	−0.222365	+	0.274871i
$969$	−42.5271	+	55.4092i	−1.36617	+	1.78000i
$970$			13.7113i			0.440242i
$971$			47.7488i			1.53233i	0.642642	+	0.766166i	$0.277838\pi$
$971$			47.7488i			1.53233i	−0.642642	+	0.766166i	$0.722162\pi$
$972$	−15.4539	−	2.04359i	−0.495685	−	0.0655481i
$973$	6.05064			0.193974
$974$	−9.83009			−0.314976
$975$	−1.20090	+	1.56467i	−0.0384596	+	0.0501096i
$976$		−	6.35346i		−	0.203369i
$977$			51.7861i			1.65678i	0.560150	+	0.828391i	$0.310744\pi$
$977$			51.7861i			1.65678i	−0.560150	+	0.828391i	$0.689256\pi$
$978$	−4.04024	−	3.10093i	−0.129193	−	0.0991567i
$979$	−2.16176	+	1.03175i	−0.0690902	+	0.0329749i
$980$			3.92876i			0.125500i
$981$	39.7281	−	10.6353i	1.26842	−	0.339559i
$982$	7.60395			0.242652
$983$			13.0802i			0.417193i	0.978002	+	0.208597i	$0.0668896\pi$
$983$			13.0802i			0.417193i	−0.978002	+	0.208597i	$0.933110\pi$
$984$	−12.2982	−	9.43896i	−0.392051	−	0.300903i
$985$		−	6.18115i		−	0.196948i
$986$	−72.1937			−2.29911
$987$	−15.6794	−	12.0341i	−0.499082	−	0.383050i
$988$	0.630782			0.0200678
$989$	1.36010			0.0432485
$990$	−25.3878	−	29.7245i	−0.806876	−	0.944706i
$991$	−21.4492			−0.681356			−0.340678	−	0.940180i	$-0.610657\pi$
$991$	−21.4492			−0.681356			−0.340678	+	0.940180i	$0.610657\pi$
$992$	−2.61516			−0.0830315
$993$	−0.688285	−	0.528265i	−0.0218421	−	0.0167640i
$994$	4.39287			0.139333
$995$			17.2219i			0.545970i
$996$	2.03400	+	1.56112i	0.0644499	+	0.0494659i
$997$		−	35.6278i		−	1.12834i	−0.825657	−	0.564172i	$-0.809195\pi$
$997$		−	35.6278i		−	1.12834i	0.825657	−	0.564172i	$-0.190805\pi$
$998$	−40.0276			−1.26705
$999$	−14.3661	+	34.6490i	−0.454523	+	1.09625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.c.b.197.10	yes	12
3.2	odd	2		462.2.c.a.197.9	✓	12
11.10	odd	2		462.2.c.a.197.10	yes	12
33.32	even	2	inner	462.2.c.b.197.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.c.a.197.9	✓	12	3.2	odd	2
462.2.c.a.197.10	yes	12	11.10	odd	2
462.2.c.b.197.9	yes	12	33.32	even	2	inner
462.2.c.b.197.10	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.37401 + 1.05456i) q^{3} +1.00000 q^{4} -3.92876i q^{5} +(1.37401 + 1.05456i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(0.775791 + 2.89796i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.37401 + 1.05456i) q^{3} +1.00000 q^{4} -3.92876i q^{5} +(1.37401 + 1.05456i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(0.775791 + 2.89796i) q^{9} -3.92876i q^{10} +(-1.42857 - 2.99319i) q^{11} +(1.37401 + 1.05456i) q^{12} -0.109128i q^{13} +1.00000i q^{14} +(4.14313 - 5.39815i) q^{15} +1.00000 q^{16} +6.97666 q^{17} +(0.775791 + 2.89796i) q^{18} +5.78023i q^{19} -3.92876i q^{20} +(-1.05456 + 1.37401i) q^{21} +(-1.42857 - 2.99319i) q^{22} -0.938770i q^{23} +(1.37401 + 1.05456i) q^{24} -10.4352 q^{25} -0.109128i q^{26} +(-1.99014 + 4.79993i) q^{27} +1.00000i q^{28} -10.3479 q^{29} +(4.14313 - 5.39815i) q^{30} -2.61516 q^{31} +1.00000 q^{32} +(1.19364 - 5.61918i) q^{33} +6.97666 q^{34} +3.92876 q^{35} +(0.775791 + 2.89796i) q^{36} +7.21864 q^{37} +5.78023i q^{38} +(0.115082 - 0.149942i) q^{39} -3.92876i q^{40} -8.95059 q^{41} +(-1.05456 + 1.37401i) q^{42} +1.44880i q^{43} +(-1.42857 - 2.99319i) q^{44} +(11.3854 - 3.04790i) q^{45} -0.938770i q^{46} +11.4115i q^{47} +(1.37401 + 1.05456i) q^{48} -1.00000 q^{49} -10.4352 q^{50} +(9.58598 + 7.35733i) q^{51} -0.109128i q^{52} -5.55158i q^{53} +(-1.99014 + 4.79993i) q^{54} +(-11.7595 + 5.61252i) q^{55} +1.00000i q^{56} +(-6.09562 + 7.94207i) q^{57} -10.3479 q^{58} +7.60516i q^{59} +(4.14313 - 5.39815i) q^{60} -6.35346i q^{61} -2.61516 q^{62} +(-2.89796 + 0.775791i) q^{63} +1.00000 q^{64} -0.428736 q^{65} +(1.19364 - 5.61918i) q^{66} +5.60544 q^{67} +6.97666 q^{68} +(0.989993 - 1.28988i) q^{69} +3.92876 q^{70} -4.39287i q^{71} +(0.775791 + 2.89796i) q^{72} +3.31566i q^{73} +7.21864 q^{74} +(-14.3380 - 11.0046i) q^{75} +5.78023i q^{76} +(2.99319 - 1.42857i) q^{77} +(0.115082 - 0.149942i) q^{78} -0.361499i q^{79} -3.92876i q^{80} +(-7.79630 + 4.49641i) q^{81} -8.95059 q^{82} +1.48034 q^{83} +(-1.05456 + 1.37401i) q^{84} -27.4097i q^{85} +1.44880i q^{86} +(-14.2181 - 10.9125i) q^{87} +(-1.42857 - 2.99319i) q^{88} -0.722227i q^{89} +(11.3854 - 3.04790i) q^{90} +0.109128 q^{91} -0.938770i q^{92} +(-3.59325 - 2.75786i) q^{93} +11.4115i q^{94} +22.7092 q^{95} +(1.37401 + 1.05456i) q^{96} -3.48997 q^{97} -1.00000 q^{98} +(7.56586 - 6.46202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^2 + 4 * q^3 + 12 * q^4 + 4 * q^6 + 12 * q^8	\( 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8} + 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} + 4 q^{17} + 8 q^{22} + 4 q^{24} - 28 q^{25} - 8 q^{27} - 8 q^{29} + 4 q^{30} + 12 q^{31} + 12 q^{32} - 16 q^{33} + 4 q^{34} + 4 q^{35} + 36 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} - 28 q^{50} - 8 q^{51} - 8 q^{54} + 4 q^{55} - 28 q^{57} - 8 q^{58} + 4 q^{60} + 12 q^{62} - 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} + 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} - 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} - 44 q^{83} - 8 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} - 24 q^{93} + 4 q^{96} - 48 q^{97} - 12 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 4 * q^3 + 12 * q^4 + 4 * q^6 + 12 * q^8 + 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 + 4 * q^17 + 8 * q^22 + 4 * q^24 - 28 * q^25 - 8 * q^27 - 8 * q^29 + 4 * q^30 + 12 * q^31 + 12 * q^32 - 16 * q^33 + 4 * q^34 + 4 * q^35 + 36 * q^39 - 20 * q^41 + 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 - 28 * q^50 - 8 * q^51 - 8 * q^54 + 4 * q^55 - 28 * q^57 - 8 * q^58 + 4 * q^60 + 12 * q^62 - 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 + 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 - 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 - 44 * q^83 - 8 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 - 24 * q^93 + 4 * q^96 - 48 * q^97 - 12 * q^98 + 20 * q^99

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