LMFDB - Embedded newform 210.3.l.b.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(43,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.l (of order $4$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.3
Root			$3.76660 + 3.76660i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.b.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.294013 + 4.99135i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.294013 + 4.99135i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(4.69734 - 5.28536i) q^{10} -3.32459 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.80162 + 7.80162i) q^{13} +3.74166i q^{14} +(-6.47322 - 5.75304i) q^{15} -4.00000 q^{16} +(-13.6628 - 13.6628i) q^{17} +(-3.00000 + 3.00000i) q^{18} -37.1623i q^{19} +(-9.98270 + 0.588026i) q^{20} +4.58258 q^{21} +(3.32459 + 3.32459i) q^{22} +(-31.5017 + 31.5017i) q^{23} +4.89898i q^{24} +(-24.8271 + 2.93504i) q^{25} +15.6032 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +55.3464i q^{29} +(0.720182 + 12.2263i) q^{30} -4.54280 q^{31} +(4.00000 + 4.00000i) q^{32} +(4.07177 - 4.07177i) q^{33} +27.3257i q^{34} +(8.78791 - 9.88801i) q^{35} +6.00000 q^{36} +(-46.8661 - 46.8661i) q^{37} +(-37.1623 + 37.1623i) q^{38} -19.1100i q^{39} +(10.5707 + 9.39467i) q^{40} +9.94537 q^{41} +(-4.58258 - 4.58258i) q^{42} +(23.0431 - 23.0431i) q^{43} -6.64917i q^{44} +(14.9740 - 0.882039i) q^{45} +63.0035 q^{46} +(-6.38149 - 6.38149i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(27.7622 + 21.8921i) q^{50} +33.4670 q^{51} +(-15.6032 - 15.6032i) q^{52} +(-42.9239 + 42.9239i) q^{53} -7.34847i q^{54} +(-0.977472 - 16.5942i) q^{55} -7.48331 q^{56} +(45.5143 + 45.5143i) q^{57} +(55.3464 - 55.3464i) q^{58} -59.2884i q^{59} +(11.5061 - 12.9464i) q^{60} +47.1648 q^{61} +(4.54280 + 4.54280i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(-41.2344 - 36.6468i) q^{65} -8.14354 q^{66} +(8.48975 + 8.48975i) q^{67} +(27.3257 - 27.3257i) q^{68} -77.1632i q^{69} +(-18.6759 + 1.10010i) q^{70} +85.6769 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-34.7848 + 34.7848i) q^{73} +93.7322i q^{74} +(26.8122 - 34.0016i) q^{75} +74.3246 q^{76} +(6.21973 + 6.21973i) q^{77} +(-19.1100 + 19.1100i) q^{78} +96.4868i q^{79} +(-1.17605 - 19.9654i) q^{80} -9.00000 q^{81} +(-9.94537 - 9.94537i) q^{82} +(19.6272 - 19.6272i) q^{83} +9.16515i q^{84} +(64.1789 - 72.2131i) q^{85} -46.0863 q^{86} +(-67.7852 - 67.7852i) q^{87} +(-6.64917 + 6.64917i) q^{88} +43.0279i q^{89} +(-15.8561 - 14.0920i) q^{90} +29.1910 q^{91} +(-63.0035 - 63.0035i) q^{92} +(5.56377 - 5.56377i) q^{93} +12.7630i q^{94} +(185.490 - 10.9262i) q^{95} -9.79796 q^{96} +(88.5610 + 88.5610i) q^{97} +(7.00000 - 7.00000i) q^{98} +9.97376i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	0.294013	+	4.99135i	0.0588026	+	0.998270i
$5$	0.294013	+	4.99135i	0.0588026	+	0.998270i
$6$	2.44949			0.408248
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	4.69734	−	5.28536i	0.469734	−	0.528536i
$11$	−3.32459			−0.302235			−0.151118	−	0.988516i	$-0.548287\pi$
$11$	−3.32459			−0.302235			−0.151118	+	0.988516i	$0.548287\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	−7.80162	+	7.80162i	−0.600124	+	0.600124i	−0.940345	−	0.340221i	$-0.889498\pi$
$13$	−7.80162	+	7.80162i	−0.600124	+	0.600124i	0.340221	+	0.940345i	$0.389498\pi$
$14$			3.74166i			0.267261i
$15$	−6.47322	−	5.75304i	−0.431548	−	0.383536i
$16$	−4.00000			−0.250000
$17$	−13.6628	−	13.6628i	−0.803697	−	0.803697i	0.179975	−	0.983671i	$-0.442398\pi$
$17$	−13.6628	−	13.6628i	−0.803697	−	0.803697i	−0.983671	+	0.179975i	$0.942398\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	37.1623i		−	1.95591i	−0.208817	−	0.977955i	$-0.566961\pi$
$19$		−	37.1623i		−	1.95591i	0.208817	−	0.977955i	$-0.433039\pi$
$20$	−9.98270	+	0.588026i	−0.499135	+	0.0294013i
$21$	4.58258			0.218218
$22$	3.32459	+	3.32459i	0.151118	+	0.151118i
$23$	−31.5017	+	31.5017i	−1.36964	+	1.36964i	−0.508693	+	0.860948i	$0.669871\pi$
$23$	−31.5017	+	31.5017i	−1.36964	+	1.36964i	−0.860948	+	0.508693i	$0.830129\pi$
$24$			4.89898i			0.204124i
$25$	−24.8271	+	2.93504i	−0.993085	+	0.117402i
$26$	15.6032			0.600124
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	3.74166	−	3.74166i	0.133631	−	0.133631i
$29$			55.3464i			1.90850i	0.299016	+	0.954248i	$0.403342\pi$
$29$			55.3464i			1.90850i	−0.299016	+	0.954248i	$0.596658\pi$
$30$	0.720182	+	12.2263i	0.0240061	+	0.407542i
$31$	−4.54280			−0.146542			−0.0732710	−	0.997312i	$-0.523344\pi$
$31$	−4.54280			−0.146542			−0.0732710	+	0.997312i	$0.523344\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	4.07177	−	4.07177i	0.123387	−	0.123387i
$34$			27.3257i			0.803697i
$35$	8.78791	−	9.88801i	0.251083	−	0.282514i
$36$	6.00000			0.166667
$37$	−46.8661	−	46.8661i	−1.26665	−	1.26665i	−0.947807	−	0.318843i	$-0.896706\pi$
$37$	−46.8661	−	46.8661i	−1.26665	−	1.26665i	−0.318843	−	0.947807i	$-0.603294\pi$
$38$	−37.1623	+	37.1623i	−0.977955	+	0.977955i
$39$		−	19.1100i		−	0.489999i
$40$	10.5707	+	9.39467i	0.264268	+	0.234867i
$41$	9.94537			0.242570			0.121285	−	0.992618i	$-0.461298\pi$
$41$	9.94537			0.242570			0.121285	+	0.992618i	$0.461298\pi$
$42$	−4.58258	−	4.58258i	−0.109109	−	0.109109i
$43$	23.0431	−	23.0431i	0.535887	−	0.535887i	−0.386431	−	0.922318i	$-0.626292\pi$
$43$	23.0431	−	23.0431i	0.535887	−	0.535887i	0.922318	+	0.386431i	$0.126292\pi$
$44$		−	6.64917i		−	0.151118i
$45$	14.9740	−	0.882039i	0.332757	−	0.0196009i
$46$	63.0035			1.36964
$47$	−6.38149	−	6.38149i	−0.135776	−	0.135776i	0.635952	−	0.771728i	$-0.280608\pi$
$47$	−6.38149	−	6.38149i	−0.135776	−	0.135776i	−0.771728	+	0.635952i	$0.780608\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			7.00000i			0.142857i
$50$	27.7622	+	21.8921i	0.555243	+	0.437841i
$51$	33.4670			0.656216
$52$	−15.6032	−	15.6032i	−0.300062	−	0.300062i
$53$	−42.9239	+	42.9239i	−0.809885	+	0.809885i	−0.984616	−	0.174731i	$-0.944094\pi$
$53$	−42.9239	+	42.9239i	−0.809885	+	0.809885i	0.174731	+	0.984616i	$0.444094\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−0.977472	−	16.5942i	−0.0177722	−	0.301712i
$56$	−7.48331			−0.133631
$57$	45.5143	+	45.5143i	0.798497	+	0.798497i
$58$	55.3464	−	55.3464i	0.954248	−	0.954248i
$59$		−	59.2884i		−	1.00489i	−0.864610	−	0.502444i	$-0.832434\pi$
$59$		−	59.2884i		−	1.00489i	0.864610	−	0.502444i	$-0.167566\pi$
$60$	11.5061	−	12.9464i	0.191768	−	0.215774i
$61$	47.1648			0.773193			0.386596	−	0.922249i	$-0.373651\pi$
$61$	47.1648			0.773193			0.386596	+	0.922249i	$0.373651\pi$
$62$	4.54280	+	4.54280i	0.0732710	+	0.0732710i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	8.00000i		−	0.125000i
$65$	−41.2344	−	36.6468i	−0.634375	−	0.563797i
$66$	−8.14354			−0.123387
$67$	8.48975	+	8.48975i	0.126713	+	0.126713i	0.767619	−	0.640906i	$-0.221441\pi$
$67$	8.48975	+	8.48975i	0.126713	+	0.126713i	−0.640906	+	0.767619i	$0.721441\pi$
$68$	27.3257	−	27.3257i	0.401848	−	0.401848i
$69$		−	77.1632i		−	1.11831i
$70$	−18.6759	+	1.10010i	−0.266799	+	0.0157157i
$71$	85.6769			1.20672			0.603358	−	0.797470i	$-0.293829\pi$
$71$	85.6769			1.20672			0.603358	+	0.797470i	$0.293829\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−34.7848	+	34.7848i	−0.476505	+	0.476505i	−0.904012	−	0.427507i	$-0.859392\pi$
$73$	−34.7848	+	34.7848i	−0.476505	+	0.476505i	0.427507	+	0.904012i	$0.359392\pi$
$74$			93.7322i			1.26665i
$75$	26.8122	−	34.0016i	0.357496	−	0.453354i
$76$	74.3246			0.977955
$77$	6.21973	+	6.21973i	0.0807757	+	0.0807757i
$78$	−19.1100	+	19.1100i	−0.245000	+	0.245000i
$79$			96.4868i			1.22135i	0.791880	+	0.610676i	$0.209102\pi$
$79$			96.4868i			1.22135i	−0.791880	+	0.610676i	$0.790898\pi$
$80$	−1.17605	−	19.9654i	−0.0147006	−	0.249567i
$81$	−9.00000			−0.111111
$82$	−9.94537	−	9.94537i	−0.121285	−	0.121285i
$83$	19.6272	−	19.6272i	0.236472	−	0.236472i	−0.578915	−	0.815388i	$-0.696524\pi$
$83$	19.6272	−	19.6272i	0.236472	−	0.236472i	0.815388	+	0.578915i	$0.196524\pi$
$84$			9.16515i			0.109109i
$85$	64.1789	−	72.2131i	0.755046	−	0.849565i
$86$	−46.0863			−0.535887
$87$	−67.7852	−	67.7852i	−0.779140	−	0.779140i
$88$	−6.64917	+	6.64917i	−0.0755588	+	0.0755588i
$89$			43.0279i			0.483460i	0.970344	+	0.241730i	$0.0777148\pi$
$89$			43.0279i			0.483460i	−0.970344	+	0.241730i	$0.922285\pi$
$90$	−15.8561	−	14.0920i	−0.176179	−	0.156578i
$91$	29.1910			0.320780
$92$	−63.0035	−	63.0035i	−0.684820	−	0.684820i
$93$	5.56377	−	5.56377i	0.0598255	−	0.0598255i
$94$			12.7630i			0.135776i
$95$	185.490	−	10.9262i	1.95252	−	0.115013i
$96$	−9.79796			−0.102062
$97$	88.5610	+	88.5610i	0.913000	+	0.913000i	0.996507	−	0.0835068i	$-0.0266120\pi$
$97$	88.5610	+	88.5610i	0.913000	+	0.913000i	−0.0835068	+	0.996507i	$0.526612\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$			9.97376i			0.100745i
$100$	−5.87008	−	49.6542i	−0.0587008	−	0.496542i
$101$	−101.113			−1.00112			−0.500558	−	0.865703i	$-0.666872\pi$
$101$	−101.113			−1.00112			−0.500558	+	0.865703i	$0.666872\pi$
$102$	−33.4670	−	33.4670i	−0.328108	−	0.328108i
$103$	−48.7475	+	48.7475i	−0.473276	+	0.473276i	−0.902973	−	0.429697i	$-0.858620\pi$
$103$	−48.7475	+	48.7475i	−0.473276	+	0.473276i	0.429697	+	0.902973i	$0.358620\pi$
$104$			31.2065i			0.300062i
$105$	1.34734	+	22.8732i	0.0128318	+	0.217840i
$106$	85.8479			0.809885
$107$	−11.0826	−	11.0826i	−0.103576	−	0.103576i	0.653420	−	0.756996i	$-0.273334\pi$
$107$	−11.0826	−	11.0826i	−0.103576	−	0.103576i	−0.756996	+	0.653420i	$0.773334\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	1.00349i		−	0.00920630i	−0.999989	−	0.00460315i	$-0.998535\pi$
$109$		−	1.00349i		−	0.00920630i	0.999989	−	0.00460315i	$-0.00146523\pi$
$110$	−15.6167	+	17.5716i	−0.141970	+	0.159742i
$111$	114.798			1.03422
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	−129.405	+	129.405i	−1.14517	+	1.14517i	−0.157683	+	0.987490i	$0.550402\pi$
$113$	−129.405	+	129.405i	−1.14517	+	1.14517i	−0.987490	+	0.157683i	$0.949598\pi$
$114$		−	91.0286i		−	0.798497i
$115$	−166.498	−	147.974i	−1.44781	−	1.28673i
$116$	−110.693			−0.954248
$117$	23.4048	+	23.4048i	0.200041	+	0.200041i
$118$	−59.2884	+	59.2884i	−0.502444	+	0.502444i
$119$			51.1217i			0.429594i
$120$	−24.4525	+	1.44036i	−0.203771	+	0.0120030i
$121$	−109.947			−0.908654
$122$	−47.1648	−	47.1648i	−0.386596	−	0.386596i
$123$	−12.1805	+	12.1805i	−0.0990288	+	0.0990288i
$124$		−	9.08560i		−	0.0732710i
$125$	−21.9493	−	123.058i	−0.175594	−	0.984463i
$126$	11.2250			0.0890871
$127$	124.878	+	124.878i	0.983289	+	0.983289i	0.999863	−	0.0165736i	$-0.00527577\pi$
$127$	124.878	+	124.878i	0.983289	+	0.983289i	−0.0165736	+	0.999863i	$0.505276\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			56.4439i			0.437550i
$130$	4.58755	+	77.8812i	0.0352889	+	0.599086i
$131$	137.486			1.04951			0.524754	−	0.851254i	$-0.324157\pi$
$131$	137.486			1.04951			0.524754	+	0.851254i	$0.324157\pi$
$132$	8.14354	+	8.14354i	0.0616935	+	0.0616935i
$133$	−69.5243	+	69.5243i	−0.522739	+	0.522739i
$134$		−	16.9795i		−	0.126713i
$135$	−17.2591	+	19.4197i	−0.127845	+	0.143849i
$136$	−54.6514			−0.401848
$137$	69.9065	+	69.9065i	0.510267	+	0.510267i	0.914608	−	0.404341i	$-0.132499\pi$
$137$	69.9065	+	69.9065i	0.510267	+	0.510267i	−0.404341	+	0.914608i	$0.632499\pi$
$138$	−77.1632	+	77.1632i	−0.559154	+	0.559154i
$139$			121.192i			0.871888i	0.899974	+	0.435944i	$0.143585\pi$
$139$			121.192i			0.871888i	−0.899974	+	0.435944i	$0.856415\pi$
$140$	19.7760	+	17.5758i	0.141257	+	0.125542i
$141$	15.6314			0.110861
$142$	−85.6769	−	85.6769i	−0.603358	−	0.603358i
$143$	25.9372	−	25.9372i	0.181379	−	0.181379i
$144$			12.0000i			0.0833333i
$145$	−276.253	+	16.2726i	−1.90519	+	0.112225i
$146$	69.5697			0.476505
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	93.7322	−	93.7322i	0.633325	−	0.633325i
$149$			131.094i			0.879823i	0.898041	+	0.439911i	$0.144990\pi$
$149$			131.094i			0.879823i	−0.898041	+	0.439911i	$0.855010\pi$
$150$	−60.8138	+	7.18936i	−0.405425	+	0.0479290i
$151$	−105.336			−0.697586			−0.348793	−	0.937200i	$-0.613408\pi$
$151$	−105.336			−0.697586			−0.348793	+	0.937200i	$0.613408\pi$
$152$	−74.3246	−	74.3246i	−0.488977	−	0.488977i
$153$	−40.9885	+	40.9885i	−0.267899	+	0.267899i
$154$		−	12.4395i		−	0.0807757i
$155$	−1.33564	−	22.6747i	−0.00861705	−	0.146288i
$156$	38.2200			0.245000
$157$	−34.7788	−	34.7788i	−0.221521	−	0.221521i	0.587618	−	0.809139i	$-0.300066\pi$
$157$	−34.7788	−	34.7788i	−0.221521	−	0.221521i	−0.809139	+	0.587618i	$0.800066\pi$
$158$	96.4868	−	96.4868i	0.610676	−	0.610676i
$159$		−	105.142i		−	0.661269i
$160$	−18.7893	+	21.1414i	−0.117433	+	0.132134i
$161$	117.869			0.732104
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	71.0414	−	71.0414i	0.435837	−	0.435837i	−0.454771	−	0.890608i	$-0.650279\pi$
$163$	71.0414	−	71.0414i	0.435837	−	0.435837i	0.890608	+	0.454771i	$0.150279\pi$
$164$			19.8907i			0.121285i
$165$	21.5208	+	19.1265i	0.130429	+	0.115918i
$166$	−39.2544			−0.236472
$167$	−155.443	−	155.443i	−0.930797	−	0.930797i	0.0669588	−	0.997756i	$-0.478670\pi$
$167$	−155.443	−	155.443i	−0.930797	−	0.930797i	−0.997756	+	0.0669588i	$0.978670\pi$
$168$	9.16515	−	9.16515i	0.0545545	−	0.0545545i
$169$			47.2696i			0.279702i
$170$	−136.392	+	8.03411i	−0.802306	+	0.0472594i
$171$	−111.487			−0.651970
$172$	46.0863	+	46.0863i	0.267944	+	0.267944i
$173$	−16.5518	+	16.5518i	−0.0956751	+	0.0956751i	−0.753324	−	0.657649i	$-0.771551\pi$
$173$	−16.5518	+	16.5518i	−0.0956751	+	0.0956751i	0.657649	+	0.753324i	$0.271551\pi$
$174$			135.570i			0.779140i
$175$	51.9382	+	40.9563i	0.296790	+	0.234036i
$176$	13.2983			0.0755588
$177$	72.6131	+	72.6131i	0.410244	+	0.410244i
$178$	43.0279	−	43.0279i	0.241730	−	0.241730i
$179$		−	184.541i		−	1.03096i	−0.856903	−	0.515478i	$-0.827614\pi$
$179$		−	184.541i		−	1.03096i	0.856903	−	0.515478i	$-0.172386\pi$
$180$	1.76408	+	29.9481i	0.00980043	+	0.166378i
$181$	−73.9362			−0.408488			−0.204244	−	0.978920i	$-0.565474\pi$
$181$	−73.9362			−0.408488			−0.204244	+	0.978920i	$0.565474\pi$
$182$	−29.1910	−	29.1910i	−0.160390	−	0.160390i
$183$	−57.7648	+	57.7648i	−0.315655	+	0.315655i
$184$			126.007i			0.684820i
$185$	220.146	−	247.704i	1.18998	−	1.33894i
$186$	−11.1275			−0.0598255
$187$	45.4233	+	45.4233i	0.242905	+	0.242905i
$188$	12.7630	−	12.7630i	0.0678882	−	0.0678882i
$189$		−	13.7477i		−	0.0727393i
$190$	−196.416	−	174.564i	−1.03377	−	0.918756i
$191$	−255.605			−1.33825			−0.669123	−	0.743152i	$-0.733330\pi$
$191$	−255.605			−1.33825			−0.669123	+	0.743152i	$0.733330\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	153.794	−	153.794i	0.796858	−	0.796858i	−0.185741	−	0.982599i	$-0.559468\pi$
$193$	153.794	−	153.794i	0.796858	−	0.796858i	0.982599	+	0.185741i	$0.0594684\pi$
$194$		−	177.122i		−	0.913000i
$195$	95.3846	−	5.61858i	0.489152	−	0.0288132i
$196$	−14.0000			−0.0714286
$197$	132.071	+	132.071i	0.670411	+	0.670411i	0.957811	−	0.287400i	$-0.0927908\pi$
$197$	132.071	+	132.071i	0.670411	+	0.670411i	−0.287400	+	0.957811i	$0.592791\pi$
$198$	9.97376	−	9.97376i	0.0503725	−	0.0503725i
$199$		−	223.530i		−	1.12327i	−0.827387	−	0.561633i	$-0.810173\pi$
$199$		−	223.530i		−	1.12327i	0.827387	−	0.561633i	$-0.189827\pi$
$200$	−43.7841	+	55.5243i	−0.218921	+	0.277622i
$201$	−20.7956			−0.103460
$202$	101.113	+	101.113i	0.500558	+	0.500558i
$203$	103.544	−	103.544i	0.510067	−	0.510067i
$204$			66.9340i			0.328108i
$205$	2.92407	+	49.6408i	0.0142638	+	0.242150i
$206$	97.4950			0.473276
$207$	94.5052	+	94.5052i	0.456547	+	0.456547i
$208$	31.2065	−	31.2065i	0.150031	−	0.150031i
$209$			123.549i			0.591145i
$210$	21.5259	−	24.2206i	0.102504	−	0.115336i
$211$	−122.409			−0.580137			−0.290069	−	0.957006i	$-0.593678\pi$
$211$	−122.409			−0.580137			−0.290069	+	0.957006i	$0.593678\pi$
$212$	−85.8479	−	85.8479i	−0.404943	−	0.404943i
$213$	−104.932	+	104.932i	−0.492640	+	0.492640i
$214$			22.1652i			0.103576i
$215$	121.791	+	108.241i	0.566471	+	0.503448i
$216$	14.6969			0.0680414
$217$	8.49880	+	8.49880i	0.0391650	+	0.0391650i
$218$	−1.00349	+	1.00349i	−0.00460315	+	0.00460315i
$219$		−	85.2051i		−	0.389064i
$220$	33.1883	−	1.95494i	0.150856	−	0.00888611i
$221$	213.185			0.964636
$222$	−114.798	−	114.798i	−0.517108	−	0.517108i
$223$	139.840	−	139.840i	0.627083	−	0.627083i	−0.320250	−	0.947333i	$-0.603767\pi$
$223$	139.840	−	139.840i	0.627083	−	0.627083i	0.947333	+	0.320250i	$0.103767\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	8.80513	+	74.4813i	0.0391339	+	0.331028i
$226$	258.809			1.14517
$227$	−61.8255	−	61.8255i	−0.272359	−	0.272359i	0.557690	−	0.830049i	$-0.311688\pi$
$227$	−61.8255	−	61.8255i	−0.272359	−	0.272359i	−0.830049	+	0.557690i	$0.811688\pi$
$228$	−91.0286	+	91.0286i	−0.399248	+	0.399248i
$229$			145.539i			0.635540i	0.948168	+	0.317770i	$0.102934\pi$
$229$			145.539i			0.635540i	−0.948168	+	0.317770i	$0.897066\pi$
$230$	18.5238	+	314.472i	0.0805384	+	1.36727i
$231$	−15.2352			−0.0659531
$232$	110.693	+	110.693i	0.477124	+	0.477124i
$233$	78.2015	−	78.2015i	0.335629	−	0.335629i	−0.519090	−	0.854719i	$-0.673729\pi$
$233$	78.2015	−	78.2015i	0.335629	−	0.335629i	0.854719	+	0.519090i	$0.173729\pi$
$234$		−	46.8097i		−	0.200041i
$235$	29.9760	−	33.7285i	0.127557	−	0.143525i
$236$	118.577			0.502444
$237$	−118.172	−	118.172i	−0.498615	−	0.498615i
$238$	51.1217	−	51.1217i	0.214797	−	0.214797i
$239$		−	183.007i		−	0.765720i	−0.923806	−	0.382860i	$-0.874939\pi$
$239$		−	183.007i		−	0.765720i	0.923806	−	0.382860i	$-0.125061\pi$
$240$	25.8929	+	23.0121i	0.107887	+	0.0958840i
$241$	39.6298			0.164439			0.0822194	−	0.996614i	$-0.473799\pi$
$241$	39.6298			0.164439			0.0822194	+	0.996614i	$0.473799\pi$
$242$	109.947	+	109.947i	0.454327	+	0.454327i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			94.3295i			0.386596i
$245$	−34.9394	+	2.05809i	−0.142610	+	0.00840037i
$246$	24.3611			0.0990288
$247$	289.926	+	289.926i	1.17379	+	1.17379i
$248$	−9.08560	+	9.08560i	−0.0366355	+	0.0366355i
$249$			48.0766i			0.193079i
$250$	−101.109	+	145.007i	−0.404434	+	0.580029i
$251$	−15.9671			−0.0636141			−0.0318070	−	0.999494i	$-0.510126\pi$
$251$	−15.9671			−0.0636141			−0.0318070	+	0.999494i	$0.510126\pi$
$252$	−11.2250	−	11.2250i	−0.0445435	−	0.0445435i
$253$	104.730	−	104.730i	0.413954	−	0.413954i
$254$		−	249.755i		−	0.983289i
$255$	9.83973	+	167.045i	0.0385872	+	0.655080i
$256$	16.0000			0.0625000
$257$	59.0712	+	59.0712i	0.229849	+	0.229849i	0.812630	−	0.582781i	$-0.198035\pi$
$257$	59.0712	+	59.0712i	0.229849	+	0.229849i	−0.582781	+	0.812630i	$0.698035\pi$
$258$	56.4439	−	56.4439i	0.218775	−	0.218775i
$259$			175.357i			0.677053i
$260$	73.2936	−	82.4687i	0.281899	−	0.317187i
$261$	166.039			0.636165
$262$	−137.486	−	137.486i	−0.524754	−	0.524754i
$263$	186.291	−	186.291i	0.708330	−	0.708330i	−0.257854	−	0.966184i	$-0.583015\pi$
$263$	186.291	−	186.291i	0.708330	−	0.708330i	0.966184	+	0.257854i	$0.0830153\pi$
$264$		−	16.2871i		−	0.0616935i
$265$	−226.868	−	201.628i	−0.856107	−	0.760861i
$266$	139.049			0.522739
$267$	−52.6982	−	52.6982i	−0.197372	−	0.197372i
$268$	−16.9795	+	16.9795i	−0.0633563	+	0.0633563i
$269$			120.015i			0.446153i	0.974801	+	0.223077i	$0.0716100\pi$
$269$			120.015i			0.446153i	−0.974801	+	0.223077i	$0.928390\pi$
$270$	36.6788	−	2.16055i	0.135847	−	0.00800202i
$271$	−457.758			−1.68914			−0.844571	−	0.535444i	$-0.820144\pi$
$271$	−457.758			−1.68914			−0.844571	+	0.535444i	$0.820144\pi$
$272$	54.6514	+	54.6514i	0.200924	+	0.200924i
$273$	−35.7515	+	35.7515i	−0.130958	+	0.130958i
$274$		−	139.813i		−	0.510267i
$275$	82.5399	−	9.75780i	0.300145	−	0.0354829i
$276$	154.326			0.559154
$277$	2.98510	+	2.98510i	0.0107766	+	0.0107766i	0.712475	−	0.701698i	$-0.247574\pi$
$277$	2.98510	+	2.98510i	0.0107766	+	0.0107766i	−0.701698	+	0.712475i	$0.747574\pi$
$278$	121.192	−	121.192i	0.435944	−	0.435944i
$279$			13.6284i			0.0488473i
$280$	−2.20019	−	37.3518i	−0.00785783	−	0.133399i
$281$	−196.044			−0.697666			−0.348833	−	0.937185i	$-0.613422\pi$
$281$	−196.044			−0.697666			−0.348833	+	0.937185i	$0.613422\pi$
$282$	−15.6314	−	15.6314i	−0.0554305	−	0.0554305i
$283$	−226.011	+	226.011i	−0.798627	+	0.798627i	−0.982879	−	0.184252i	$-0.941014\pi$
$283$	−226.011	+	226.011i	−0.798627	+	0.798627i	0.184252	+	0.982879i	$0.441014\pi$
$284$			171.354i			0.603358i
$285$	−213.796	+	240.560i	−0.750161	+	0.844069i
$286$	−51.8743			−0.181379
$287$	−18.6061	−	18.6061i	−0.0648296	−	0.0648296i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$			84.3465i			0.291856i
$290$	292.526	+	259.981i	1.00871	+	0.896485i
$291$	−216.929			−0.745462
$292$	−69.5697	−	69.5697i	−0.238252	−	0.238252i
$293$	−106.875	+	106.875i	−0.364762	+	0.364762i	−0.865563	−	0.500801i	$-0.833039\pi$
$293$	−106.875	+	106.875i	−0.364762	+	0.364762i	0.500801	+	0.865563i	$0.333039\pi$
$294$			17.1464i			0.0583212i
$295$	295.929	−	17.4316i	1.00315	−	0.0590900i
$296$	−187.464			−0.633325
$297$	−12.2153	−	12.2153i	−0.0411290	−	0.0411290i
$298$	131.094	−	131.094i	0.439911	−	0.439911i
$299$		−	491.529i		−	1.64391i
$300$	68.0031	+	53.6244i	0.226677	+	0.178748i
$301$	−86.2196			−0.286444
$302$	105.336	+	105.336i	0.348793	+	0.348793i
$303$	123.837	−	123.837i	0.408704	−	0.408704i
$304$			148.649i			0.488977i
$305$	13.8671	+	235.416i	0.0454658	+	0.771855i
$306$	81.9771			0.267899
$307$	−169.042	−	169.042i	−0.550624	−	0.550624i	0.375997	−	0.926621i	$-0.377300\pi$
$307$	−169.042	−	169.042i	−0.550624	−	0.550624i	−0.926621	+	0.375997i	$0.877300\pi$
$308$	−12.4395	+	12.4395i	−0.0403879	+	0.0403879i
$309$		−	119.406i		−	0.386429i
$310$	−21.3391	+	24.0103i	−0.0688357	+	0.0774527i
$311$	184.053			0.591810			0.295905	−	0.955217i	$-0.404379\pi$
$311$	184.053			0.591810			0.295905	+	0.955217i	$0.404379\pi$
$312$	−38.2200	−	38.2200i	−0.122500	−	0.122500i
$313$	208.497	−	208.497i	0.666124	−	0.666124i	−0.290692	−	0.956817i	$-0.593886\pi$
$313$	208.497	−	208.497i	0.666124	−	0.666124i	0.956817	+	0.290692i	$0.0938856\pi$
$314$			69.5576i			0.221521i
$315$	−29.6640	−	26.3637i	−0.0941715	−	0.0836944i
$316$	−192.974			−0.610676
$317$	−403.707	−	403.707i	−1.27352	−	1.27352i	−0.944227	−	0.329296i	$-0.893189\pi$
$317$	−403.707	−	403.707i	−1.27352	−	1.27352i	−0.329296	−	0.944227i	$-0.606811\pi$
$318$	−105.142	+	105.142i	−0.330634	+	0.330634i
$319$		−	184.004i		−	0.576815i
$320$	39.9308	−	2.35210i	0.124784	−	0.00735032i
$321$	27.1467			0.0845691
$322$	−117.869	−	117.869i	−0.366052	−	0.366052i
$323$	−507.742	+	507.742i	−1.57196	+	1.57196i
$324$		−	18.0000i		−	0.0555556i
$325$	170.794	−	216.590i	0.525519	−	0.666430i
$326$	−142.083			−0.435837
$327$	1.22901	+	1.22901i	0.00375846	+	0.00375846i
$328$	19.8907	−	19.8907i	0.0606425	−	0.0606425i
$329$			23.8773i			0.0725755i
$330$	−2.39431	−	40.6473i	−0.00725548	−	0.123173i
$331$	−26.7859			−0.0809241			−0.0404620	−	0.999181i	$-0.512883\pi$
$331$	−26.7859			−0.0809241			−0.0404620	+	0.999181i	$0.512883\pi$
$332$	39.2544	+	39.2544i	0.118236	+	0.118236i
$333$	−140.598	+	140.598i	−0.422217	+	0.422217i
$334$			310.886i			0.930797i
$335$	−39.8792	+	44.8714i	−0.119042	+	0.133944i
$336$	−18.3303			−0.0545545
$337$	325.031	+	325.031i	0.964485	+	0.964485i	0.999391	−	0.0349056i	$-0.0111130\pi$
$337$	325.031	+	325.031i	0.964485	+	0.964485i	−0.0349056	+	0.999391i	$0.511113\pi$
$338$	47.2696	−	47.2696i	0.139851	−	0.139851i
$339$		−	316.975i		−	0.935030i
$340$	144.426	+	128.358i	0.424783	+	0.377523i
$341$	15.1029			0.0442901
$342$	111.487	+	111.487i	0.325985	+	0.325985i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$		−	92.1726i		−	0.267944i
$345$	385.148	−	22.6870i	1.11637	−	0.0657594i
$346$	33.1036			0.0956751
$347$	−119.676	−	119.676i	−0.344887	−	0.344887i	0.513314	−	0.858201i	$-0.328418\pi$
$347$	−119.676	−	119.676i	−0.344887	−	0.344887i	−0.858201	+	0.513314i	$0.828418\pi$
$348$	135.570	−	135.570i	0.389570	−	0.389570i
$349$		−	592.030i		−	1.69636i	−0.529708	−	0.848180i	$-0.677698\pi$
$349$		−	592.030i		−	1.69636i	0.529708	−	0.848180i	$-0.322302\pi$
$350$	−10.9819	−	92.8945i	−0.0313769	−	0.265413i
$351$	−57.3299			−0.163333
$352$	−13.2983	−	13.2983i	−0.0377794	−	0.0377794i
$353$	92.2147	−	92.2147i	0.261231	−	0.261231i	−0.564323	−	0.825554i	$-0.690863\pi$
$353$	92.2147	−	92.2147i	0.261231	−	0.261231i	0.825554	+	0.564323i	$0.190863\pi$
$354$		−	145.226i		−	0.410244i
$355$	25.1901	+	427.643i	0.0709581	+	1.20463i
$356$	−86.0558			−0.241730
$357$	−62.6110	−	62.6110i	−0.175381	−	0.175381i
$358$	−184.541	+	184.541i	−0.515478	+	0.515478i
$359$			464.557i			1.29403i	0.762477	+	0.647016i	$0.223983\pi$
$359$			464.557i			1.29403i	−0.762477	+	0.647016i	$0.776017\pi$
$360$	28.1840	−	31.7122i	0.0782889	−	0.0880894i
$361$	−1020.03			−2.82558
$362$	73.9362	+	73.9362i	0.204244	+	0.204244i
$363$	134.657	−	134.657i	0.370956	−	0.370956i
$364$			58.3820i			0.160390i
$365$	−183.850	−	163.396i	−0.503700	−	0.447660i
$366$	115.530			0.315655
$367$	450.255	+	450.255i	1.22685	+	1.22685i	0.965148	+	0.261705i	$0.0842847\pi$
$367$	450.255	+	450.255i	1.22685	+	1.22685i	0.261705	+	0.965148i	$0.415715\pi$
$368$	126.007	−	126.007i	0.342410	−	0.342410i
$369$		−	29.8361i		−	0.0808567i
$370$	−467.850	+	27.5585i	−1.26446	+	0.0744824i
$371$	160.607			0.432902
$372$	11.1275	+	11.1275i	0.0299128	+	0.0299128i
$373$	447.933	−	447.933i	1.20089	−	1.20089i	0.226997	−	0.973895i	$-0.427109\pi$
$373$	447.933	−	447.933i	1.20089	−	1.20089i	0.973895	−	0.226997i	$-0.0728907\pi$
$374$		−	90.8466i		−	0.242905i
$375$	177.597	+	123.832i	0.473591	+	0.330219i
$376$	−25.5259			−0.0678882
$377$	−431.791	−	431.791i	−1.14534	−	1.14534i
$378$	−13.7477	+	13.7477i	−0.0363696	+	0.0363696i
$379$		−	200.204i		−	0.528242i	−0.964490	−	0.264121i	$-0.914918\pi$
$379$		−	200.204i		−	0.528242i	0.964490	−	0.264121i	$-0.0850818\pi$
$380$	21.8524	+	370.980i	0.0575063	+	0.976262i
$381$	−305.887			−0.802852
$382$	255.605	+	255.605i	0.669123	+	0.669123i
$383$	−260.633	+	260.633i	−0.680503	+	0.680503i	−0.960114	−	0.279610i	$-0.909795\pi$
$383$	−260.633	+	260.633i	−0.680503	+	0.680503i	0.279610	+	0.960114i	$0.409795\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−29.2162	+	32.8735i	−0.0758862	+	0.0853858i
$386$	−307.587			−0.796858
$387$	−69.1294	−	69.1294i	−0.178629	−	0.178629i
$388$	−177.122	+	177.122i	−0.456500	+	0.456500i
$389$		−	192.566i		−	0.495028i	−0.968884	−	0.247514i	$-0.920386\pi$
$389$		−	192.566i		−	0.495028i	0.968884	−	0.247514i	$-0.0796136\pi$
$390$	−101.003	−	89.7660i	−0.258982	−	0.230169i
$391$	860.807			2.20155
$392$	14.0000	+	14.0000i	0.0357143	+	0.0357143i
$393$	−168.385	+	168.385i	−0.428460	+	0.428460i
$394$		−	264.142i		−	0.670411i
$395$	−481.599	+	28.3684i	−1.21924	+	0.0718187i
$396$	−19.9475			−0.0503725
$397$	−183.256	−	183.256i	−0.461602	−	0.461602i	0.437578	−	0.899180i	$-0.355836\pi$
$397$	−183.256	−	183.256i	−0.461602	−	0.461602i	−0.899180	+	0.437578i	$0.855836\pi$
$398$	−223.530	+	223.530i	−0.561633	+	0.561633i
$399$		−	170.299i		−	0.426814i
$400$	99.3085	−	11.7402i	0.248271	−	0.0293504i
$401$	−327.614			−0.816992			−0.408496	−	0.912760i	$-0.633947\pi$
$401$	−327.614			−0.816992			−0.408496	+	0.912760i	$0.633947\pi$
$402$	20.7956	+	20.7956i	0.0517302	+	0.0517302i
$403$	35.4412	−	35.4412i	0.0879434	−	0.0879434i
$404$		−	202.225i		−	0.500558i
$405$	−2.64612	−	44.9221i	−0.00653362	−	0.110919i
$406$	−207.087			−0.510067
$407$	155.810	+	155.810i	0.382826	+	0.382826i
$408$	66.9340	−	66.9340i	0.164054	−	0.164054i
$409$			637.257i			1.55809i	0.626971	+	0.779043i	$0.284295\pi$
$409$			637.257i			1.55809i	−0.626971	+	0.779043i	$0.715705\pi$
$410$	46.7168	−	52.5649i	0.113943	−	0.128207i
$411$	−171.235			−0.416631
$412$	−97.4950	−	97.4950i	−0.236638	−	0.236638i
$413$	−110.918	+	110.918i	−0.268568	+	0.268568i
$414$		−	189.010i		−	0.456547i
$415$	103.737	+	92.1955i	0.249968	+	0.222158i
$416$	−62.4129			−0.150031
$417$	−148.430	−	148.430i	−0.355947	−	0.355947i
$418$	123.549	−	123.549i	0.295572	−	0.295572i
$419$		−	332.788i		−	0.794244i	−0.917766	−	0.397122i	$-0.870009\pi$
$419$		−	332.788i		−	0.794244i	0.917766	−	0.397122i	$-0.129991\pi$
$420$	−45.7465	+	2.69467i	−0.108920	+	0.00641589i
$421$	−287.551			−0.683018			−0.341509	−	0.939879i	$-0.610938\pi$
$421$	−287.551			−0.683018			−0.341509	+	0.939879i	$0.610938\pi$
$422$	122.409	+	122.409i	0.290069	+	0.290069i
$423$	−19.1445	+	19.1445i	−0.0452588	+	0.0452588i
$424$			171.696i			0.404943i
$425$	379.310	+	299.108i	0.892494	+	0.703783i
$426$	209.865			0.492640
$427$	−88.2372	−	88.2372i	−0.206645	−	0.206645i
$428$	22.1652	−	22.1652i	0.0517878	−	0.0517878i
$429$			63.5328i			0.148095i
$430$	−13.5500	−	230.033i	−0.0315116	−	0.534960i
$431$	−321.978			−0.747049			−0.373524	−	0.927620i	$-0.621851\pi$
$431$	−321.978			−0.747049			−0.373524	+	0.927620i	$0.621851\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	285.044	−	285.044i	0.658300	−	0.658300i	−0.296678	−	0.954978i	$-0.595879\pi$
$433$	285.044	−	285.044i	0.658300	−	0.658300i	0.954978	+	0.296678i	$0.0958788\pi$
$434$		−	16.9976i		−	0.0391650i
$435$	318.410	−	358.269i	0.731977	−	0.823608i
$436$	2.00697			0.00460315
$437$	1170.68	+	1170.68i	2.67889	+	2.67889i
$438$	−85.2051	+	85.2051i	−0.194532	+	0.194532i
$439$			342.297i			0.779721i	0.920874	+	0.389860i	$0.127477\pi$
$439$			342.297i			0.779721i	−0.920874	+	0.389860i	$0.872523\pi$
$440$	−35.1433	−	31.2334i	−0.0798711	−	0.0709850i
$441$	21.0000			0.0476190
$442$	−213.185	−	213.185i	−0.482318	−	0.482318i
$443$	−545.221	+	545.221i	−1.23075	+	1.23075i	−0.267070	+	0.963677i	$0.586055\pi$
$443$	−545.221	+	545.221i	−1.23075	+	1.23075i	−0.963677	+	0.267070i	$0.913945\pi$
$444$			229.596i			0.517108i
$445$	−214.767	+	12.6508i	−0.482623	+	0.0284287i
$446$	−279.679			−0.627083
$447$	−160.556	−	160.556i	−0.359186	−	0.359186i
$448$	−14.9666	+	14.9666i	−0.0334077	+	0.0334077i
$449$		−	65.3316i		−	0.145505i	−0.997350	−	0.0727523i	$-0.976822\pi$
$449$		−	65.3316i		−	0.145505i	0.997350	−	0.0727523i	$-0.0231783\pi$
$450$	65.6762	−	83.2865i	0.145947	−	0.185081i
$451$	−33.0643			−0.0733132
$452$	−258.809	−	258.809i	−0.572586	−	0.572586i
$453$	129.009	−	129.009i	0.284788	−	0.284788i
$454$			123.651i			0.272359i
$455$	8.58253	+	145.702i	0.0188627	+	0.320225i
$456$	182.057			0.399248
$457$	147.331	+	147.331i	0.322387	+	0.322387i	0.849682	−	0.527295i	$-0.176794\pi$
$457$	147.331	+	147.331i	0.322387	+	0.322387i	−0.527295	+	0.849682i	$0.676794\pi$
$458$	145.539	−	145.539i	0.317770	−	0.317770i
$459$		−	100.401i		−	0.218739i
$460$	295.948	−	332.996i	0.643366	−	0.723905i
$461$	−52.5087			−0.113902			−0.0569509	−	0.998377i	$-0.518138\pi$
$461$	−52.5087			−0.113902			−0.0569509	+	0.998377i	$0.518138\pi$
$462$	15.2352	+	15.2352i	0.0329766	+	0.0329766i
$463$	−76.6237	+	76.6237i	−0.165494	+	0.165494i	−0.784995	−	0.619502i	$-0.787335\pi$
$463$	−76.6237	+	76.6237i	−0.165494	+	0.165494i	0.619502	+	0.784995i	$0.287335\pi$
$464$		−	221.386i		−	0.477124i
$465$	29.4066	+	26.1349i	0.0632399	+	0.0562041i
$466$	−156.403			−0.335629
$467$	54.4091	+	54.4091i	0.116508	+	0.116508i	0.762957	−	0.646449i	$-0.223747\pi$
$467$	54.4091	+	54.4091i	0.116508	+	0.116508i	−0.646449	+	0.762957i	$0.723747\pi$
$468$	−46.8097	+	46.8097i	−0.100021	+	0.100021i
$469$		−	31.7657i		−	0.0677308i
$470$	−63.7045	+	3.75248i	−0.135541	+	0.00798400i
$471$	85.1904			0.180871
$472$	−118.577	−	118.577i	−0.251222	−	0.251222i
$473$	−76.6089	+	76.6089i	−0.161964	+	0.161964i
$474$			236.343i			0.498615i
$475$	109.073	+	922.632i	0.229627	+	1.94238i
$476$	−102.243			−0.214797
$477$	128.772	+	128.772i	0.269962	+	0.269962i
$478$	−183.007	+	183.007i	−0.382860	+	0.382860i
$479$		−	165.940i		−	0.346430i	−0.984884	−	0.173215i	$-0.944584\pi$
$479$		−	165.940i		−	0.346430i	0.984884	−	0.173215i	$-0.0554156\pi$
$480$	−2.88073	−	48.9050i	−0.00600152	−	0.101885i
$481$	731.262			1.52030
$482$	−39.6298	−	39.6298i	−0.0822194	−	0.0822194i
$483$	−144.359	+	144.359i	−0.298880	+	0.298880i
$484$		−	219.894i		−	0.454327i
$485$	−416.001	+	468.077i	−0.857734	+	0.965107i
$486$	−22.0454			−0.0453609
$487$	−49.2440	−	49.2440i	−0.101117	−	0.101117i	0.654738	−	0.755856i	$-0.272779\pi$
$487$	−49.2440	−	49.2440i	−0.101117	−	0.101117i	−0.755856	+	0.654738i	$0.772779\pi$
$488$	94.3295	−	94.3295i	0.193298	−	0.193298i
$489$			174.015i			0.355859i
$490$	36.9975	+	32.8813i	0.0755052	+	0.0671048i
$491$	−207.513			−0.422633			−0.211316	−	0.977418i	$-0.567775\pi$
$491$	−207.513			−0.422633			−0.211316	+	0.977418i	$0.567775\pi$
$492$	−24.3611	−	24.3611i	−0.0495144	−	0.0495144i
$493$	756.189	−	756.189i	1.53385	−	1.53385i
$494$		−	579.852i		−	1.17379i
$495$	−49.7825	+	2.93242i	−0.100571	+	0.00592407i
$496$	18.1712			0.0366355
$497$	−160.287	−	160.287i	−0.322509	−	0.322509i
$498$	48.0766	−	48.0766i	0.0965393	−	0.0965393i
$499$			299.711i			0.600624i	0.953841	+	0.300312i	$0.0970908\pi$
$499$			299.711i			0.600624i	−0.953841	+	0.300312i	$0.902909\pi$
$500$	246.116	−	43.8986i	0.492231	−	0.0877972i
$501$	380.756			0.759993
$502$	15.9671	+	15.9671i	0.0318070	+	0.0318070i
$503$	−354.819	+	354.819i	−0.705406	+	0.705406i	−0.965566	−	0.260160i	$-0.916225\pi$
$503$	−354.819	+	354.819i	−0.705406	+	0.705406i	0.260160	+	0.965566i	$0.416225\pi$
$504$			22.4499i			0.0445435i
$505$	−29.7284	−	504.688i	−0.0588682	−	0.999383i
$506$	−209.461			−0.413954
$507$	−57.8932	−	57.8932i	−0.114188	−	0.114188i
$508$	−249.755	+	249.755i	−0.491645	+	0.491645i
$509$			46.3713i			0.0911027i	0.998962	+	0.0455514i	$0.0145045\pi$
$509$			46.3713i			0.0911027i	−0.998962	+	0.0455514i	$0.985496\pi$
$510$	157.206	−	176.885i	0.308246	−	0.346834i
$511$	130.153			0.254702
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	136.543	−	136.543i	0.266166	−	0.266166i
$514$		−	118.142i		−	0.229849i
$515$	−257.648	−	228.983i	−0.500287	−	0.444628i
$516$	−112.888			−0.218775
$517$	21.2158	+	21.2158i	0.0410364	+	0.0410364i
$518$	175.357	−	175.357i	0.338527	−	0.338527i
$519$		−	40.5435i		−	0.0781184i
$520$	−155.762	+	9.17511i	−0.299543	+	0.0176444i
$521$	784.619			1.50599			0.752993	−	0.658028i	$-0.228609\pi$
$521$	784.619			1.50599			0.752993	+	0.658028i	$0.228609\pi$
$522$	−166.039	−	166.039i	−0.318083	−	0.318083i
$523$	271.744	−	271.744i	0.519587	−	0.519587i	−0.397859	−	0.917446i	$-0.630247\pi$
$523$	271.744	−	271.744i	0.519587	−	0.519587i	0.917446	+	0.397859i	$0.130247\pi$
$524$			274.971i			0.524754i
$525$	−113.772	+	13.4501i	−0.216709	+	0.0256192i
$526$	−372.582			−0.708330
$527$	62.0676	+	62.0676i	0.117775	+	0.117775i
$528$	−16.2871	+	16.2871i	−0.0308467	+	0.0308467i
$529$		−	1455.72i		−	2.75183i
$530$	25.2404	+	428.497i	0.0476234	+	0.808484i
$531$	−177.865			−0.334963
$532$	−139.049	−	139.049i	−0.261369	−	0.261369i
$533$	−77.5900	+	77.5900i	−0.145572	+	0.145572i
$534$			105.396i			0.197372i
$535$	52.0586	−	58.5755i	0.0973058	−	0.109487i
$536$	33.9590			0.0633563
$537$	226.016	+	226.016i	0.420886	+	0.420886i
$538$	120.015	−	120.015i	0.223077	−	0.223077i
$539$		−	23.2721i		−	0.0431765i
$540$	−38.8393	−	34.5182i	−0.0719247	−	0.0639226i
$541$	545.359			1.00806			0.504029	−	0.863687i	$-0.331851\pi$
$541$	545.359			1.00806			0.504029	+	0.863687i	$0.331851\pi$
$542$	457.758	+	457.758i	0.844571	+	0.844571i
$543$	90.5530	−	90.5530i	0.166764	−	0.166764i
$544$		−	109.303i		−	0.200924i
$545$	5.00875	−	0.295038i	0.00919037	−	0.000541354i
$546$	71.5030			0.130958
$547$	93.2739	+	93.2739i	0.170519	+	0.170519i	0.787207	−	0.616688i	$-0.211526\pi$
$547$	93.2739	+	93.2739i	0.170519	+	0.170519i	−0.616688	+	0.787207i	$0.711526\pi$
$548$	−139.813	+	139.813i	−0.255133	+	0.255133i
$549$		−	141.494i		−	0.257731i
$550$	−92.2977	−	72.7821i	−0.167814	−	0.132331i
$551$	2056.80			3.73285
$552$	−154.326	−	154.326i	−0.279577	−	0.279577i
$553$	180.510	−	180.510i	0.326420	−	0.326420i
$554$		−	5.97021i		−	0.0107766i
$555$	33.7521	+	572.997i	0.0608146	+	1.03243i
$556$	−242.385			−0.435944
$557$	549.179	+	549.179i	0.985958	+	0.985958i	0.999903	−	0.0139446i	$-0.00443886\pi$
$557$	549.179	+	549.179i	0.985958	+	0.985958i	−0.0139446	+	0.999903i	$0.504439\pi$
$558$	13.6284	−	13.6284i	0.0244237	−	0.0244237i
$559$			359.548i			0.643198i
$560$	−35.1516	+	39.5520i	−0.0627708	+	0.0706286i
$561$	−111.264			−0.198331
$562$	196.044	+	196.044i	0.348833	+	0.348833i
$563$	−45.1575	+	45.1575i	−0.0802088	+	0.0802088i	−0.746073	−	0.665864i	$-0.768063\pi$
$563$	−45.1575	+	45.1575i	−0.0802088	+	0.0802088i	0.665864	+	0.746073i	$0.268063\pi$
$564$			31.2628i			0.0554305i
$565$	−683.950	−	607.856i	−1.21053	−	1.07585i
$566$	452.023			0.798627
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	171.354	−	171.354i	0.301679	−	0.301679i
$569$			392.758i			0.690260i	0.938555	+	0.345130i	$0.112165\pi$
$569$			392.758i			0.690260i	−0.938555	+	0.345130i	$0.887835\pi$
$570$	454.356	−	26.7636i	0.797115	−	0.0469537i
$571$	−0.726963			−0.00127314			−0.000636570	−	1.00000i	$-0.500203\pi$
$571$	−0.726963			−0.00127314			−0.000636570		1.00000i	$0.500203\pi$
$572$	51.8743	+	51.8743i	0.0906893	+	0.0906893i
$573$	313.051	−	313.051i	0.546337	−	0.546337i
$574$			37.2122i			0.0648296i
$575$	689.638	−	874.556i	1.19937	−	1.52097i
$576$	−24.0000			−0.0416667
$577$	−184.973	−	184.973i	−0.320577	−	0.320577i	0.528411	−	0.848988i	$-0.322788\pi$
$577$	−184.973	−	184.973i	−0.320577	−	0.320577i	−0.848988	+	0.528411i	$0.822788\pi$
$578$	84.3465	−	84.3465i	0.145928	−	0.145928i
$579$			376.716i			0.650632i
$580$	−32.5451	−	552.506i	−0.0561123	−	0.952597i
$581$	−73.4382			−0.126400
$582$	216.929	+	216.929i	0.372731	+	0.372731i
$583$	142.704	−	142.704i	0.244776	−	0.244776i
$584$			139.139i			0.238252i
$585$	−109.940	+	123.703i	−0.187932	+	0.211458i
$586$	213.751			0.364762
$587$	−703.941	−	703.941i	−1.19922	−	1.19922i	−0.974401	−	0.224817i	$-0.927822\pi$
$587$	−703.941	−	703.941i	−1.19922	−	1.19922i	−0.224817	−	0.974401i	$-0.572178\pi$
$588$	17.1464	−	17.1464i	0.0291606	−	0.0291606i
$589$			168.821i			0.286623i
$590$	−313.361	−	278.497i	−0.531120	−	0.472030i
$591$	−323.506			−0.547388
$592$	187.464	+	187.464i	0.316663	+	0.316663i
$593$	730.917	−	730.917i	1.23257	−	1.23257i	0.269603	−	0.962972i	$-0.413107\pi$
$593$	730.917	−	730.917i	1.23257	−	1.23257i	0.962972	−	0.269603i	$-0.0868925\pi$
$594$			24.4306i			0.0411290i
$595$	−255.166	+	15.0304i	−0.428851	+	0.0252612i
$596$	−262.187			−0.439911
$597$	273.767	+	273.767i	0.458571	+	0.458571i
$598$	−491.529	+	491.529i	−0.821955	+	0.821955i
$599$			646.505i			1.07931i	0.841887	+	0.539654i	$0.181445\pi$
$599$			646.505i			1.07931i	−0.841887	+	0.539654i	$0.818555\pi$
$600$	−14.3787	−	121.628i	−0.0239645	−	0.202713i
$601$	−133.146			−0.221541			−0.110771	−	0.993846i	$-0.535332\pi$
$601$	−133.146			−0.221541			−0.110771	+	0.993846i	$0.535332\pi$
$602$	86.2196	+	86.2196i	0.143222	+	0.143222i
$603$	25.4692	−	25.4692i	0.0422376	−	0.0422376i
$604$		−	210.671i		−	0.348793i
$605$	−32.3259	−	548.784i	−0.0534312	−	0.907082i
$606$	−247.674			−0.408704
$607$	−1.17531	−	1.17531i	−0.00193627	−	0.00193627i	0.706138	−	0.708074i	$-0.250436\pi$
$607$	−1.17531	−	1.17531i	−0.00193627	−	0.00193627i	−0.708074	+	0.706138i	$0.750436\pi$
$608$	148.649	−	148.649i	0.244489	−	0.244489i
$609$			253.629i			0.416468i
$610$	221.549	−	249.283i	0.363195	−	0.408660i
$611$	99.5718			0.162965
$612$	−81.9771	−	81.9771i	−0.133949	−	0.133949i
$613$	−464.748	+	464.748i	−0.758153	+	0.758153i	−0.975986	−	0.217833i	$-0.930101\pi$
$613$	−464.748	+	464.748i	−0.758153	+	0.758153i	0.217833	+	0.975986i	$0.430101\pi$
$614$			338.083i			0.550624i
$615$	−64.3786	−	57.2161i	−0.104681	−	0.0930343i
$616$	24.8789			0.0403879
$617$	−591.643	−	591.643i	−0.958903	−	0.958903i	0.0402851	−	0.999188i	$-0.487173\pi$
$617$	−591.643	−	591.643i	−0.958903	−	0.958903i	−0.999188	+	0.0402851i	$0.987173\pi$
$618$	−119.406	+	119.406i	−0.193214	+	0.193214i
$619$			1133.85i			1.83175i	0.401466	+	0.915874i	$0.368501\pi$
$619$			1133.85i			1.83175i	−0.401466	+	0.915874i	$0.631499\pi$
$620$	45.3494	−	2.67129i	0.0731442	−	0.00430853i
$621$	−231.490			−0.372769
$622$	−184.053	−	184.053i	−0.295905	−	0.295905i
$623$	80.4978	−	80.4978i	0.129210	−	0.129210i
$624$			76.4399i			0.122500i
$625$	607.771	−	145.737i	0.972434	−	0.233180i
$626$	−416.994			−0.666124
$627$	−151.316	−	151.316i	−0.241334	−	0.241334i
$628$	69.5576	−	69.5576i	0.110761	−	0.110761i
$629$			1280.65i			2.03601i
$630$	3.30029	+	56.0277i	0.00523855	+	0.0889329i
$631$	−383.255			−0.607377			−0.303689	−	0.952771i	$-0.598218\pi$
$631$	−383.255			−0.607377			−0.303689	+	0.952771i	$0.598218\pi$
$632$	192.974	+	192.974i	0.305338	+	0.305338i
$633$	149.920	−	149.920i	0.236840	−	0.236840i
$634$			807.414i			1.27352i
$635$	−586.592	+	660.024i	−0.923768	+	1.03941i
$636$	210.283			0.330634
$637$	−54.6113	−	54.6113i	−0.0857320	−	0.0857320i
$638$	−184.004	+	184.004i	−0.288407	+	0.288407i
$639$		−	257.031i		−	0.402239i
$640$	−42.2829	−	37.5787i	−0.0660670	−	0.0587167i
$641$	−129.610			−0.202199			−0.101100	−	0.994876i	$-0.532236\pi$
$641$	−129.610			−0.202199			−0.101100	+	0.994876i	$0.532236\pi$
$642$	−27.1467	−	27.1467i	−0.0422845	−	0.0422845i
$643$	233.464	−	233.464i	0.363085	−	0.363085i	−0.501862	−	0.864948i	$-0.667352\pi$
$643$	233.464	−	233.464i	0.363085	−	0.363085i	0.864948	+	0.501862i	$0.167352\pi$
$644$			235.737i			0.366052i
$645$	−281.731	+	16.5953i	−0.436793	+	0.0257291i
$646$	1015.48			1.57196
$647$	−430.823	−	430.823i	−0.665878	−	0.665878i	0.290881	−	0.956759i	$-0.406052\pi$
$647$	−430.823	−	430.823i	−0.665878	−	0.665878i	−0.956759	+	0.290881i	$0.906052\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			197.109i			0.303712i
$650$	−387.383	+	45.7962i	−0.595974	+	0.0704556i
$651$	−20.8177			−0.0319781
$652$	142.083	+	142.083i	0.217918	+	0.217918i
$653$	170.000	−	170.000i	0.260337	−	0.260337i	−0.564854	−	0.825191i	$-0.691068\pi$
$653$	170.000	−	170.000i	0.260337	−	0.260337i	0.825191	+	0.564854i	$0.191068\pi$
$654$		−	2.45803i		−	0.00375846i
$655$	40.4225	+	686.238i	0.0617138	+	1.04769i
$656$	−39.7815			−0.0606425
$657$	104.355	+	104.355i	0.158835	+	0.158835i
$658$	23.8773	−	23.8773i	0.0362878	−	0.0362878i
$659$		−	532.095i		−	0.807429i	−0.914885	−	0.403714i	$-0.867719\pi$
$659$		−	532.095i		−	0.807429i	0.914885	−	0.403714i	$-0.132281\pi$
$660$	−38.2529	+	43.0416i	−0.0579590	+	0.0652145i
$661$	1235.23			1.86872			0.934362	−	0.356325i	$-0.115971\pi$
$661$	1235.23			1.86872			0.934362	+	0.356325i	$0.115971\pi$
$662$	26.7859	+	26.7859i	0.0404620	+	0.0404620i
$663$	−261.097	+	261.097i	−0.393811	+	0.393811i
$664$		−	78.5087i		−	0.118236i
$665$	−367.461	−	326.579i	−0.552573	−	0.491096i
$666$	281.196			0.422217
$667$	−1743.51	−	1743.51i	−2.61395	−	2.61395i
$668$	310.886	−	310.886i	0.465398	−	0.465398i
$669$			342.536i			0.512011i
$670$	84.7506	−	4.99219i	0.126493	−	0.00745103i
$671$	−156.803			−0.233686
$672$	18.3303	+	18.3303i	0.0272772	+	0.0272772i
$673$	−350.867	+	350.867i	−0.521347	+	0.521347i	−0.917978	−	0.396631i	$-0.870179\pi$
$673$	−350.867	+	350.867i	−0.521347	+	0.521347i	0.396631	+	0.917978i	$0.370179\pi$
$674$		−	650.063i		−	0.964485i
$675$	−102.005	−	80.4366i	−0.151118	−	0.119165i
$676$	−94.5391			−0.139851
$677$	−721.673	−	721.673i	−1.06599	−	1.06599i	−0.997663	−	0.0683230i	$-0.978235\pi$
$677$	−721.673	−	721.673i	−1.06599	−	1.06599i	−0.0683230	−	0.997663i	$-0.521765\pi$
$678$	−316.975	+	316.975i	−0.467515	+	0.467515i
$679$		−	331.365i		−	0.488019i
$680$	−16.0682	−	272.784i	−0.0236297	−	0.401153i
$681$	151.441			0.222380
$682$	−15.1029	−	15.1029i	−0.0221451	−	0.0221451i
$683$	314.116	−	314.116i	0.459906	−	0.459906i	−0.438719	−	0.898624i	$-0.644568\pi$
$683$	314.116	−	314.116i	0.459906	−	0.459906i	0.898624	+	0.438719i	$0.144568\pi$
$684$		−	222.974i		−	0.325985i
$685$	−328.374	+	369.481i	−0.479379	+	0.539389i
$686$	−26.1916			−0.0381802
$687$	−178.248	−	178.248i	−0.259458	−	0.259458i
$688$	−92.1726	+	92.1726i	−0.133972	+	0.133972i
$689$		−	669.752i		−	0.972064i
$690$	−407.835	−	362.461i	−0.591066	−	0.525306i
$691$	−1255.23			−1.81654			−0.908269	−	0.418387i	$-0.862595\pi$
$691$	−1255.23			−1.81654			−0.908269	+	0.418387i	$0.862595\pi$
$692$	−33.1036	−	33.1036i	−0.0478376	−	0.0478376i
$693$	18.6592	−	18.6592i	0.0269252	−	0.0269252i
$694$			239.351i			0.344887i
$695$	−604.914	+	35.6322i	−0.870380	+	0.0512693i
$696$	−271.141			−0.389570
$697$	−135.882	−	135.882i	−0.194953	−	0.194953i
$698$	−592.030	+	592.030i	−0.848180	+	0.848180i
$699$			191.554i			0.274040i
$700$	−81.9126	+	103.876i	−0.117018	+	0.148395i
$701$	275.772			0.393398			0.196699	−	0.980464i	$-0.436978\pi$
$701$	275.772			0.393398			0.196699	+	0.980464i	$0.436978\pi$
$702$	57.3299	+	57.3299i	0.0816666	+	0.0816666i
$703$	−1741.65	+	1741.65i	−2.47745	+	2.47745i
$704$			26.5967i			0.0377794i
$705$	4.59583	+	78.0217i	0.00651891	+	0.110669i
$706$	−184.429			−0.261231
$707$	189.164	+	189.164i	0.267559	+	0.267559i
$708$	−145.226	+	145.226i	−0.205122	+	0.205122i
$709$			533.450i			0.752398i	0.926539	+	0.376199i	$0.122769\pi$
$709$			533.450i			0.752398i	−0.926539	+	0.376199i	$0.877231\pi$
$710$	402.453	−	452.833i	0.566835	−	0.637793i
$711$	289.460			0.407117
$712$	86.0558	+	86.0558i	0.120865	+	0.120865i
$713$	143.106	−	143.106i	0.200710	−	0.200710i
$714$			125.222i			0.175381i
$715$	137.087	+	121.835i	0.191730	+	0.170399i
$716$	369.082			0.515478
$717$	224.137	+	224.137i	0.312604	+	0.312604i
$718$	464.557	−	464.557i	0.647016	−	0.647016i
$719$			260.982i			0.362979i	0.983393	+	0.181490i	$0.0580919\pi$
$719$			260.982i			0.362979i	−0.983393	+	0.181490i	$0.941908\pi$
$720$	−59.8962	+	3.52816i	−0.0831891	+	0.00490022i
$721$	182.396			0.252977
$722$	1020.03	+	1020.03i	1.41279	+	1.41279i
$723$	−48.5363	+	48.5363i	−0.0671319	+	0.0671319i
$724$		−	147.872i		−	0.204244i
$725$	−162.444	−	1374.09i	−0.224061	−	1.89530i
$726$	−269.314			−0.370956
$727$	293.600	+	293.600i	0.403852	+	0.403852i	0.879588	−	0.475736i	$-0.157818\pi$
$727$	293.600	+	293.600i	0.403852	+	0.403852i	−0.475736	+	0.879588i	$0.657818\pi$
$728$	58.3820	−	58.3820i	0.0801950	−	0.0801950i
$729$			27.0000i			0.0370370i
$730$	20.4544	+	347.246i	0.0280197	+	0.475680i
$731$	−629.670			−0.861381
$732$	−115.530	−	115.530i	−0.157827	−	0.157827i
$733$	416.677	−	416.677i	0.568455	−	0.568455i	−0.363241	−	0.931695i	$-0.618330\pi$
$733$	416.677	−	416.677i	0.568455	−	0.568455i	0.931695	+	0.363241i	$0.118330\pi$
$734$		−	900.510i		−	1.22685i
$735$	40.2713	−	45.3125i	0.0547908	−	0.0616497i
$736$	−252.014			−0.342410
$737$	−28.2249	−	28.2249i	−0.0382970	−	0.0382970i
$738$	−29.8361	+	29.8361i	−0.0404283	+	0.0404283i
$739$		−	96.5954i		−	0.130711i	−0.997862	−	0.0653555i	$-0.979182\pi$
$739$		−	96.5954i		−	0.130711i	0.997862	−	0.0653555i	$-0.0208181\pi$
$740$	495.408	+	440.291i	0.669471	+	0.594988i
$741$	−710.170			−0.958395
$742$	−160.607	−	160.607i	−0.216451	−	0.216451i
$743$	−517.336	+	517.336i	−0.696280	+	0.696280i	−0.963606	−	0.267326i	$-0.913860\pi$
$743$	−517.336	+	517.336i	−0.696280	+	0.696280i	0.267326	+	0.963606i	$0.413860\pi$
$744$		−	22.2551i		−	0.0299128i
$745$	−654.334	+	38.5432i	−0.878300	+	0.0517359i
$746$	−895.866			−1.20089
$747$	−58.8816	−	58.8816i	−0.0788240	−	0.0788240i
$748$	−90.8466	+	90.8466i	−0.121453	+	0.121453i
$749$			41.4672i			0.0553635i
$750$	−53.7646	−	301.429i	−0.0716862	−	0.401905i
$751$	429.736			0.572218			0.286109	−	0.958197i	$-0.407638\pi$
$751$	429.736			0.572218			0.286109	+	0.958197i	$0.407638\pi$
$752$	25.5259	+	25.5259i	0.0339441	+	0.0339441i
$753$	19.5557	−	19.5557i	0.0259703	−	0.0259703i
$754$			863.583i			1.14534i
$755$	−30.9700	−	525.766i	−0.0410199	−	0.696379i
$756$	27.4955			0.0363696
$757$	400.880	+	400.880i	0.529565	+	0.529565i	0.920443	−	0.390878i	$-0.127829\pi$
$757$	400.880	+	400.880i	0.529565	+	0.529565i	−0.390878	+	0.920443i	$0.627829\pi$
$758$	−200.204	+	200.204i	−0.264121	+	0.264121i
$759$			256.536i			0.337992i
$760$	349.127	−	392.832i	0.459378	−	0.516884i
$761$	−45.5634			−0.0598730			−0.0299365	−	0.999552i	$-0.509531\pi$
$761$	−45.5634			−0.0598730			−0.0299365	+	0.999552i	$0.509531\pi$
$762$	305.887	+	305.887i	0.401426	+	0.401426i
$763$	−1.87735	+	1.87735i	−0.00246049	+	0.00246049i
$764$		−	511.210i		−	0.669123i
$765$	−216.639	−	192.537i	−0.283188	−	0.251682i
$766$	521.265			0.680503
$767$	462.545	+	462.545i	0.603058	+	0.603058i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			1217.00i			1.58257i	0.611445	+	0.791287i	$0.290588\pi$
$769$			1217.00i			1.58257i	−0.611445	+	0.791287i	$0.709412\pi$
$770$	62.0897	−	3.65736i	0.0806360	−	0.00474982i
$771$	−144.694			−0.187671
$772$	307.587	+	307.587i	0.398429	+	0.398429i
$773$	141.860	−	141.860i	0.183519	−	0.183519i	−0.609368	−	0.792887i	$-0.708577\pi$
$773$	141.860	−	141.860i	0.183519	−	0.183519i	0.792887	+	0.609368i	$0.208577\pi$
$774$			138.259i			0.178629i
$775$	112.785	−	13.3333i	0.145529	−	0.0172043i
$776$	354.244			0.456500
$777$	−214.767	−	214.767i	−0.276406	−	0.276406i
$778$	−192.566	+	192.566i	−0.247514	+	0.247514i
$779$		−	369.593i		−	0.474445i
$780$	11.2372	+	190.769i	0.0144066	+	0.244576i
$781$	−284.840			−0.364712
$782$	−860.807	−	860.807i	−1.10078	−	1.10078i
$783$	−203.356	+	203.356i	−0.259713	+	0.259713i
$784$		−	28.0000i		−	0.0357143i
$785$	163.368	−	183.819i	0.208112	−	0.234164i
$786$	336.769			0.428460
$787$	41.2990	+	41.2990i	0.0524765	+	0.0524765i	0.732858	−	0.680382i	$-0.238186\pi$
$787$	41.2990	+	41.2990i	0.0524765	+	0.0524765i	−0.680382	+	0.732858i	$0.738186\pi$
$788$	−264.142	+	264.142i	−0.335205	+	0.335205i
$789$			456.317i			0.578349i
$790$	509.968	+	453.231i	0.645529	+	0.573710i
$791$	484.187			0.612121
$792$	19.9475	+	19.9475i	0.0251863	+	0.0251863i
$793$	−367.961	+	367.961i	−0.464012	+	0.464012i
$794$			366.512i			0.461602i
$795$	524.799	−	30.9130i	0.660124	−	0.0388843i
$796$	447.060			0.561633
$797$	−320.603	−	320.603i	−0.402262	−	0.402262i	0.476768	−	0.879029i	$-0.341808\pi$
$797$	−320.603	−	320.603i	−0.402262	−	0.402262i	−0.879029	+	0.476768i	$0.841808\pi$
$798$	−170.299	+	170.299i	−0.213407	+	0.213407i
$799$			174.379i			0.218246i
$800$	−111.049	−	87.5683i	−0.138811	−	0.109460i
$801$	129.084			0.161153
$802$	327.614	+	327.614i	0.408496	+	0.408496i
$803$	115.645	−	115.645i	0.144016	−	0.144016i
$804$		−	41.5911i		−	0.0517302i
$805$	34.6549	+	588.324i	0.0430496	+	0.730837i
$806$	−70.8824			−0.0879434
$807$	−146.988	−	146.988i	−0.182141	−	0.182141i
$808$	−202.225	+	202.225i	−0.250279	+	0.250279i
$809$			1036.57i			1.28130i	0.767834	+	0.640649i	$0.221335\pi$
$809$			1036.57i			1.28130i	−0.767834	+	0.640649i	$0.778665\pi$
$810$	−42.2760	+	47.5683i	−0.0521926	+	0.0587262i
$811$	591.042			0.728782			0.364391	−	0.931246i	$-0.381277\pi$
$811$	591.042			0.728782			0.364391	+	0.931246i	$0.381277\pi$
$812$	207.087	+	207.087i	0.255034	+	0.255034i
$813$	560.636	−	560.636i	0.689589	−	0.689589i
$814$		−	311.621i		−	0.382826i
$815$	375.480	+	333.705i	0.460711	+	0.409454i
$816$	−133.868			−0.164054
$817$	−856.336	−	856.336i	−1.04815	−	1.04815i
$818$	637.257	−	637.257i	0.779043	−	0.779043i
$819$		−	87.5729i		−	0.106927i
$820$	−99.2816	+	5.84814i	−0.121075	+	0.00713188i
$821$	550.566			0.670604			0.335302	−	0.942111i	$-0.391162\pi$
$821$	550.566			0.670604			0.335302	+	0.942111i	$0.391162\pi$
$822$	171.235	+	171.235i	0.208316	+	0.208316i
$823$	−828.295	+	828.295i	−1.00643	+	1.00643i	−0.00645489	+	0.999979i	$0.502055\pi$
$823$	−828.295	+	828.295i	−1.00643	+	1.00643i	−0.999979	+	0.00645489i	$0.997945\pi$
$824$			194.990i			0.236638i
$825$	−89.1395	+	113.041i	−0.108048	+	0.137020i
$826$	221.837			0.268568
$827$	266.349	+	266.349i	0.322066	+	0.322066i	0.849559	−	0.527493i	$-0.176868\pi$
$827$	266.349	+	266.349i	0.322066	+	0.322066i	−0.527493	+	0.849559i	$0.676868\pi$
$828$	−189.010	+	189.010i	−0.228273	+	0.228273i
$829$		−	1568.25i		−	1.89174i	−0.324551	−	0.945868i	$-0.605213\pi$
$829$		−	1568.25i		−	1.89174i	0.324551	−	0.945868i	$-0.394787\pi$
$830$	−11.5413	−	195.932i	−0.0139052	−	0.236063i
$831$	−7.31198			−0.00879902
$832$	62.4129	+	62.4129i	0.0750155	+	0.0750155i
$833$	95.6399	−	95.6399i	0.114814	−	0.114814i
$834$			296.860i			0.355947i
$835$	730.168	−	821.573i	0.874453	−	0.983920i
$836$	−247.098			−0.295572
$837$	−16.6913	−	16.6913i	−0.0199418	−	0.0199418i
$838$	−332.788	+	332.788i	−0.397122	+	0.397122i
$839$		−	660.770i		−	0.787568i	−0.919203	−	0.393784i	$-0.871166\pi$
$839$		−	660.770i		−	0.787568i	0.919203	−	0.393784i	$-0.128834\pi$
$840$	48.4411	+	43.0518i	0.0576680	+	0.0512521i
$841$	−2222.22			−2.64236
$842$	287.551	+	287.551i	0.341509	+	0.341509i
$843$	240.104	−	240.104i	0.284821	−	0.284821i
$844$		−	244.818i		−	0.290069i
$845$	−235.939	+	13.8979i	−0.279218	+	0.0164472i
$846$	38.2889			0.0452588
$847$	205.692	+	205.692i	0.242848	+	0.242848i
$848$	171.696	−	171.696i	0.202471	−	0.202471i
$849$		−	553.613i		−	0.652076i
$850$	−80.2020	−	678.418i	−0.0943553	−	0.798139i
$851$	2952.73			3.46971
$852$	−209.865	−	209.865i	−0.246320	−	0.246320i
$853$	−338.010	+	338.010i	−0.396261	+	0.396261i	−0.876912	−	0.480651i	$-0.840400\pi$
$853$	−338.010	+	338.010i	−0.396261	+	0.396261i	0.480651	+	0.876912i	$0.340400\pi$
$854$			176.474i			0.206645i
$855$	−32.7786	−	556.470i	−0.0383375	−	0.650842i
$856$	−44.3303			−0.0517878
$857$	−19.5395	−	19.5395i	−0.0227999	−	0.0227999i	0.695615	−	0.718415i	$-0.255132\pi$
$857$	−19.5395	−	19.5395i	−0.0227999	−	0.0227999i	−0.718415	+	0.695615i	$0.755132\pi$
$858$	63.5328	−	63.5328i	0.0740475	−	0.0740475i
$859$		−	749.310i		−	0.872305i	−0.899873	−	0.436153i	$-0.856341\pi$
$859$		−	749.310i		−	0.872305i	0.899873	−	0.436153i	$-0.143659\pi$
$860$	−216.483	+	243.583i	−0.251724	+	0.283236i
$861$	45.5754			0.0529331
$862$	321.978	+	321.978i	0.373524	+	0.373524i
$863$	937.685	−	937.685i	1.08654	−	1.08654i	0.0906593	−	0.995882i	$-0.471103\pi$
$863$	937.685	−	937.685i	1.08654	−	1.08654i	0.995882	−	0.0906593i	$-0.0288974\pi$
$864$			29.3939i			0.0340207i
$865$	−87.4822	−	77.7493i	−0.101136	−	0.0898836i
$866$	−570.087			−0.658300
$867$	−103.303	−	103.303i	−0.119150	−	0.119150i
$868$	−16.9976	+	16.9976i	−0.0195825	+	0.0195825i
$869$		−	320.779i		−	0.369136i
$870$	−676.679	+	39.8595i	−0.777792	+	0.0458155i
$871$	−132.468			−0.152087
$872$	−2.00697	−	2.00697i	−0.00230157	−	0.00230157i
$873$	265.683	−	265.683i	0.304333	−	0.304333i
$874$		−	2341.35i		−	2.67889i
$875$	−189.157	+	271.284i	−0.216179	+	0.310038i
$876$	170.410			0.194532
$877$	−282.933	−	282.933i	−0.322615	−	0.322615i	0.527155	−	0.849769i	$-0.323259\pi$
$877$	−282.933	−	282.933i	−0.322615	−	0.322615i	−0.849769	+	0.527155i	$0.823259\pi$
$878$	342.297	−	342.297i	0.389860	−	0.389860i
$879$		−	261.790i		−	0.297827i
$880$	3.90989	+	66.3767i	0.00444305	+	0.0754280i
$881$	1193.56			1.35478			0.677391	−	0.735623i	$-0.263110\pi$
$881$	1193.56			1.35478			0.677391	+	0.735623i	$0.263110\pi$
$882$	−21.0000	−	21.0000i	−0.0238095	−	0.0238095i
$883$	28.7690	−	28.7690i	0.0325809	−	0.0325809i	−0.690629	−	0.723210i	$-0.742666\pi$
$883$	28.7690	−	28.7690i	0.0325809	−	0.0325809i	0.723210	+	0.690629i	$0.242666\pi$
$884$			426.369i			0.482318i
$885$	−341.088	+	383.787i	−0.385410	+	0.433657i
$886$	1090.44			1.23075
$887$	−774.170	−	774.170i	−0.872796	−	0.872796i	0.119980	−	0.992776i	$-0.461717\pi$
$887$	−774.170	−	774.170i	−0.872796	−	0.872796i	−0.992776	+	0.119980i	$0.961717\pi$
$888$	229.596	−	229.596i	0.258554	−	0.258554i
$889$		−	467.250i		−	0.525590i
$890$	227.418	+	202.116i	0.255526	+	0.227097i
$891$	29.9213			0.0335817
$892$	279.679	+	279.679i	0.313542	+	0.313542i
$893$	−237.151	+	237.151i	−0.265566	+	0.265566i
$894$			321.112i			0.359186i
$895$	921.109	−	54.2575i	1.02917	−	0.0606229i
$896$	29.9333			0.0334077
$897$	601.998	+	601.998i	0.671123	+	0.671123i
$898$	−65.3316	+	65.3316i	−0.0727523	+	0.0727523i
$899$		−	251.428i		−	0.279675i
$900$	−148.963	+	17.6103i	−0.165514	+	0.0195669i
$901$	1172.93			1.30180
$902$	33.0643	+	33.0643i	0.0366566	+	0.0366566i
$903$	105.597	−	105.597i	0.116940	−	0.116940i
$904$			517.618i			0.572586i
$905$	−21.7382	−	369.042i	−0.0240201	−	0.407781i
$906$	−258.018			−0.284788
$907$	−386.610	−	386.610i	−0.426252	−	0.426252i	0.461098	−	0.887349i	$-0.347456\pi$
$907$	−386.610	−	386.610i	−0.426252	−	0.426252i	−0.887349	+	0.461098i	$0.847456\pi$
$908$	123.651	−	123.651i	0.136180	−	0.136180i
$909$			303.338i			0.333705i
$910$	137.120	−	154.285i	0.150681	−	0.169544i
$911$	1028.20			1.12865			0.564324	−	0.825553i	$-0.309137\pi$
$911$	1028.20			1.12865			0.564324	+	0.825553i	$0.309137\pi$
$912$	−182.057	−	182.057i	−0.199624	−	0.199624i
$913$	−65.2523	+	65.2523i	−0.0714702	+	0.0714702i
$914$		−	294.662i		−	0.322387i
$915$	−305.308	−	271.341i	−0.333670	−	0.296547i
$916$	−291.077			−0.317770
$917$	−257.212	−	257.212i	−0.280493	−	0.280493i
$918$	−100.401	+	100.401i	−0.109369	+	0.109369i
$919$			334.758i			0.364263i	0.983274	+	0.182132i	$0.0582997\pi$
$919$			334.758i			0.364263i	−0.983274	+	0.182132i	$0.941700\pi$
$920$	−628.945	+	37.0477i	−0.683635	+	0.0402692i
$921$	414.066			0.449583
$922$	52.5087	+	52.5087i	0.0569509	+	0.0569509i
$923$	−668.418	+	668.418i	−0.724180	+	0.724180i
$924$		−	30.4703i		−	0.0329766i
$925$	1301.10	+	1026.00i	1.40660	+	1.10918i
$926$	153.247			0.165494
$927$	146.242	+	146.242i	0.157759	+	0.157759i
$928$	−221.386	+	221.386i	−0.238562	+	0.238562i
$929$			829.100i			0.892465i	0.894917	+	0.446233i	$0.147235\pi$
$929$			829.100i			0.892465i	−0.894917	+	0.446233i	$0.852765\pi$
$930$	−3.27164	−	55.5415i	−0.00351790	−	0.0597220i
$931$	260.136			0.279416
$932$	156.403	+	156.403i	0.167814	+	0.167814i
$933$	−225.418	+	225.418i	−0.241605	+	0.241605i
$934$		−	108.818i		−	0.116508i
$935$	−213.368	+	240.079i	−0.228202	+	0.256769i
$936$	93.6194			0.100021
$937$	−602.614	−	602.614i	−0.643132	−	0.643132i	0.308192	−	0.951324i	$-0.400276\pi$
$937$	−602.614	−	602.614i	−0.643132	−	0.643132i	−0.951324	+	0.308192i	$0.900276\pi$
$938$	−31.7657	+	31.7657i	−0.0338654	+	0.0338654i
$939$			510.711i			0.543888i
$940$	67.4569	+	59.9520i	0.0717627	+	0.0637787i
$941$	−1339.85			−1.42386			−0.711928	−	0.702252i	$-0.752178\pi$
$941$	−1339.85			−1.42386			−0.711928	+	0.702252i	$0.752178\pi$
$942$	−85.1904	−	85.1904i	−0.0904356	−	0.0904356i
$943$	−313.297	+	313.297i	−0.332234	+	0.332234i
$944$			237.154i			0.251222i
$945$	68.6197	−	4.04201i	0.0726134	−	0.00427726i
$946$	153.218			0.161964
$947$	−617.006	−	617.006i	−0.651537	−	0.651537i	0.301826	−	0.953363i	$-0.402404\pi$
$947$	−617.006	−	617.006i	−0.651537	−	0.651537i	−0.953363	+	0.301826i	$0.902404\pi$
$948$	236.343	−	236.343i	0.249307	−	0.249307i
$949$		−	542.756i		−	0.571924i
$950$	813.559	−	1031.70i	0.856378	−	1.08601i
$951$	988.876			1.03983
$952$	102.243	+	102.243i	0.107398	+	0.107398i
$953$	−324.856	+	324.856i	−0.340877	+	0.340877i	−0.856697	−	0.515820i	$-0.827487\pi$
$953$	−324.856	+	324.856i	−0.340877	+	0.340877i	0.515820	+	0.856697i	$0.327487\pi$
$954$		−	257.544i		−	0.269962i
$955$	−75.1512	−	1275.81i	−0.0786923	−	1.33593i
$956$	366.014			0.382860
$957$	225.358	+	225.358i	0.235484	+	0.235484i
$958$	−165.940	+	165.940i	−0.173215	+	0.173215i
$959$		−	261.566i		−	0.272749i
$960$	−46.0243	+	51.7858i	−0.0479420	+	0.0539435i
$961$	−940.363			−0.978525
$962$	−731.262	−	731.262i	−0.760148	−	0.760148i
$963$	−33.2478	+	33.2478i	−0.0345252	+	0.0345252i
$964$			79.2595i			0.0822194i
$965$	812.855	+	722.420i	0.842337	+	0.748622i
$966$	288.718			0.298880
$967$	834.219	+	834.219i	0.862688	+	0.862688i	0.991650	−	0.128962i	$-0.0411644\pi$
$967$	834.219	+	834.219i	0.862688	+	0.862688i	−0.128962	+	0.991650i	$0.541164\pi$
$968$	−219.894	+	219.894i	−0.227163	+	0.227163i
$969$		−	1243.71i		−	1.28350i
$970$	884.078	−	52.0762i	0.911421	−	0.0536868i
$971$	−1357.06			−1.39759			−0.698796	−	0.715321i	$-0.746280\pi$
$971$	−1357.06			−1.39759			−0.698796	+	0.715321i	$0.746280\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	226.730	−	226.730i	0.233022	−	0.233022i
$974$			98.4881i			0.101117i
$975$	56.0886	+	474.446i	0.0575268	+	0.486611i
$976$	−188.659			−0.193298
$977$	1099.64	+	1099.64i	1.12553	+	1.12553i	0.990895	+	0.134634i	$0.0429859\pi$
$977$	1099.64	+	1099.64i	1.12553	+	1.12553i	0.134634	+	0.990895i	$0.457014\pi$
$978$	174.015	−	174.015i	0.177930	−	0.177930i
$979$		−	143.050i		−	0.146118i
$980$	−4.11618	−	69.8789i	−0.00420019	−	0.0713050i
$981$	−3.01046			−0.00306877
$982$	207.513	+	207.513i	0.211316	+	0.211316i
$983$	329.200	−	329.200i	0.334893	−	0.334893i	−0.519548	−	0.854441i	$-0.673900\pi$
$983$	329.200	−	329.200i	0.334893	−	0.334893i	0.854441	+	0.519548i	$0.173900\pi$
$984$			48.7222i			0.0495144i
$985$	−620.382	+	698.043i	−0.629829	+	0.708673i
$986$	−1512.38			−1.53385
$987$	−29.2436	−	29.2436i	−0.0296288	−	0.0296288i
$988$	−579.852	+	579.852i	−0.586894	+	0.586894i
$989$			1451.80i			1.46795i
$990$	52.7149	+	46.8501i	0.0532474	+	0.0473233i
$991$	1117.81			1.12796			0.563978	−	0.825789i	$-0.309270\pi$
$991$	1117.81			1.12796			0.563978	+	0.825789i	$0.309270\pi$
$992$	−18.1712	−	18.1712i	−0.0183177	−	0.0183177i
$993$	32.8058	−	32.8058i	0.0330371	−	0.0330371i
$994$			320.574i			0.322509i
$995$	1115.72	−	65.7207i	1.12132	−	0.0660509i
$996$	−96.1532			−0.0965393
$997$	1308.85	+	1308.85i	1.31278	+	1.31278i	0.919355	+	0.393428i	$0.128711\pi$
$997$	1308.85	+	1308.85i	1.31278	+	1.31278i	0.393428	+	0.919355i	$0.371289\pi$
$998$	299.711	−	299.711i	0.300312	−	0.300312i
$999$		−	344.394i		−	0.344739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.b.127.3	yes	16
3.2	odd	2		630.3.o.f.127.3		16
5.2	odd	4		1050.3.l.h.43.7		16
5.3	odd	4	inner	210.3.l.b.43.3	✓	16
5.4	even	2		1050.3.l.h.757.7		16
15.8	even	4		630.3.o.f.253.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.3	✓	16	5.3	odd	4	inner
210.3.l.b.127.3	yes	16	1.1	even	1	trivial
630.3.o.f.127.3		16	3.2	odd	2
630.3.o.f.253.3		16	15.8	even	4
1050.3.l.h.43.7		16	5.2	odd	4
1050.3.l.h.757.7		16	5.4	even	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.294013 + 4.99135i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.294013 + 4.99135i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(4.69734 - 5.28536i) q^{10} -3.32459 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.80162 + 7.80162i) q^{13} +3.74166i q^{14} +(-6.47322 - 5.75304i) q^{15} -4.00000 q^{16} +(-13.6628 - 13.6628i) q^{17} +(-3.00000 + 3.00000i) q^{18} -37.1623i q^{19} +(-9.98270 + 0.588026i) q^{20} +4.58258 q^{21} +(3.32459 + 3.32459i) q^{22} +(-31.5017 + 31.5017i) q^{23} +4.89898i q^{24} +(-24.8271 + 2.93504i) q^{25} +15.6032 q^{26} +(3.67423 + 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +55.3464i q^{29} +(0.720182 + 12.2263i) q^{30} -4.54280 q^{31} +(4.00000 + 4.00000i) q^{32} +(4.07177 - 4.07177i) q^{33} +27.3257i q^{34} +(8.78791 - 9.88801i) q^{35} +6.00000 q^{36} +(-46.8661 - 46.8661i) q^{37} +(-37.1623 + 37.1623i) q^{38} -19.1100i q^{39} +(10.5707 + 9.39467i) q^{40} +9.94537 q^{41} +(-4.58258 - 4.58258i) q^{42} +(23.0431 - 23.0431i) q^{43} -6.64917i q^{44} +(14.9740 - 0.882039i) q^{45} +63.0035 q^{46} +(-6.38149 - 6.38149i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(27.7622 + 21.8921i) q^{50} +33.4670 q^{51} +(-15.6032 - 15.6032i) q^{52} +(-42.9239 + 42.9239i) q^{53} -7.34847i q^{54} +(-0.977472 - 16.5942i) q^{55} -7.48331 q^{56} +(45.5143 + 45.5143i) q^{57} +(55.3464 - 55.3464i) q^{58} -59.2884i q^{59} +(11.5061 - 12.9464i) q^{60} +47.1648 q^{61} +(4.54280 + 4.54280i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(-41.2344 - 36.6468i) q^{65} -8.14354 q^{66} +(8.48975 + 8.48975i) q^{67} +(27.3257 - 27.3257i) q^{68} -77.1632i q^{69} +(-18.6759 + 1.10010i) q^{70} +85.6769 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-34.7848 + 34.7848i) q^{73} +93.7322i q^{74} +(26.8122 - 34.0016i) q^{75} +74.3246 q^{76} +(6.21973 + 6.21973i) q^{77} +(-19.1100 + 19.1100i) q^{78} +96.4868i q^{79} +(-1.17605 - 19.9654i) q^{80} -9.00000 q^{81} +(-9.94537 - 9.94537i) q^{82} +(19.6272 - 19.6272i) q^{83} +9.16515i q^{84} +(64.1789 - 72.2131i) q^{85} -46.0863 q^{86} +(-67.7852 - 67.7852i) q^{87} +(-6.64917 + 6.64917i) q^{88} +43.0279i q^{89} +(-15.8561 - 14.0920i) q^{90} +29.1910 q^{91} +(-63.0035 - 63.0035i) q^{92} +(5.56377 - 5.56377i) q^{93} +12.7630i q^{94} +(185.490 - 10.9262i) q^{95} -9.79796 q^{96} +(88.5610 + 88.5610i) q^{97} +(7.00000 - 7.00000i) q^{98} +9.97376i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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