LMFDB - Embedded newform 483.2.i.f.415.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, degree $2$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - x^{11} + 8 x^{10} - 3 x^{9} + 42 x^{8} - 15 x^{7} + 101 x^{6} + 6 x^{5} + 150 x^{4} - 28 x^{3} + \cdots + 4 $ x^12 - x^11 + 8x^10 - 3x^9 + 42x^8 - 15x^7 + 101x^6 + 6x^5 + 150x^4 - 28x^3 + 40x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.2
Root			$-0.682743 - 1.18255i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.f.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.682743 + 1.18255i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.0677246 + 0.117302i) q^{4} +(0.663106 - 1.14853i) q^{5} -1.36549 q^{6} +(2.35341 + 1.20891i) q^{7} -2.91593 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.682743 + 1.18255i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.0677246 + 0.117302i) q^{4} +(0.663106 - 1.14853i) q^{5} -1.36549 q^{6} +(2.35341 + 1.20891i) q^{7} -2.91593 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.905461 + 1.56830i) q^{10} +(0.710043 + 1.22983i) q^{11} +(-0.0677246 + 0.117302i) q^{12} +3.16661 q^{13} +(-3.03637 + 1.95764i) q^{14} +1.32621 q^{15} +(1.85538 - 3.21361i) q^{16} +(-0.579802 - 1.00425i) q^{17} +(-0.682743 - 1.18255i) q^{18} +(-4.28943 + 7.42951i) q^{19} +0.179634 q^{20} +(0.129755 + 2.64257i) q^{21} -1.93911 q^{22} +(0.500000 - 0.866025i) q^{23} +(-1.45796 - 2.52527i) q^{24} +(1.62058 + 2.80693i) q^{25} +(-2.16198 + 3.74466i) q^{26} -1.00000 q^{27} +(0.0175752 + 0.357934i) q^{28} +7.45480 q^{29} +(-0.905461 + 1.56830i) q^{30} +(-0.933210 - 1.61637i) q^{31} +(-0.382434 - 0.662395i) q^{32} +(-0.710043 + 1.22983i) q^{33} +1.58342 q^{34} +(2.94903 - 1.90133i) q^{35} -0.135449 q^{36} +(3.89919 - 6.75360i) q^{37} +(-5.85715 - 10.1449i) q^{38} +(1.58330 + 2.74236i) q^{39} +(-1.93357 + 3.34903i) q^{40} -11.2258 q^{41} +(-3.21355 - 1.65075i) q^{42} -11.8479 q^{43} +(-0.0961748 + 0.166580i) q^{44} +(0.663106 + 1.14853i) q^{45} +(0.682743 + 1.18255i) q^{46} +(-0.868249 + 1.50385i) q^{47} +3.71076 q^{48} +(4.07706 + 5.69013i) q^{49} -4.42576 q^{50} +(0.579802 - 1.00425i) q^{51} +(0.214457 + 0.371451i) q^{52} +(2.07449 + 3.59312i) q^{53} +(0.682743 - 1.18255i) q^{54} +1.88333 q^{55} +(-6.86236 - 3.52510i) q^{56} -8.57886 q^{57} +(-5.08971 + 8.81564i) q^{58} +(-6.34357 - 10.9874i) q^{59} +(0.0898171 + 0.155568i) q^{60} +(6.90738 - 11.9639i) q^{61} +2.54857 q^{62} +(-2.22365 + 1.43366i) q^{63} +8.46593 q^{64} +(2.09980 - 3.63695i) q^{65} +(-0.969554 - 1.67932i) q^{66} +(4.04647 + 7.00870i) q^{67} +(0.0785337 - 0.136024i) q^{68} +1.00000 q^{69} +(0.234977 + 4.78548i) q^{70} -5.18979 q^{71} +(1.45796 - 2.52527i) q^{72} +(5.68430 + 9.84549i) q^{73} +(5.32429 + 9.22194i) q^{74} +(-1.62058 + 2.80693i) q^{75} -1.16200 q^{76} +(0.184264 + 3.75267i) q^{77} -4.32396 q^{78} +(5.86823 - 10.1641i) q^{79} +(-2.46062 - 4.26192i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.66430 - 13.2750i) q^{82} +5.70566 q^{83} +(-0.301192 + 0.194187i) q^{84} -1.53788 q^{85} +(8.08906 - 14.0107i) q^{86} +(3.72740 + 6.45604i) q^{87} +(-2.07043 - 3.58609i) q^{88} +(3.17756 - 5.50369i) q^{89} -1.81092 q^{90} +(7.45232 + 3.82815i) q^{91} +0.135449 q^{92} +(0.933210 - 1.61637i) q^{93} +(-1.18558 - 2.05349i) q^{94} +(5.68869 + 9.85310i) q^{95} +(0.382434 - 0.662395i) q^{96} +0.408396 q^{97} +(-9.51242 + 0.936415i) q^{98} -1.42009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} - q^{14} - 6 q^{15} + 7 q^{16} - 15 q^{17} + q^{18} + q^{19} + 34 q^{20} - 4 q^{21} - 12 q^{22} + 6 q^{23} - 3 q^{24} - 9 q^{25} + 15 q^{26} - 12 q^{27} - 2 q^{28} - 12 q^{29} - 3 q^{30} + 11 q^{31} - 3 q^{32} - 14 q^{33} + 30 q^{34} - q^{35} + 6 q^{36} + 5 q^{37} - 14 q^{38} + 17 q^{40} + 36 q^{41} - 17 q^{42} - 74 q^{43} + 10 q^{44} - 3 q^{45} - q^{46} - 3 q^{47} + 14 q^{48} - 6 q^{49} - 60 q^{50} + 15 q^{51} + 7 q^{52} + 15 q^{53} - q^{54} - 4 q^{55} - 21 q^{56} + 2 q^{57} - 4 q^{58} + 2 q^{59} + 17 q^{60} + 12 q^{61} + 72 q^{62} - 2 q^{63} - 46 q^{64} + 17 q^{65} - 6 q^{66} + 10 q^{67} + q^{68} + 12 q^{69} - 56 q^{70} - 42 q^{71} + 3 q^{72} + 8 q^{73} + 16 q^{74} + 9 q^{75} + 36 q^{76} - 40 q^{77} + 30 q^{78} + 17 q^{79} - 3 q^{80} - 6 q^{81} + 48 q^{82} + 24 q^{83} - 25 q^{84} - 26 q^{85} - 22 q^{86} - 6 q^{87} + 2 q^{88} - 18 q^{89} - 6 q^{90} + 22 q^{91} - 6 q^{92} - 11 q^{93} - 3 q^{94} + 16 q^{95} + 3 q^{96} - 4 q^{97} - 62 q^{98} - 28 q^{99}+O(q^{100}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 - q^14 - 6 * q^15 + 7 * q^16 - 15 * q^17 + q^18 + q^19 + 34 * q^20 - 4 * q^21 - 12 * q^22 + 6 * q^23 - 3 * q^24 - 9 * q^25 + 15 * q^26 - 12 * q^27 - 2 * q^28 - 12 * q^29 - 3 * q^30 + 11 * q^31 - 3 * q^32 - 14 * q^33 + 30 * q^34 - q^35 + 6 * q^36 + 5 * q^37 - 14 * q^38 + 17 * q^40 + 36 * q^41 - 17 * q^42 - 74 * q^43 + 10 * q^44 - 3 * q^45 - q^46 - 3 * q^47 + 14 * q^48 - 6 * q^49 - 60 * q^50 + 15 * q^51 + 7 * q^52 + 15 * q^53 - q^54 - 4 * q^55 - 21 * q^56 + 2 * q^57 - 4 * q^58 + 2 * q^59 + 17 * q^60 + 12 * q^61 + 72 * q^62 - 2 * q^63 - 46 * q^64 + 17 * q^65 - 6 * q^66 + 10 * q^67 + q^68 + 12 * q^69 - 56 * q^70 - 42 * q^71 + 3 * q^72 + 8 * q^73 + 16 * q^74 + 9 * q^75 + 36 * q^76 - 40 * q^77 + 30 * q^78 + 17 * q^79 - 3 * q^80 - 6 * q^81 + 48 * q^82 + 24 * q^83 - 25 * q^84 - 26 * q^85 - 22 * q^86 - 6 * q^87 + 2 * q^88 - 18 * q^89 - 6 * q^90 + 22 * q^91 - 6 * q^92 - 11 * q^93 - 3 * q^94 + 16 * q^95 + 3 * q^96 - 4 * q^97 - 62 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.682743	+	1.18255i	−0.482772	+	0.836186i	−0.999804	−	0.0197802i	$-0.993703\pi$
$2$	−0.682743	+	1.18255i	−0.482772	+	0.836186i	0.517032	+	0.855966i	$0.327037\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.0677246	+	0.117302i	0.0338623	+	0.0586512i
$5$	0.663106	−	1.14853i	0.296550	−	0.513639i	−0.678794	−	0.734328i	$-0.737497\pi$
$5$	0.663106	−	1.14853i	0.296550	−	0.513639i	0.975344	+	0.220689i	$0.0708306\pi$
$6$	−1.36549			−0.557457
$7$	2.35341	+	1.20891i	0.889505	+	0.456926i
$7$	2.35341	+	1.20891i	0.889505	+	0.456926i
$8$	−2.91593			−1.03094
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.905461	+	1.56830i	0.286332	+	0.495941i
$11$	0.710043	+	1.22983i	0.214086	+	0.370808i	0.952989	−	0.303003i	$-0.0979894\pi$
$11$	0.710043	+	1.22983i	0.214086	+	0.370808i	−0.738903	+	0.673811i	$0.764656\pi$
$12$	−0.0677246	+	0.117302i	−0.0195504	+	0.0338623i
$13$	3.16661			0.878259			0.439129	−	0.898424i	$-0.355287\pi$
$13$	3.16661			0.878259			0.439129	+	0.898424i	$0.355287\pi$
$14$	−3.03637	+	1.95764i	−0.811503	+	0.523200i
$15$	1.32621			0.342426
$16$	1.85538	−	3.21361i	0.463844	−	0.803402i
$17$	−0.579802	−	1.00425i	−0.140623	−	0.243565i	0.787109	−	0.616814i	$-0.211577\pi$
$17$	−0.579802	−	1.00425i	−0.140623	−	0.243565i	−0.927731	+	0.373249i	$0.878244\pi$
$18$	−0.682743	−	1.18255i	−0.160924	−	0.278729i
$19$	−4.28943	+	7.42951i	−0.984063	+	1.70445i	−0.338033	+	0.941134i	$0.609762\pi$
$19$	−4.28943	+	7.42951i	−0.984063	+	1.70445i	−0.646030	+	0.763312i	$0.723572\pi$
$20$	0.179634			0.0401674
$21$	0.129755	+	2.64257i	0.0283149	+	0.576656i
$22$	−1.93911			−0.413419
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	−1.45796	−	2.52527i	−0.297605	−	0.515468i
$25$	1.62058	+	2.80693i	0.324116	+	0.561386i
$26$	−2.16198	+	3.74466i	−0.423999	+	0.734388i
$27$	−1.00000			−0.192450
$28$	0.0175752	+	0.357934i	0.00332141	+	0.0676431i
$29$	7.45480			1.38432			0.692161	−	0.721743i	$-0.256659\pi$
$29$	7.45480			1.38432			0.692161	+	0.721743i	$0.256659\pi$
$30$	−0.905461	+	1.56830i	−0.165314	+	0.286332i
$31$	−0.933210	−	1.61637i	−0.167609	−	0.290308i	0.769969	−	0.638081i	$-0.220271\pi$
$31$	−0.933210	−	1.61637i	−0.167609	−	0.290308i	−0.937579	+	0.347773i	$0.886938\pi$
$32$	−0.382434	−	0.662395i	−0.0676054	−	0.117096i
$33$	−0.710043	+	1.22983i	−0.123603	+	0.214086i
$34$	1.58342			0.271555
$35$	2.94903	−	1.90133i	0.498478	−	0.321383i
$36$	−0.135449			−0.0225749
$37$	3.89919	−	6.75360i	0.641023	−	1.11028i	−0.344182	−	0.938903i	$-0.611844\pi$
$37$	3.89919	−	6.75360i	0.641023	−	1.11028i	0.985205	−	0.171382i	$-0.0548231\pi$
$38$	−5.85715	−	10.1449i	−0.950156	−	1.64572i
$39$	1.58330	+	2.74236i	0.253532	+	0.439129i
$40$	−1.93357	+	3.34903i	−0.305724	+	0.529529i
$41$	−11.2258			−1.75317			−0.876584	−	0.481248i	$-0.840183\pi$
$41$	−11.2258			−1.75317			−0.876584	+	0.481248i	$0.840183\pi$
$42$	−3.21355	−	1.65075i	−0.495861	−	0.254717i
$43$	−11.8479			−1.80679			−0.903393	−	0.428814i	$-0.858932\pi$
$43$	−11.8479			−1.80679			−0.903393	+	0.428814i	$0.858932\pi$
$44$	−0.0961748	+	0.166580i	−0.0144989	+	0.0251128i
$45$	0.663106	+	1.14853i	0.0988499	+	0.171213i
$46$	0.682743	+	1.18255i	0.100665	+	0.174357i
$47$	−0.868249	+	1.50385i	−0.126647	+	0.219359i	−0.922376	−	0.386294i	$-0.873755\pi$
$47$	−0.868249	+	1.50385i	−0.126647	+	0.219359i	0.795728	+	0.605654i	$0.207088\pi$
$48$	3.71076			0.535601
$49$	4.07706	+	5.69013i	0.582437	+	0.812876i
$50$	−4.42576			−0.625897
$51$	0.579802	−	1.00425i	0.0811885	−	0.140623i
$52$	0.214457	+	0.371451i	0.0297399	+	0.0515110i
$53$	2.07449	+	3.59312i	0.284953	+	0.493553i	0.972598	−	0.232494i	$-0.0746886\pi$
$53$	2.07449	+	3.59312i	0.284953	+	0.493553i	−0.687645	+	0.726047i	$0.741355\pi$
$54$	0.682743	−	1.18255i	0.0929095	−	0.160924i
$55$	1.88333			0.253949
$56$	−6.86236	−	3.52510i	−0.917022	−	0.471061i
$57$	−8.57886			−1.13630
$58$	−5.08971	+	8.81564i	−0.668312	+	1.15755i
$59$	−6.34357	−	10.9874i	−0.825862	−	1.43044i	−0.901259	−	0.433281i	$-0.857356\pi$
$59$	−6.34357	−	10.9874i	−0.825862	−	1.43044i	0.0753966	−	0.997154i	$-0.475978\pi$
$60$	0.0898171	+	0.155568i	0.0115953	+	0.0200837i
$61$	6.90738	−	11.9639i	0.884399	−	1.53182i	0.0379985	−	0.999278i	$-0.487902\pi$
$61$	6.90738	−	11.9639i	0.884399	−	1.53182i	0.846401	−	0.532547i	$-0.178765\pi$
$62$	2.54857			0.323669
$63$	−2.22365	+	1.43366i	−0.280154	+	0.180624i
$64$	8.46593			1.05824
$65$	2.09980	−	3.63695i	0.260448	−	0.451108i
$66$	−0.969554	−	1.67932i	−0.119344	−	0.206710i
$67$	4.04647	+	7.00870i	0.494355	+	0.856249i	0.999979	−	0.00650550i	$-0.00207078\pi$
$67$	4.04647	+	7.00870i	0.494355	+	0.856249i	−0.505623	+	0.862754i	$0.668737\pi$
$68$	0.0785337	−	0.136024i	0.00952361	−	0.0164954i
$69$	1.00000			0.120386
$70$	0.234977	+	4.78548i	0.0280851	+	0.571975i
$71$	−5.18979			−0.615915			−0.307957	−	0.951400i	$-0.599645\pi$
$71$	−5.18979			−0.615915			−0.307957	+	0.951400i	$0.599645\pi$
$72$	1.45796	−	2.52527i	0.171823	−	0.297605i
$73$	5.68430	+	9.84549i	0.665297	+	1.15233i	0.979205	+	0.202874i	$0.0650282\pi$
$73$	5.68430	+	9.84549i	0.665297	+	1.15233i	−0.313908	+	0.949453i	$0.601638\pi$
$74$	5.32429	+	9.22194i	0.618936	+	1.07203i
$75$	−1.62058	+	2.80693i	−0.187129	+	0.324116i
$76$	−1.16200			−0.133291
$77$	0.184264	+	3.75267i	0.0209988	+	0.427657i
$78$	−4.32396			−0.489592
$79$	5.86823	−	10.1641i	0.660228	−	1.14355i	−0.320328	−	0.947307i	$-0.603793\pi$
$79$	5.86823	−	10.1641i	0.660228	−	1.14355i	0.980556	−	0.196242i	$-0.0628737\pi$
$80$	−2.46062	−	4.26192i	−0.275106	−	0.476497i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.66430	−	13.2750i	0.846381	−	1.46597i
$83$	5.70566			0.626277			0.313139	−	0.949707i	$-0.398620\pi$
$83$	5.70566			0.626277			0.313139	+	0.949707i	$0.398620\pi$
$84$	−0.301192	+	0.194187i	−0.0328627	+	0.0211876i
$85$	−1.53788			−0.166806
$86$	8.08906	−	14.0107i	0.872266	−	1.51081i
$87$	3.72740	+	6.45604i	0.399619	+	0.692161i
$88$	−2.07043	−	3.58609i	−0.220709	−	0.382279i
$89$	3.17756	−	5.50369i	0.336820	−	0.583390i	−0.647012	−	0.762479i	$-0.723982\pi$
$89$	3.17756	−	5.50369i	0.336820	−	0.583390i	0.983833	+	0.179089i	$0.0573151\pi$
$90$	−1.81092			−0.190888
$91$	7.45232	+	3.82815i	0.781215	+	0.401299i
$92$	0.135449			0.0141216
$93$	0.933210	−	1.61637i	0.0967694	−	0.167609i
$94$	−1.18558	−	2.05349i	−0.122283	−	0.211801i
$95$	5.68869	+	9.85310i	0.583647	+	1.01091i
$96$	0.382434	−	0.662395i	0.0390320	−	0.0676054i
$97$	0.408396			0.0414663			0.0207331	−	0.999785i	$-0.493400\pi$
$97$	0.408396			0.0414663			0.0207331	+	0.999785i	$0.493400\pi$
$98$	−9.51242	+	0.936415i	−0.960899	+	0.0945922i
$99$	−1.42009			−0.142724
$100$	−0.219507	+	0.380196i	−0.0219507	+	0.0380196i
$101$	0.361914	+	0.626853i	0.0360117	+	0.0623742i	0.883470	−	0.468489i	$-0.155201\pi$
$101$	0.361914	+	0.626853i	0.0360117	+	0.0623742i	−0.847458	+	0.530863i	$0.821868\pi$
$102$	0.791711	+	1.37128i	0.0783911	+	0.135777i
$103$	7.13695	−	12.3616i	0.703225	−	1.21802i	−0.264103	−	0.964494i	$-0.585076\pi$
$103$	7.13695	−	12.3616i	0.703225	−	1.21802i	0.967328	−	0.253527i	$-0.0815907\pi$
$104$	−9.23359			−0.905428
$105$	3.12112	+	1.60327i	0.304590	+	0.156463i
$106$	−5.66537			−0.550270
$107$	−6.99797	+	12.1208i	−0.676520	+	1.17177i	0.299503	+	0.954095i	$0.403179\pi$
$107$	−6.99797	+	12.1208i	−0.676520	+	1.17177i	−0.976022	+	0.217671i	$0.930154\pi$
$108$	−0.0677246	−	0.117302i	−0.00651680	−	0.0112874i
$109$	−1.45473	−	2.51966i	−0.139338	−	0.241340i	0.787908	−	0.615792i	$-0.211164\pi$
$109$	−1.45473	−	2.51966i	−0.139338	−	0.241340i	−0.927246	+	0.374453i	$0.877831\pi$
$110$	−1.28583	+	2.22713i	−0.122599	+	0.212348i
$111$	7.79838			0.740190
$112$	8.25143	−	5.31994i	0.779687	−	0.502687i
$113$	18.6624			1.75561			0.877804	−	0.479020i	$-0.159008\pi$
$113$	18.6624			1.75561			0.877804	+	0.479020i	$0.159008\pi$
$114$	5.85715	−	10.1449i	0.548573	−	0.950156i
$115$	−0.663106	−	1.14853i	−0.0618349	−	0.107101i
$116$	0.504873	+	0.874466i	0.0468763	+	0.0811921i
$117$	−1.58330	+	2.74236i	−0.146376	+	0.253532i
$118$	17.3241			1.59481
$119$	−0.150465	−	3.06433i	−0.0137931	−	0.280907i
$120$	−3.86713			−0.353019
$121$	4.49168	−	7.77981i	0.408334	−	0.707256i
$122$	9.43193	+	16.3366i	0.853926	+	1.47904i
$123$	−5.61288	−	9.72179i	−0.506096	−	0.876584i
$124$	0.126403	−	0.218936i	0.0113513	−	0.0196610i
$125$	10.9295			0.977566
$126$	−0.177179	−	3.60839i	−0.0157844	−	0.321461i
$127$	1.06631			0.0946196			0.0473098	−	0.998880i	$-0.484935\pi$
$127$	1.06631			0.0946196			0.0473098	+	0.998880i	$0.484935\pi$
$128$	−5.01518	+	8.68655i	−0.443284	+	0.767790i
$129$	−5.92394	−	10.2606i	−0.521574	−	0.903393i
$130$	2.86724	+	4.96620i	0.251474	+	0.435565i
$131$	8.00721	−	13.8689i	0.699593	−	1.21173i	−0.269014	−	0.963136i	$-0.586698\pi$
$131$	8.00721	−	13.8689i	0.699593	−	1.21173i	0.968608	−	0.248595i	$-0.0799688\pi$
$132$	−0.192350			−0.0167419
$133$	−19.0764	+	12.2991i	−1.65413	+	1.06647i
$134$	−11.0508			−0.954644
$135$	−0.663106	+	1.14853i	−0.0570710	+	0.0988499i
$136$	1.69066	+	2.92831i	0.144973	+	0.251100i
$137$	−0.463790	−	0.803307i	−0.0396242	−	0.0686312i	0.845533	−	0.533923i	$-0.179283\pi$
$137$	−0.463790	−	0.803307i	−0.0396242	−	0.0686312i	−0.885157	+	0.465292i	$0.845949\pi$
$138$	−0.682743	+	1.18255i	−0.0581189	+	0.100665i
$139$	−4.22569			−0.358418			−0.179209	−	0.983811i	$-0.557354\pi$
$139$	−4.22569			−0.358418			−0.179209	+	0.983811i	$0.557354\pi$
$140$	0.422753	+	0.217162i	0.0357291	+	0.0183535i
$141$	−1.73650			−0.146239
$142$	3.54329	−	6.13716i	0.297346	−	0.515019i
$143$	2.24843	+	3.89439i	0.188023	+	0.325665i
$144$	1.85538	+	3.21361i	0.154615	+	0.267801i
$145$	4.94332	−	8.56208i	0.410520	−	0.711042i
$146$	−15.5237			−1.28475
$147$	−2.88927	+	6.37590i	−0.238303	+	0.525876i
$148$	1.05628			0.0868261
$149$	8.22319	−	14.2430i	0.673670	−	1.16683i	−0.303186	−	0.952931i	$-0.598050\pi$
$149$	8.22319	−	14.2430i	0.673670	−	1.16683i	0.976856	−	0.213899i	$-0.0686164\pi$
$150$	−2.21288	−	3.83282i	−0.180681	−	0.312949i
$151$	4.09419	+	7.09135i	0.333180	+	0.577086i	0.983134	−	0.182889i	$-0.0585448\pi$
$151$	4.09419	+	7.09135i	0.333180	+	0.577086i	−0.649953	+	0.759974i	$0.725211\pi$
$152$	12.5077	−	21.6639i	1.01450	−	1.75717i
$153$	1.15960			0.0937484
$154$	−4.56351	−	2.34421i	−0.367738	−	0.188902i
$155$	−2.47527			−0.198818
$156$	−0.214457	+	0.371451i	−0.0171703	+	0.0297399i
$157$	−11.2576	−	19.4987i	−0.898452	−	1.55616i	−0.829473	−	0.558546i	$-0.811359\pi$
$157$	−11.2576	−	19.4987i	−0.898452	−	1.55616i	−0.0689787	−	0.997618i	$-0.521974\pi$
$158$	8.01299	+	13.8789i	0.637479	+	1.10415i
$159$	−2.07449	+	3.59312i	−0.164518	+	0.284953i
$160$	−1.01438			−0.0801935
$161$	2.22365	−	1.43366i	0.175248	−	0.112988i
$162$	1.36549			0.107283
$163$	0.730753	−	1.26570i	0.0572370	−	0.0991373i	−0.835987	−	0.548749i	$-0.815104\pi$
$163$	0.730753	−	1.26570i	0.0572370	−	0.0991373i	0.893224	+	0.449612i	$0.148438\pi$
$164$	−0.760260	−	1.31681i	−0.0593663	−	0.102825i
$165$	0.941667	+	1.63102i	0.0733087	+	0.126974i
$166$	−3.89550	+	6.74720i	−0.302349	+	0.523684i
$167$	2.76301			0.213808			0.106904	−	0.994269i	$-0.465906\pi$
$167$	2.76301			0.213808			0.106904	+	0.994269i	$0.465906\pi$
$168$	−0.378357	−	7.70553i	−0.0291908	−	0.594494i
$169$	−2.97260			−0.228661
$170$	1.04998	−	1.81861i	0.0805295	−	0.139481i
$171$	−4.28943	−	7.42951i	−0.328021	−	0.568149i
$172$	−0.802394	−	1.38979i	−0.0611819	−	0.105970i
$173$	−9.43306	+	16.3385i	−0.717182	+	1.24220i	0.244930	+	0.969541i	$0.421235\pi$
$173$	−9.43306	+	16.3385i	−0.717182	+	1.24220i	−0.962112	+	0.272655i	$0.912098\pi$
$174$	−10.1794			−0.771700
$175$	0.420558	+	8.56500i	0.0317912	+	0.647453i
$176$	5.26959			0.397210
$177$	6.34357	−	10.9874i	0.476812	−	0.825862i
$178$	4.33891	+	7.51521i	0.325215	+	0.563289i
$179$	10.3591	+	17.9425i	0.774276	+	1.34109i	0.935200	+	0.354119i	$0.115219\pi$
$179$	10.3591	+	17.9425i	0.774276	+	1.34109i	−0.160924	+	0.986967i	$0.551447\pi$
$180$	−0.0898171	+	0.155568i	−0.00669457	+	0.0115953i
$181$	0.686865			0.0510543			0.0255271	−	0.999674i	$-0.491874\pi$
$181$	0.686865			0.0510543			0.0255271	+	0.999674i	$0.491874\pi$
$182$	−9.61498	+	6.19906i	−0.712710	+	0.459505i
$183$	13.8148			1.02122
$184$	−1.45796	+	2.52527i	−0.107482	+	0.186165i
$185$	−5.17115	−	8.95670i	−0.380191	−	0.658509i
$186$	1.27428	+	2.20713i	0.0934351	+	0.161834i
$187$	0.823369	−	1.42612i	0.0602107	−	0.104288i
$188$	−0.235207			−0.0171542
$189$	−2.35341	−	1.20891i	−0.171185	−	0.0879354i
$190$	−15.5356			−1.12707
$191$	−0.546501	+	0.946568i	−0.0395434	+	0.0684912i	−0.885120	−	0.465363i	$-0.845924\pi$
$191$	−0.546501	+	0.946568i	−0.0395434	+	0.0684912i	0.845576	+	0.533855i	$0.179257\pi$
$192$	4.23296	+	7.33171i	0.305488	+	0.529120i
$193$	−3.70697	−	6.42066i	−0.266833	−	0.462169i	0.701209	−	0.712956i	$-0.252644\pi$
$193$	−3.70697	−	6.42066i	−0.266833	−	0.462169i	−0.968042	+	0.250787i	$0.919311\pi$
$194$	−0.278829	+	0.482946i	−0.0200188	+	0.0346735i
$195$	4.19959			0.300739
$196$	−0.391349	+	0.863611i	−0.0279535	+	0.0616865i
$197$	3.16080			0.225198			0.112599	−	0.993641i	$-0.464082\pi$
$197$	3.16080			0.225198			0.112599	+	0.993641i	$0.464082\pi$
$198$	0.969554	−	1.67932i	0.0689032	−	0.119344i
$199$	0.904642	+	1.56689i	0.0641283	+	0.111074i	0.896307	−	0.443434i	$-0.146240\pi$
$199$	0.904642	+	1.56689i	0.0641283	+	0.111074i	−0.832179	+	0.554508i	$0.812907\pi$
$200$	−4.72550	−	8.18480i	−0.334143	−	0.578753i
$201$	−4.04647	+	7.00870i	−0.285416	+	0.494355i
$202$	−0.988375			−0.0695419
$203$	17.5442	+	9.01220i	1.23136	+	0.632532i
$204$	0.157067			0.0109969
$205$	−7.44386	+	12.8931i	−0.519902	+	0.900496i
$206$	9.74541	+	16.8795i	0.678995	+	1.17605i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	5.87525	−	10.1762i	0.407375	−	0.705595i
$209$	−12.1827			−0.842696
$210$	−4.02686	+	2.59624i	−0.277880	+	0.179157i
$211$	−22.5516			−1.55252			−0.776260	−	0.630413i	$-0.782885\pi$
$211$	−22.5516			−1.55252			−0.776260	+	0.630413i	$0.782885\pi$
$212$	−0.280988	+	0.486686i	−0.0192983	+	0.0334257i
$213$	−2.59489	−	4.49449i	−0.177799	−	0.307957i
$214$	−9.55563	−	16.5508i	−0.653210	−	1.13139i
$215$	−7.85640	+	13.6077i	−0.535802	+	0.928036i
$216$	2.91593			0.198404
$217$	−0.242178	−	4.93214i	−0.0164401	−	0.334816i
$218$	3.97282			0.269073
$219$	−5.68430	+	9.84549i	−0.384109	+	0.665297i
$220$	0.127548	+	0.220920i	0.00859929	+	0.0148944i
$221$	−1.83600	−	3.18005i	−0.123503	−	0.213914i
$222$	−5.32429	+	9.22194i	−0.357343	+	0.618936i
$223$	−14.4484			−0.967535			−0.483767	−	0.875197i	$-0.660732\pi$
$223$	−14.4484			−0.967535			−0.483767	+	0.875197i	$0.660732\pi$
$224$	−0.0992456	−	2.02121i	−0.00663113	−	0.135048i
$225$	−3.24116			−0.216078
$226$	−12.7416	+	22.0691i	−0.847558	+	1.46801i
$227$	1.63940	+	2.83953i	0.108811	+	0.188466i	0.915289	−	0.402798i	$-0.131962\pi$
$227$	1.63940	+	2.83953i	0.108811	+	0.188466i	−0.806478	+	0.591264i	$0.798629\pi$
$228$	−0.581000	−	1.00632i	−0.0384777	−	0.0666453i
$229$	0.131966	−	0.228573i	0.00872059	−	0.0151045i	−0.861632	−	0.507533i	$-0.830557\pi$
$229$	0.131966	−	0.228573i	0.00872059	−	0.0151045i	0.870353	+	0.492429i	$0.163891\pi$
$230$	1.81092			0.119409
$231$	−3.15778	+	2.03591i	−0.207767	+	0.133953i
$232$	−21.7376			−1.42715
$233$	−8.92547	+	15.4594i	−0.584727	+	1.01278i	0.410183	+	0.912003i	$0.365465\pi$
$233$	−8.92547	+	15.4594i	−0.584727	+	1.01278i	−0.994909	+	0.100773i	$0.967868\pi$
$234$	−2.16198	−	3.74466i	−0.141333	−	0.244796i
$235$	1.15148	+	1.99442i	0.0751143	+	0.130102i
$236$	0.859231	−	1.48823i	0.0559312	−	0.0968756i
$237$	11.7365			0.762366
$238$	3.72644	+	1.91422i	0.241549	+	0.124080i
$239$	1.68846			0.109217			0.0546086	−	0.998508i	$-0.482609\pi$
$239$	1.68846			0.109217			0.0546086	+	0.998508i	$0.482609\pi$
$240$	2.46062	−	4.26192i	0.158832	−	0.275106i
$241$	−9.52098	−	16.4908i	−0.613300	−	1.06227i	−0.990680	−	0.136208i	$-0.956508\pi$
$241$	−9.52098	−	16.4908i	−0.613300	−	1.06227i	0.377380	−	0.926058i	$-0.376825\pi$
$242$	6.13332	+	10.6232i	0.394265	+	0.682887i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.87120			0.119791
$245$	9.23882	−	0.909481i	0.590247	−	0.0581046i
$246$	15.3286			0.977316
$247$	−13.5829	+	23.5263i	−0.864262	+	1.49695i
$248$	2.72117	+	4.71321i	0.172795	+	0.299289i
$249$	2.85283	+	4.94125i	0.180791	+	0.313139i
$250$	−7.46205	+	12.9247i	−0.471942	+	0.817427i
$251$	−20.3390			−1.28379			−0.641895	−	0.766793i	$-0.721851\pi$
$251$	−20.3390			−1.28379			−0.641895	+	0.766793i	$0.721851\pi$
$252$	−0.318767	−	0.163746i	−0.0200805	−	0.0103150i
$253$	1.42009			0.0892801
$254$	−0.728015	+	1.26096i	−0.0456797	+	0.0791196i
$255$	−0.768940	−	1.33184i	−0.0481529	−	0.0834032i
$256$	1.61777	+	2.80205i	0.101110	+	0.175128i
$257$	4.81478	−	8.33944i	0.300337	−	0.520200i	−0.675875	−	0.737016i	$-0.736234\pi$
$257$	4.81478	−	8.33944i	0.300337	−	0.520200i	0.976212	+	0.216817i	$0.0695674\pi$
$258$	16.1781			1.00721
$259$	17.3409	−	11.1802i	1.07751	−	0.694703i
$260$	0.568831			0.0352774
$261$	−3.72740	+	6.45604i	−0.230720	+	0.399619i
$262$	10.9337	+	18.9378i	0.675488	+	1.16998i
$263$	2.42754	+	4.20462i	0.149688	+	0.259268i	0.931112	−	0.364733i	$-0.118840\pi$
$263$	2.42754	+	4.20462i	0.149688	+	0.259268i	−0.781424	+	0.624000i	$0.785506\pi$
$264$	2.07043	−	3.58609i	0.127426	−	0.220709i
$265$	5.50243			0.338011
$266$	−1.51999	−	30.9559i	−0.0931968	−	1.89803i
$267$	6.35511			0.388927
$268$	−0.548092	+	0.949323i	−0.0334800	+	0.0579891i
$269$	−6.36928	−	11.0319i	−0.388342	−	0.672628i	0.603885	−	0.797072i	$-0.293619\pi$
$269$	−6.36928	−	11.0319i	−0.388342	−	0.672628i	−0.992227	+	0.124444i	$0.960285\pi$
$270$	−0.905461	−	1.56830i	−0.0551046	−	0.0954440i
$271$	11.0010	−	19.0543i	0.668265	−	1.15747i	−0.310124	−	0.950696i	$-0.600371\pi$
$271$	11.0010	−	19.0543i	0.668265	−	1.15747i	0.978389	−	0.206773i	$-0.0662960\pi$
$272$	−4.30301			−0.260908
$273$	0.410884	+	8.36797i	0.0248678	+	0.506453i
$274$	1.26660			0.0765179
$275$	−2.30137	+	3.98608i	−0.138778	+	0.240370i
$276$	0.0677246	+	0.117302i	0.00407654	+	0.00706078i
$277$	−0.0827222	−	0.143279i	−0.00497030	−	0.00860881i	0.863530	−	0.504298i	$-0.168249\pi$
$277$	−0.0827222	−	0.143279i	−0.00497030	−	0.00860881i	−0.868500	+	0.495689i	$0.834915\pi$
$278$	2.88506	−	4.99707i	0.173034	−	0.299704i
$279$	1.86642			0.111740
$280$	−8.59916	+	5.54413i	−0.513898	+	0.331325i
$281$	−20.9797			−1.25155			−0.625773	−	0.780006i	$-0.715216\pi$
$281$	−20.9797			−1.25155			−0.625773	+	0.780006i	$0.715216\pi$
$282$	1.18558	−	2.05349i	0.0706003	−	0.122283i
$283$	0.407411	+	0.705657i	0.0242181	+	0.0419470i	0.877880	−	0.478880i	$-0.158957\pi$
$283$	0.407411	+	0.705657i	0.0242181	+	0.0419470i	−0.853662	+	0.520827i	$0.825624\pi$
$284$	−0.351476	−	0.608775i	−0.0208563	−	0.0361242i
$285$	−5.68869	+	9.85310i	−0.336969	+	0.583647i
$286$	−6.14039			−0.363089
$287$	−26.4188	−	13.5710i	−1.55945	−	0.801068i
$288$	0.764868			0.0450703
$289$	7.82766	−	13.5579i	0.460451	−	0.797524i
$290$	6.75003	+	11.6914i	0.396375	+	0.686542i
$291$	0.204198	+	0.353681i	0.0119703	+	0.0207331i
$292$	−0.769933	+	1.33356i	−0.0450569	+	0.0780409i
$293$	−12.6589			−0.739543			−0.369771	−	0.929123i	$-0.620564\pi$
$293$	−12.6589			−0.739543			−0.369771	+	0.929123i	$0.620564\pi$
$294$	−5.56717	−	7.76979i	−0.324684	−	0.453143i
$295$	−16.8258			−0.979637
$296$	−11.3698	+	19.6930i	−0.660853	+	1.14463i
$297$	−0.710043	−	1.22983i	−0.0412009	−	0.0713620i
$298$	11.2286	+	19.4486i	0.650458	+	1.12663i
$299$	1.58330	−	2.74236i	0.0915648	−	0.158595i
$300$	−0.439013			−0.0253464
$301$	−27.8829	−	14.3231i	−1.60714	−	0.825567i
$302$	−11.1811			−0.643401
$303$	−0.361914	+	0.626853i	−0.0207914	+	0.0360117i
$304$	15.9170	+	27.5691i	0.912904	+	1.58120i
$305$	−9.16064	−	15.8667i	−0.524537	−	0.908525i
$306$	−0.791711	+	1.37128i	−0.0452591	+	0.0783911i
$307$	−3.03467			−0.173198			−0.0865989	−	0.996243i	$-0.527600\pi$
$307$	−3.03467			−0.173198			−0.0865989	+	0.996243i	$0.527600\pi$
$308$	−0.427719	+	0.275763i	−0.0243715	+	0.0157131i
$309$	14.2739			0.812014
$310$	1.68997	−	2.92712i	0.0959839	−	0.166249i
$311$	−13.7383	−	23.7955i	−0.779029	−	1.34932i	−0.932502	−	0.361164i	$-0.882379\pi$
$311$	−13.7383	−	23.7955i	−0.779029	−	1.34932i	0.153474	−	0.988153i	$-0.450954\pi$
$312$	−4.61679	−	7.99652i	−0.261375	−	0.452714i
$313$	−0.671013	+	1.16223i	−0.0379279	+	0.0656930i	−0.884366	−	0.466794i	$-0.845409\pi$
$313$	−0.671013	+	1.16223i	−0.0379279	+	0.0656930i	0.846438	+	0.532487i	$0.178742\pi$
$314$	30.7441			1.73499
$315$	0.172083	+	3.50460i	0.00969577	+	0.197462i
$316$	1.58970			0.0894274
$317$	−0.254308	+	0.440475i	−0.0142834	+	0.0247395i	−0.873079	−	0.487579i	$-0.837880\pi$
$317$	−0.254308	+	0.440475i	−0.0142834	+	0.0247395i	0.858795	+	0.512319i	$0.171213\pi$
$318$	−2.83269	−	4.90636i	−0.158849	−	0.275135i
$319$	5.29323	+	9.16814i	0.296364	+	0.513317i
$320$	5.61380	−	9.72339i	0.313821	−	0.543554i
$321$	−13.9959			−0.781178
$322$	0.177179	+	3.60839i	0.00987380	+	0.201088i
$323$	9.94808			0.553526
$324$	0.0677246	−	0.117302i	0.00376248	−	0.00651680i
$325$	5.13175	+	8.88845i	0.284658	+	0.493042i
$326$	0.997832	+	1.72830i	0.0552648	+	0.0957215i
$327$	1.45473	−	2.51966i	0.0804466	−	0.139338i
$328$	32.7335			1.80740
$329$	−3.86137	+	2.48954i	−0.212884	+	0.137253i
$330$	−2.57167			−0.141566
$331$	−3.09517	+	5.36099i	−0.170126	+	0.294666i	−0.938464	−	0.345378i	$-0.887751\pi$
$331$	−3.09517	+	5.36099i	−0.170126	+	0.294666i	0.768338	+	0.640044i	$0.221084\pi$
$332$	0.386413	+	0.669288i	0.0212072	+	0.0367319i
$333$	3.89919	+	6.75360i	0.213674	+	0.370095i
$334$	−1.88642	+	3.26738i	−0.103220	+	0.178783i
$335$	10.7330			0.586404
$336$	8.73292	+	4.48598i	0.476420	+	0.244730i
$337$	−5.07603			−0.276509			−0.138254	−	0.990397i	$-0.544149\pi$
$337$	−5.07603			−0.276509			−0.138254	+	0.990397i	$0.544149\pi$
$338$	2.02952	−	3.51523i	0.110391	−	0.191203i
$339$	9.33118	+	16.1621i	0.506800	+	0.877804i
$340$	−0.104152	−	0.180397i	−0.00564845	−	0.00978340i
$341$	1.32524	−	2.29538i	0.0717657	−	0.124302i
$342$	11.7143			0.633437
$343$	2.71612	+	18.3200i	0.146657	+	0.989187i
$344$	34.5476			1.86268
$345$	0.663106	−	1.14853i	0.0357004	−	0.0618349i
$346$	−12.8807	−	22.3100i	−0.692471	−	1.19939i
$347$	12.7476	+	22.0795i	0.684326	+	1.18529i	0.973648	+	0.228055i	$0.0732367\pi$
$347$	12.7476	+	22.0795i	0.684326	+	1.18529i	−0.289322	+	0.957232i	$0.593430\pi$
$348$	−0.504873	+	0.874466i	−0.0270640	+	0.0468763i
$349$	−11.0135			−0.589541			−0.294771	−	0.955568i	$-0.595243\pi$
$349$	−11.0135			−0.589541			−0.294771	+	0.955568i	$0.595243\pi$
$350$	−10.4156	−	5.35036i	−0.556739	−	0.285989i
$351$	−3.16661			−0.169021
$352$	0.543089	−	0.940658i	0.0289467	−	0.0501372i
$353$	3.32390	+	5.75717i	0.176914	+	0.306423i	0.940822	−	0.338902i	$-0.110055\pi$
$353$	3.32390	+	5.75717i	0.176914	+	0.306423i	−0.763908	+	0.645325i	$0.776722\pi$
$354$	8.66205	+	15.0031i	0.460383	+	0.797406i
$355$	−3.44138	+	5.96064i	−0.182649	+	0.316358i
$356$	0.860795			0.0456221
$357$	2.57856	−	1.66247i	0.136472	−	0.0879873i
$358$	−28.2904			−1.49520
$359$	3.92736	−	6.80239i	0.207278	−	0.359017i	−0.743578	−	0.668649i	$-0.766873\pi$
$359$	3.92736	−	6.80239i	0.207278	−	0.359017i	0.950856	+	0.309633i	$0.100206\pi$
$360$	−1.93357	−	3.34903i	−0.101908	−	0.176510i
$361$	−27.2984	−	47.2822i	−1.43676	−	2.48854i
$362$	−0.468952	+	0.812249i	−0.0246476	+	0.0426909i
$363$	8.98335			0.471504
$364$	0.0556539	+	1.13344i	0.00291706	+	0.0594082i
$365$	15.0772			0.789174
$366$	−9.43193	+	16.3366i	−0.493015	+	0.853926i
$367$	−0.936185	−	1.62152i	−0.0488684	−	0.0846426i	0.840556	−	0.541724i	$-0.182228\pi$
$367$	−0.936185	−	1.62152i	−0.0488684	−	0.0846426i	−0.889425	+	0.457081i	$0.848895\pi$
$368$	−1.85538	−	3.21361i	−0.0967182	−	0.167521i
$369$	5.61288	−	9.72179i	0.292195	−	0.506096i
$370$	14.1223			0.734182
$371$	0.538352	+	10.9640i	0.0279499	+	0.569221i
$372$	0.252805			0.0131073
$373$	11.6887	−	20.2455i	0.605220	−	1.04827i	−0.386796	−	0.922165i	$-0.626418\pi$
$373$	11.6887	−	20.2455i	0.605220	−	1.04827i	0.992017	−	0.126107i	$-0.0402484\pi$
$374$	1.12430	+	1.94734i	0.0581361	+	0.100695i
$375$	5.46476	+	9.46524i	0.282199	+	0.488783i
$376$	2.53175	−	4.38512i	0.130565	−	0.226145i
$377$	23.6064			1.21579
$378$	3.03637	−	1.95764i	0.156174	−	0.100690i
$379$	20.9257			1.07488			0.537441	−	0.843301i	$-0.319391\pi$
$379$	20.9257			1.07488			0.537441	+	0.843301i	$0.319391\pi$
$380$	−0.770528	+	1.33459i	−0.0395273	+	0.0684633i
$381$	0.533154	+	0.923450i	0.0273143	+	0.0473098i
$382$	−0.746239	−	1.29252i	−0.0381809	−	0.0661313i
$383$	13.4095	−	23.2259i	0.685191	−	1.18679i	−0.288185	−	0.957575i	$-0.593052\pi$
$383$	13.4095	−	23.2259i	0.685191	−	1.18679i	0.973377	−	0.229211i	$-0.0736147\pi$
$384$	−10.0304			−0.511860
$385$	4.43225	+	2.27679i	0.225889	+	0.116036i
$386$	10.1236			0.515279
$387$	5.92394	−	10.2606i	0.301131	−	0.521574i
$388$	0.0276584	+	0.0479058i	0.00140414	+	0.00243205i
$389$	12.8169	+	22.1995i	0.649842	+	1.12556i	0.983160	+	0.182744i	$0.0584981\pi$
$389$	12.8169	+	22.1995i	0.649842	+	1.12556i	−0.333319	+	0.942814i	$0.608169\pi$
$390$	−2.86724	+	4.96620i	−0.145188	+	0.251474i
$391$	−1.15960			−0.0586437
$392$	−11.8884	−	16.5920i	−0.600455	−	0.838022i
$393$	16.0144			0.807821
$394$	−2.15802	+	3.73779i	−0.108719	+	0.188307i
$395$	−7.78252	−	13.4797i	−0.391581	−	0.678238i
$396$	−0.0961748	−	0.166580i	−0.00483296	−	0.00837094i
$397$	−5.09522	+	8.82518i	−0.255722	+	0.442923i	−0.965091	−	0.261914i	$-0.915646\pi$
$397$	−5.09522	+	8.82518i	−0.255722	+	0.442923i	0.709369	+	0.704837i	$0.248980\pi$
$398$	−2.47055			−0.123837
$399$	−20.1896	−	10.3711i	−1.01074	−	0.519204i
$400$	12.0272			0.601358
$401$	−11.8908	+	20.5954i	−0.593796	+	1.02849i	0.399919	+	0.916550i	$0.369038\pi$
$401$	−11.8908	+	20.5954i	−0.593796	+	1.02849i	−0.993716	+	0.111935i	$0.964295\pi$
$402$	−5.52540	−	9.57028i	−0.275582	−	0.477322i
$403$	−2.95511	−	5.11840i	−0.147205	−	0.254966i
$404$	−0.0490209	+	0.0849067i	−0.00243888	+	0.00422427i
$405$	−1.32621			−0.0659000
$406$	−22.6355	+	14.5938i	−1.12338	+	0.724277i
$407$	11.0744			0.548937
$408$	−1.69066	+	2.92831i	−0.0837001	+	0.144973i
$409$	7.21835	+	12.5026i	0.356925	+	0.618211i	0.987445	−	0.157961i	$-0.0504920\pi$
$409$	7.21835	+	12.5026i	0.356925	+	0.618211i	−0.630521	+	0.776172i	$0.717159\pi$
$410$	−10.1645	−	17.6054i	−0.501988	−	0.869469i
$411$	0.463790	−	0.803307i	0.0228771	−	0.0396242i
$412$	1.93339			0.0952513
$413$	−1.64622	−	33.5266i	−0.0810053	−	1.64974i
$414$	−1.36549			−0.0671100
$415$	3.78345	−	6.55314i	0.185722	−	0.321681i
$416$	−1.21102	−	2.09754i	−0.0593750	−	0.102841i
$417$	−2.11284	−	3.65955i	−0.103466	−	0.179209i
$418$	8.31766	−	14.4066i	0.406830	−	0.704651i
$419$	18.5772			0.907558			0.453779	−	0.891114i	$-0.350076\pi$
$419$	18.5772			0.907558			0.453779	+	0.891114i	$0.350076\pi$
$420$	0.0233085	+	0.474696i	0.00113734	+	0.0231628i
$421$	−7.98595			−0.389211			−0.194606	−	0.980882i	$-0.562343\pi$
$421$	−7.98595			−0.389211			−0.194606	+	0.980882i	$0.562343\pi$
$422$	15.3970	−	26.6683i	0.749513	−	1.29819i
$423$	−0.868249	−	1.50385i	−0.0422157	−	0.0731197i
$424$	−6.04906	−	10.4773i	−0.293768	−	0.508822i
$425$	1.87923	−	3.25493i	0.0911562	−	0.157887i
$426$	7.08658			0.343346
$427$	30.7192	−	19.8056i	1.48661	−	0.958460i
$428$	−1.89574			−0.0916340
$429$	−2.24843	+	3.89439i	−0.108555	+	0.188023i
$430$	−10.7278	−	18.5811i	−0.517341	−	0.896060i
$431$	9.01713	+	15.6181i	0.434340	+	0.752299i	0.997242	−	0.0742252i	$-0.0236484\pi$
$431$	9.01713	+	15.6181i	0.434340	+	0.752299i	−0.562902	+	0.826524i	$0.690315\pi$
$432$	−1.85538	+	3.21361i	−0.0892669	+	0.154615i
$433$	−13.6502			−0.655989			−0.327995	−	0.944680i	$-0.606373\pi$
$433$	−13.6502			−0.655989			−0.327995	+	0.944680i	$0.606373\pi$
$434$	5.99783	+	3.08100i	0.287905	+	0.147893i
$435$	9.88664			0.474028
$436$	0.197042	−	0.341286i	0.00943658	−	0.0163446i
$437$	4.28943	+	7.42951i	0.205191	+	0.355402i
$438$	−7.76183	−	13.4439i	−0.370874	−	0.642373i
$439$	−5.43271	+	9.40973i	−0.259289	+	0.449102i	−0.966052	−	0.258349i	$-0.916822\pi$
$439$	−5.43271	+	9.40973i	−0.259289	+	0.449102i	0.706762	+	0.707451i	$0.250155\pi$
$440$	−5.49166			−0.261805
$441$	−6.96633	+	0.685774i	−0.331730	+	0.0326559i
$442$	5.01408			0.238495
$443$	−7.55614	+	13.0876i	−0.359003	+	0.621812i	−0.987795	−	0.155762i	$-0.950217\pi$
$443$	−7.55614	+	13.0876i	−0.359003	+	0.621812i	0.628791	+	0.777574i	$0.283550\pi$
$444$	0.528142	+	0.914770i	0.0250645	+	0.0434130i
$445$	−4.21411	−	7.29906i	−0.199768	−	0.346008i
$446$	9.86452	−	17.0859i	0.467099	−	0.809039i
$447$	16.4464			0.777887
$448$	19.9238	+	10.2346i	0.941310	+	0.483538i
$449$	6.14432			0.289968			0.144984	−	0.989434i	$-0.453687\pi$
$449$	6.14432			0.289968			0.144984	+	0.989434i	$0.453687\pi$
$450$	2.21288	−	3.83282i	0.104316	−	0.180681i
$451$	−7.97077	−	13.8058i	−0.375329	−	0.650089i
$452$	1.26390	+	2.18914i	0.0594489	+	0.102969i
$453$	−4.09419	+	7.09135i	−0.192362	+	0.333180i
$454$	−4.47717			−0.210124
$455$	9.33843	−	6.02076i	0.437792	−	0.282258i
$456$	25.0153			1.17145
$457$	−14.7924	+	25.6212i	−0.691960	+	1.19851i	0.279235	+	0.960223i	$0.409919\pi$
$457$	−14.7924	+	25.6212i	−0.691960	+	1.19851i	−0.971195	+	0.238287i	$0.923414\pi$
$458$	0.180198	+	0.312112i	0.00842011	+	0.0145841i
$459$	0.579802	+	1.00425i	0.0270628	+	0.0468742i
$460$	0.0898171	−	0.155568i	0.00418774	−	0.00725339i
$461$	−34.7997			−1.62078			−0.810391	−	0.585890i	$-0.800745\pi$
$461$	−34.7997			−1.62078			−0.810391	+	0.585890i	$0.800745\pi$
$462$	−0.251609	−	5.12422i	−0.0117059	−	0.238400i
$463$	15.8969			0.738793			0.369397	−	0.929272i	$-0.379564\pi$
$463$	15.8969			0.738793			0.369397	+	0.929272i	$0.379564\pi$
$464$	13.8315	−	23.9568i	0.642110	−	1.11217i
$465$	−1.23763	−	2.14364i	−0.0573939	−	0.0994091i
$466$	−12.1876	−	21.1095i	−0.564579	−	0.977880i
$467$	−3.64308	+	6.31000i	−0.168582	+	0.291992i	−0.937921	−	0.346848i	$-0.887252\pi$
$467$	−3.64308	+	6.31000i	−0.168582	+	0.291992i	0.769340	+	0.638840i	$0.220585\pi$
$468$	−0.428914			−0.0198266
$469$	1.05010	+	21.3862i	0.0484892	+	0.987521i
$470$	−3.14466			−0.145052
$471$	11.2576	−	19.4987i	0.518721	−	0.898452i
$472$	18.4974	+	32.0384i	0.851410	+	1.47469i
$473$	−8.41251	−	14.5709i	−0.386808	−	0.669971i
$474$	−8.01299	+	13.8789i	−0.368049	+	0.637479i
$475$	−27.8055			−1.27580
$476$	0.349263	−	0.225180i	0.0160085	−	0.0103211i
$477$	−4.14898			−0.189969
$478$	−1.15278	+	1.99668i	−0.0527270	+	0.0913259i
$479$	9.30781	+	16.1216i	0.425285	+	0.736614i	0.996447	−	0.0842227i	$-0.0268407\pi$
$479$	9.30781	+	16.1216i	0.425285	+	0.736614i	−0.571162	+	0.820837i	$0.693507\pi$
$480$	−0.507188	−	0.878475i	−0.0231499	−	0.0400967i
$481$	12.3472	−	21.3860i	0.562984	−	0.975117i
$482$	26.0015			1.18434
$483$	2.35341	+	1.20891i	0.107084	+	0.0550074i
$484$	1.21679			0.0553086
$485$	0.270809	−	0.469056i	0.0122968	−	0.0212987i
$486$	0.682743	+	1.18255i	0.0309698	+	0.0536413i
$487$	−4.81446	−	8.33888i	−0.218164	−	0.377871i	0.736083	−	0.676892i	$-0.236673\pi$
$487$	−4.81446	−	8.33888i	−0.218164	−	0.377871i	−0.954247	+	0.299021i	$0.903340\pi$
$488$	−20.1414	+	34.8859i	−0.911758	+	1.57921i
$489$	1.46151			0.0660915
$490$	−5.23224	+	11.5463i	−0.236368	+	0.521607i
$491$	−4.61117			−0.208099			−0.104050	−	0.994572i	$-0.533180\pi$
$491$	−4.61117			−0.208099			−0.104050	+	0.994572i	$0.533180\pi$
$492$	0.760260	−	1.31681i	0.0342752	−	0.0593663i
$493$	−4.32231	−	7.48645i	−0.194667	−	0.337173i
$494$	−18.5473	−	32.1249i	−0.834483	−	1.44537i
$495$	−0.941667	+	1.63102i	−0.0423248	+	0.0733087i
$496$	−6.92583			−0.310979
$497$	−12.2137	−	6.27400i	−0.547859	−	0.281427i
$498$	−7.79099			−0.349123
$499$	−6.42833	+	11.1342i	−0.287771	+	0.498435i	−0.973277	−	0.229632i	$-0.926248\pi$
$499$	−6.42833	+	11.1342i	−0.287771	+	0.498435i	0.685506	+	0.728067i	$0.259581\pi$
$500$	0.740198	+	1.28206i	0.0331026	+	0.0573355i
$501$	1.38150	+	2.39283i	0.0617210	+	0.106904i
$502$	13.8863	−	24.0518i	0.619777	−	1.07349i
$503$	15.4383			0.688360			0.344180	−	0.938904i	$-0.388157\pi$
$503$	15.4383			0.688360			0.344180	+	0.938904i	$0.388157\pi$
$504$	6.48401	−	4.18043i	0.288821	−	0.186211i
$505$	0.959948			0.0427171
$506$	−0.969554	+	1.67932i	−0.0431019	+	0.0746547i
$507$	−1.48630	−	2.57434i	−0.0660088	−	0.114331i
$508$	0.0722153	+	0.125081i	0.00320404	+	0.00554956i
$509$	−5.70161	+	9.87549i	−0.252720	+	0.437723i	−0.964274	−	0.264908i	$-0.914658\pi$
$509$	−5.70161	+	9.87549i	−0.252720	+	0.437723i	0.711554	+	0.702631i	$0.247992\pi$
$510$	2.09995			0.0929874
$511$	1.47513	+	30.0423i	0.0652561	+	1.32899i
$512$	−24.4788			−1.08182
$513$	4.28943	−	7.42951i	0.189383	−	0.328021i
$514$	6.57451	+	11.3874i	0.289989	+	0.502276i
$515$	−9.46511	−	16.3940i	−0.417083	−	0.722408i
$516$	0.802394	−	1.38979i	0.0353234	−	0.0611819i
$517$	−2.46598			−0.108454
$518$	1.38171	+	28.1396i	0.0607088	+	1.23638i
$519$	−18.8661			−0.828131
$520$	−6.12284	+	10.6051i	−0.268505	+	0.465063i
$521$	−7.48785	−	12.9693i	−0.328049	−	0.568197i	0.654076	−	0.756429i	$-0.273058\pi$
$521$	−7.48785	−	12.9693i	−0.328049	−	0.568197i	−0.982125	+	0.188232i	$0.939724\pi$
$522$	−5.08971	−	8.81564i	−0.222771	−	0.385850i
$523$	5.70754	−	9.88575i	0.249573	−	0.432274i	−0.713834	−	0.700315i	$-0.753043\pi$
$523$	5.70754	−	9.88575i	0.249573	−	0.432274i	0.963407	+	0.268041i	$0.0863763\pi$
$524$	2.16914			0.0947593
$525$	−7.20722	+	4.64671i	−0.314549	+	0.202799i
$526$	−6.62953			−0.289061
$527$	−1.08215	+	1.87435i	−0.0471394	+	0.0816478i
$528$	2.63480	+	4.56360i	0.114665	+	0.198605i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−3.75674	+	6.50687i	−0.163182	+	0.282640i
$531$	12.6871			0.550575
$532$	−2.73466	−	1.40476i	−0.118563	−	0.0609039i
$533$	−35.5476			−1.53974
$534$	−4.33891	+	7.51521i	−0.187763	+	0.325215i
$535$	9.28079	+	16.0748i	0.401244	+	0.694974i
$536$	−11.7992	−	20.4368i	−0.509648	−	0.882737i
$537$	−10.3591	+	17.9425i	−0.447029	+	0.774276i
$538$	17.3943			0.749923
$539$	−4.10301	+	9.05433i	−0.176729	+	0.389998i
$540$	−0.179634			−0.00773023
$541$	−9.06483	+	15.7007i	−0.389727	+	0.675027i	−0.992413	−	0.122951i	$-0.960764\pi$
$541$	−9.06483	+	15.7007i	−0.389727	+	0.675027i	0.602685	+	0.797979i	$0.294097\pi$
$542$	15.0217	+	26.0184i	0.645239	+	1.11759i
$543$	0.343433	+	0.594843i	0.0147381	+	0.0255271i
$544$	−0.443472	+	0.768115i	−0.0190137	+	0.0329327i
$545$	−3.85855			−0.165282
$546$	−10.1760	−	5.22729i	−0.435494	−	0.223707i
$547$	−13.0632			−0.558543			−0.279271	−	0.960212i	$-0.590093\pi$
$547$	−13.0632			−0.558543			−0.279271	+	0.960212i	$0.590093\pi$
$548$	0.0628199	−	0.108807i	0.00268353	−	0.00464802i
$549$	6.90738	+	11.9639i	0.294800	+	0.510608i
$550$	−3.14248	−	5.44294i	−0.133996	−	0.232088i
$551$	−31.9768	+	55.3855i	−1.36226	+	2.35950i
$552$	−2.91593			−0.124110
$553$	26.0978	−	16.8260i	1.10979	−	0.715516i
$554$	0.225912			0.00959808
$555$	5.17115	−	8.95670i	0.219503	−	0.380191i
$556$	−0.286183	−	0.495684i	−0.0121369	−	0.0210217i
$557$	13.4457	+	23.2886i	0.569711	+	0.986768i	0.996594	+	0.0824615i	$0.0262781\pi$
$557$	13.4457	+	23.2886i	0.569711	+	0.986768i	−0.426883	+	0.904307i	$0.640389\pi$
$558$	−1.27428	+	2.20713i	−0.0539448	+	0.0934351i
$559$	−37.5176			−1.58683
$560$	−0.638557	−	13.0047i	−0.0269840	−	0.549550i
$561$	1.64674			0.0695253
$562$	14.3238	−	24.8095i	0.604211	−	1.04652i
$563$	−4.88702	−	8.46457i	−0.205963	−	0.356739i	0.744476	−	0.667649i	$-0.232699\pi$
$563$	−4.88702	−	8.46457i	−0.205963	−	0.356739i	−0.950439	+	0.310910i	$0.899366\pi$
$564$	−0.117604	−	0.203695i	−0.00495200	−	0.00857712i
$565$	12.3751	−	21.4343i	0.520625	−	0.901749i
$566$	−1.11263			−0.0467673
$567$	−0.129755	−	2.64257i	−0.00544921	−	0.110977i
$568$	15.1330			0.634968
$569$	21.9945	−	38.0956i	0.922057	−	1.59705i	0.125830	−	0.992052i	$-0.459841\pi$
$569$	21.9945	−	38.0956i	0.922057	−	1.59705i	0.796227	−	0.604998i	$-0.206826\pi$
$570$	−7.76782	−	13.4543i	−0.325358	−	0.563537i
$571$	−3.09960	−	5.36867i	−0.129714	−	0.224672i	0.793852	−	0.608112i	$-0.208073\pi$
$571$	−3.09960	−	5.36867i	−0.129714	−	0.224672i	−0.923566	+	0.383440i	$0.874739\pi$
$572$	−0.304548	+	0.527492i	−0.0127338	+	0.0220556i
$573$	−1.09300			−0.0456608
$574$	34.0855	−	21.9759i	1.42270	−	0.917258i
$575$	3.24116			0.135166
$576$	−4.23296	+	7.33171i	−0.176373	+	0.305488i
$577$	−7.28016	−	12.6096i	−0.303077	−	0.524945i	0.673754	−	0.738956i	$-0.264681\pi$
$577$	−7.28016	−	12.6096i	−0.303077	−	0.524945i	−0.976831	+	0.214010i	$0.931347\pi$
$578$	10.6886	+	18.5131i	0.444585	+	0.770044i
$579$	3.70697	−	6.42066i	0.154056	−	0.266833i
$580$	1.33914			0.0556046
$581$	13.4277	+	6.89764i	0.557077	+	0.286162i
$582$	−0.557658			−0.0231157
$583$	−2.94596	+	5.10255i	−0.122009	+	0.211326i
$584$	−16.5750	−	28.7087i	−0.685878	−	1.18797i
$585$	2.09980	+	3.63695i	0.0868158	+	0.150369i
$586$	8.64280	−	14.9698i	0.357031	−	0.618395i
$587$	−16.3784			−0.676009			−0.338004	−	0.941145i	$-0.609752\pi$
$587$	−16.3784			−0.676009			−0.338004	+	0.941145i	$0.609752\pi$
$588$	−0.943583	+	0.0928876i	−0.0389127	+	0.00383062i
$589$	16.0118			0.659753
$590$	11.4877	−	19.8973i	0.472941	−	0.819158i
$591$	1.58040	+	2.73734i	0.0650091	+	0.112599i
$592$	−14.4689	−	25.0609i	−0.594670	−	1.03000i
$593$	−13.6157	+	23.5830i	−0.559129	+	0.968440i	0.438440	+	0.898760i	$0.355531\pi$
$593$	−13.6157	+	23.5830i	−0.559129	+	0.968440i	−0.997569	+	0.0696795i	$0.977802\pi$
$594$	1.93911			0.0795625
$595$	−3.61926	−	1.85916i	−0.148375	−	0.0762182i
$596$	2.22765			0.0912481
$597$	−0.904642	+	1.56689i	−0.0370245	+	0.0641283i
$598$	2.16198	+	3.74466i	0.0884099	+	0.153130i
$599$	−20.2644	−	35.0990i	−0.827981	−	1.43411i	−0.899620	−	0.436675i	$-0.856156\pi$
$599$	−20.2644	−	35.0990i	−0.827981	−	1.43411i	0.0716385	−	0.997431i	$-0.477177\pi$
$600$	4.72550	−	8.18480i	0.192918	−	0.334143i
$601$	8.69739			0.354774			0.177387	−	0.984141i	$-0.443236\pi$
$601$	8.69739			0.354774			0.177387	+	0.984141i	$0.443236\pi$
$602$	35.9745	−	23.1938i	1.46621	−	0.945311i
$603$	−8.09295			−0.329570
$604$	−0.554555	+	0.960517i	−0.0225645	+	0.0390829i
$605$	−5.95691	−	10.3177i	−0.242183	−	0.419473i
$606$	−0.494188	−	0.855958i	−0.0200750	−	0.0347709i
$607$	−10.0215	+	17.3578i	−0.406761	+	0.704530i	−0.994525	−	0.104502i	$-0.966675\pi$
$607$	−10.0215	+	17.3578i	−0.406761	+	0.704530i	0.587764	+	0.809033i	$0.300008\pi$
$608$	6.56169			0.266112
$609$	0.967299	+	19.6998i	0.0391969	+	0.798277i
$610$	25.0175			1.01293
$611$	−2.74940	+	4.76210i	−0.111229	+	0.192654i
$612$	0.0785337	+	0.136024i	0.00317454	+	0.00549846i
$613$	10.0301	+	17.3726i	0.405111	+	0.701672i	0.994334	−	0.106298i	$-0.0338997\pi$
$613$	10.0301	+	17.3726i	0.405111	+	0.701672i	−0.589224	+	0.807970i	$0.700566\pi$
$614$	2.07190	−	3.58863i	0.0836150	−	0.144825i
$615$	−14.8877			−0.600331
$616$	−0.537299	−	10.9425i	−0.0216484	−	0.440887i
$617$	35.9585			1.44764			0.723818	−	0.689991i	$-0.242385\pi$
$617$	35.9585			1.44764			0.723818	+	0.689991i	$0.242385\pi$
$618$	−9.74541	+	16.8795i	−0.392018	+	0.678995i
$619$	7.40997	+	12.8344i	0.297832	+	0.515860i	0.975640	−	0.219379i	$-0.0704033\pi$
$619$	7.40997	+	12.8344i	0.297832	+	0.515860i	−0.677808	+	0.735239i	$0.737070\pi$
$620$	−0.167636	−	0.290355i	−0.00673244	−	0.0116609i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	37.5190			1.50437
$623$	14.1316	−	9.11104i	0.566169	−	0.365026i
$624$	11.7505			0.470397
$625$	−0.855482	+	1.48174i	−0.0342193	+	0.0592695i
$626$	−0.916258	−	1.58701i	−0.0366211	−	0.0634295i
$627$	−6.09136	−	10.5505i	−0.243266	−	0.421348i
$628$	1.52483	−	2.64108i	0.0608473	−	0.105391i
$629$	−9.04303			−0.360569
$630$	−4.26184	−	2.18925i	−0.169796	−	0.0872217i
$631$	−25.6933			−1.02284			−0.511418	−	0.859332i	$-0.670880\pi$
$631$	−25.6933			−1.02284			−0.511418	+	0.859332i	$0.670880\pi$
$632$	−17.1113	+	29.6377i	−0.680652	+	1.17892i
$633$	−11.2758	−	19.5303i	−0.448174	−	0.776260i
$634$	−0.347254	−	0.601462i	−0.0137912	−	0.0238871i
$635$	0.707075	−	1.22469i	0.0280594	−	0.0486004i
$636$	−0.561976			−0.0222838
$637$	12.9105	+	18.0184i	0.511531	+	0.713915i
$638$	−14.4557			−0.572305
$639$	2.59489	−	4.49449i	0.102652	−	0.177799i
$640$	6.65119	+	11.5202i	0.262911	+	0.455376i
$641$	−9.87984	−	17.1124i	−0.390230	−	0.675899i	0.602249	−	0.798308i	$-0.294271\pi$
$641$	−9.87984	−	17.1124i	−0.390230	−	0.675899i	−0.992480	+	0.122409i	$0.960938\pi$
$642$	9.55563	−	16.5508i	0.377131	−	0.653210i
$643$	−6.27845			−0.247598			−0.123799	−	0.992307i	$-0.539508\pi$
$643$	−6.27845			−0.247598			−0.123799	+	0.992307i	$0.539508\pi$
$644$	0.318767	+	0.163746i	0.0125612	+	0.00645251i
$645$	−15.7128			−0.618691
$646$	−6.79198	+	11.7641i	−0.267227	+	0.462850i
$647$	23.4542	+	40.6238i	0.922078	+	1.59709i	0.796195	+	0.605041i	$0.206843\pi$
$647$	23.4542	+	40.6238i	0.922078	+	1.59709i	0.125883	+	0.992045i	$0.459823\pi$
$648$	1.45796	+	2.52527i	0.0572742	+	0.0992018i
$649$	9.00841	−	15.6030i	0.353611	−	0.612472i
$650$	−14.0147			−0.549700
$651$	4.15027	−	2.67580i	0.162662	−	0.104873i
$652$	0.197960			0.00775270
$653$	−14.6588	+	25.3898i	−0.573643	+	0.993579i	0.422544	+	0.906342i	$0.361137\pi$
$653$	−14.6588	+	25.3898i	−0.573643	+	0.993579i	−0.996188	+	0.0872370i	$0.972196\pi$
$654$	1.98641	+	3.44056i	0.0776747	+	0.134537i
$655$	−10.6193	−	18.3931i	−0.414929	−	0.718677i
$656$	−20.8280	+	36.0752i	−0.813197	+	1.40850i
$657$	−11.3686			−0.443531
$658$	−0.307671	−	6.26596i	−0.0119943	−	0.244272i
$659$	−8.04283			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$659$	−8.04283			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$660$	−0.127548	+	0.220920i	−0.00496480	+	0.00859929i
$661$	−6.43869	−	11.1521i	−0.250436	−	0.433768i	0.713210	−	0.700951i	$-0.247241\pi$
$661$	−6.43869	−	11.1521i	−0.250436	−	0.433768i	−0.963646	+	0.267182i	$0.913907\pi$
$662$	−4.22641	−	7.32035i	−0.164264	−	0.284513i
$663$	1.83600	−	3.18005i	0.0713045	−	0.123503i
$664$	−16.6373			−0.645651
$665$	1.47627	+	30.0655i	0.0572475	+	1.16589i
$666$	−10.6486			−0.412624
$667$	3.72740	−	6.45604i	0.144325	−	0.249979i
$668$	0.187123	+	0.324107i	0.00724002	+	0.0125401i
$669$	−7.22419	−	12.5127i	−0.279303	−	0.483767i
$670$	−7.32785	+	12.6922i	−0.283100	+	0.490343i
$671$	19.6181			0.757350
$672$	1.70080	−	1.09656i	0.0656098	−	0.0423006i
$673$	42.5924			1.64182			0.820909	−	0.571059i	$-0.193467\pi$
$673$	42.5924			1.64182			0.820909	+	0.571059i	$0.193467\pi$
$674$	3.46562	−	6.00263i	0.133491	−	0.231213i
$675$	−1.62058	−	2.80693i	−0.0623762	−	0.108039i
$676$	−0.201318	−	0.348693i	−0.00774300	−	0.0134113i
$677$	−5.81225	+	10.0671i	−0.223383	+	0.386911i	−0.955833	−	0.293910i	$-0.905043\pi$
$677$	−5.81225	+	10.0671i	−0.223383	+	0.386911i	0.732450	+	0.680821i	$0.238377\pi$
$678$	−25.4832			−0.978676
$679$	0.961122	+	0.493715i	0.0368845	+	0.0189470i
$680$	4.48434			0.171967
$681$	−1.63940	+	2.83953i	−0.0628221	+	0.108811i
$682$	1.80959	+	3.13431i	0.0692930	+	0.120019i
$683$	−4.42079	−	7.65703i	−0.169157	−	0.292988i	0.768967	−	0.639289i	$-0.220771\pi$
$683$	−4.42079	−	7.65703i	−0.169157	−	0.292988i	−0.938124	+	0.346301i	$0.887438\pi$
$684$	0.581000	−	1.00632i	0.0222151	−	0.0384777i
$685$	−1.23017			−0.0470022
$686$	−23.5186	−	9.29592i	−0.897946	−	0.354920i
$687$	0.263933			0.0100697
$688$	−21.9823	+	38.0745i	−0.838068	+	1.45158i
$689$	6.56910	+	11.3780i	0.250263	+	0.433468i
$690$	0.905461	+	1.56830i	0.0344703	+	0.0597043i
$691$	−12.6339	+	21.8825i	−0.480615	+	0.832450i	−0.999753	−	0.0222409i	$-0.992920\pi$
$691$	−12.6339	+	21.8825i	−0.480615	+	0.832450i	0.519138	+	0.854691i	$0.326253\pi$
$692$	−2.55540			−0.0971417
$693$	−3.34204	−	1.71676i	−0.126954	−	0.0652143i
$694$	−34.8133			−1.32149
$695$	−2.80208	+	4.85334i	−0.106289	+	0.184098i
$696$	−10.8688	−	18.8253i	−0.411981	−	0.713573i
$697$	6.50871	+	11.2734i	0.246535	+	0.427011i
$698$	7.51941	−	13.0240i	0.284614	−	0.492966i
$699$	−17.8509			−0.675184
$700$	−0.976213	+	0.629393i	−0.0368974	+	0.0237888i
$701$	17.9512			0.678009			0.339005	−	0.940785i	$-0.389910\pi$
$701$	17.9512			0.678009			0.339005	+	0.940785i	$0.389910\pi$
$702$	2.16198	−	3.74466i	0.0815986	−	0.141333i
$703$	33.4506	+	57.9382i	1.26161	+	2.18518i
$704$	6.01117	+	10.4117i	0.226555	+	0.392404i
$705$	−1.15148	+	1.99442i	−0.0433673	+	0.0751143i
$706$	−9.07748			−0.341636
$707$	0.0939204	+	1.91276i	0.00353224	+	0.0719368i
$708$	1.71846			0.0645838
$709$	18.7313	−	32.4436i	0.703470	−	1.21845i	−0.263770	−	0.964585i	$-0.584966\pi$
$709$	18.7313	−	32.4436i	0.703470	−	1.21845i	0.967241	−	0.253861i	$-0.0817005\pi$
$710$	−4.69915	−	8.13917i	−0.176356	−	0.305458i
$711$	5.86823	+	10.1641i	0.220076	+	0.381183i
$712$	−9.26552	+	16.0484i	−0.347240	+	0.601437i
$713$	−1.86642			−0.0698980
$714$	0.205457	+	4.18430i	0.00768905	+	0.156593i
$715$	5.96378			0.223033
$716$	−1.40313	+	2.43030i	−0.0524376	+	0.0908245i
$717$	0.844229	+	1.46225i	0.0315283	+	0.0546086i
$718$	5.36276	+	9.28857i	0.200136	+	0.346646i
$719$	−15.8091	+	27.3822i	−0.589580	+	1.02118i	0.404707	+	0.914446i	$0.367373\pi$
$719$	−15.8091	+	27.3822i	−0.589580	+	1.02118i	−0.994287	+	0.106736i	$0.965960\pi$
$720$	4.92124			0.183404
$721$	31.7402	−	20.4639i	1.18207	−	0.762114i
$722$	74.5512			2.77451
$723$	9.52098	−	16.4908i	0.354089	−	0.613300i
$724$	0.0465177	+	0.0805710i	0.00172882	+	0.00299440i
$725$	12.0811	+	20.9251i	0.448681	+	0.777139i
$726$	−6.13332	+	10.6232i	−0.227629	+	0.394265i
$727$	0.00894509			0.000331755			0.000165878	−	1.00000i	$-0.499947\pi$
$727$	0.00894509			0.000331755			0.000165878		1.00000i	$0.499947\pi$
$728$	−21.7304	−	11.1626i	−0.805382	−	0.413714i
$729$	1.00000			0.0370370
$730$	−10.2938	+	17.8294i	−0.380991	+	0.659896i
$731$	6.86943	+	11.8982i	0.254075	+	0.440071i
$732$	0.935599	+	1.62050i	0.0345807	+	0.0598956i
$733$	−12.8555	+	22.2663i	−0.474828	+	0.822426i	−0.999584	−	0.0288262i	$-0.990823\pi$
$733$	−12.8555	+	22.2663i	−0.474828	+	0.822426i	0.524756	+	0.851252i	$0.324156\pi$
$734$	2.55669			0.0943693
$735$	5.40704	+	7.54631i	0.199442	+	0.278350i
$736$	−0.764868			−0.0281934
$737$	−5.74634	+	9.95296i	−0.211669	+	0.366622i
$738$	7.66430	+	13.2750i	0.282127	+	0.488658i
$739$	8.38289	+	14.5196i	0.308370	+	0.534112i	0.978006	−	0.208577i	$-0.0668833\pi$
$739$	8.38289	+	14.5196i	0.308370	+	0.534112i	−0.669636	+	0.742689i	$0.733550\pi$
$740$	0.700428	−	1.21318i	0.0257483	−	0.0445973i
$741$	−27.1659			−0.997964
$742$	−13.3329	−	6.84894i	−0.489468	−	0.251433i
$743$	13.6484			0.500712			0.250356	−	0.968154i	$-0.419452\pi$
$743$	13.6484			0.500712			0.250356	+	0.968154i	$0.419452\pi$
$744$	−2.72117	+	4.71321i	−0.0997630	+	0.172795i
$745$	−10.9057	−	18.8892i	−0.399553	−	0.692047i
$746$	15.9608	+	27.6449i	0.584367	+	1.01215i
$747$	−2.85283	+	4.94125i	−0.104380	+	0.180791i
$748$	0.223049			0.00815549
$749$	−31.1221	+	20.0654i	−1.13718	+	0.733172i
$750$	−14.9241			−0.544951
$751$	9.75722	−	16.9000i	0.356046	−	0.616690i	−0.631250	−	0.775579i	$-0.717458\pi$
$751$	9.75722	−	16.9000i	0.356046	−	0.616690i	0.987296	+	0.158889i	$0.0507913\pi$
$752$	3.22186	+	5.58042i	0.117489	+	0.203497i
$753$	−10.1695	−	17.6141i	−0.370598	−	0.641895i
$754$	−16.1171	+	27.9157i	−0.586951	+	1.01663i
$755$	10.8595			0.395218
$756$	−0.0175752	−	0.357934i	−0.000639206	−	0.0130179i
$757$	11.1059			0.403652			0.201826	−	0.979421i	$-0.435312\pi$
$757$	11.1059			0.403652			0.201826	+	0.979421i	$0.435312\pi$
$758$	−14.2869	+	24.7456i	−0.518923	+	0.898801i
$759$	0.710043	+	1.22983i	0.0257729	+	0.0446400i
$760$	−16.5878	−	28.7309i	−0.601702	−	1.04218i
$761$	−14.6605	+	25.3927i	−0.531442	+	0.920485i	0.467884	+	0.883790i	$0.345016\pi$
$761$	−14.6605	+	25.3927i	−0.531442	+	0.920485i	−0.999327	+	0.0366951i	$0.988317\pi$
$762$	−1.45603			−0.0527464
$763$	−0.377517	−	7.68843i	−0.0136670	−	0.278340i
$764$	−0.148046			−0.00535613
$765$	0.768940	−	1.33184i	0.0278011	−	0.0481529i
$766$	18.3104	+	31.7146i	0.661582	+	1.14589i
$767$	−20.0876	−	34.7927i	−0.725321	−	1.25629i
$768$	−1.61777	+	2.80205i	−0.0583761	+	0.101110i
$769$	−9.29965			−0.335354			−0.167677	−	0.985842i	$-0.553627\pi$
$769$	−9.29965			−0.335354			−0.167677	+	0.985842i	$0.553627\pi$
$770$	−5.71849	+	3.68688i	−0.206080	+	0.132866i
$771$	9.62955			0.346800
$772$	0.502106	−	0.869673i	0.0180712	−	0.0313002i
$773$	−16.7718	−	29.0496i	−0.603240	−	1.04484i	−0.992327	−	0.123642i	$-0.960543\pi$
$773$	−16.7718	−	29.0496i	−0.603240	−	1.04484i	0.389087	−	0.921201i	$-0.372791\pi$
$774$	8.08906	+	14.0107i	0.290755	+	0.503603i
$775$	3.02469	−	5.23891i	0.108650	−	0.188187i
$776$	−1.19085			−0.0427491
$777$	18.3528	+	9.42756i	0.658402	+	0.338212i
$778$	−35.0025			−1.25490
$779$	48.1521	−	83.4019i	1.72523	−	2.98818i
$780$	0.284416	+	0.492622i	0.0101837	+	0.0176387i
$781$	−3.68497	−	6.38256i	−0.131859	−	0.228386i
$782$	0.791711	−	1.37128i	0.0283115	−	0.0490370i
$783$	−7.45480			−0.266413
$784$	25.8503	−	2.54474i	0.923226	−	0.0908836i
$785$	−29.8598			−1.06574
$786$	−10.9337	+	18.9378i	−0.389993	+	0.675488i
$787$	15.2595	+	26.4302i	0.543943	+	0.942136i	0.998673	+	0.0515070i	$0.0164024\pi$
$787$	15.2595	+	26.4302i	0.543943	+	0.942136i	−0.454730	+	0.890629i	$0.650264\pi$
$788$	0.214064	+	0.370770i	0.00762572	+	0.0132081i
$789$	−2.42754	+	4.20462i	−0.0864226	+	0.149688i
$790$	21.2538			0.756177
$791$	43.9202	+	22.5612i	1.56162	+	0.802183i
$792$	4.14087			0.147139
$793$	21.8730	−	37.8851i	0.776731	−	1.34534i
$794$	−6.95745	−	12.0507i	−0.246911	−	0.427662i
$795$	2.75121	+	4.76524i	0.0975755	+	0.169006i
$796$	−0.122533	+	0.212233i	−0.00434307	+	0.00752241i
$797$	−41.6491			−1.47529			−0.737643	−	0.675191i	$-0.764061\pi$
$797$	−41.6491			−1.47529			−0.737643	+	0.675191i	$0.764061\pi$
$798$	26.0486	−	16.7943i	0.922109	−	0.594511i
$799$	2.01365			0.0712378
$800$	1.23953	−	2.14693i	0.0438240	−	0.0759054i
$801$	3.17756	+	5.50369i	0.112273	+	0.194463i
$802$	−16.2367	−	28.1227i	−0.573336	−	0.993048i
$803$	−8.07219	+	13.9814i	−0.284861	+	0.493395i
$804$	−1.09618			−0.0386594
$805$	−0.172083	−	3.50460i	−0.00606512	−	0.123521i
$806$	8.07032			0.284265
$807$	6.36928	−	11.0319i	0.224209	−	0.388342i
$808$	−1.05531	−	1.82786i	−0.0371258	−	0.0643037i
$809$	15.7710	+	27.3162i	0.554479	+	0.960385i	0.997944	+	0.0640937i	$0.0204157\pi$
$809$	15.7710	+	27.3162i	0.554479	+	0.960385i	−0.443465	+	0.896292i	$0.646251\pi$
$810$	0.905461	−	1.56830i	0.0318147	−	0.0551046i
$811$	−22.0480			−0.774211			−0.387106	−	0.922035i	$-0.626525\pi$
$811$	−22.0480			−0.774211			−0.387106	+	0.922035i	$0.626525\pi$
$812$	0.131020	+	2.66832i	0.00459790	+	0.0936398i
$813$	22.0021			0.771646
$814$	−7.56095	+	13.0960i	−0.265011	+	0.459013i
$815$	−0.969132	−	1.67859i	−0.0339472	−	0.0587983i
$816$	−2.15150	−	3.72651i	−0.0753177	−	0.130454i
$817$	50.8207	−	88.0240i	1.77799	−	3.07957i
$818$	−19.7131			−0.689253
$819$	−7.04144	+	4.53982i	−0.246048	+	0.158634i
$820$	−2.01653			−0.0704203
$821$	−26.0497	+	45.1195i	−0.909142	+	1.57468i	−0.0938828	+	0.995583i	$0.529928\pi$
$821$	−26.0497	+	45.1195i	−0.909142	+	1.57468i	−0.815259	+	0.579097i	$0.803405\pi$
$822$	0.633298	+	1.09690i	0.0220888	+	0.0382589i
$823$	19.2488	+	33.3399i	0.670970	+	1.16215i	0.977629	+	0.210335i	$0.0674555\pi$
$823$	19.2488	+	33.3399i	0.670970	+	1.16215i	−0.306659	+	0.951819i	$0.599211\pi$
$824$	−20.8108	+	36.0454i	−0.724979	+	1.25570i
$825$	−4.60273			−0.160247
$826$	40.7707	+	20.9433i	1.41859	+	0.728711i
$827$	−36.5676			−1.27158			−0.635790	−	0.771862i	$-0.719325\pi$
$827$	−36.5676			−1.27158			−0.635790	+	0.771862i	$0.719325\pi$
$828$	−0.0677246	+	0.117302i	−0.00235359	+	0.00407654i
$829$	−13.7595	−	23.8322i	−0.477888	−	0.827727i	0.521790	−	0.853074i	$-0.325264\pi$
$829$	−13.7595	−	23.8322i	−0.477888	−	0.827727i	−0.999679	+	0.0253469i	$0.991931\pi$
$830$	5.16625	+	8.94821i	0.179323	+	0.310597i
$831$	0.0827222	−	0.143279i	0.00286960	−	0.00497030i
$832$	26.8083			0.929409
$833$	3.35040	−	7.39352i	0.116085	−	0.256170i
$834$	5.77012			0.199803
$835$	1.83216	−	3.17340i	0.0634047	−	0.109820i
$836$	−0.825070	−	1.42906i	−0.0285356	−	0.0494252i
$837$	0.933210	+	1.61637i	0.0322565	+	0.0558698i
$838$	−12.6835	+	21.9684i	−0.438144	+	0.758887i
$839$	2.02614			0.0699502			0.0349751	−	0.999388i	$-0.488865\pi$
$839$	2.02614			0.0699502			0.0349751	+	0.999388i	$0.488865\pi$
$840$	−9.10094	−	4.67502i	−0.314012	−	0.161304i
$841$	26.5740			0.916345
$842$	5.45235	−	9.44375i	0.187900	−	0.325453i
$843$	−10.4899	−	18.1690i	−0.361290	−	0.625773i
$844$	−1.52730	−	2.64536i	−0.0525719	−	0.0910571i
$845$	−1.97115	+	3.41412i	−0.0678095	+	0.117449i
$846$	2.37116			0.0815222
$847$	19.9759	−	12.8790i	0.686379	−	0.442529i
$848$	15.3959			0.528696
$849$	−0.407411	+	0.705657i	−0.0139823	+	0.0242181i
$850$	2.56607	+	4.44456i	0.0880153	+	0.152447i
$851$	−3.89919	−	6.75360i	−0.133663	−	0.231510i
$852$	0.351476	−	0.608775i	0.0120414	−	0.0208563i
$853$	−38.6105			−1.32200			−0.660999	−	0.750387i	$-0.729867\pi$
$853$	−38.6105			−1.32200			−0.660999	+	0.750387i	$0.729867\pi$
$854$	2.44768	+	49.8490i	0.0837580	+	1.70580i
$855$	−11.3774			−0.389098
$856$	20.4056	−	35.3435i	0.697448	−	1.20802i
$857$	−20.9898	−	36.3554i	−0.716997	−	1.24188i	−0.962184	−	0.272400i	$-0.912183\pi$
$857$	−20.9898	−	36.3554i	−0.716997	−	1.24188i	0.245187	−	0.969476i	$-0.421151\pi$
$858$	−3.07020	−	5.31774i	−0.104815	−	0.181544i
$859$	−20.4314	+	35.3883i	−0.697111	+	1.20743i	0.272353	+	0.962198i	$0.412198\pi$
$859$	−20.4314	+	35.3883i	−0.697111	+	1.20743i	−0.969464	+	0.245235i	$0.921135\pi$
$860$	−2.12829			−0.0725740
$861$	−1.45660	−	29.6648i	−0.0496408	−	1.01097i
$862$	−24.6255			−0.838748
$863$	16.6323	−	28.8079i	0.566169	−	0.980633i	−0.430771	−	0.902461i	$-0.641758\pi$
$863$	16.6323	−	28.8079i	0.566169	−	0.980633i	0.996940	−	0.0781719i	$-0.0249083\pi$
$864$	0.382434	+	0.662395i	0.0130107	+	0.0225351i
$865$	12.5102	+	21.6683i	0.425360	+	0.736746i
$866$	9.31961	−	16.1420i	0.316693	−	0.548529i
$867$	15.6553			0.531683
$868$	0.562151	−	0.362435i	0.0190806	−	0.0123019i
$869$	16.6668			0.565382
$870$	−6.75003	+	11.6914i	−0.228847	+	0.396375i
$871$	12.8136	+	22.1938i	0.434172	+	0.752008i
$872$	4.24188	+	7.34714i	0.143648	+	0.248806i
$873$	−0.204198	+	0.353681i	−0.00691105	+	0.0119703i
$874$	−11.7143			−0.396242
$875$	25.7216	+	13.2128i	0.869550	+	0.446675i
$876$	−1.53987			−0.0520273
$877$	−9.13437	+	15.8212i	−0.308446	+	0.534244i	−0.978023	−	0.208499i	$-0.933142\pi$
$877$	−9.13437	+	15.8212i	−0.308446	+	0.534244i	0.669577	+	0.742743i	$0.266476\pi$
$878$	−7.41829	−	12.8489i	−0.250355	−	0.433628i
$879$	−6.32947	−	10.9630i	−0.213488	−	0.369771i
$880$	3.49430	−	6.05230i	0.117793	−	0.204023i
$881$	27.6269			0.930775			0.465387	−	0.885107i	$-0.345915\pi$
$881$	27.6269			0.930775			0.465387	+	0.885107i	$0.345915\pi$
$882$	3.94525	−	8.70620i	0.132844	−	0.293153i
$883$	−46.7892			−1.57458			−0.787290	−	0.616582i	$-0.788517\pi$
$883$	−46.7892			−1.57458			−0.787290	+	0.616582i	$0.788517\pi$
$884$	0.248685	−	0.430736i	0.00836419	−	0.0144872i
$885$	−8.41291	−	14.5716i	−0.282797	−	0.489819i
$886$	−10.3178	−	17.8710i	−0.346633	−	0.600387i
$887$	10.9311	−	18.9333i	0.367032	−	0.635718i	−0.622068	−	0.782963i	$-0.713707\pi$
$887$	10.9311	−	18.9333i	0.367032	−	0.635718i	0.989100	+	0.147245i	$0.0470406\pi$
$888$	−22.7395			−0.763088
$889$	2.50946	+	1.28907i	0.0841646	+	0.0432342i
$890$	11.5086			0.385770
$891$	0.710043	−	1.22983i	0.0237873	−	0.0412009i
$892$	−0.978510	−	1.69483i	−0.0327629	−	0.0567471i
$893$	−7.44858	−	12.9013i	−0.249257	−	0.431726i
$894$	−11.2286	+	19.4486i	−0.375542	+	0.650458i
$895$	27.4767			0.918446
$896$	−22.3041	+	14.3801i	−0.745126	+	0.480405i
$897$	3.16661			0.105730
$898$	−4.19499	+	7.26594i	−0.139989	+	0.242467i
$899$	−6.95689	−	12.0497i	−0.232025	−	0.401880i
$900$	−0.219507	−	0.380196i	−0.00731688	−	0.0126732i
$901$	2.40559	−	4.16660i	0.0801417	−	0.138810i
$902$	21.7679			0.724793
$903$	−1.53733	−	31.3088i	−0.0511590	−	1.04189i
$904$	−54.4181			−1.80992
$905$	0.455464	−	0.788887i	0.0151401	−	0.0262235i
$906$	−5.59056	−	9.68313i	−0.185734	−	0.321700i
$907$	25.5763	+	44.2994i	0.849246	+	1.47094i	0.881882	+	0.471469i	$0.156276\pi$
$907$	25.5763	+	44.2994i	0.849246	+	1.47094i	−0.0326367	+	0.999467i	$0.510390\pi$
$908$	−0.222056	+	0.384612i	−0.00736919	+	0.0127638i
$909$	−0.723827			−0.0240078
$910$	0.744079	+	15.1537i	0.0246660	+	0.502342i
$911$	−26.2401			−0.869373			−0.434686	−	0.900582i	$-0.643141\pi$
$911$	−26.2401			−0.869373			−0.434686	+	0.900582i	$0.643141\pi$
$912$	−15.9170	+	27.5691i	−0.527065	+	0.912904i
$913$	4.05126	+	7.01700i	0.134077	+	0.232229i
$914$	−20.1988	−	34.9854i	−0.668118	−	1.15721i
$915$	9.16064	−	15.8667i	0.302842	−	0.524537i
$916$	0.0357495			0.00118120
$917$	35.6105	−	22.9592i	1.17596	−	0.758178i
$918$	−1.58342			−0.0522607
$919$	−15.9701	+	27.6609i	−0.526803	+	0.912450i	0.472709	+	0.881219i	$0.343276\pi$
$919$	−15.9701	+	27.6609i	−0.526803	+	0.912450i	−0.999512	+	0.0312315i	$0.990057\pi$
$920$	1.93357	+	3.34903i	0.0637478	+	0.110414i
$921$	−1.51733	−	2.62810i	−0.0499979	−	0.0865989i
$922$	23.7592	−	41.1522i	0.782468	−	1.35527i
$923$	−16.4340			−0.540933
$924$	−0.452677	−	0.232534i	−0.0148920	−	0.00764980i
$925$	25.2758			0.831065
$926$	−10.8535	+	18.7988i	−0.356669	+	0.617768i
$927$	7.13695	+	12.3616i	0.234408	+	0.406007i
$928$	−2.85097	−	4.93802i	−0.0935876	−	0.162098i
$929$	6.70763	−	11.6180i	0.220070	−	0.381173i	−0.734759	−	0.678328i	$-0.762705\pi$
$929$	6.70763	−	11.6180i	0.220070	−	0.381173i	0.954829	+	0.297156i	$0.0960380\pi$
$930$	3.37994			0.110833
$931$	−59.7631	+	5.88316i	−1.95866	+	0.192813i
$932$	−2.41789			−0.0792008
$933$	13.7383	−	23.7955i	0.449772	−	0.779029i
$934$	−4.97458	−	8.61622i	−0.162773	−	0.281931i
$935$	−1.09196	−	1.89133i	−0.0357109	−	0.0618532i
$936$	4.61679	−	7.99652i	0.150905	−	0.261375i
$937$	21.3033			0.695950			0.347975	−	0.937504i	$-0.386869\pi$
$937$	21.3033			0.695950			0.347975	+	0.937504i	$0.386869\pi$
$938$	−26.0071	−	13.3595i	−0.849160	−	0.436202i
$939$	−1.34203			−0.0437954
$940$	−0.155967	+	0.270143i	−0.00508709	+	0.00881110i
$941$	−2.61286	−	4.52561i	−0.0851770	−	0.147531i	0.820290	−	0.571948i	$-0.193812\pi$
$941$	−2.61286	−	4.52561i	−0.0851770	−	0.147531i	−0.905467	+	0.424418i	$0.860479\pi$
$942$	15.3721	+	26.6252i	0.500848	+	0.867495i
$943$	−5.61288	+	9.72179i	−0.182780	+	0.316585i
$944$	−47.0788			−1.53229
$945$	−2.94903	+	1.90133i	−0.0959321	+	0.0618503i
$946$	22.9743			0.746960
$947$	7.38044	−	12.7833i	0.239832	−	0.415401i	−0.720834	−	0.693108i	$-0.756241\pi$
$947$	7.38044	−	12.7833i	0.239832	−	0.415401i	0.960666	+	0.277707i	$0.0895743\pi$
$948$	0.794848	+	1.37672i	0.0258155	+	0.0447137i
$949$	17.9999	+	31.1768i	0.584303	+	1.01204i
$950$	18.9840	−	32.8812i	0.615922	−	1.06681i
$951$	−0.508616			−0.0164930
$952$	0.438744	+	8.93536i	0.0142198	+	0.289597i
$953$	−33.6944			−1.09147			−0.545735	−	0.837958i	$-0.683749\pi$
$953$	−33.6944			−1.09147			−0.545735	+	0.837958i	$0.683749\pi$
$954$	2.83269	−	4.90636i	0.0917116	−	0.158849i
$955$	0.724776	+	1.25535i	0.0234532	+	0.0406221i
$956$	0.114350	+	0.198060i	0.00369835	+	0.00640572i
$957$	−5.29323	+	9.16814i	−0.171106	+	0.296364i
$958$	−25.4193			−0.821262
$959$	−0.120358	−	2.45119i	−0.00388657	−	0.0791531i
$960$	11.2276			0.362369
$961$	13.7582	−	23.8300i	0.443814	−	0.768709i
$962$	16.8599	+	29.2023i	0.543586	+	0.941519i
$963$	−6.99797	−	12.1208i	−0.225507	−	0.390589i
$964$	1.28961	−	2.23367i	0.0415355	−	0.0719416i
$965$	−9.83244			−0.316518
$966$	−3.03637	+	1.95764i	−0.0976935	+	0.0629859i
$967$	49.9879			1.60750			0.803751	−	0.594966i	$-0.202835\pi$
$967$	49.9879			1.60750			0.803751	+	0.594966i	$0.202835\pi$
$968$	−13.0974	+	22.6854i	−0.420966	+	0.729135i
$969$	4.97404	+	8.61529i	0.159789	+	0.276763i
$970$	0.369786	+	0.640489i	0.0118731	+	0.0205649i
$971$	5.71414	−	9.89717i	0.183375	−	0.317615i	−0.759652	−	0.650329i	$-0.774631\pi$
$971$	5.71414	−	9.89717i	0.183375	−	0.317615i	0.943028	+	0.332714i	$0.107964\pi$
$972$	0.135449			0.00434454
$973$	−9.94477	−	5.10849i	−0.318815	−	0.163771i
$974$	13.1481			0.421294
$975$	−5.13175	+	8.88845i	−0.164347	+	0.284658i
$976$	−25.6316	−	44.3952i	−0.820447	−	1.42106i
$977$	−2.49391	−	4.31958i	−0.0797873	−	0.138196i	0.823371	−	0.567504i	$-0.192091\pi$
$977$	−2.49391	−	4.31958i	−0.0797873	−	0.138196i	−0.903158	+	0.429308i	$0.858757\pi$
$978$	−0.997832	+	1.72830i	−0.0319072	+	0.0552648i
$979$	9.02481			0.288434
$980$	0.732380	+	1.02214i	0.0233950	+	0.0326511i
$981$	2.90945			0.0928917
$982$	3.14825	−	5.45292i	0.100465	−	0.174010i
$983$	−22.9278	−	39.7121i	−0.731282	−	1.26662i	−0.956335	−	0.292272i	$-0.905589\pi$
$983$	−22.9278	−	39.7121i	−0.731282	−	1.26662i	0.225053	−	0.974347i	$-0.427744\pi$
$984$	16.3667	+	28.3480i	0.521752	+	0.903702i
$985$	2.09595	−	3.63029i	0.0667824	−	0.115671i
$986$	11.8041			0.375919
$987$	−4.08669	−	2.09927i	−0.130081	−	0.0668206i
$988$	−3.67960			−0.117064
$989$	−5.92394	+	10.2606i	−0.188370	+	0.326267i
$990$	−1.28583	−	2.22713i	−0.0408665	−	0.0707828i
$991$	−16.7032	−	28.9308i	−0.530596	−	0.919018i	−0.999363	−	0.0356967i	$-0.988635\pi$
$991$	−16.7032	−	28.9308i	−0.530596	−	0.919018i	0.468767	−	0.883322i	$-0.344698\pi$
$992$	−0.713782	+	1.23631i	−0.0226626	+	0.0392528i
$993$	−6.19033			−0.196444
$994$	15.7581	−	10.1597i	0.499817	−	0.322247i
$995$	2.39949			0.0760690
$996$	−0.386413	+	0.669288i	−0.0122440	+	0.0212072i
$997$	10.9486	+	18.9636i	0.346747	+	0.600584i	0.985670	−	0.168687i	$-0.0539529\pi$
$997$	10.9486	+	18.9636i	0.346747	+	0.600584i	−0.638922	+	0.769271i	$0.720620\pi$
$998$	−8.77779	−	15.2036i	−0.277856	−	0.481261i
$999$	−3.89919	+	6.75360i	−0.123365	+	0.213674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.f.415.2	yes	12
7.2	even	3		3381.2.a.bc.1.5		6
7.4	even	3	inner	483.2.i.f.277.2	✓	12
7.5	odd	6		3381.2.a.bd.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.2	✓	12	7.4	even	3	inner
483.2.i.f.415.2	yes	12	1.1	even	1	trivial
3381.2.a.bc.1.5		6	7.2	even	3
3381.2.a.bd.1.5		6	7.5	odd	6

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.682743 + 1.18255i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.0677246 + 0.117302i) q^{4} +(0.663106 - 1.14853i) q^{5} -1.36549 q^{6} +(2.35341 + 1.20891i) q^{7} -2.91593 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.682743 + 1.18255i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.0677246 + 0.117302i) q^{4} +(0.663106 - 1.14853i) q^{5} -1.36549 q^{6} +(2.35341 + 1.20891i) q^{7} -2.91593 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.905461 + 1.56830i) q^{10} +(0.710043 + 1.22983i) q^{11} +(-0.0677246 + 0.117302i) q^{12} +3.16661 q^{13} +(-3.03637 + 1.95764i) q^{14} +1.32621 q^{15} +(1.85538 - 3.21361i) q^{16} +(-0.579802 - 1.00425i) q^{17} +(-0.682743 - 1.18255i) q^{18} +(-4.28943 + 7.42951i) q^{19} +0.179634 q^{20} +(0.129755 + 2.64257i) q^{21} -1.93911 q^{22} +(0.500000 - 0.866025i) q^{23} +(-1.45796 - 2.52527i) q^{24} +(1.62058 + 2.80693i) q^{25} +(-2.16198 + 3.74466i) q^{26} -1.00000 q^{27} +(0.0175752 + 0.357934i) q^{28} +7.45480 q^{29} +(-0.905461 + 1.56830i) q^{30} +(-0.933210 - 1.61637i) q^{31} +(-0.382434 - 0.662395i) q^{32} +(-0.710043 + 1.22983i) q^{33} +1.58342 q^{34} +(2.94903 - 1.90133i) q^{35} -0.135449 q^{36} +(3.89919 - 6.75360i) q^{37} +(-5.85715 - 10.1449i) q^{38} +(1.58330 + 2.74236i) q^{39} +(-1.93357 + 3.34903i) q^{40} -11.2258 q^{41} +(-3.21355 - 1.65075i) q^{42} -11.8479 q^{43} +(-0.0961748 + 0.166580i) q^{44} +(0.663106 + 1.14853i) q^{45} +(0.682743 + 1.18255i) q^{46} +(-0.868249 + 1.50385i) q^{47} +3.71076 q^{48} +(4.07706 + 5.69013i) q^{49} -4.42576 q^{50} +(0.579802 - 1.00425i) q^{51} +(0.214457 + 0.371451i) q^{52} +(2.07449 + 3.59312i) q^{53} +(0.682743 - 1.18255i) q^{54} +1.88333 q^{55} +(-6.86236 - 3.52510i) q^{56} -8.57886 q^{57} +(-5.08971 + 8.81564i) q^{58} +(-6.34357 - 10.9874i) q^{59} +(0.0898171 + 0.155568i) q^{60} +(6.90738 - 11.9639i) q^{61} +2.54857 q^{62} +(-2.22365 + 1.43366i) q^{63} +8.46593 q^{64} +(2.09980 - 3.63695i) q^{65} +(-0.969554 - 1.67932i) q^{66} +(4.04647 + 7.00870i) q^{67} +(0.0785337 - 0.136024i) q^{68} +1.00000 q^{69} +(0.234977 + 4.78548i) q^{70} -5.18979 q^{71} +(1.45796 - 2.52527i) q^{72} +(5.68430 + 9.84549i) q^{73} +(5.32429 + 9.22194i) q^{74} +(-1.62058 + 2.80693i) q^{75} -1.16200 q^{76} +(0.184264 + 3.75267i) q^{77} -4.32396 q^{78} +(5.86823 - 10.1641i) q^{79} +(-2.46062 - 4.26192i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.66430 - 13.2750i) q^{82} +5.70566 q^{83} +(-0.301192 + 0.194187i) q^{84} -1.53788 q^{85} +(8.08906 - 14.0107i) q^{86} +(3.72740 + 6.45604i) q^{87} +(-2.07043 - 3.58609i) q^{88} +(3.17756 - 5.50369i) q^{89} -1.81092 q^{90} +(7.45232 + 3.82815i) q^{91} +0.135449 q^{92} +(0.933210 - 1.61637i) q^{93} +(-1.18558 - 2.05349i) q^{94} +(5.68869 + 9.85310i) q^{95} +(0.382434 - 0.662395i) q^{96} +0.408396 q^{97} +(-9.51242 + 0.936415i) q^{98} -1.42009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} - q^{14} - 6 q^{15} + 7 q^{16} - 15 q^{17} + q^{18} + q^{19} + 34 q^{20} - 4 q^{21} - 12 q^{22} + 6 q^{23} - 3 q^{24} - 9 q^{25} + 15 q^{26} - 12 q^{27} - 2 q^{28} - 12 q^{29} - 3 q^{30} + 11 q^{31} - 3 q^{32} - 14 q^{33} + 30 q^{34} - q^{35} + 6 q^{36} + 5 q^{37} - 14 q^{38} + 17 q^{40} + 36 q^{41} - 17 q^{42} - 74 q^{43} + 10 q^{44} - 3 q^{45} - q^{46} - 3 q^{47} + 14 q^{48} - 6 q^{49} - 60 q^{50} + 15 q^{51} + 7 q^{52} + 15 q^{53} - q^{54} - 4 q^{55} - 21 q^{56} + 2 q^{57} - 4 q^{58} + 2 q^{59} + 17 q^{60} + 12 q^{61} + 72 q^{62} - 2 q^{63} - 46 q^{64} + 17 q^{65} - 6 q^{66} + 10 q^{67} + q^{68} + 12 q^{69} - 56 q^{70} - 42 q^{71} + 3 q^{72} + 8 q^{73} + 16 q^{74} + 9 q^{75} + 36 q^{76} - 40 q^{77} + 30 q^{78} + 17 q^{79} - 3 q^{80} - 6 q^{81} + 48 q^{82} + 24 q^{83} - 25 q^{84} - 26 q^{85} - 22 q^{86} - 6 q^{87} + 2 q^{88} - 18 q^{89} - 6 q^{90} + 22 q^{91} - 6 q^{92} - 11 q^{93} - 3 q^{94} + 16 q^{95} + 3 q^{96} - 4 q^{97} - 62 q^{98} - 28 q^{99}+O(q^{100}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 - q^14 - 6 * q^15 + 7 * q^16 - 15 * q^17 + q^18 + q^19 + 34 * q^20 - 4 * q^21 - 12 * q^22 + 6 * q^23 - 3 * q^24 - 9 * q^25 + 15 * q^26 - 12 * q^27 - 2 * q^28 - 12 * q^29 - 3 * q^30 + 11 * q^31 - 3 * q^32 - 14 * q^33 + 30 * q^34 - q^35 + 6 * q^36 + 5 * q^37 - 14 * q^38 + 17 * q^40 + 36 * q^41 - 17 * q^42 - 74 * q^43 + 10 * q^44 - 3 * q^45 - q^46 - 3 * q^47 + 14 * q^48 - 6 * q^49 - 60 * q^50 + 15 * q^51 + 7 * q^52 + 15 * q^53 - q^54 - 4 * q^55 - 21 * q^56 + 2 * q^57 - 4 * q^58 + 2 * q^59 + 17 * q^60 + 12 * q^61 + 72 * q^62 - 2 * q^63 - 46 * q^64 + 17 * q^65 - 6 * q^66 + 10 * q^67 + q^68 + 12 * q^69 - 56 * q^70 - 42 * q^71 + 3 * q^72 + 8 * q^73 + 16 * q^74 + 9 * q^75 + 36 * q^76 - 40 * q^77 + 30 * q^78 + 17 * q^79 - 3 * q^80 - 6 * q^81 + 48 * q^82 + 24 * q^83 - 25 * q^84 - 26 * q^85 - 22 * q^86 - 6 * q^87 + 2 * q^88 - 18 * q^89 - 6 * q^90 + 22 * q^91 - 6 * q^92 - 11 * q^93 - 3 * q^94 + 16 * q^95 + 3 * q^96 - 4 * q^97 - 62 * q^98 - 28 * q^99

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