LMFDB - Embedded newform 483.2.i.h.415.1

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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 245x^16 - 416x^15 + 1707x^14 - 2021x^13 + 7135x^12 - 6640x^11 + 20315x^10 - 10565x^9 + 29358x^8 - 9009x^7 + 30661x^6 - 4026x^5 + 15786x^4 - 84x^3 + 5800x^2 + 152*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.1
Root			$1.39981 + 2.42454i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.h.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39981 + 2.42454i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.91893 - 5.05574i) q^{4} +(0.973538 - 1.68622i) q^{5} -2.79962 q^{6} +(-2.64333 - 0.113245i) q^{7} +10.7446 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.39981 + 2.42454i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.91893 - 5.05574i) q^{4} +(0.973538 - 1.68622i) q^{5} -2.79962 q^{6} +(-2.64333 - 0.113245i) q^{7} +10.7446 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.72553 + 4.72076i) q^{10} +(1.34384 + 2.32760i) q^{11} +(2.91893 - 5.05574i) q^{12} +4.19039 q^{13} +(3.97472 - 6.25033i) q^{14} +1.94708 q^{15} +(-9.20247 + 15.9391i) q^{16} +(0.316198 + 0.547671i) q^{17} +(-1.39981 - 2.42454i) q^{18} +(-2.77713 + 4.81013i) q^{19} -11.3668 q^{20} +(-1.22359 - 2.34581i) q^{21} -7.52450 q^{22} +(-0.500000 + 0.866025i) q^{23} +(5.37228 + 9.30506i) q^{24} +(0.604448 + 1.04694i) q^{25} +(-5.86574 + 10.1598i) q^{26} -1.00000 q^{27} +(7.14315 + 13.6945i) q^{28} +5.57812 q^{29} +(-2.72553 + 4.72076i) q^{30} +(2.79909 + 4.84817i) q^{31} +(-15.0188 - 26.0134i) q^{32} +(-1.34384 + 2.32760i) q^{33} -1.77047 q^{34} +(-2.76433 + 4.34697i) q^{35} +5.83786 q^{36} +(-2.05806 + 3.56466i) q^{37} +(-7.77490 - 13.4665i) q^{38} +(2.09519 + 3.62898i) q^{39} +(10.4602 - 18.1177i) q^{40} +5.19481 q^{41} +(7.40031 + 0.317043i) q^{42} -1.98626 q^{43} +(7.84517 - 13.5882i) q^{44} +(0.973538 + 1.68622i) q^{45} +(-1.39981 - 2.42454i) q^{46} +(0.146293 - 0.253388i) q^{47} -18.4049 q^{48} +(6.97435 + 0.598687i) q^{49} -3.38445 q^{50} +(-0.316198 + 0.547671i) q^{51} +(-12.2315 - 21.1855i) q^{52} +(5.08608 + 8.80935i) q^{53} +(1.39981 - 2.42454i) q^{54} +5.23313 q^{55} +(-28.4014 - 1.21677i) q^{56} -5.55426 q^{57} +(-7.80831 + 13.5244i) q^{58} +(-3.65980 - 6.33896i) q^{59} +(-5.68338 - 9.84391i) q^{60} +(3.14346 - 5.44464i) q^{61} -15.6728 q^{62} +(1.41974 - 2.23257i) q^{63} +47.2842 q^{64} +(4.07950 - 7.06590i) q^{65} +(-3.76225 - 6.51640i) q^{66} +(-1.57437 - 2.72690i) q^{67} +(1.84592 - 3.19723i) q^{68} -1.00000 q^{69} +(-6.66987 - 12.7872i) q^{70} +6.00227 q^{71} +(-5.37228 + 9.30506i) q^{72} +(-6.93126 - 12.0053i) q^{73} +(-5.76178 - 9.97970i) q^{74} +(-0.604448 + 1.04694i) q^{75} +32.4250 q^{76} +(-3.28863 - 6.30480i) q^{77} -11.7315 q^{78} +(-7.89510 + 13.6747i) q^{79} +(17.9179 + 31.0347i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.27175 + 12.5950i) q^{82} +12.4983 q^{83} +(-8.28823 + 13.0334i) q^{84} +1.23132 q^{85} +(2.78038 - 4.81577i) q^{86} +(2.78906 + 4.83079i) q^{87} +(14.4390 + 25.0091i) q^{88} +(-0.905775 + 1.56885i) q^{89} -5.45107 q^{90} +(-11.0766 - 0.474541i) q^{91} +5.83786 q^{92} +(-2.79909 + 4.84817i) q^{93} +(0.409566 + 0.709389i) q^{94} +(5.40728 + 9.36568i) q^{95} +(15.0188 - 26.0134i) q^{96} -2.95190 q^{97} +(-11.2143 + 16.0716i) q^{98} -2.68769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * 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 $

$2$	−1.39981	+	2.42454i	−0.989815	+	1.71441i	−0.371618	+	0.928386i	$0.621197\pi$
$2$	−1.39981	+	2.42454i	−0.989815	+	1.71441i	−0.618196	+	0.786024i	$0.712136\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.91893	−	5.05574i	−1.45947	−	2.52787i
$5$	0.973538	−	1.68622i	0.435379	−	0.754099i	−0.561947	−	0.827173i	$-0.689948\pi$
$5$	0.973538	−	1.68622i	0.435379	−	0.754099i	0.997327	+	0.0730740i	$0.0232809\pi$
$6$	−2.79962			−1.14294
$7$	−2.64333	−	0.113245i	−0.999084	−	0.0428026i
$7$	−2.64333	−	0.113245i	−0.999084	−	0.0428026i
$8$	10.7446			3.79878
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.72553	+	4.72076i	0.861890	+	1.49284i
$11$	1.34384	+	2.32760i	0.405184	+	0.701799i	0.994343	−	0.106218i	$-0.0338742\pi$
$11$	1.34384	+	2.32760i	0.405184	+	0.701799i	−0.589159	+	0.808017i	$0.700541\pi$
$12$	2.91893	−	5.05574i	0.842623	−	1.45947i
$13$	4.19039			1.16220			0.581102	−	0.813831i	$-0.302622\pi$
$13$	4.19039			1.16220			0.581102	+	0.813831i	$0.302622\pi$
$14$	3.97472	−	6.25033i	1.06229	−	1.67047i
$15$	1.94708			0.502733
$16$	−9.20247	+	15.9391i	−2.30062	+	3.98479i
$17$	0.316198	+	0.547671i	0.0766893	+	0.132830i	0.901820	−	0.432113i	$-0.142232\pi$
$17$	0.316198	+	0.547671i	0.0766893	+	0.132830i	−0.825130	+	0.564942i	$0.808898\pi$
$18$	−1.39981	−	2.42454i	−0.329938	−	0.571470i
$19$	−2.77713	+	4.81013i	−0.637117	+	1.10352i	0.348946	+	0.937143i	$0.386540\pi$
$19$	−2.77713	+	4.81013i	−0.637117	+	1.10352i	−0.986062	+	0.166376i	$0.946794\pi$
$20$	−11.3668			−2.54169
$21$	−1.22359	−	2.34581i	−0.267009	−	0.511898i
$22$	−7.52450			−1.60423
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	5.37228	+	9.30506i	1.09661	+	1.89939i
$25$	0.604448	+	1.04694i	0.120890	+	0.209387i
$26$	−5.86574	+	10.1598i	−1.15037	+	1.99249i
$27$	−1.00000			−0.192450
$28$	7.14315	+	13.6945i	1.34993	+	2.58802i
$29$	5.57812			1.03583			0.517915	−	0.855432i	$-0.326708\pi$
$29$	5.57812			1.03583			0.517915	+	0.855432i	$0.326708\pi$
$30$	−2.72553	+	4.72076i	−0.497612	+	0.861890i
$31$	2.79909	+	4.84817i	0.502732	+	0.870757i	0.999995	+	0.00315709i	$0.00100493\pi$
$31$	2.79909	+	4.84817i	0.502732	+	0.870757i	−0.497263	+	0.867600i	$0.665662\pi$
$32$	−15.0188	−	26.0134i	−2.65498	−	4.59856i
$33$	−1.34384	+	2.32760i	−0.233933	+	0.405184i
$34$	−1.77047			−0.303633
$35$	−2.76433	+	4.34697i	−0.467258	+	0.734773i
$36$	5.83786			0.972977
$37$	−2.05806	+	3.56466i	−0.338343	+	0.586027i	−0.984121	−	0.177498i	$-0.943200\pi$
$37$	−2.05806	+	3.56466i	−0.338343	+	0.586027i	0.645778	+	0.763525i	$0.276533\pi$
$38$	−7.77490	−	13.4665i	−1.26126	−	2.18456i
$39$	2.09519	+	3.62898i	0.335500	+	0.581102i
$40$	10.4602	−	18.1177i	1.65391	−	2.86465i
$41$	5.19481			0.811293			0.405647	−	0.914030i	$-0.367046\pi$
$41$	5.19481			0.811293			0.405647	+	0.914030i	$0.367046\pi$
$42$	7.40031	+	0.317043i	1.14189	+	0.0489208i
$43$	−1.98626			−0.302902			−0.151451	−	0.988465i	$-0.548395\pi$
$43$	−1.98626			−0.302902			−0.151451	+	0.988465i	$0.548395\pi$
$44$	7.84517	−	13.5882i	1.18270	−	2.04850i
$45$	0.973538	+	1.68622i	0.145126	+	0.251366i
$46$	−1.39981	−	2.42454i	−0.206391	−	0.357479i
$47$	0.146293	−	0.253388i	0.0213391	−	0.0369604i	−0.855159	−	0.518366i	$-0.826540\pi$
$47$	0.146293	−	0.253388i	0.0213391	−	0.0369604i	0.876498	+	0.481406i	$0.159874\pi$
$48$	−18.4049			−2.65652
$49$	6.97435	+	0.598687i	0.996336	+	0.0855268i
$50$	−3.38445			−0.478633
$51$	−0.316198	+	0.547671i	−0.0442766	+	0.0766893i
$52$	−12.2315	−	21.1855i	−1.69620	−	2.93790i
$53$	5.08608	+	8.80935i	0.698627	+	1.21006i	0.968943	+	0.247286i	$0.0795387\pi$
$53$	5.08608	+	8.80935i	0.698627	+	1.21006i	−0.270315	+	0.962772i	$0.587128\pi$
$54$	1.39981	−	2.42454i	0.190490	−	0.329938i
$55$	5.23313			0.705635
$56$	−28.4014	−	1.21677i	−3.79529	−	0.162597i
$57$	−5.55426			−0.735679
$58$	−7.80831	+	13.5244i	−1.02528	+	1.77584i
$59$	−3.65980	−	6.33896i	−0.476466	−	0.825262i	0.523171	−	0.852228i	$-0.324749\pi$
$59$	−3.65980	−	6.33896i	−0.476466	−	0.825262i	−0.999636	+	0.0269653i	$0.991416\pi$
$60$	−5.68338	−	9.84391i	−0.733721	−	1.27084i
$61$	3.14346	−	5.44464i	0.402479	−	0.697114i	−0.591545	−	0.806272i	$-0.701482\pi$
$61$	3.14346	−	5.44464i	0.402479	−	0.697114i	0.994024	+	0.109158i	$0.0348153\pi$
$62$	−15.6728			−1.99044
$63$	1.41974	−	2.23257i	0.178870	−	0.281277i
$64$	47.2842			5.91053
$65$	4.07950	−	7.06590i	0.506000	−	0.876417i
$66$	−3.76225	−	6.51640i	−0.463101	−	0.802114i
$67$	−1.57437	−	2.72690i	−0.192340	−	0.333143i	0.753685	−	0.657236i	$-0.228274\pi$
$67$	−1.57437	−	2.72690i	−0.192340	−	0.333143i	−0.946025	+	0.324092i	$0.894941\pi$
$68$	1.84592	−	3.19723i	0.223851	−	0.387721i
$69$	−1.00000			−0.120386
$70$	−6.66987	−	12.7872i	−0.797203	−	1.52836i
$71$	6.00227			0.712338			0.356169	−	0.934422i	$-0.384083\pi$
$71$	6.00227			0.712338			0.356169	+	0.934422i	$0.384083\pi$
$72$	−5.37228	+	9.30506i	−0.633129	+	1.09661i
$73$	−6.93126	−	12.0053i	−0.811243	−	1.40511i	−0.911994	−	0.410202i	$-0.865458\pi$
$73$	−6.93126	−	12.0053i	−0.811243	−	1.40511i	0.100752	−	0.994912i	$-0.467875\pi$
$74$	−5.76178	−	9.97970i	−0.669793	−	1.16012i
$75$	−0.604448	+	1.04694i	−0.0697957	+	0.120890i
$76$	32.4250			3.71940
$77$	−3.28863	−	6.30480i	−0.374774	−	0.718499i
$78$	−11.7315			−1.32833
$79$	−7.89510	+	13.6747i	−0.888268	+	1.53852i	−0.0463457	+	0.998925i	$0.514758\pi$
$79$	−7.89510	+	13.6747i	−0.888268	+	1.53852i	−0.841922	+	0.539599i	$0.818576\pi$
$80$	17.9179	+	31.0347i	2.00328	+	3.46979i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.27175	+	12.5950i	−0.803030	+	1.39089i
$83$	12.4983			1.37186			0.685931	−	0.727666i	$-0.259395\pi$
$83$	12.4983			1.37186			0.685931	+	0.727666i	$0.259395\pi$
$84$	−8.28823	+	13.0334i	−0.904320	+	1.42206i
$85$	1.23132			0.133556
$86$	2.78038	−	4.81577i	0.299816	−	0.519297i
$87$	2.78906	+	4.83079i	0.299019	+	0.517915i
$88$	14.4390	+	25.0091i	1.53920	+	2.66598i
$89$	−0.905775	+	1.56885i	−0.0960119	+	0.166298i	−0.910030	−	0.414541i	$-0.863942\pi$
$89$	−0.905775	+	1.56885i	−0.0960119	+	0.166298i	0.814019	+	0.580839i	$0.197275\pi$
$90$	−5.45107			−0.574593
$91$	−11.0766	−	0.474541i	−1.16114	−	0.0497454i
$92$	5.83786			0.608639
$93$	−2.79909	+	4.84817i	−0.290252	+	0.502732i
$94$	0.409566	+	0.709389i	0.0422435	+	0.0731679i
$95$	5.40728	+	9.36568i	0.554775	+	0.960898i
$96$	15.0188	−	26.0134i	1.53285	−	2.65498i
$97$	−2.95190			−0.299720			−0.149860	−	0.988707i	$-0.547882\pi$
$97$	−2.95190			−0.299720			−0.149860	+	0.988707i	$0.547882\pi$
$98$	−11.2143	+	16.0716i	−1.13282	+	1.62347i
$99$	−2.68769			−0.270123
$100$	3.52869	−	6.11187i	0.352869	−	0.611187i
$101$	6.40066	+	11.0863i	0.636889	+	1.10312i	0.986112	+	0.166084i	$0.0531124\pi$
$101$	6.40066	+	11.0863i	0.636889	+	1.10312i	−0.349222	+	0.937040i	$0.613554\pi$
$102$	−0.885234	−	1.53327i	−0.0876512	−	0.151816i
$103$	−6.52904	+	11.3086i	−0.643325	+	1.11427i	0.341360	+	0.939933i	$0.389112\pi$
$103$	−6.52904	+	11.3086i	−0.643325	+	1.11427i	−0.984686	+	0.174340i	$0.944221\pi$
$104$	45.0239			4.41495
$105$	−5.14676	−	0.220497i	−0.502272	−	0.0215183i
$106$	−28.4782			−2.76605
$107$	6.86084	−	11.8833i	0.663263	−	1.14880i	−0.316491	−	0.948596i	$-0.602505\pi$
$107$	6.86084	−	11.8833i	0.663263	−	1.14880i	0.979753	−	0.200209i	$-0.0641621\pi$
$108$	2.91893	+	5.05574i	0.280874	+	0.486489i
$109$	2.25296	+	3.90223i	0.215794	+	0.373766i	0.953518	−	0.301336i	$-0.0974327\pi$
$109$	2.25296	+	3.90223i	0.215794	+	0.373766i	−0.737724	+	0.675103i	$0.764099\pi$
$110$	−7.32538	+	12.6879i	−0.698448	+	1.20975i
$111$	−4.11612			−0.390685
$112$	26.1302	−	41.0902i	2.46907	−	3.88266i
$113$	−16.4013			−1.54290			−0.771451	−	0.636288i	$-0.780469\pi$
$113$	−16.4013			−1.54290			−0.771451	+	0.636288i	$0.780469\pi$
$114$	7.77490	−	13.4665i	0.728186	−	1.26126i
$115$	0.973538	+	1.68622i	0.0907829	+	0.157241i
$116$	−16.2822	−	28.2015i	−1.51176	−	2.61845i
$117$	−2.09519	+	3.62898i	−0.193701	+	0.335500i
$118$	20.4921			1.88645
$119$	−0.773794	−	1.48348i	−0.0709335	−	0.135990i
$120$	20.9205			1.90977
$121$	1.88817	−	3.27041i	0.171652	−	0.297310i
$122$	8.80049	+	15.2429i	0.796759	+	1.38003i
$123$	2.59741	+	4.49884i	0.234200	+	0.405647i
$124$	16.3407	−	28.3030i	1.46744	−	2.54168i
$125$	12.0892			1.08129
$126$	3.42559	+	6.56738i	0.305175	+	0.585068i
$127$	−18.2031			−1.61527			−0.807634	−	0.589685i	$-0.799252\pi$
$127$	−18.2031			−1.61527			−0.807634	+	0.589685i	$0.799252\pi$
$128$	−36.1512	+	62.6157i	−3.19534	+	5.53450i
$129$	−0.993129	−	1.72015i	−0.0874402	−	0.151451i
$130$	11.4210	+	19.7818i	1.00169	+	1.73498i
$131$	4.16420	−	7.21261i	0.363828	−	0.630169i	−0.624759	−	0.780817i	$-0.714803\pi$
$131$	4.16420	−	7.21261i	0.363828	−	0.630169i	0.988587	+	0.150649i	$0.0481362\pi$
$132$	15.6903			1.36567
$133$	7.88558	−	12.4002i	0.683766	−	1.07524i
$134$	8.81530			0.761526
$135$	−0.973538	+	1.68622i	−0.0837888	+	0.145126i
$136$	3.39741	+	5.88448i	0.291325	+	0.504590i
$137$	6.65217	+	11.5219i	0.568333	+	0.984382i	0.996731	+	0.0807919i	$0.0257449\pi$
$137$	6.65217	+	11.5219i	0.568333	+	0.984382i	−0.428398	+	0.903590i	$0.640922\pi$
$138$	1.39981	−	2.42454i	0.119160	−	0.206391i
$139$	−5.93319			−0.503247			−0.251623	−	0.967825i	$-0.580964\pi$
$139$	−5.93319			−0.503247			−0.251623	+	0.967825i	$0.580964\pi$
$140$	30.0461	+	1.28723i	2.53936	+	0.108791i
$141$	0.292587			0.0246403
$142$	−8.40203	+	14.5527i	−0.705083	+	1.22124i
$143$	5.63122	+	9.75356i	0.470907	+	0.815634i
$144$	−9.20247	−	15.9391i	−0.766872	−	1.32826i
$145$	5.43051	−	9.40592i	0.450979	−	0.781119i
$146$	38.8098			3.21192
$147$	2.96870	+	6.33931i	0.244854	+	0.522857i
$148$	24.0293			1.97520
$149$	2.41533	−	4.18348i	0.197872	−	0.342724i	−0.749967	−	0.661476i	$-0.769930\pi$
$149$	2.41533	−	4.18348i	0.197872	−	0.342724i	0.947838	+	0.318752i	$0.103264\pi$
$150$	−1.69222	−	2.93102i	−0.138170	−	0.239317i
$151$	−10.4923	−	18.1732i	−0.853854	−	1.47892i	−0.877705	−	0.479202i	$-0.840926\pi$
$151$	−10.4923	−	18.1732i	−0.853854	−	1.47892i	0.0238510	−	0.999716i	$-0.492407\pi$
$152$	−29.8390	+	51.6827i	−2.42026	+	4.19202i
$153$	−0.632396			−0.0511262
$154$	19.8897	+	0.852112i	1.60276	+	0.0686651i
$155$	10.9001			0.875516
$156$	12.2315	−	21.1855i	0.979300	−	1.69620i
$157$	−0.797219	−	1.38082i	−0.0636250	−	0.110202i	0.832458	−	0.554088i	$-0.186933\pi$
$157$	−0.797219	−	1.38082i	−0.0636250	−	0.110202i	−0.896083	+	0.443886i	$0.853599\pi$
$158$	−22.1033	−	38.2840i	−1.75844	−	3.04571i
$159$	−5.08608	+	8.80935i	−0.403353	+	0.698627i
$160$	−58.4857			−4.62370
$161$	1.41974	−	2.23257i	0.111891	−	0.175951i
$162$	2.79962			0.219959
$163$	5.44883	−	9.43766i	0.426786	−	0.739214i	−0.569800	−	0.821784i	$-0.692979\pi$
$163$	5.44883	−	9.43766i	0.426786	−	0.739214i	0.996585	+	0.0825692i	$0.0263125\pi$
$164$	−15.1633	−	26.2636i	−1.18406	−	2.05084i
$165$	2.61656	+	4.53202i	0.203699	+	0.352817i
$166$	−17.4952	+	30.3026i	−1.35789	+	2.35193i
$167$	−15.5931			−1.20663			−0.603313	−	0.797504i	$-0.706153\pi$
$167$	−15.5931			−1.20663			−0.603313	+	0.797504i	$0.706153\pi$
$168$	−13.1469	−	25.2047i	−1.01431	−	1.94458i
$169$	4.55935			0.350719
$170$	−1.72362	+	2.98539i	−0.132195	+	0.228969i
$171$	−2.77713	−	4.81013i	−0.212372	−	0.367840i
$172$	5.79776	+	10.0420i	0.442075	+	0.765696i
$173$	5.63605	−	9.76193i	0.428501	−	0.742186i	−0.568239	−	0.822864i	$-0.692375\pi$
$173$	5.63605	−	9.76193i	0.428501	−	0.742186i	0.996740	+	0.0806777i	$0.0257084\pi$
$174$	−15.6166			−1.18389
$175$	−1.47919	−	2.83584i	−0.111817	−	0.214370i
$176$	−49.4667			−3.72869
$177$	3.65980	−	6.33896i	0.275087	−	0.476466i
$178$	−2.53582	−	4.39218i	−0.190068	−	0.329207i
$179$	−4.08754	−	7.07983i	−0.305517	−	0.529171i	0.671859	−	0.740679i	$-0.265496\pi$
$179$	−4.08754	−	7.07983i	−0.305517	−	0.529171i	−0.977376	+	0.211508i	$0.932163\pi$
$180$	5.68338	−	9.84391i	0.423614	−	0.733721i
$181$	−3.00094			−0.223058			−0.111529	−	0.993761i	$-0.535575\pi$
$181$	−3.00094			−0.223058			−0.111529	+	0.993761i	$0.535575\pi$
$182$	16.6556	−	26.1913i	1.23460	−	1.94143i
$183$	6.28692			0.464743
$184$	−5.37228	+	9.30506i	−0.396050	+	0.685978i
$185$	4.00720	+	6.94067i	0.294615	+	0.510288i
$186$	−7.83639	−	13.5730i	−0.574592	−	0.995222i
$187$	−0.849841	+	1.47197i	−0.0621465	+	0.107641i
$188$	−1.70808			−0.124575
$189$	2.64333	+	0.113245i	0.192274	+	0.00823737i
$190$	−30.2766			−2.19650
$191$	5.78941	−	10.0276i	0.418907	−	0.725568i	−0.576923	−	0.816799i	$-0.695747\pi$
$191$	5.78941	−	10.0276i	0.418907	−	0.725568i	0.995830	+	0.0912304i	$0.0290800\pi$
$192$	23.6421	+	40.9493i	1.70622	+	2.95526i
$193$	−2.84965	−	4.93573i	−0.205122	−	0.355282i	0.745050	−	0.667009i	$-0.232426\pi$
$193$	−2.84965	−	4.93573i	−0.205122	−	0.355282i	−0.950172	+	0.311727i	$0.899092\pi$
$194$	4.13210	−	7.15700i	0.296667	−	0.513843i
$195$	8.15900			0.584278
$196$	−17.3309	−	37.0080i	−1.23792	−	2.64343i
$197$	−12.9883			−0.925379			−0.462689	−	0.886521i	$-0.653115\pi$
$197$	−12.9883			−0.925379			−0.462689	+	0.886521i	$0.653115\pi$
$198$	3.76225	−	6.51640i	0.267371	−	0.463101i
$199$	10.6628	+	18.4685i	0.755864	+	1.30919i	0.944944	+	0.327233i	$0.106116\pi$
$199$	10.6628	+	18.4685i	0.755864	+	1.30919i	−0.189080	+	0.981962i	$0.560551\pi$
$200$	6.49453	+	11.2489i	0.459233	+	0.795414i
$201$	1.57437	−	2.72690i	0.111048	−	0.192340i
$202$	−35.8388			−2.52161
$203$	−14.7448	−	0.631695i	−1.03488	−	0.0443363i
$204$	3.69184			0.258481
$205$	5.05735	−	8.75958i	0.353220	−	0.611796i
$206$	−18.2788	−	31.6598i	−1.27355	−	2.20585i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	−38.5619	+	66.7912i	−2.67379	+	4.63114i
$209$	−14.9281			−1.03260
$210$	7.73908	−	12.1699i	0.534047	−	0.839801i
$211$	7.69191			0.529533			0.264766	−	0.964313i	$-0.414705\pi$
$211$	7.69191			0.529533			0.264766	+	0.964313i	$0.414705\pi$
$212$	29.6919	−	51.4278i	2.03925	−	3.53208i
$213$	3.00113	+	5.19812i	0.205634	+	0.356169i
$214$	19.2077	+	33.2688i	1.31301	+	2.27421i
$215$	−1.93370	+	3.34926i	−0.131877	+	0.228418i
$216$	−10.7446			−0.731075
$217$	−6.84988	−	13.1323i	−0.465000	−	0.891477i
$218$	−12.6148			−0.854384
$219$	6.93126	−	12.0053i	0.468371	−	0.811243i
$220$	−15.2751	−	26.4573i	−1.02985	−	1.78375i
$221$	1.32499	+	2.29495i	0.0891286	+	0.154375i
$222$	5.76178	−	9.97970i	0.386705	−	0.669793i
$223$	20.9689			1.40418			0.702091	−	0.712087i	$-0.252250\pi$
$223$	20.9689			1.40418			0.702091	+	0.712087i	$0.252250\pi$
$224$	36.7538	+	70.4627i	2.45572	+	4.70799i
$225$	−1.20890			−0.0805931
$226$	22.9587	−	39.7656i	1.52719	−	2.64517i
$227$	12.0879	+	20.9369i	0.802302	+	1.38963i	0.918097	+	0.396355i	$0.129725\pi$
$227$	12.0879	+	20.9369i	0.802302	+	1.38963i	−0.115795	+	0.993273i	$0.536941\pi$
$228$	16.2125	+	28.0809i	1.07370	+	1.85970i
$229$	4.33927	−	7.51584i	0.286747	−	0.496661i	−0.686284	−	0.727334i	$-0.740759\pi$
$229$	4.33927	−	7.51584i	0.286747	−	0.496661i	0.973031	+	0.230673i	$0.0740927\pi$
$230$	−5.45107			−0.359433
$231$	3.81581	−	6.00043i	0.251062	−	0.394800i
$232$	59.9344			3.93489
$233$	−1.34590	+	2.33117i	−0.0881729	+	0.152720i	−0.906739	−	0.421693i	$-0.861436\pi$
$233$	−1.34590	+	2.33117i	−0.0881729	+	0.152720i	0.818566	+	0.574413i	$0.194769\pi$
$234$	−5.86574	−	10.1598i	−0.383456	−	0.664165i
$235$	−0.284844	−	0.493365i	−0.0185812	−	0.0321836i
$236$	−21.3654	+	37.0060i	−1.39077	+	2.40889i
$237$	−15.7902			−1.02568
$238$	4.67992	+	0.200497i	0.303354	+	0.0129963i
$239$	−0.0523580			−0.00338675			−0.00169338	−	0.999999i	$-0.500539\pi$
$239$	−0.0523580			−0.00338675			−0.00169338	+	0.999999i	$0.500539\pi$
$240$	−17.9179	+	31.0347i	−1.15660	+	2.00328i
$241$	0.149776	+	0.259419i	0.00964789	+	0.0167106i	0.870809	−	0.491621i	$-0.163596\pi$
$241$	0.149776	+	0.259419i	0.00964789	+	0.0167106i	−0.861161	+	0.508332i	$0.830262\pi$
$242$	5.28616	+	9.15590i	0.339807	+	0.588564i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−36.7022			−2.34962
$245$	7.79931	−	11.1774i	0.498280	−	0.714099i
$246$	−14.5435			−0.927259
$247$	−11.6372	+	20.1563i	−0.740460	+	1.28251i
$248$	30.0750	+	52.0914i	1.90976	+	3.30781i
$249$	6.24913	+	10.8238i	0.396023	+	0.685931i
$250$	−16.9226	+	29.3107i	−1.07028	+	1.85377i
$251$	−5.72848			−0.361579			−0.180789	−	0.983522i	$-0.557865\pi$
$251$	−5.72848			−0.361579			−0.180789	+	0.983522i	$0.557865\pi$
$252$	−15.4314	−	0.661109i	−0.972086	−	0.0416460i
$253$	−2.68769			−0.168973
$254$	25.4809	−	44.1343i	1.59882	−	2.76923i
$255$	0.615661	+	1.06636i	0.0385542	+	0.0667779i
$256$	−53.9253	−	93.4014i	−3.37033	−	5.83759i
$257$	8.61484	−	14.9213i	0.537379	−	0.930768i	−0.461665	−	0.887054i	$-0.652748\pi$
$257$	8.61484	−	14.9213i	0.537379	−	0.930768i	0.999044	−	0.0437133i	$-0.0139188\pi$
$258$	5.56077			0.346198
$259$	5.84380	−	9.18950i	0.363116	−	0.571008i
$260$	−47.6312			−2.95396
$261$	−2.78906	+	4.83079i	−0.172638	+	0.299019i
$262$	11.6582	+	20.1926i	0.720245	+	1.24750i
$263$	−11.7608	−	20.3703i	−0.725202	−	1.25609i	−0.958891	−	0.283775i	$-0.908413\pi$
$263$	−11.7608	−	20.3703i	−0.725202	−	1.25609i	0.233689	−	0.972311i	$-0.424920\pi$
$264$	−14.4390	+	25.0091i	−0.888659	+	1.53920i
$265$	19.8060			1.21667
$266$	19.0266	+	36.4769i	1.16659	+	2.23654i
$267$	−1.81155			−0.110865
$268$	−9.19098	+	15.9193i	−0.561429	+	0.972423i
$269$	6.90462	+	11.9592i	0.420982	+	0.729163i	0.996036	−	0.0889531i	$-0.0283521\pi$
$269$	6.90462	+	11.9592i	0.420982	+	0.729163i	−0.575054	+	0.818116i	$0.695019\pi$
$270$	−2.72553	−	4.72076i	−0.165871	−	0.287297i
$271$	11.2211	−	19.4355i	0.681634	−	1.18062i	−0.292848	−	0.956159i	$-0.594603\pi$
$271$	11.2211	−	19.4355i	0.681634	−	1.18062i	0.974482	−	0.224466i	$-0.0720637\pi$
$272$	−11.6392			−0.705731
$273$	−5.12732	−	9.82986i	−0.310319	−	0.594930i
$274$	−37.2471			−2.25018
$275$	−1.62457	+	2.81383i	−0.0979651	+	0.169681i
$276$	2.91893	+	5.05574i	0.175699	+	0.304320i
$277$	−11.1138	−	19.2497i	−0.667765	−	1.15660i	−0.978528	−	0.206115i	$-0.933918\pi$
$277$	−11.1138	−	19.2497i	−0.667765	−	1.15660i	0.310763	−	0.950487i	$-0.399415\pi$
$278$	8.30534	−	14.3853i	0.498121	−	0.862771i
$279$	−5.59818			−0.335154
$280$	−29.7015	+	46.7063i	−1.77501	+	2.79124i
$281$	6.99680			0.417394			0.208697	−	0.977980i	$-0.433078\pi$
$281$	6.99680			0.417394			0.208697	+	0.977980i	$0.433078\pi$
$282$	−0.409566	+	0.709389i	−0.0243893	+	0.0422435i
$283$	−4.03188	−	6.98343i	−0.239671	−	0.415122i	0.720949	−	0.692988i	$-0.243706\pi$
$283$	−4.03188	−	6.98343i	−0.239671	−	0.415122i	−0.960620	+	0.277866i	$0.910373\pi$
$284$	−17.5202	−	30.3459i	−1.03963	−	1.80070i
$285$	−5.40728	+	9.36568i	−0.320299	+	0.554775i
$286$	−31.5306			−1.86444
$287$	−13.7316	−	0.588287i	−0.810550	−	0.0347255i
$288$	30.0377			1.76999
$289$	8.30004	−	14.3761i	0.488238	−	0.845652i
$290$	15.2034	+	26.3330i	0.892772	+	1.54633i
$291$	−1.47595	−	2.55642i	−0.0865217	−	0.149860i
$292$	−40.4638	+	70.0853i	−2.36796	+	4.10143i
$293$	−13.1458			−0.767986			−0.383993	−	0.923336i	$-0.625451\pi$
$293$	−13.1458			−0.767986			−0.383993	+	0.923336i	$0.625451\pi$
$294$	−19.5255	−	1.67610i	−1.13875	−	0.0977519i
$295$	−14.2518			−0.829773
$296$	−22.1129	+	38.3007i	−1.28529	+	2.22618i
$297$	−1.34384	−	2.32760i	−0.0779777	−	0.135061i
$298$	6.76200	+	11.7121i	0.391712	+	0.678466i
$299$	−2.09519	+	3.62898i	−0.121168	+	0.209869i
$300$	7.05738			0.407458
$301$	5.25033	+	0.224934i	0.302624	+	0.0129650i
$302$	58.7490			3.38063
$303$	−6.40066	+	11.0863i	−0.367708	+	0.636889i
$304$	−51.1129	−	88.5301i	−2.93152	−	5.07755i
$305$	−6.12056	−	10.6011i	−0.350462	−	0.607018i
$306$	0.885234	−	1.53327i	0.0506054	−	0.0876512i
$307$	15.1086			0.862293			0.431147	−	0.902282i	$-0.358109\pi$
$307$	15.1086			0.862293			0.431147	+	0.902282i	$0.358109\pi$
$308$	−22.2762	+	35.0297i	−1.26930	+	1.99600i
$309$	−13.0581			−0.742848
$310$	−15.2580	+	26.4277i	−0.866598	+	1.50099i
$311$	10.7414	+	18.6047i	0.609090	+	1.05497i	0.991391	+	0.130937i	$0.0417985\pi$
$311$	10.7414	+	18.6047i	0.609090	+	1.05497i	−0.382301	+	0.924038i	$0.624868\pi$
$312$	22.5119	+	38.9918i	1.27449	+	2.20748i
$313$	−7.41912	+	12.8503i	−0.419353	+	0.726341i	−0.995875	−	0.0907410i	$-0.971076\pi$
$313$	−7.41912	+	12.8503i	−0.419353	+	0.726341i	0.576521	+	0.817082i	$0.304410\pi$
$314$	4.46382			0.251908
$315$	−2.38242	−	4.56747i	−0.134234	−	0.257348i
$316$	92.1810			5.18559
$317$	2.35086	−	4.07181i	0.132038	−	0.228696i	−0.792424	−	0.609970i	$-0.791181\pi$
$317$	2.35086	−	4.07181i	0.132038	−	0.228696i	0.924462	+	0.381274i	$0.124515\pi$
$318$	−14.2391	−	24.6628i	−0.798489	−	1.38302i
$319$	7.49612	+	12.9837i	0.419702	+	0.726945i
$320$	46.0330	−	79.7314i	2.57332	−	4.45712i
$321$	13.7217			0.765870
$322$	3.42559	+	6.56738i	0.190900	+	0.365986i
$323$	−3.51249			−0.195440
$324$	−2.91893	+	5.05574i	−0.162163	+	0.280874i
$325$	2.53287	+	4.38706i	0.140499	+	0.243351i
$326$	15.2547	+	26.4218i	0.844877	+	1.46337i
$327$	−2.25296	+	3.90223i	−0.124589	+	0.215794i
$328$	55.8160			3.08192
$329$	−0.415396	+	0.653219i	−0.0229015	+	0.0360132i
$330$	−14.6508			−0.806498
$331$	3.93932	−	6.82310i	0.216524	−	0.375031i	−0.737219	−	0.675654i	$-0.763861\pi$
$331$	3.93932	−	6.82310i	0.216524	−	0.375031i	0.953743	+	0.300623i	$0.0971946\pi$
$332$	−36.4816	−	63.1880i	−2.00219	−	3.46789i
$333$	−2.05806	−	3.56466i	−0.112781	−	0.195342i
$334$	21.8273	−	37.8060i	1.19434	−	2.06865i
$335$	−6.13085			−0.334964
$336$	48.6503	+	2.08427i	2.65409	+	0.113706i
$337$	−18.3857			−1.00153			−0.500767	−	0.865582i	$-0.666949\pi$
$337$	−18.3857			−1.00153			−0.500767	+	0.865582i	$0.666949\pi$
$338$	−6.38222	+	11.0543i	−0.347147	+	0.601276i
$339$	−8.20064	−	14.2039i	−0.445398	−	0.771451i
$340$	−3.59415	−	6.22525i	−0.194920	−	0.337611i
$341$	−7.52308	+	13.0304i	−0.407398	+	0.705633i
$342$	15.5498			0.840837
$343$	−18.3677	−	2.37234i	−0.991762	−	0.128094i
$344$	−21.3415			−1.15066
$345$	−0.973538	+	1.68622i	−0.0524135	+	0.0907829i
$346$	15.7788	+	27.3297i	0.848274	+	1.46925i
$347$	−3.01039	−	5.21415i	−0.161606	−	0.279910i	0.773839	−	0.633383i	$-0.218334\pi$
$347$	−3.01039	−	5.21415i	−0.161606	−	0.279910i	−0.935445	+	0.353473i	$0.885001\pi$
$348$	16.2822	−	28.2015i	0.872815	−	1.51176i
$349$	13.3378			0.713956			0.356978	−	0.934113i	$-0.383807\pi$
$349$	13.3378			0.713956			0.356978	+	0.934113i	$0.383807\pi$
$350$	8.94621	+	0.383272i	0.478195	+	0.0204868i
$351$	−4.19039			−0.223666
$352$	40.3659	−	69.9159i	2.15151	−	3.72653i
$353$	−8.74350	−	15.1442i	−0.465369	−	0.806043i	0.533849	−	0.845580i	$-0.320745\pi$
$353$	−8.74350	−	15.1442i	−0.465369	−	0.806043i	−0.999218	+	0.0395367i	$0.987412\pi$
$354$	10.2460	+	17.7467i	0.544571	+	0.943225i
$355$	5.84343	−	10.1211i	0.310137	−	0.537174i
$356$	10.5756			0.560505
$357$	0.897836	−	1.41187i	0.0475185	−	0.0747238i
$358$	22.8871			1.20962
$359$	4.28362	−	7.41944i	0.226081	−	0.391583i	−0.730562	−	0.682846i	$-0.760742\pi$
$359$	4.28362	−	7.41944i	0.226081	−	0.391583i	0.956643	+	0.291263i	$0.0940754\pi$
$360$	10.4602	+	18.1177i	0.551303	+	0.954884i
$361$	−5.92488	−	10.2622i	−0.311836	−	0.540115i
$362$	4.20075	−	7.27591i	0.220787	−	0.382413i
$363$	3.77634			0.198207
$364$	29.9326	+	57.3854i	1.56889	+	3.00781i
$365$	−26.9914			−1.41279
$366$	−8.80049	+	15.2429i	−0.460009	+	0.796759i
$367$	9.85576	+	17.0707i	0.514467	+	0.891082i	0.999859	+	0.0167860i	$0.00534340\pi$
$367$	9.85576	+	17.0707i	0.514467	+	0.891082i	−0.485392	+	0.874296i	$0.661323\pi$
$368$	−9.20247	−	15.9391i	−0.479712	−	0.830885i
$369$	−2.59741	+	4.49884i	−0.135216	+	0.234200i
$370$	−22.4372			−1.16646
$371$	−12.4466	−	23.8620i	−0.646193	−	1.23885i
$372$	32.6814			1.69445
$373$	−10.9629	+	18.9883i	−0.567639	+	0.983179i	0.429160	+	0.903228i	$0.358810\pi$
$373$	−10.9629	+	18.9883i	−0.567639	+	0.983179i	−0.996799	+	0.0799507i	$0.974524\pi$
$374$	−2.37923	−	4.12095i	−0.123027	−	0.213089i
$375$	6.04460	+	10.4695i	0.312142	+	0.540645i
$376$	1.57186	−	2.72254i	0.0810624	−	0.140404i
$377$	23.3745			1.20385
$378$	−3.97472	+	6.25033i	−0.204438	+	0.321482i
$379$	9.89943			0.508500			0.254250	−	0.967139i	$-0.418171\pi$
$379$	9.89943			0.508500			0.254250	+	0.967139i	$0.418171\pi$
$380$	31.5670	−	54.6756i	1.61935	−	2.80480i
$381$	−9.10157	−	15.7644i	−0.466288	−	0.807634i
$382$	16.2081	+	28.0733i	0.829281	+	1.43636i
$383$	8.76893	−	15.1882i	0.448071	−	0.776083i	−0.550189	−	0.835040i	$-0.685444\pi$
$383$	8.76893	−	15.1882i	0.448071	−	0.776083i	0.998260	+	0.0589576i	$0.0187777\pi$
$384$	−72.3024			−3.68966
$385$	−13.8329	−	0.592626i	−0.704988	−	0.0302030i
$386$	15.9558			0.812131
$387$	0.993129	−	1.72015i	0.0504836	−	0.0874402i
$388$	8.61639	+	14.9240i	0.437431	+	0.757653i
$389$	−9.62382	−	16.6689i	−0.487947	−	0.845149i	0.511957	−	0.859011i	$-0.328921\pi$
$389$	−9.62382	−	16.6689i	−0.487947	−	0.845149i	−0.999904	+	0.0138623i	$0.995587\pi$
$390$	−11.4210	+	19.7818i	−0.578327	+	1.00169i
$391$	−0.632396			−0.0319816
$392$	74.9363	+	6.43263i	3.78486	+	0.324897i
$393$	8.32841			0.420113
$394$	18.1812	−	31.4907i	0.915953	−	1.58648i
$395$	15.3723	+	26.6257i	0.773467	+	1.33968i
$396$	7.84517	+	13.5882i	0.394235	+	0.682835i
$397$	12.2997	−	21.3037i	0.617304	−	1.06920i	−0.372671	−	0.927963i	$-0.621558\pi$
$397$	12.2997	−	21.3037i	0.617304	−	1.06920i	0.989976	−	0.141239i	$-0.0451086\pi$
$398$	−59.7034			−2.99266
$399$	14.6817	+	0.628992i	0.735005	+	0.0314890i
$400$	−22.2497			−1.11248
$401$	3.94256	−	6.82871i	0.196882	−	0.341010i	−0.750634	−	0.660718i	$-0.770252\pi$
$401$	3.94256	−	6.82871i	0.196882	−	0.341010i	0.947516	+	0.319709i	$0.103585\pi$
$402$	4.40765	+	7.63427i	0.219833	+	0.380763i
$403$	11.7293	+	20.3157i	0.584277	+	1.01200i
$404$	37.3662	−	64.7201i	1.85904	−	3.21995i
$405$	−1.94708			−0.0967510
$406$	22.1715	−	34.8651i	1.10035	−	1.73033i
$407$	−11.0628			−0.548364
$408$	−3.39741	+	5.88448i	−0.168197	+	0.291325i
$409$	−2.40339	−	4.16279i	−0.118840	−	0.205836i	0.800468	−	0.599375i	$-0.204584\pi$
$409$	−2.40339	−	4.16279i	−0.118840	−	0.205836i	−0.919308	+	0.393538i	$0.871251\pi$
$410$	14.1586	+	24.5235i	0.699245	+	1.21113i
$411$	−6.65217	+	11.5219i	−0.328127	+	0.568333i
$412$	76.2313			3.75565
$413$	8.95619	+	17.1704i	0.440705	+	0.844900i
$414$	2.79962			0.137594
$415$	12.1675	−	21.0748i	0.597281	−	1.03452i
$416$	−62.9348	−	109.006i	−3.08563	−	5.34447i
$417$	−2.96660	−	5.13830i	−0.145275	−	0.251623i
$418$	20.8965	−	36.1938i	1.02208	−	1.77030i
$419$	4.37312			0.213641			0.106820	−	0.994278i	$-0.465933\pi$
$419$	4.37312			0.213641			0.106820	+	0.994278i	$0.465933\pi$
$420$	13.9083	+	26.6643i	0.678654	+	1.30108i
$421$	−15.6894			−0.764655			−0.382327	−	0.924027i	$-0.624877\pi$
$421$	−15.6894			−0.764655			−0.382327	+	0.924027i	$0.624877\pi$
$422$	−10.7672	+	18.6493i	−0.524139	+	0.907836i
$423$	0.146293	+	0.253388i	0.00711303	+	0.0123201i
$424$	54.6477	+	94.6526i	2.65393	+	4.59674i
$425$	−0.382251	+	0.662078i	−0.0185419	+	0.0321155i
$426$	−16.8041			−0.814159
$427$	−8.92577	+	14.0360i	−0.431948	+	0.679248i
$428$	−80.1053			−3.87204
$429$	−5.63122	+	9.75356i	−0.271878	+	0.470907i
$430$	−5.41362	−	9.37666i	−0.261068	−	0.452183i
$431$	1.67317	+	2.89801i	0.0805935	+	0.139592i	0.903505	−	0.428577i	$-0.140985\pi$
$431$	1.67317	+	2.89801i	0.0805935	+	0.139592i	−0.822912	+	0.568170i	$0.807652\pi$
$432$	9.20247	−	15.9391i	0.442754	−	0.766872i
$433$	−15.2273			−0.731779			−0.365889	−	0.930658i	$-0.619235\pi$
$433$	−15.2273			−0.731779			−0.365889	+	0.930658i	$0.619235\pi$
$434$	41.4283	+	1.77486i	1.98862	+	0.0851962i
$435$	10.8610			0.520746
$436$	13.1524	−	22.7807i	0.629888	−	1.09100i
$437$	−2.77713	−	4.81013i	−0.132848	−	0.230100i
$438$	19.4049	+	33.6103i	0.927202	+	1.60596i
$439$	−10.7457	+	18.6121i	−0.512865	+	0.888308i	0.487024	+	0.873389i	$0.338083\pi$
$439$	−10.7457	+	18.6121i	−0.512865	+	0.888308i	−0.999889	+	0.0149196i	$0.995251\pi$
$440$	56.2276			2.68055
$441$	−4.00565	+	5.74062i	−0.190745	+	0.273363i
$442$	−7.41895			−0.352883
$443$	−11.8923	+	20.5980i	−0.565019	+	0.978642i	0.432029	+	0.901860i	$0.357798\pi$
$443$	−11.8923	+	20.5980i	−0.565019	+	0.978642i	−0.997048	+	0.0767822i	$0.975535\pi$
$444$	12.0147	+	20.8100i	0.570191	+	0.987600i
$445$	1.76361	+	3.05467i	0.0836032	+	0.144805i
$446$	−29.3525	+	50.8400i	−1.38988	+	2.40734i
$447$	4.83066			0.228482
$448$	−124.988	−	5.35470i	−5.90511	−	0.252986i
$449$	−8.36232			−0.394642			−0.197321	−	0.980339i	$-0.563224\pi$
$449$	−8.36232			−0.394642			−0.197321	+	0.980339i	$0.563224\pi$
$450$	1.69222	−	2.93102i	0.0797722	−	0.138170i
$451$	6.98101	+	12.0915i	0.328723	+	0.569365i
$452$	47.8742	+	82.9206i	2.25181	+	3.90026i
$453$	10.4923	−	18.1732i	0.492973	−	0.853854i
$454$	−67.6831			−3.17652
$455$	−11.5836	+	18.2155i	−0.543049	+	0.853956i
$456$	−59.6780			−2.79468
$457$	7.96569	−	13.7970i	0.372619	−	0.645395i	−0.617349	−	0.786690i	$-0.711793\pi$
$457$	7.96569	−	13.7970i	0.372619	−	0.645395i	0.989968	+	0.141295i	$0.0451265\pi$
$458$	12.1483	+	21.0415i	0.567653	+	0.983204i
$459$	−0.316198	−	0.547671i	−0.0147589	−	0.0255631i
$460$	5.68338	−	9.84391i	0.264989	−	0.458975i
$461$	−11.6774			−0.543873			−0.271936	−	0.962315i	$-0.587664\pi$
$461$	−11.6774			−0.543873			−0.271936	+	0.962315i	$0.587664\pi$
$462$	9.20690	+	17.6510i	0.428344	+	0.821201i
$463$	−6.74188			−0.313322			−0.156661	−	0.987652i	$-0.550073\pi$
$463$	−6.74188			−0.313322			−0.156661	+	0.987652i	$0.550073\pi$
$464$	−51.3325	+	88.9105i	−2.38305	+	4.12756i
$465$	5.45004	+	9.43975i	0.252740	+	0.437758i
$466$	−3.76801	−	6.52638i	−0.174550	−	0.302329i
$467$	−7.73999	+	13.4061i	−0.358164	+	0.620358i	−0.987654	−	0.156650i	$-0.949931\pi$
$467$	−7.73999	+	13.4061i	−0.358164	+	0.620358i	0.629490	+	0.777009i	$0.283264\pi$
$468$	24.4629			1.13080
$469$	3.85278	+	7.38637i	0.177905	+	0.341071i
$470$	1.59491			0.0735678
$471$	0.797219	−	1.38082i	0.0367339	−	0.0636250i
$472$	−39.3229	−	68.1093i	−1.80999	−	3.13499i
$473$	−2.66922	−	4.62322i	−0.122731	−	0.212576i
$474$	22.1033	−	38.2840i	1.01524	−	1.75844i
$475$	−6.71452			−0.308083
$476$	−5.24144	+	8.24228i	−0.240241	+	0.377784i
$477$	−10.1722			−0.465751
$478$	0.0732912	−	0.126944i	0.00335226	−	0.00580628i
$479$	−9.28598	−	16.0838i	−0.424287	−	0.734887i	0.572066	−	0.820207i	$-0.306142\pi$
$479$	−9.28598	−	16.0838i	−0.424287	−	0.734887i	−0.996354	+	0.0853204i	$0.972809\pi$
$480$	−29.2428	−	50.6501i	−1.33475	−	2.31185i
$481$	−8.62407	+	14.9373i	−0.393224	+	0.681083i
$482$	−0.838629			−0.0381985
$483$	2.64333	+	0.113245i	0.120276	+	0.00515283i
$484$	−22.0458			−1.00208
$485$	−2.87379	+	4.97754i	−0.130492	+	0.226019i
$486$	1.39981	+	2.42454i	0.0634966	+	0.109979i
$487$	−9.08084	−	15.7285i	−0.411492	−	0.712725i	0.583561	−	0.812069i	$-0.301659\pi$
$487$	−9.08084	−	15.7285i	−0.411492	−	0.712725i	−0.995053	+	0.0993441i	$0.968326\pi$
$488$	33.7751	−	58.5002i	1.52893	−	2.64818i
$489$	10.8977			0.492810
$490$	16.1826	+	34.5560i	0.731054	+	1.56108i
$491$	14.1905			0.640410			0.320205	−	0.947348i	$-0.396248\pi$
$491$	14.1905			0.640410			0.320205	+	0.947348i	$0.396248\pi$
$492$	15.1633	−	26.2636i	0.683615	−	1.18406i
$493$	1.76379	+	3.05497i	0.0794371	+	0.137589i
$494$	−32.5798	−	56.4299i	−1.46584	−	2.53890i
$495$	−2.61656	+	4.53202i	−0.117606	+	0.203699i
$496$	−103.034			−4.62637
$497$	−15.8660	−	0.679727i	−0.711685	−	0.0304899i
$498$	−34.9904			−1.56796
$499$	−7.16937	+	12.4177i	−0.320945	+	0.555893i	−0.980683	−	0.195603i	$-0.937334\pi$
$499$	−7.16937	+	12.4177i	−0.320945	+	0.555893i	0.659738	+	0.751495i	$0.270667\pi$
$500$	−35.2875	−	61.1198i	−1.57811	−	2.73336i
$501$	−7.79653	−	13.5040i	−0.348323	−	0.603313i
$502$	8.01878	−	13.8889i	0.357896	−	0.619894i
$503$	10.8254			0.482681			0.241341	−	0.970440i	$-0.422413\pi$
$503$	10.8254			0.482681			0.241341	+	0.970440i	$0.422413\pi$
$504$	15.2544	−	23.9879i	0.679487	−	1.06851i
$505$	24.9251			1.10915
$506$	3.76225	−	6.51640i	0.167252	−	0.289690i
$507$	2.27968	+	3.94851i	0.101244	+	0.175360i
$508$	53.1337	+	92.0303i	2.35743	+	4.08319i
$509$	−13.7751	+	23.8592i	−0.610570	+	1.05754i	0.380574	+	0.924750i	$0.375726\pi$
$509$	−13.7751	+	23.8592i	−0.610570	+	1.05754i	−0.991144	+	0.132788i	$0.957607\pi$
$510$	−3.44723			−0.152646
$511$	16.9621	+	32.5189i	0.750357	+	1.43855i
$512$	157.336			6.95333
$513$	2.77713	−	4.81013i	0.122613	−	0.212372i
$514$	24.1183	+	41.7741i	1.06381	+	1.84257i
$515$	12.7125	+	22.0187i	0.560181	+	0.970262i
$516$	−5.79776	+	10.0420i	−0.255232	+	0.442075i
$517$	0.786382			0.0345850
$518$	14.1001	+	27.0321i	0.619524	+	1.18772i
$519$	11.2721			0.494791
$520$	43.8324	−	75.9200i	1.92218	−	3.32931i
$521$	6.81822	+	11.8095i	0.298712	+	0.517384i	0.975841	−	0.218480i	$-0.0701098\pi$
$521$	6.81822	+	11.8095i	0.298712	+	0.517384i	−0.677130	+	0.735864i	$0.736776\pi$
$522$	−7.80831	−	13.5244i	−0.341760	−	0.591946i
$523$	5.28178	−	9.14831i	0.230956	−	0.400028i	−0.727134	−	0.686496i	$-0.759148\pi$
$523$	5.28178	−	9.14831i	0.230956	−	0.400028i	0.958090	+	0.286468i	$0.0924813\pi$
$524$	−48.6201			−2.12398
$525$	1.71631	−	2.69894i	0.0749061	−	0.117791i
$526$	65.8515			2.87126
$527$	−1.77013	+	3.06596i	−0.0771083	+	0.133555i
$528$	−24.7333	−	42.8394i	−1.07638	−	1.86435i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−27.7246	+	48.0204i	−1.20428	+	2.08587i
$531$	7.31960			0.317644
$532$	−85.7098	−	3.67197i	−3.71599	−	0.159200i
$533$	21.7683			0.942889
$534$	2.53582	−	4.39218i	0.109736	−	0.190068i
$535$	−13.3586	−	23.1377i	−0.577542	−	1.00033i
$536$	−16.9160	−	29.2993i	−0.730658	−	1.26554i
$537$	4.08754	−	7.07983i	0.176390	−	0.305517i
$538$	−38.6606			−1.66678
$539$	7.97893	+	17.0381i	0.343677	+	0.733882i
$540$	11.3668			0.489148
$541$	−15.8326	+	27.4229i	−0.680696	+	1.17900i	0.294072	+	0.955783i	$0.404989\pi$
$541$	−15.8326	+	27.4229i	−0.680696	+	1.17900i	−0.974769	+	0.223218i	$0.928344\pi$
$542$	31.4148	+	54.4121i	1.34938	+	2.33720i
$543$	−1.50047	−	2.59889i	−0.0643914	−	0.111529i
$544$	9.49786	−	16.4508i	0.407217	−	0.705321i
$545$	8.77335			0.375809
$546$	31.0102	+	1.32853i	1.32711	+	0.0568560i
$547$	−30.4882			−1.30358			−0.651792	−	0.758398i	$-0.725982\pi$
$547$	−30.4882			−1.30358			−0.651792	+	0.758398i	$0.725982\pi$
$548$	38.8345	−	67.2633i	1.65893	−	2.87335i
$549$	3.14346	+	5.44464i	0.134160	+	0.232371i
$550$	−4.54817	−	7.87766i	−0.193935	−	0.335905i
$551$	−15.4912	+	26.8315i	−0.659945	+	1.14306i
$552$	−10.7446			−0.457319
$553$	22.4179	−	35.2526i	0.953307	−	1.49909i
$554$	62.2289			2.64385
$555$	−4.00720	+	6.94067i	−0.170096	+	0.294615i
$556$	17.3186	+	29.9967i	0.734472	+	1.27214i
$557$	−7.06138	−	12.2307i	−0.299200	−	0.518230i	0.676753	−	0.736210i	$-0.263387\pi$
$557$	−7.06138	−	12.2307i	−0.299200	−	0.518230i	−0.975953	+	0.217980i	$0.930053\pi$
$558$	7.83639	−	13.5730i	0.331741	−	0.574592i
$559$	−8.32319			−0.352034
$560$	−43.8483	−	84.0640i	−1.85293	−	3.55235i
$561$	−1.69968			−0.0717606
$562$	−9.79418	+	16.9640i	−0.413143	+	0.715584i
$563$	8.64204	+	14.9685i	0.364219	+	0.630845i	0.988650	−	0.150234i	$-0.0480027\pi$
$563$	8.64204	+	14.9685i	0.364219	+	0.630845i	−0.624432	+	0.781079i	$0.714669\pi$
$564$	−0.854041	−	1.47924i	−0.0359616	−	0.0622874i
$565$	−15.9673	+	27.6561i	−0.671748	+	1.16350i
$566$	22.5755			0.948918
$567$	1.22359	+	2.34581i	0.0513860	+	0.0985148i
$568$	64.4917			2.70601
$569$	−1.37078	+	2.37427i	−0.0574662	+	0.0995345i	−0.893327	−	0.449406i	$-0.851635\pi$
$569$	−1.37078	+	2.37427i	−0.0574662	+	0.0995345i	0.835861	+	0.548941i	$0.184969\pi$
$570$	−15.1383	−	26.2203i	−0.634074	−	1.09825i
$571$	−15.5954	−	27.0120i	−0.652647	−	1.13042i	−0.982478	−	0.186377i	$-0.940325\pi$
$571$	−15.5954	−	27.0120i	−0.652647	−	1.13042i	0.329832	−	0.944040i	$-0.393008\pi$
$572$	32.8743	−	56.9400i	1.37454	−	2.38078i
$573$	11.5788			0.483712
$574$	20.6479	−	32.4693i	0.861828	−	1.35524i
$575$	−1.20890			−0.0504145
$576$	−23.6421	+	40.9493i	−0.985088	+	1.70622i
$577$	2.12410	+	3.67904i	0.0884273	+	0.153161i	0.906847	−	0.421461i	$-0.138483\pi$
$577$	2.12410	+	3.67904i	0.0884273	+	0.153161i	−0.818419	+	0.574622i	$0.805149\pi$
$578$	23.2369	+	40.2476i	0.966529	+	1.67408i
$579$	2.84965	−	4.93573i	0.118427	−	0.205122i
$580$	−63.4052			−2.63276
$581$	−33.0370	−	1.41537i	−1.37061	−	0.0587193i
$582$	8.26419			0.342562
$583$	−13.6698	+	23.6768i	−0.566145	+	0.980592i
$584$	−74.4734	−	128.992i	−3.08173	−	5.33771i
$585$	4.07950	+	7.06590i	0.168667	+	0.292139i
$586$	18.4016	−	31.8725i	0.760164	−	1.31664i
$587$	−27.9648			−1.15423			−0.577116	−	0.816662i	$-0.695822\pi$
$587$	−27.9648			−1.15423			−0.577116	+	0.816662i	$0.695822\pi$
$588$	23.3845	−	33.5130i	0.964359	−	1.38205i
$589$	−31.0937			−1.28119
$590$	19.9498	−	34.5541i	0.821321	−	1.42257i
$591$	−6.49415	−	11.2482i	−0.267134	−	0.462689i
$592$	−37.8784	−	65.6074i	−1.55679	−	2.69645i
$593$	12.2413	−	21.2026i	0.502690	−	0.870685i	−0.497305	−	0.867576i	$-0.665677\pi$
$593$	12.2413	−	21.2026i	0.502690	−	0.870685i	0.999995	−	0.00310888i	$-0.000989590\pi$
$594$	7.52450			0.308734
$595$	−3.25479	−	0.139441i	−0.133433	−	0.00571653i
$596$	−28.2007			−1.15515
$597$	−10.6628	+	18.4685i	−0.436398	+	0.755864i
$598$	−5.86574	−	10.1598i	−0.239868	−	0.415464i
$599$	21.9951	+	38.0966i	0.898696	+	1.55659i	0.829163	+	0.559007i	$0.188817\pi$
$599$	21.9951	+	38.0966i	0.898696	+	1.55659i	0.0695327	+	0.997580i	$0.477849\pi$
$600$	−6.49453	+	11.2489i	−0.265138	+	0.459233i
$601$	9.57098			0.390408			0.195204	−	0.980763i	$-0.437463\pi$
$601$	9.57098			0.390408			0.195204	+	0.980763i	$0.437463\pi$
$602$	−7.89482	+	12.4148i	−0.321769	+	0.505989i
$603$	3.14875			0.128227
$604$	−61.2528	+	106.093i	−2.49234	+	4.31686i
$605$	−3.67641	−	6.36774i	−0.149467	−	0.258885i
$606$	−17.9194	−	31.0373i	−0.727926	−	1.26080i
$607$	0.795419	−	1.37771i	0.0322851	−	0.0559194i	−0.849431	−	0.527699i	$-0.823055\pi$
$607$	0.795419	−	1.37771i	0.0322851	−	0.0559194i	0.881716	+	0.471780i	$0.156388\pi$
$608$	166.837			6.76613
$609$	−6.82533	−	13.0852i	−0.276576	−	0.530240i
$610$	34.2705			1.38757
$611$	0.613026	−	1.06179i	0.0248004	−	0.0429555i
$612$	1.84592	+	3.19723i	0.0746169	+	0.129240i
$613$	−8.61461	−	14.9209i	−0.347941	−	0.602651i	0.637943	−	0.770084i	$-0.279786\pi$
$613$	−8.61461	−	14.9209i	−0.347941	−	0.602651i	−0.985883	+	0.167433i	$0.946452\pi$
$614$	−21.1492	+	36.6314i	−0.853511	+	1.47832i
$615$	10.1147			0.407864
$616$	−35.3348	−	67.7423i	−1.42368	−	2.72942i
$617$	−28.9242			−1.16444			−0.582222	−	0.813030i	$-0.697817\pi$
$617$	−28.9242			−1.16444			−0.582222	+	0.813030i	$0.697817\pi$
$618$	18.2788	−	31.6598i	0.735282	−	1.27355i
$619$	10.9323	+	18.9352i	0.439404	+	0.761071i	0.997644	−	0.0686093i	$-0.0218562\pi$
$619$	10.9323	+	18.9352i	0.439404	+	0.761071i	−0.558239	+	0.829680i	$0.688523\pi$
$620$	−31.8166	−	55.1080i	−1.27779	−	2.21319i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	−60.1438			−2.41154
$623$	2.57192	−	4.04440i	0.103042	−	0.162036i
$624$	−77.1238			−3.08742
$625$	8.74704	−	15.1503i	0.349882	−	0.606013i
$626$	−20.7707	−	35.9759i	−0.830164	−	1.43789i
$627$	−7.46405	−	12.9281i	−0.298085	−	0.516299i
$628$	−4.65406	+	8.06107i	−0.185717	+	0.321672i
$629$	−2.60302			−0.103789
$630$	14.4090	+	0.617307i	0.574067	+	0.0245941i
$631$	−11.5152			−0.458412			−0.229206	−	0.973378i	$-0.573613\pi$
$631$	−11.5152			−0.458412			−0.229206	+	0.973378i	$0.573613\pi$
$632$	−84.8293	+	146.929i	−3.37433	+	5.84451i
$633$	3.84595	+	6.66139i	0.152863	+	0.264766i
$634$	6.58152	+	11.3995i	0.261386	+	0.452733i
$635$	−17.7214	+	30.6944i	−0.703254	+	1.21807i
$636$	59.3837			2.35472
$637$	29.2252	+	2.50873i	1.15795	+	0.0993996i
$638$	−41.9725			−1.66171
$639$	−3.00113	+	5.19812i	−0.118723	+	0.205634i
$640$	70.3891	+	121.917i	2.78237	+	4.81921i
$641$	−4.63400	−	8.02633i	−0.183032	−	0.317021i	0.759879	−	0.650064i	$-0.225258\pi$
$641$	−4.63400	−	8.02633i	−0.183032	−	0.317021i	−0.942912	+	0.333043i	$0.891925\pi$
$642$	−19.2077	+	33.2688i	−0.758069	+	1.31301i
$643$	13.8712			0.547025			0.273513	−	0.961868i	$-0.411814\pi$
$643$	13.8712			0.547025			0.273513	+	0.961868i	$0.411814\pi$
$644$	−15.4314	−	0.661109i	−0.608082	−	0.0260514i
$645$	−3.86740			−0.152279
$646$	4.91681	−	8.51617i	0.193449	−	0.335064i
$647$	3.65031	+	6.32253i	0.143509	+	0.248564i	0.928816	−	0.370542i	$-0.120828\pi$
$647$	3.65031	+	6.32253i	0.143509	+	0.248564i	−0.785307	+	0.619107i	$0.787495\pi$
$648$	−5.37228	−	9.30506i	−0.211043	−	0.365537i
$649$	9.83640	−	17.0371i	0.386112	−	0.668766i
$650$	−14.1822			−0.556270
$651$	7.94794	−	12.4983i	0.311504	−	0.489847i
$652$	−63.6191			−2.49152
$653$	14.1389	−	24.4892i	0.553296	−	0.958337i	−0.444737	−	0.895661i	$-0.646703\pi$
$653$	14.1389	−	24.4892i	0.553296	−	0.958337i	0.998034	−	0.0626765i	$-0.0199636\pi$
$654$	−6.30742	−	10.9248i	−0.246639	−	0.427192i
$655$	−8.10802	−	14.0435i	−0.316806	−	0.548725i
$656$	−47.8051	+	82.8008i	−1.86648	+	3.23283i
$657$	13.8625			0.540829
$658$	−1.00228	−	1.92153i	−0.0390730	−	0.0749090i
$659$	26.3606			1.02686			0.513431	−	0.858131i	$-0.328374\pi$
$659$	26.3606			1.02686			0.513431	+	0.858131i	$0.328374\pi$
$660$	15.2751	−	26.4573i	0.594584	−	1.02985i
$661$	8.46466	+	14.6612i	0.329237	+	0.570255i	0.982361	−	0.186996i	$-0.0598751\pi$
$661$	8.46466	+	14.6612i	0.329237	+	0.570255i	−0.653124	+	0.757251i	$0.726542\pi$
$662$	11.0286	+	19.1021i	0.428638	+	0.742423i
$663$	−1.32499	+	2.29495i	−0.0514584	+	0.0891286i
$664$	134.288			5.21140
$665$	−13.2326	−	25.3689i	−0.513138	−	0.983764i
$666$	11.5236			0.446529
$667$	−2.78906	+	4.83079i	−0.107993	+	0.187049i
$668$	45.5151	+	78.8344i	1.76103	+	3.05020i
$669$	10.4845	+	18.1596i	0.405353	+	0.702091i
$670$	8.58202	−	14.8645i	0.331552	−	0.574266i
$671$	16.8973			0.652312
$672$	−42.6456	+	67.0611i	−1.64509	+	2.58694i
$673$	−23.7746			−0.916444			−0.458222	−	0.888838i	$-0.651513\pi$
$673$	−23.7746			−0.916444			−0.458222	+	0.888838i	$0.651513\pi$
$674$	25.7365	−	44.5770i	0.991334	−	1.71704i
$675$	−0.604448	−	1.04694i	−0.0232652	−	0.0402966i
$676$	−13.3084	−	23.0509i	−0.511863	−	0.886573i
$677$	−11.3542	+	19.6661i	−0.436377	+	0.755828i	−0.997407	−	0.0719679i	$-0.977072\pi$
$677$	−11.3542	+	19.6661i	−0.436377	+	0.755828i	0.561030	+	0.827796i	$0.310405\pi$
$678$	45.9173			1.76344
$679$	7.80283	+	0.334288i	0.299445	+	0.0128288i
$680$	13.2300			0.507348
$681$	−12.0879	+	20.9369i	−0.463210	+	0.802302i
$682$	−21.0618	−	36.4800i	−0.806496	−	1.39689i
$683$	−5.42079	−	9.38908i	−0.207421	−	0.359263i	0.743481	−	0.668757i	$-0.233174\pi$
$683$	−5.42079	−	9.38908i	−0.207421	−	0.359263i	−0.950901	+	0.309494i	$0.899840\pi$
$684$	−16.2125	+	28.0809i	−0.619900	+	1.07370i
$685$	25.9046			0.989762
$686$	31.4631	−	41.2124i	1.20127	−	1.57350i
$687$	8.67855			0.331107
$688$	18.2785	−	31.6593i	0.696861	−	1.20700i
$689$	21.3127	+	36.9146i	0.811948	+	1.40633i
$690$	−2.72553	−	4.72076i	−0.103759	−	0.179716i
$691$	−7.50102	+	12.9921i	−0.285352	+	0.494245i	−0.972695	−	0.232089i	$-0.925444\pi$
$691$	−7.50102	+	12.9921i	−0.285352	+	0.494245i	0.687342	+	0.726334i	$0.258777\pi$
$692$	−65.8050			−2.50153
$693$	7.10443	+	0.304367i	0.269875	+	0.0115620i
$694$	16.8559			0.639841
$695$	−5.77619	+	10.0047i	−0.219103	+	0.379498i
$696$	29.9672	+	51.9047i	1.13590	+	1.96744i
$697$	1.64259	+	2.84505i	0.0622175	+	0.107764i
$698$	−18.6704	+	32.3380i	−0.706684	+	1.22401i
$699$	−2.69180			−0.101813
$700$	−10.0196	+	15.7561i	−0.378706	+	0.595523i
$701$	−8.60412			−0.324973			−0.162486	−	0.986711i	$-0.551951\pi$
$701$	−8.60412			−0.324973			−0.162486	+	0.986711i	$0.551951\pi$
$702$	5.86574	−	10.1598i	0.221388	−	0.383456i
$703$	−11.4310	−	19.7990i	−0.431128	−	0.746735i
$704$	63.5425	+	110.059i	2.39485	+	4.14800i
$705$	0.284844	−	0.493365i	0.0107279	−	0.0185812i
$706$	48.9569			1.84252
$707$	−15.6636	−	30.0295i	−0.589089	−	1.12937i
$708$	−42.7308			−1.60592
$709$	14.5604	−	25.2194i	0.546829	−	0.947135i	−0.451661	−	0.892190i	$-0.649168\pi$
$709$	14.5604	−	25.2194i	0.546829	−	0.947135i	0.998489	−	0.0549454i	$-0.0174985\pi$
$710$	16.3594	+	28.3353i	0.613957	+	1.06340i
$711$	−7.89510	−	13.6747i	−0.296089	−	0.512842i
$712$	−9.73215	+	16.8566i	−0.364728	+	0.631727i
$713$	−5.59818			−0.209654
$714$	2.16633	+	4.15318i	0.0810727	+	0.155429i
$715$	21.9288			0.820092
$716$	−23.8625	+	41.3311i	−0.891784	+	1.54462i
$717$	−0.0261790	−	0.0453433i	−0.000977672	−	0.00169338i
$718$	11.9925	+	20.7716i	0.447556	+	0.775189i
$719$	7.65789	−	13.2639i	0.285591	−	0.494658i	−0.687161	−	0.726505i	$-0.741143\pi$
$719$	7.65789	−	13.2639i	0.285591	−	0.494658i	0.972752	+	0.231847i	$0.0744767\pi$
$720$	−35.8358			−1.33552
$721$	18.5390	−	29.1530i	0.690429	−	1.08571i
$722$	33.1748			1.23464
$723$	−0.149776	+	0.259419i	−0.00557021	+	0.00964789i
$724$	8.75955	+	15.1720i	0.325546	+	0.563863i
$725$	3.37169	+	5.83993i	0.125221	+	0.216890i
$726$	−5.28616	+	9.15590i	−0.196188	+	0.339807i
$727$	32.6484			1.21086			0.605432	−	0.795897i	$-0.293000\pi$
$727$	32.6484			1.21086			0.605432	+	0.795897i	$0.293000\pi$
$728$	−119.013	−	5.09873i	−4.41091	−	0.188972i
$729$	1.00000			0.0370370
$730$	37.7828	−	65.4417i	1.39840	−	2.42211i
$731$	−0.628051	−	1.08782i	−0.0232293	−	0.0402343i
$732$	−18.3511	−	31.7850i	−0.678276	−	1.17481i
$733$	21.7266	−	37.6316i	0.802490	−	1.38995i	−0.115482	−	0.993310i	$-0.536841\pi$
$733$	21.7266	−	37.6316i	0.802490	−	1.38995i	0.917972	−	0.396644i	$-0.129825\pi$
$734$	−55.1848			−2.03691
$735$	13.5796	+	1.16569i	0.500891	+	0.0429971i
$736$	30.0377			1.10720
$737$	4.23142	−	7.32904i	0.155867	−	0.269969i
$738$	−7.27175	−	12.5950i	−0.267677	−	0.463630i
$739$	−1.74434	−	3.02129i	−0.0641667	−	0.111140i	0.832157	−	0.554540i	$-0.187106\pi$
$739$	−1.74434	−	3.02129i	−0.0641667	−	0.111140i	−0.896324	+	0.443400i	$0.853772\pi$
$740$	23.3935	−	40.5187i	0.859961	−	1.48950i
$741$	−23.2745			−0.855010
$742$	75.2771	+	3.22501i	2.76351	+	0.118394i
$743$	22.0130			0.807577			0.403789	−	0.914852i	$-0.367693\pi$
$743$	22.0130			0.807577			0.403789	+	0.914852i	$0.367693\pi$
$744$	−30.0750	+	52.0914i	−1.10260	+	1.90976i
$745$	−4.70283	−	8.14554i	−0.172298	−	0.298430i
$746$	−30.6920	−	53.1601i	−1.12371	−	1.94633i
$747$	−6.24913	+	10.8238i	−0.228644	+	0.396023i
$748$	9.92251			0.362803
$749$	−19.4812	+	30.6346i	−0.711827	+	1.11936i
$750$	−33.8451			−1.23585
$751$	−7.71696	+	13.3662i	−0.281596	+	0.487739i	−0.971778	−	0.235897i	$-0.924197\pi$
$751$	−7.71696	+	13.3662i	−0.281596	+	0.487739i	0.690182	+	0.723636i	$0.257530\pi$
$752$	2.69252	+	4.66358i	0.0981862	+	0.170063i
$753$	−2.86424	−	4.96101i	−0.104379	−	0.180789i
$754$	−32.7198	+	56.6724i	−1.19159	+	2.06389i
$755$	−40.8587			−1.48700
$756$	−7.14315	−	13.6945i	−0.259794	−	0.498065i
$757$	−13.1778			−0.478955			−0.239478	−	0.970902i	$-0.576976\pi$
$757$	−13.1778			−0.478955			−0.239478	+	0.970902i	$0.576976\pi$
$758$	−13.8573	+	24.0016i	−0.503321	+	0.871777i
$759$	−1.34384	−	2.32760i	−0.0487784	−	0.0844867i
$760$	58.0988	+	100.630i	2.10747	+	3.65024i
$761$	−5.35343	+	9.27241i	−0.194062	+	0.336125i	−0.946592	−	0.322432i	$-0.895499\pi$
$761$	−5.35343	+	9.27241i	−0.194062	+	0.336125i	0.752531	+	0.658557i	$0.228833\pi$
$762$	50.9618			1.84615
$763$	−5.51339	−	10.5700i	−0.199598	−	0.382660i
$764$	−67.5956			−2.44552
$765$	−0.615661	+	1.06636i	−0.0222593	+	0.0385542i
$766$	24.5497	+	42.5213i	0.887015	+	1.53636i
$767$	−15.3360	−	26.5627i	−0.553750	−	0.959124i
$768$	53.9253	−	93.4014i	1.94586	−	3.37033i
$769$	30.1544			1.08739			0.543697	−	0.839282i	$-0.317024\pi$
$769$	30.1544			1.08739			0.543697	+	0.839282i	$0.317024\pi$
$770$	20.8002	−	32.7088i	0.749588	−	1.17874i
$771$	17.2297			0.620512
$772$	−16.6358	+	28.8141i	−0.598737	+	1.03704i
$773$	−23.1191	−	40.0435i	−0.831537	−	1.44026i	−0.896819	−	0.442398i	$-0.854128\pi$
$773$	−23.1191	−	40.0435i	−0.831537	−	1.44026i	0.0652818	−	0.997867i	$-0.479205\pi$
$774$	2.78038	+	4.81577i	0.0999388	+	0.173099i
$775$	−3.38381	+	5.86093i	−0.121550	+	0.210531i
$776$	−31.7169			−1.13857
$777$	10.8802	+	0.466130i	0.390327	+	0.0167223i
$778$	53.8860			1.93191
$779$	−14.4267	+	24.9877i	−0.516889	+	0.895277i
$780$	−23.8156	−	41.2498i	−0.852734	−	1.47698i
$781$	8.06611	+	13.9709i	0.288628	+	0.499918i
$782$	0.885234	−	1.53327i	0.0316559	−	0.0548296i
$783$	−5.57812			−0.199346
$784$	−73.7238	+	105.656i	−2.63299	+	3.77342i
$785$	−3.10449			−0.110804
$786$	−11.6582	+	20.1926i	−0.415834	+	0.720245i
$787$	−18.3653	−	31.8096i	−0.654651	−	1.13389i	−0.981981	−	0.188978i	$-0.939482\pi$
$787$	−18.3653	−	31.8096i	−0.654651	−	1.13389i	0.327330	−	0.944910i	$-0.393851\pi$
$788$	37.9120	+	65.6655i	1.35056	+	2.33924i
$789$	11.7608	−	20.3703i	0.418695	−	0.725202i
$790$	−86.0734			−3.06236
$791$	43.3539	+	1.85736i	1.54149	+	0.0660403i
$792$	−28.8780			−1.02614
$793$	13.1723	−	22.8151i	0.467763	−	0.810189i
$794$	34.4345	+	59.6423i	1.22203	+	2.11662i
$795$	9.90299	+	17.1525i	0.351223	+	0.608336i
$796$	62.2478	−	107.816i	2.20631	−	3.82145i
$797$	−32.2468			−1.14224			−0.571120	−	0.820867i	$-0.693491\pi$
$797$	−32.2468			−1.14224			−0.571120	+	0.820867i	$0.693491\pi$
$798$	−22.0766	+	34.7159i	−0.781504	+	1.22893i
$799$	0.185031			0.00654592
$800$	18.1562	−	31.4475i	0.641920	−	1.11184i
$801$	−0.905775	−	1.56885i	−0.0320040	−	0.0554325i
$802$	11.0377	+	19.1178i	0.389753	+	0.675073i
$803$	18.6291	−	32.2665i	0.657405	−	1.13866i
$804$	−18.3820			−0.648282
$805$	−2.38242	−	4.56747i	−0.0839694	−	0.160982i
$806$	−65.6750			−2.31330
$807$	−6.90462	+	11.9592i	−0.243054	+	0.420982i
$808$	68.7722	+	119.117i	2.41940	+	4.19052i
$809$	−3.40031	−	5.88951i	−0.119548	−	0.207064i	0.800040	−	0.599946i	$-0.204811\pi$
$809$	−3.40031	−	5.88951i	−0.119548	−	0.207064i	−0.919589	+	0.392882i	$0.871478\pi$
$810$	2.72553	−	4.72076i	0.0957655	−	0.165871i
$811$	−32.1358			−1.12844			−0.564220	−	0.825625i	$-0.690823\pi$
$811$	−32.1358			−1.12844			−0.564220	+	0.825625i	$0.690823\pi$
$812$	39.8454	+	76.3897i	1.39830	+	2.68075i
$813$	22.4422			0.787083
$814$	15.4859	−	26.8223i	0.542779	−	0.940121i
$815$	−10.6093	−	18.3758i	−0.371627	−	0.643677i
$816$	−5.81960	−	10.0799i	−0.203727	−	0.352865i
$817$	5.51609	−	9.55416i	0.192984	−	0.334258i
$818$	13.4571			0.470517
$819$	5.94925	−	9.35532i	0.207883	−	0.326901i
$820$	−59.0482			−2.06205
$821$	15.3962	−	26.6670i	0.537331	−	0.930684i	−0.461716	−	0.887028i	$-0.652766\pi$
$821$	15.3962	−	26.6670i	0.537331	−	0.930684i	0.999047	−	0.0436564i	$-0.0139007\pi$
$822$	−18.6235	−	32.2569i	−0.649571	−	1.12509i
$823$	27.6175	+	47.8350i	0.962687	+	1.66742i	0.715705	+	0.698402i	$0.246105\pi$
$823$	27.6175	+	47.8350i	0.962687	+	1.66742i	0.246981	+	0.969020i	$0.420561\pi$
$824$	−70.1516	+	121.506i	−2.44385	+	4.23287i
$825$	−3.24913			−0.113120
$826$	−54.1673	−	2.32063i	−1.88472	−	0.0807450i
$827$	25.1429			0.874303			0.437152	−	0.899388i	$-0.355987\pi$
$827$	25.1429			0.874303			0.437152	+	0.899388i	$0.355987\pi$
$828$	−2.91893	+	5.05574i	−0.101440	+	0.175699i
$829$	−9.89887	−	17.1453i	−0.343802	−	0.595482i	0.641333	−	0.767262i	$-0.278382\pi$
$829$	−9.89887	−	17.1453i	−0.343802	−	0.595482i	−0.985135	+	0.171780i	$0.945048\pi$
$830$	34.0645	+	59.0014i	1.18239	+	2.04797i
$831$	11.1138	−	19.2497i	0.385534	−	0.667765i
$832$	198.139			6.86924
$833$	1.87739	+	4.00895i	0.0650478	+	0.138902i
$834$	16.6107			0.575181
$835$	−15.1804	+	26.2933i	−0.525340	+	0.909916i
$836$	43.5741	+	75.4726i	1.50704	+	2.61027i
$837$	−2.79909	−	4.84817i	−0.0967507	−	0.167577i
$838$	−6.12153	+	10.6028i	−0.211465	+	0.366268i
$839$	32.6430			1.12696			0.563480	−	0.826130i	$-0.309462\pi$
$839$	32.6430			1.12696			0.563480	+	0.826130i	$0.309462\pi$
$840$	−55.2996	−	2.36914i	−1.90802	−	0.0817431i
$841$	2.11543			0.0729458
$842$	21.9622	−	38.0396i	0.756866	−	1.31093i
$843$	3.49840	+	6.05940i	0.120491	+	0.208697i
$844$	−22.4522	−	38.8883i	−0.772835	−	1.33859i
$845$	4.43870	−	7.68805i	0.152696	−	0.264477i
$846$	−0.819132			−0.0281623
$847$	−5.36141	+	8.43094i	−0.184220	+	0.289690i
$848$	−187.218			−6.42909
$849$	4.03188	−	6.98343i	0.138374	−	0.239671i
$850$	−1.07016	−	1.85356i	−0.0367061	−	0.0635768i
$851$	−2.05806	−	3.56466i	−0.0705494	−	0.122195i
$852$	17.5202	−	30.3459i	0.600233	−	1.03963i
$853$	50.0984			1.71534			0.857668	−	0.514204i	$-0.171913\pi$
$853$	50.0984			1.71534			0.857668	+	0.514204i	$0.171913\pi$
$854$	−21.5364	−	41.2886i	−0.736960	−	1.41287i
$855$	−10.8146			−0.369850
$856$	73.7167	−	127.681i	2.51959	−	4.36405i
$857$	−1.80216	−	3.12143i	−0.0615605	−	0.106626i	0.833603	−	0.552365i	$-0.186274\pi$
$857$	−1.80216	−	3.12143i	−0.0615605	−	0.106626i	−0.895163	+	0.445739i	$0.852941\pi$
$858$	−15.7653	−	27.3063i	−0.538218	−	0.932220i
$859$	−2.20328	+	3.81619i	−0.0751749	+	0.130207i	−0.901162	−	0.433482i	$-0.857285\pi$
$859$	−2.20328	+	3.81619i	−0.0751749	+	0.130207i	0.825987	+	0.563689i	$0.190618\pi$
$860$	22.5773			0.769881
$861$	−6.35632	−	12.1860i	−0.216623	−	0.415299i
$862$	−9.36845			−0.319091
$863$	−23.5854	+	40.8511i	−0.802857	+	1.39059i	0.114871	+	0.993380i	$0.463354\pi$
$863$	−23.5854	+	40.8511i	−0.802857	+	1.39059i	−0.917728	+	0.397209i	$0.869979\pi$
$864$	15.0188	+	26.0134i	0.510951	+	0.884994i
$865$	−10.9738	−	19.0072i	−0.373121	−	0.646265i
$866$	21.3154	−	36.9193i	0.724325	−	1.25457i
$867$	16.6001			0.563768
$868$	−46.3990	+	72.9634i	−1.57489	+	2.47654i
$869$	−42.4391			−1.43965
$870$	−15.2034	+	26.3330i	−0.515442	+	0.892772i
$871$	−6.59724	−	11.4268i	−0.223539	−	0.387181i
$872$	24.2070	+	41.9278i	0.819753	+	1.41985i
$873$	1.47595	−	2.55642i	0.0499533	−	0.0865217i
$874$	15.5498			0.525980
$875$	−31.9557	−	1.36904i	−1.08030	−	0.0462820i
$876$	−80.9276			−2.73429
$877$	−20.5203	+	35.5421i	−0.692920	+	1.20017i	0.277957	+	0.960594i	$0.410343\pi$
$877$	−20.5203	+	35.5421i	−0.692920	+	1.20017i	−0.970877	+	0.239579i	$0.922991\pi$
$878$	−30.0839	−	52.1069i	−1.01528	−	1.75852i
$879$	−6.57290	−	11.3846i	−0.221699	−	0.383993i
$880$	−48.1577	+	83.4116i	−1.62340	+	2.81180i
$881$	50.3825			1.69743			0.848715	−	0.528851i	$-0.177377\pi$
$881$	50.3825			1.69743			0.848715	+	0.528851i	$0.177377\pi$
$882$	−8.31122	−	17.7476i	−0.279853	−	0.597594i
$883$	7.65081			0.257470			0.128735	−	0.991679i	$-0.458908\pi$
$883$	7.65081			0.257470			0.128735	+	0.991679i	$0.458908\pi$
$884$	7.73513	−	13.3976i	0.260160	−	0.450611i
$885$	−7.12591	−	12.3424i	−0.239535	−	0.414886i
$886$	−33.2938	−	57.6666i	−1.11853	−	1.93735i
$887$	18.6564	−	32.3138i	0.626421	−	1.08499i	−0.361843	−	0.932239i	$-0.617852\pi$
$887$	18.6564	−	32.3138i	0.626421	−	1.08499i	0.988264	−	0.152754i	$-0.0488142\pi$
$888$	−44.2259			−1.48412
$889$	48.1168	+	2.06142i	1.61379	+	0.0691377i
$890$	−9.87488			−0.331007
$891$	1.34384	−	2.32760i	0.0450204	−	0.0779777i
$892$	−61.2068	−	106.013i	−2.04936	−	3.54959i
$893$	0.812551	+	1.40738i	0.0271910	+	0.0470962i
$894$	−6.76200	+	11.7121i	−0.226155	+	0.391712i
$895$	−15.9175			−0.532064
$896$	102.650	−	161.420i	3.42931	−	5.39266i
$897$	−4.19039			−0.139913
$898$	11.7057	−	20.2748i	0.390623	−	0.676578i
$899$	15.6137	+	27.0437i	0.520745	+	0.901957i
$900$	3.52869	+	6.11187i	0.117623	+	0.203729i
$901$	−3.21642	+	5.57100i	−0.107154	+	0.185597i
$902$	−39.0883			−1.30150
$903$	2.43037	+	4.65939i	0.0808775	+	0.155055i
$904$	−176.225			−5.86114
$905$	−2.92153	+	5.06024i	−0.0971150	+	0.168208i
$906$	29.3745	+	50.8782i	0.975903	+	1.69031i
$907$	−25.0612	−	43.4073i	−0.832144	−	1.44132i	−0.896335	−	0.443378i	$-0.853780\pi$
$907$	−25.0612	−	43.4073i	−0.832144	−	1.44132i	0.0641906	−	0.997938i	$-0.479553\pi$
$908$	70.5676	−	122.227i	2.34187	−	4.05623i
$909$	−12.8013			−0.424593
$910$	−27.9494	−	53.5832i	−0.926512	−	1.77627i
$911$	33.1001			1.09666			0.548328	−	0.836264i	$-0.315265\pi$
$911$	33.1001			1.09666			0.548328	+	0.836264i	$0.315265\pi$
$912$	51.1129	−	88.5301i	1.69252	−	2.93152i
$913$	16.7957	+	29.0910i	0.555857	+	0.962772i
$914$	22.3009	+	38.6263i	0.737648	+	1.27764i
$915$	6.12056	−	10.6011i	0.202339	−	0.350462i
$916$	−50.6642			−1.67399
$917$	−11.8241	+	18.5937i	−0.390468	+	0.614018i
$918$	1.77047			0.0584341
$919$	22.9767	−	39.7968i	0.757931	−	1.31278i	−0.185972	−	0.982555i	$-0.559543\pi$
$919$	22.9767	−	39.7968i	0.757931	−	1.31278i	0.943904	−	0.330221i	$-0.107123\pi$
$920$	10.4602	+	18.1177i	0.344864	+	0.597321i
$921$	7.55430	+	13.0844i	0.248923	+	0.431147i
$922$	16.3462	−	28.3124i	0.538333	−	0.932420i
$923$	25.1518			0.827883
$924$	−41.4747	−	1.77685i	−1.36442	−	0.0584542i
$925$	−4.97596			−0.163609
$926$	9.43735	−	16.3460i	0.310131	−	0.537162i
$927$	−6.52904	−	11.3086i	−0.214442	−	0.371424i
$928$	−83.7769	−	145.106i	−2.75011	−	4.76333i
$929$	11.2680	−	19.5168i	0.369692	−	0.640325i	−0.619826	−	0.784740i	$-0.712797\pi$
$929$	11.2680	−	19.5168i	0.369692	−	0.640325i	0.989517	+	0.144415i	$0.0461300\pi$
$930$	−30.5161			−1.00066
$931$	−22.2484	+	31.8849i	−0.729163	+	1.04498i
$932$	15.7144			0.514741
$933$	−10.7414	+	18.6047i	−0.351658	+	0.609090i
$934$	−21.6690	−	37.5319i	−0.709032	−	1.22808i
$935$	1.65470	+	2.86603i	0.0541146	+	0.0937293i
$936$	−22.5119	+	38.9918i	−0.735826	+	1.27449i
$937$	−20.5555			−0.671520			−0.335760	−	0.941948i	$-0.608993\pi$
$937$	−20.5555			−0.671520			−0.335760	+	0.941948i	$0.608993\pi$
$938$	−23.3017	−	0.998289i	−0.760828	−	0.0325953i
$939$	−14.8382			−0.484227
$940$	−1.66288	+	2.88020i	−0.0542373	+	0.0939417i
$941$	19.9421	+	34.5407i	0.650093	+	1.12599i	0.983100	+	0.183070i	$0.0586034\pi$
$941$	19.9421	+	34.5407i	0.650093	+	1.12599i	−0.333007	+	0.942924i	$0.608063\pi$
$942$	2.23191	+	3.86578i	0.0727196	+	0.125954i
$943$	−2.59741	+	4.49884i	−0.0845832	+	0.146502i
$944$	134.717			4.38466
$945$	2.76433	−	4.34697i	0.0899238	−	0.141407i
$946$	14.9456			0.485923
$947$	−1.36901	+	2.37120i	−0.0444869	+	0.0770536i	−0.887411	−	0.460978i	$-0.847499\pi$
$947$	−1.36901	+	2.37120i	−0.0444869	+	0.0770536i	0.842925	+	0.538032i	$0.180832\pi$
$948$	46.0905	+	79.8311i	1.49695	+	2.59279i
$949$	−29.0447	−	50.3069i	−0.942830	−	1.63303i
$950$	9.39905	−	16.2796i	0.304945	−	0.528181i
$951$	4.70173			0.152464
$952$	−8.31407	−	15.9394i	−0.269461	−	0.516597i
$953$	20.6225			0.668027			0.334014	−	0.942568i	$-0.391597\pi$
$953$	20.6225			0.668027			0.334014	+	0.942568i	$0.391597\pi$
$954$	14.2391	−	24.6628i	0.461008	−	0.798489i
$955$	−11.2724	−	19.5244i	−0.364767	−	0.631795i
$956$	0.152829	+	0.264708i	0.00494285	+	0.00856127i
$957$	−7.49612	+	12.9837i	−0.242315	+	0.419702i
$958$	51.9944			1.67986
$959$	−16.2791	−	31.2095i	−0.525678	−	1.00781i
$960$	92.0659			2.97141
$961$	−0.169823	+	0.294143i	−0.00547817	+	0.00948847i
$962$	−24.1441	−	41.8188i	−0.778437	−	1.34829i
$963$	6.86084	+	11.8833i	0.221088	+	0.382935i
$964$	0.874370	−	1.51445i	0.0281615	−	0.0487772i
$965$	−11.0969			−0.357223
$966$	−3.97472	+	6.25033i	−0.127885	+	0.201101i
$967$	46.6896			1.50144			0.750719	−	0.660622i	$-0.229707\pi$
$967$	46.6896			1.50144			0.750719	+	0.660622i	$0.229707\pi$
$968$	20.2876	−	35.1391i	0.652067	−	1.12941i
$969$	−1.75624	−	3.04190i	−0.0564187	−	0.0977201i
$970$	−8.04550	−	13.9352i	−0.258326	−	0.447433i
$971$	19.9032	−	34.4733i	0.638723	−	1.10630i	−0.346991	−	0.937869i	$-0.612796\pi$
$971$	19.9032	−	34.4733i	0.638723	−	1.10630i	0.985713	−	0.168432i	$-0.0538702\pi$
$972$	−5.83786			−0.187250
$973$	15.6834	+	0.671905i	0.502786	+	0.0215403i
$974$	50.8458			1.62920
$975$	−2.53287	+	4.38706i	−0.0811169	+	0.140499i
$976$	57.8552	+	100.208i	1.85190	+	3.20759i
$977$	16.1499	+	27.9725i	0.516683	+	0.894921i	0.999812	+	0.0193718i	$0.00616661\pi$
$977$	16.1499	+	27.9725i	0.516683	+	0.894921i	−0.483130	+	0.875549i	$0.660500\pi$
$978$	−15.2547	+	26.4218i	−0.487790	+	0.844877i
$979$	−4.86888			−0.155610
$980$	−79.2758	−	6.80514i	−2.53237	−	0.217382i
$981$	−4.50591			−0.143863
$982$	−19.8641	+	34.4056i	−0.633887	+	1.09793i
$983$	−28.5393	−	49.4314i	−0.910261	−	1.57662i	−0.813696	−	0.581291i	$-0.802548\pi$
$983$	−28.5393	−	49.4314i	−0.910261	−	1.57662i	−0.0965653	−	0.995327i	$-0.530786\pi$
$984$	27.9080	+	48.3380i	0.889674	+	1.54096i
$985$	−12.6446	+	21.9011i	−0.402891	+	0.697827i
$986$	−9.87588			−0.314512
$987$	−0.773403	−	0.0331340i	−0.0246177	−	0.00105467i
$988$	135.873			4.32271
$989$	0.993129	−	1.72015i	0.0315797	−	0.0546976i
$990$	−7.32538	−	12.6879i	−0.232816	−	0.403249i
$991$	18.5164	+	32.0714i	0.588193	+	1.01878i	0.994469	+	0.105030i	$0.0334938\pi$
$991$	18.5164	+	32.0714i	0.588193	+	1.01878i	−0.406276	+	0.913750i	$0.633173\pi$
$992$	84.0782	−	145.628i	2.66949	−	4.62369i
$993$	7.87864			0.250021
$994$	23.8573	−	37.5162i	0.756709	−	1.18994i
$995$	41.5224			1.31635
$996$	36.4816	−	63.1880i	1.15596	−	2.00219i
$997$	23.5094	+	40.7195i	0.744550	+	1.28960i	0.950405	+	0.311016i	$0.100669\pi$
$997$	23.5094	+	40.7195i	0.744550	+	1.28960i	−0.205855	+	0.978583i	$0.565997\pi$
$998$	−20.0715	−	34.7648i	−0.635352	−	1.10046i
$999$	2.05806	−	3.56466i	0.0651141	−	0.112781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.415.1	yes	20
7.2	even	3		3381.2.a.bi.1.10		10
7.4	even	3	inner	483.2.i.h.277.1	✓	20
7.5	odd	6		3381.2.a.bj.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.1	✓	20	7.4	even	3	inner
483.2.i.h.415.1	yes	20	1.1	even	1	trivial
3381.2.a.bi.1.10		10	7.2	even	3
3381.2.a.bj.1.10		10	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)

\(f(q)\)	\(=\)	\(q+(-1.39981 + 2.42454i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.91893 - 5.05574i) q^{4} +(0.973538 - 1.68622i) q^{5} -2.79962 q^{6} +(-2.64333 - 0.113245i) q^{7} +10.7446 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.39981 + 2.42454i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.91893 - 5.05574i) q^{4} +(0.973538 - 1.68622i) q^{5} -2.79962 q^{6} +(-2.64333 - 0.113245i) q^{7} +10.7446 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.72553 + 4.72076i) q^{10} +(1.34384 + 2.32760i) q^{11} +(2.91893 - 5.05574i) q^{12} +4.19039 q^{13} +(3.97472 - 6.25033i) q^{14} +1.94708 q^{15} +(-9.20247 + 15.9391i) q^{16} +(0.316198 + 0.547671i) q^{17} +(-1.39981 - 2.42454i) q^{18} +(-2.77713 + 4.81013i) q^{19} -11.3668 q^{20} +(-1.22359 - 2.34581i) q^{21} -7.52450 q^{22} +(-0.500000 + 0.866025i) q^{23} +(5.37228 + 9.30506i) q^{24} +(0.604448 + 1.04694i) q^{25} +(-5.86574 + 10.1598i) q^{26} -1.00000 q^{27} +(7.14315 + 13.6945i) q^{28} +5.57812 q^{29} +(-2.72553 + 4.72076i) q^{30} +(2.79909 + 4.84817i) q^{31} +(-15.0188 - 26.0134i) q^{32} +(-1.34384 + 2.32760i) q^{33} -1.77047 q^{34} +(-2.76433 + 4.34697i) q^{35} +5.83786 q^{36} +(-2.05806 + 3.56466i) q^{37} +(-7.77490 - 13.4665i) q^{38} +(2.09519 + 3.62898i) q^{39} +(10.4602 - 18.1177i) q^{40} +5.19481 q^{41} +(7.40031 + 0.317043i) q^{42} -1.98626 q^{43} +(7.84517 - 13.5882i) q^{44} +(0.973538 + 1.68622i) q^{45} +(-1.39981 - 2.42454i) q^{46} +(0.146293 - 0.253388i) q^{47} -18.4049 q^{48} +(6.97435 + 0.598687i) q^{49} -3.38445 q^{50} +(-0.316198 + 0.547671i) q^{51} +(-12.2315 - 21.1855i) q^{52} +(5.08608 + 8.80935i) q^{53} +(1.39981 - 2.42454i) q^{54} +5.23313 q^{55} +(-28.4014 - 1.21677i) q^{56} -5.55426 q^{57} +(-7.80831 + 13.5244i) q^{58} +(-3.65980 - 6.33896i) q^{59} +(-5.68338 - 9.84391i) q^{60} +(3.14346 - 5.44464i) q^{61} -15.6728 q^{62} +(1.41974 - 2.23257i) q^{63} +47.2842 q^{64} +(4.07950 - 7.06590i) q^{65} +(-3.76225 - 6.51640i) q^{66} +(-1.57437 - 2.72690i) q^{67} +(1.84592 - 3.19723i) q^{68} -1.00000 q^{69} +(-6.66987 - 12.7872i) q^{70} +6.00227 q^{71} +(-5.37228 + 9.30506i) q^{72} +(-6.93126 - 12.0053i) q^{73} +(-5.76178 - 9.97970i) q^{74} +(-0.604448 + 1.04694i) q^{75} +32.4250 q^{76} +(-3.28863 - 6.30480i) q^{77} -11.7315 q^{78} +(-7.89510 + 13.6747i) q^{79} +(17.9179 + 31.0347i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.27175 + 12.5950i) q^{82} +12.4983 q^{83} +(-8.28823 + 13.0334i) q^{84} +1.23132 q^{85} +(2.78038 - 4.81577i) q^{86} +(2.78906 + 4.83079i) q^{87} +(14.4390 + 25.0091i) q^{88} +(-0.905775 + 1.56885i) q^{89} -5.45107 q^{90} +(-11.0766 - 0.474541i) q^{91} +5.83786 q^{92} +(-2.79909 + 4.84817i) q^{93} +(0.409566 + 0.709389i) q^{94} +(5.40728 + 9.36568i) q^{95} +(15.0188 - 26.0134i) q^{96} -2.95190 q^{97} +(-11.2143 + 16.0716i) q^{98} -2.68769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Introduction

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