LMFDB - Embedded newform 210.3.l.b.43.4

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			43.4
Root			$0.170157 - 0.170157i$ of defining polynomial
Character	$\chi$	$=$	210.43
Dual form			210.3.l.b.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(4.80148 - 1.39490i) q^{5} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(4.80148 - 1.39490i) q^{5} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-3.40658 + 6.19639i) q^{10} -11.5078 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-7.70521 - 7.70521i) q^{13} +3.74166i q^{14} +(-7.58899 - 4.17219i) q^{15} -4.00000 q^{16} +(21.0749 - 21.0749i) q^{17} +(-3.00000 - 3.00000i) q^{18} -24.1173i q^{19} +(-2.78980 - 9.60297i) q^{20} -4.58258 q^{21} +(11.5078 - 11.5078i) q^{22} +(30.1762 + 30.1762i) q^{23} -4.89898i q^{24} +(21.1085 - 13.3952i) q^{25} +15.4104 q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -51.1392i q^{29} +(11.7612 - 3.41680i) q^{30} -46.9852 q^{31} +(4.00000 - 4.00000i) q^{32} +(14.0941 + 14.0941i) q^{33} +42.1499i q^{34} +(6.37313 - 11.5924i) q^{35} +6.00000 q^{36} +(-8.50020 + 8.50020i) q^{37} +(24.1173 + 24.1173i) q^{38} +18.8738i q^{39} +(12.3928 + 6.81316i) q^{40} +18.6089 q^{41} +(4.58258 - 4.58258i) q^{42} +(-26.1383 - 26.1383i) q^{43} +23.0156i q^{44} +(4.18471 + 14.4045i) q^{45} -60.3523 q^{46} +(50.1311 - 50.1311i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} +(-7.71330 + 34.5037i) q^{50} -51.6228 q^{51} +(-15.4104 + 15.4104i) q^{52} +(7.08527 + 7.08527i) q^{53} +7.34847i q^{54} +(-55.2546 + 16.0523i) q^{55} +7.48331 q^{56} +(-29.5376 + 29.5376i) q^{57} +(51.1392 + 51.1392i) q^{58} +94.3487i q^{59} +(-8.34439 + 15.1780i) q^{60} +8.09003 q^{61} +(46.9852 - 46.9852i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} +(-47.7445 - 26.2484i) q^{65} -28.1883 q^{66} +(-20.6469 + 20.6469i) q^{67} +(-42.1499 - 42.1499i) q^{68} -73.9162i q^{69} +(5.21925 + 17.9655i) q^{70} -63.7595 q^{71} +(-6.00000 + 6.00000i) q^{72} +(50.1883 + 50.1883i) q^{73} -17.0004i q^{74} +(-42.2582 - 9.44682i) q^{75} -48.2346 q^{76} +(-21.5292 + 21.5292i) q^{77} +(-18.8738 - 18.8738i) q^{78} -1.06121i q^{79} +(-19.2059 + 5.57961i) q^{80} -9.00000 q^{81} +(-18.6089 + 18.6089i) q^{82} +(53.6243 + 53.6243i) q^{83} +9.16515i q^{84} +(71.7935 - 130.588i) q^{85} +52.2765 q^{86} +(-62.6325 + 62.6325i) q^{87} +(-23.0156 - 23.0156i) q^{88} +145.154i q^{89} +(-18.5892 - 10.2197i) q^{90} -28.8303 q^{91} +(60.3523 - 60.3523i) q^{92} +(57.5449 + 57.5449i) q^{93} +100.262i q^{94} +(-33.6413 - 115.799i) q^{95} -9.79796 q^{96} +(23.7872 - 23.7872i) q^{97} +(7.00000 + 7.00000i) q^{98} -34.5235i 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$5$	4.80148	−	1.39490i	0.960297	−	0.278980i
$5$	4.80148	−	1.39490i	0.960297	−	0.278980i
$6$	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
$10$	−3.40658	+	6.19639i	−0.340658	+	0.619639i
$11$	−11.5078			−1.04617			−0.523083	−	0.852282i	$-0.675218\pi$
$11$	−11.5078			−1.04617			−0.523083	+	0.852282i	$0.675218\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−7.70521	−	7.70521i	−0.592708	−	0.592708i	0.345654	−	0.938362i	$-0.387657\pi$
$13$	−7.70521	−	7.70521i	−0.592708	−	0.592708i	−0.938362	+	0.345654i	$0.887657\pi$
$14$			3.74166i			0.267261i
$15$	−7.58899	−	4.17219i	−0.505933	−	0.278146i
$16$	−4.00000			−0.250000
$17$	21.0749	−	21.0749i	1.23970	−	1.23970i	0.279579	−	0.960123i	$-0.409805\pi$
$17$	21.0749	−	21.0749i	1.23970	−	1.23970i	0.960123	−	0.279579i	$-0.0901950\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	24.1173i		−	1.26933i	−0.772786	−	0.634666i	$-0.781138\pi$
$19$		−	24.1173i		−	1.26933i	0.772786	−	0.634666i	$-0.218862\pi$
$20$	−2.78980	−	9.60297i	−0.139490	−	0.480148i
$21$	−4.58258			−0.218218
$22$	11.5078	−	11.5078i	0.523083	−	0.523083i
$23$	30.1762	+	30.1762i	1.31201	+	1.31201i	0.919934	+	0.392073i	$0.128242\pi$
$23$	30.1762	+	30.1762i	1.31201	+	1.31201i	0.392073	+	0.919934i	$0.371758\pi$
$24$		−	4.89898i		−	0.204124i
$25$	21.1085	−	13.3952i	0.844340	−	0.535808i
$26$	15.4104			0.592708
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$		−	51.1392i		−	1.76342i	−0.471790	−	0.881711i	$-0.656392\pi$
$29$		−	51.1392i		−	1.76342i	0.471790	−	0.881711i	$-0.343608\pi$
$30$	11.7612	−	3.41680i	0.392040	−	0.113893i
$31$	−46.9852			−1.51565			−0.757826	−	0.652457i	$-0.773738\pi$
$31$	−46.9852			−1.51565			−0.757826	+	0.652457i	$0.773738\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	14.0941	+	14.0941i	0.427095	+	0.427095i
$34$			42.1499i			1.23970i
$35$	6.37313	−	11.5924i	0.182089	−	0.331211i
$36$	6.00000			0.166667
$37$	−8.50020	+	8.50020i	−0.229735	+	0.229735i	−0.812582	−	0.582847i	$-0.801939\pi$
$37$	−8.50020	+	8.50020i	−0.229735	+	0.229735i	0.582847	+	0.812582i	$0.301939\pi$
$38$	24.1173	+	24.1173i	0.634666	+	0.634666i
$39$			18.8738i			0.483944i
$40$	12.3928	+	6.81316i	0.309819	+	0.170329i
$41$	18.6089			0.453875			0.226937	−	0.973909i	$-0.427129\pi$
$41$	18.6089			0.453875			0.226937	+	0.973909i	$0.427129\pi$
$42$	4.58258	−	4.58258i	0.109109	−	0.109109i
$43$	−26.1383	−	26.1383i	−0.607867	−	0.607867i	0.334522	−	0.942388i	$-0.391425\pi$
$43$	−26.1383	−	26.1383i	−0.607867	−	0.607867i	−0.942388	+	0.334522i	$0.891425\pi$
$44$			23.0156i			0.523083i
$45$	4.18471	+	14.4045i	0.0929935	+	0.320099i
$46$	−60.3523			−1.31201
$47$	50.1311	−	50.1311i	1.06662	−	1.06662i	0.0690016	−	0.997617i	$-0.478019\pi$
$47$	50.1311	−	50.1311i	1.06662	−	1.06662i	0.997617	−	0.0690016i	$-0.0219813\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$	−7.71330	+	34.5037i	−0.154266	+	0.690074i
$51$	−51.6228			−1.01221
$52$	−15.4104	+	15.4104i	−0.296354	+	0.296354i
$53$	7.08527	+	7.08527i	0.133684	+	0.133684i	0.770783	−	0.637098i	$-0.219865\pi$
$53$	7.08527	+	7.08527i	0.133684	+	0.133684i	−0.637098	+	0.770783i	$0.719865\pi$
$54$			7.34847i			0.136083i
$55$	−55.2546	+	16.0523i	−1.00463	+	0.291860i
$56$	7.48331			0.133631
$57$	−29.5376	+	29.5376i	−0.518203	+	0.518203i
$58$	51.1392	+	51.1392i	0.881711	+	0.881711i
$59$			94.3487i			1.59913i	0.600579	+	0.799565i	$0.294937\pi$
$59$			94.3487i			1.59913i	−0.600579	+	0.799565i	$0.705063\pi$
$60$	−8.34439	+	15.1780i	−0.139073	+	0.252966i
$61$	8.09003			0.132623			0.0663117	−	0.997799i	$-0.478877\pi$
$61$	8.09003			0.132623			0.0663117	+	0.997799i	$0.478877\pi$
$62$	46.9852	−	46.9852i	0.757826	−	0.757826i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$			8.00000i			0.125000i
$65$	−47.7445	−	26.2484i	−0.734530	−	0.403822i
$66$	−28.1883			−0.427095
$67$	−20.6469	+	20.6469i	−0.308163	+	0.308163i	−0.844197	−	0.536034i	$-0.819922\pi$
$67$	−20.6469	+	20.6469i	−0.308163	+	0.308163i	0.536034	+	0.844197i	$0.319922\pi$
$68$	−42.1499	−	42.1499i	−0.619851	−	0.619851i
$69$		−	73.9162i		−	1.07125i
$70$	5.21925	+	17.9655i	0.0745607	+	0.256650i
$71$	−63.7595			−0.898021			−0.449011	−	0.893526i	$-0.648223\pi$
$71$	−63.7595			−0.898021			−0.449011	+	0.893526i	$0.648223\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	50.1883	+	50.1883i	0.687511	+	0.687511i	0.961681	−	0.274170i	$-0.0884031\pi$
$73$	50.1883	+	50.1883i	0.687511	+	0.687511i	−0.274170	+	0.961681i	$0.588403\pi$
$74$		−	17.0004i		−	0.229735i
$75$	−42.2582	−	9.44682i	−0.563443	−	0.125958i
$76$	−48.2346			−0.634666
$77$	−21.5292	+	21.5292i	−0.279599	+	0.279599i
$78$	−18.8738	−	18.8738i	−0.241972	−	0.241972i
$79$		−	1.06121i		−	0.0134331i	−0.999977	−	0.00671653i	$-0.997862\pi$
$79$		−	1.06121i		−	0.0134331i	0.999977	−	0.00671653i	$-0.00213796\pi$
$80$	−19.2059	+	5.57961i	−0.240074	+	0.0697451i
$81$	−9.00000			−0.111111
$82$	−18.6089	+	18.6089i	−0.226937	+	0.226937i
$83$	53.6243	+	53.6243i	0.646075	+	0.646075i	0.952042	−	0.305967i	$-0.0989796\pi$
$83$	53.6243	+	53.6243i	0.646075	+	0.646075i	−0.305967	+	0.952042i	$0.598980\pi$
$84$			9.16515i			0.109109i
$85$	71.7935	−	130.588i	0.844629	−	1.53633i
$86$	52.2765			0.607867
$87$	−62.6325	+	62.6325i	−0.719914	+	0.719914i
$88$	−23.0156	−	23.0156i	−0.261541	−	0.261541i
$89$			145.154i			1.63095i	0.578794	+	0.815473i	$0.303523\pi$
$89$			145.154i			1.63095i	−0.578794	+	0.815473i	$0.696477\pi$
$90$	−18.5892	−	10.2197i	−0.206546	−	0.113553i
$91$	−28.8303			−0.316816
$92$	60.3523	−	60.3523i	0.656003	−	0.656003i
$93$	57.5449	+	57.5449i	0.618762	+	0.618762i
$94$			100.262i			1.06662i
$95$	−33.6413	−	115.799i	−0.354119	−	1.21894i
$96$	−9.79796			−0.102062
$97$	23.7872	−	23.7872i	0.245229	−	0.245229i	−0.573780	−	0.819009i	$-0.694524\pi$
$97$	23.7872	−	23.7872i	0.245229	−	0.245229i	0.819009	+	0.573780i	$0.194524\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$		−	34.5235i		−	0.348722i
$100$	−26.7904	−	42.2170i	−0.267904	−	0.422170i
$101$	50.1467			0.496502			0.248251	−	0.968696i	$-0.420144\pi$
$101$	50.1467			0.496502			0.248251	+	0.968696i	$0.420144\pi$
$102$	51.6228	−	51.6228i	0.506106	−	0.506106i
$103$	56.3876	+	56.3876i	0.547453	+	0.547453i	0.925703	−	0.378251i	$-0.123474\pi$
$103$	56.3876	+	56.3876i	0.547453	+	0.547453i	−0.378251	+	0.925703i	$0.623474\pi$
$104$		−	30.8208i		−	0.296354i
$105$	−22.0032	+	6.39224i	−0.209554	+	0.0608785i
$106$	−14.1705			−0.133684
$107$	−135.365	+	135.365i	−1.26510	+	1.26510i	−0.316506	+	0.948590i	$0.602510\pi$
$107$	−135.365	+	135.365i	−1.26510	+	1.26510i	−0.948590	+	0.316506i	$0.897490\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			100.934i			0.926001i	0.886358	+	0.463001i	$0.153227\pi$
$109$			100.934i			0.926001i	−0.886358	+	0.463001i	$0.846773\pi$
$110$	39.2023	−	71.3069i	0.356385	−	0.648245i
$111$	20.8211			0.187578
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	25.3174	+	25.3174i	0.224048	+	0.224048i	0.810201	−	0.586153i	$-0.199358\pi$
$113$	25.3174	+	25.3174i	0.224048	+	0.224048i	−0.586153	+	0.810201i	$0.699358\pi$
$114$		−	59.0751i		−	0.518203i
$115$	186.983	+	102.798i	1.62594	+	0.893892i
$116$	−102.278			−0.881711
$117$	23.1156	−	23.1156i	0.197569	−	0.197569i
$118$	−94.3487	−	94.3487i	−0.799565	−	0.799565i
$119$		−	78.8552i		−	0.662649i
$120$	−6.83360	−	23.5224i	−0.0569466	−	0.196020i
$121$	11.4299			0.0944623
$122$	−8.09003	+	8.09003i	−0.0663117	+	0.0663117i
$123$	−22.7911	−	22.7911i	−0.185294	−	0.185294i
$124$			93.9704i			0.757826i
$125$	82.6671	−	93.7611i	0.661337	−	0.750089i
$126$	−11.2250			−0.0890871
$127$	116.746	−	116.746i	0.919262	−	0.919262i	−0.0777140	−	0.996976i	$-0.524762\pi$
$127$	116.746	−	116.746i	0.919262	−	0.919262i	0.996976	+	0.0777140i	$0.0247621\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			64.0254i			0.496321i
$130$	73.9929	−	21.4960i	0.569176	−	0.165354i
$131$	34.8004			0.265652			0.132826	−	0.991139i	$-0.457595\pi$
$131$	34.8004			0.265652			0.132826	+	0.991139i	$0.457595\pi$
$132$	28.1883	−	28.1883i	0.213548	−	0.213548i
$133$	−45.1194	−	45.1194i	−0.339243	−	0.339243i
$134$		−	41.2938i		−	0.308163i
$135$	12.5166	−	22.7670i	0.0927154	−	0.168644i
$136$	84.2997			0.619851
$137$	131.552	−	131.552i	0.960235	−	0.960235i	−0.0390044	−	0.999239i	$-0.512419\pi$
$137$	131.552	−	131.552i	0.960235	−	0.960235i	0.999239	+	0.0390044i	$0.0124186\pi$
$138$	73.9162	+	73.9162i	0.535625	+	0.535625i
$139$		−	89.4407i		−	0.643458i	−0.946832	−	0.321729i	$-0.895736\pi$
$139$		−	89.4407i		−	0.643458i	0.946832	−	0.321729i	$-0.104264\pi$
$140$	−23.1848	−	12.7463i	−0.165605	−	0.0910447i
$141$	−122.795			−0.870890
$142$	63.7595	−	63.7595i	0.449011	−	0.449011i
$143$	88.6702	+	88.6702i	0.620071	+	0.620071i
$144$		−	12.0000i		−	0.0833333i
$145$	−71.3342	−	245.544i	−0.491960	−	1.69341i
$146$	−100.377			−0.687511
$147$	−8.57321	+	8.57321i	−0.0583212	+	0.0583212i
$148$	17.0004	+	17.0004i	0.114868	+	0.114868i
$149$			55.7399i			0.374093i	0.982351	+	0.187047i	$0.0598915\pi$
$149$			55.7399i			0.374093i	−0.982351	+	0.187047i	$0.940108\pi$
$150$	51.7050	−	32.8114i	0.344700	−	0.218743i
$151$	82.9665			0.549447			0.274724	−	0.961523i	$-0.411414\pi$
$151$	82.9665			0.549447			0.274724	+	0.961523i	$0.411414\pi$
$152$	48.2346	−	48.2346i	0.317333	−	0.317333i
$153$	63.2248	+	63.2248i	0.413234	+	0.413234i
$154$		−	43.0583i		−	0.279599i
$155$	−225.599	+	65.5398i	−1.45548	+	0.422837i
$156$	37.7477			0.241972
$157$	−99.7950	+	99.7950i	−0.635637	+	0.635637i	−0.949476	−	0.313839i	$-0.898385\pi$
$157$	−99.7950	+	99.7950i	−0.635637	+	0.635637i	0.313839	+	0.949476i	$0.398385\pi$
$158$	1.06121	+	1.06121i	0.00671653	+	0.00671653i
$159$		−	17.3553i		−	0.109153i
$160$	13.6263	−	24.7855i	0.0851645	−	0.154910i
$161$	112.909			0.701297
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−45.3884	−	45.3884i	−0.278457	−	0.278457i	0.554036	−	0.832493i	$-0.313087\pi$
$163$	−45.3884	−	45.3884i	−0.278457	−	0.278457i	−0.832493	+	0.554036i	$0.813087\pi$
$164$		−	37.2177i		−	0.226937i
$165$	87.3328	+	48.0129i	0.529289	+	0.290987i
$166$	−107.249			−0.646075
$167$	−99.2501	+	99.2501i	−0.594312	+	0.594312i	−0.938793	−	0.344481i	$-0.888055\pi$
$167$	−99.2501	+	99.2501i	−0.594312	+	0.594312i	0.344481	+	0.938793i	$0.388055\pi$
$168$	−9.16515	−	9.16515i	−0.0545545	−	0.0545545i
$169$		−	50.2595i		−	0.297393i
$170$	58.7949	+	202.382i	0.345853	+	1.19048i
$171$	72.3520			0.423111
$172$	−52.2765	+	52.2765i	−0.303933	+	0.303933i
$173$	−80.5404	−	80.5404i	−0.465551	−	0.465551i	0.434919	−	0.900470i	$-0.356777\pi$
$173$	−80.5404	−	80.5404i	−0.465551	−	0.465551i	−0.900470	+	0.434919i	$0.856777\pi$
$174$		−	125.265i		−	0.719914i
$175$	14.4303	−	64.5505i	0.0824586	−	0.368860i
$176$	46.0313			0.261541
$177$	115.553	−	115.553i	0.652842	−	0.652842i
$178$	−145.154	−	145.154i	−0.815473	−	0.815473i
$179$		−	154.267i		−	0.861824i	−0.902394	−	0.430912i	$-0.858192\pi$
$179$		−	154.267i		−	0.861824i	0.902394	−	0.430912i	$-0.141808\pi$
$180$	28.8089	−	8.36941i	0.160049	−	0.0464967i
$181$	166.548			0.920155			0.460078	−	0.887879i	$-0.347822\pi$
$181$	166.548			0.920155			0.460078	+	0.887879i	$0.347822\pi$
$182$	28.8303	−	28.8303i	0.158408	−	0.158408i
$183$	−9.90822	−	9.90822i	−0.0541433	−	0.0541433i
$184$			120.705i			0.656003i
$185$	−28.9566	+	52.6705i	−0.156522	+	0.284705i
$186$	−115.090			−0.618762
$187$	−242.527	+	242.527i	−1.29693	+	1.29693i
$188$	−100.262	−	100.262i	−0.533309	−	0.533309i
$189$		−	13.7477i		−	0.0727393i
$190$	149.440	+	82.1576i	0.786528	+	0.432409i
$191$	−235.646			−1.23375			−0.616873	−	0.787063i	$-0.711601\pi$
$191$	−235.646			−1.23375			−0.616873	+	0.787063i	$0.711601\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	−16.2211	−	16.2211i	−0.0840471	−	0.0840471i	0.663833	−	0.747880i	$-0.268928\pi$
$193$	−16.2211	−	16.2211i	−0.0840471	−	0.0840471i	−0.747880	+	0.663833i	$0.768928\pi$
$194$			47.5744i			0.245229i
$195$	26.3271	+	90.6224i	0.135011	+	0.464730i
$196$	−14.0000			−0.0714286
$197$	−6.68134	+	6.68134i	−0.0339154	+	0.0339154i	−0.723861	−	0.689946i	$-0.757634\pi$
$197$	−6.68134	+	6.68134i	−0.0339154	+	0.0339154i	0.689946	+	0.723861i	$0.257634\pi$
$198$	34.5235	+	34.5235i	0.174361	+	0.174361i
$199$			32.0712i			0.161162i	0.996748	+	0.0805808i	$0.0256775\pi$
$199$			32.0712i			0.161162i	−0.996748	+	0.0805808i	$0.974322\pi$
$200$	69.0074	+	15.4266i	0.345037	+	0.0771330i
$201$	50.5744			0.251614
$202$	−50.1467	+	50.1467i	−0.248251	+	0.248251i
$203$	−95.6728	−	95.6728i	−0.471294	−	0.471294i
$204$			103.246i			0.506106i
$205$	89.3502	−	25.9575i	0.435855	−	0.126622i
$206$	−112.775			−0.547453
$207$	−90.5285	+	90.5285i	−0.437336	+	0.437336i
$208$	30.8208	+	30.8208i	0.148177	+	0.148177i
$209$			277.538i			1.32793i
$210$	15.6109	−	28.3954i	0.0743377	−	0.135216i
$211$	123.531			0.585457			0.292728	−	0.956196i	$-0.405437\pi$
$211$	123.531			0.585457			0.292728	+	0.956196i	$0.405437\pi$
$212$	14.1705	−	14.1705i	0.0668422	−	0.0668422i
$213$	78.0891	+	78.0891i	0.366616	+	0.366616i
$214$		−	270.731i		−	1.26510i
$215$	−161.963	−	89.0421i	−0.753315	−	0.414149i
$216$	14.6969			0.0680414
$217$	−87.9013	+	87.9013i	−0.405075	+	0.405075i
$218$	−100.934	−	100.934i	−0.463001	−	0.463001i
$219$		−	122.936i		−	0.561350i
$220$	32.1046	+	110.509i	0.145930	+	0.502315i
$221$	−324.774			−1.46956
$222$	−20.8211	+	20.8211i	−0.0937890	+	0.0937890i
$223$	−81.9590	−	81.9590i	−0.367529	−	0.367529i	0.499046	−	0.866575i	$-0.333684\pi$
$223$	−81.9590	−	81.9590i	−0.367529	−	0.367529i	−0.866575	+	0.499046i	$0.833684\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	40.1856	+	63.3255i	0.178603	+	0.281447i
$226$	−50.6348			−0.224048
$227$	93.6089	−	93.6089i	0.412374	−	0.412374i	−0.470191	−	0.882565i	$-0.655815\pi$
$227$	93.6089	−	93.6089i	0.412374	−	0.412374i	0.882565	+	0.470191i	$0.155815\pi$
$228$	59.0751	+	59.0751i	0.259101	+	0.259101i
$229$			348.973i			1.52390i	0.647635	+	0.761950i	$0.275758\pi$
$229$			348.973i			1.52390i	−0.647635	+	0.761950i	$0.724242\pi$
$230$	−289.781	+	84.1856i	−1.25992	+	0.366024i
$231$	52.7355			0.228292
$232$	102.278	−	102.278i	0.440856	−	0.440856i
$233$	208.319	+	208.319i	0.894074	+	0.894074i	0.994904	−	0.100829i	$-0.0321496\pi$
$233$	208.319	+	208.319i	0.894074	+	0.894074i	−0.100829	+	0.994904i	$0.532150\pi$
$234$			46.2313i			0.197569i
$235$	170.776	−	310.631i	0.726704	−	1.32184i
$236$	188.697			0.799565
$237$	−1.29971	+	1.29971i	−0.00548403	+	0.00548403i
$238$	78.8552	+	78.8552i	0.331324	+	0.331324i
$239$			330.793i			1.38407i	0.721864	+	0.692035i	$0.243285\pi$
$239$			330.793i			1.38407i	−0.721864	+	0.692035i	$0.756715\pi$
$240$	30.3560	+	16.6888i	0.126483	+	0.0695366i
$241$	375.584			1.55844			0.779221	−	0.626749i	$-0.215615\pi$
$241$	375.584			1.55844			0.779221	+	0.626749i	$0.215615\pi$
$242$	−11.4299	+	11.4299i	−0.0472312	+	0.0472312i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		−	16.1801i		−	0.0663117i
$245$	−9.76432	−	33.6104i	−0.0398543	−	0.137185i
$246$	45.5822			0.185294
$247$	−185.829	+	185.829i	−0.752344	+	0.752344i
$248$	−93.9704	−	93.9704i	−0.378913	−	0.378913i
$249$		−	131.352i		−	0.527518i
$250$	11.0940	+	176.428i	0.0443761	+	0.705713i
$251$	41.2876			0.164493			0.0822463	−	0.996612i	$-0.473791\pi$
$251$	41.2876			0.164493			0.0822463	+	0.996612i	$0.473791\pi$
$252$	11.2250	−	11.2250i	0.0445435	−	0.0445435i
$253$	−347.262	−	347.262i	−1.37258	−	1.37258i
$254$			233.492i			0.919262i
$255$	−247.866	+	72.0088i	−0.972024	+	0.282387i
$256$	16.0000			0.0625000
$257$	−101.370	+	101.370i	−0.394437	+	0.394437i	−0.876266	−	0.481828i	$-0.839973\pi$
$257$	−101.370	+	101.370i	−0.394437	+	0.394437i	0.481828	+	0.876266i	$0.339973\pi$
$258$	−64.0254	−	64.0254i	−0.248161	−	0.248161i
$259$			31.8048i			0.122799i
$260$	−52.4969	+	95.4889i	−0.201911	+	0.367265i
$261$	153.418			0.587807
$262$	−34.8004	+	34.8004i	−0.132826	+	0.132826i
$263$	164.594	+	164.594i	0.625833	+	0.625833i	0.947017	−	0.321184i	$-0.104081\pi$
$263$	164.594	+	164.594i	0.625833	+	0.625833i	−0.321184	+	0.947017i	$0.604081\pi$
$264$			56.3766i			0.213548i
$265$	43.9031	+	24.1366i	0.165672	+	0.0910813i
$266$	90.2387			0.339243
$267$	177.777	−	177.777i	0.665831	−	0.665831i
$268$	41.2938	+	41.2938i	0.154081	+	0.154081i
$269$		−	254.148i		−	0.944788i	−0.881387	−	0.472394i	$-0.843390\pi$
$269$		−	254.148i		−	0.944788i	0.881387	−	0.472394i	$-0.156610\pi$
$270$	10.2504	+	35.2836i	0.0379644	+	0.130680i
$271$	22.4723			0.0829237			0.0414619	−	0.999140i	$-0.486798\pi$
$271$	22.4723			0.0829237			0.0414619	+	0.999140i	$0.486798\pi$
$272$	−84.2997	+	84.2997i	−0.309925	+	0.309925i
$273$	35.3097	+	35.3097i	0.129340	+	0.129340i
$274$			263.104i			0.960235i
$275$	−242.913	+	154.150i	−0.883319	+	0.560544i
$276$	−147.832			−0.535625
$277$	47.3949	−	47.3949i	0.171101	−	0.171101i	−0.616362	−	0.787463i	$-0.711394\pi$
$277$	47.3949	−	47.3949i	0.171101	−	0.171101i	0.787463	+	0.616362i	$0.211394\pi$
$278$	89.4407	+	89.4407i	0.321729	+	0.321729i
$279$		−	140.956i		−	0.505217i
$280$	35.9310	−	10.4385i	0.128325	−	0.0372803i
$281$	−18.8810			−0.0671920			−0.0335960	−	0.999435i	$-0.510696\pi$
$281$	−18.8810			−0.0671920			−0.0335960	+	0.999435i	$0.510696\pi$
$282$	122.795	−	122.795i	0.435445	−	0.435445i
$283$	−115.825	−	115.825i	−0.409277	−	0.409277i	0.472209	−	0.881486i	$-0.343457\pi$
$283$	−115.825	−	115.825i	−0.409277	−	0.409277i	−0.881486	+	0.472209i	$0.843457\pi$
$284$			127.519i			0.449011i
$285$	−100.622	+	183.026i	−0.353060	+	0.642197i
$286$	−177.340			−0.620071
$287$	34.8140	−	34.8140i	0.121303	−	0.121303i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	599.306i		−	2.07372i
$290$	316.879	+	174.210i	1.09268	+	0.600724i
$291$	−58.2665			−0.200228
$292$	100.377	−	100.377i	0.343756	−	0.343756i
$293$	224.451	+	224.451i	0.766043	+	0.766043i	0.977407	−	0.211364i	$-0.0677906\pi$
$293$	224.451	+	224.451i	0.766043	+	0.766043i	−0.211364	+	0.977407i	$0.567791\pi$
$294$		−	17.1464i		−	0.0583212i
$295$	131.607	+	453.014i	0.446126	+	1.53564i
$296$	−34.0008			−0.114868
$297$	−42.2824	+	42.2824i	−0.142365	+	0.142365i
$298$	−55.7399	−	55.7399i	−0.187047	−	0.187047i
$299$		−	465.027i		−	1.55528i
$300$	−18.8936	+	84.5165i	−0.0629788	+	0.281722i
$301$	−97.8004			−0.324918
$302$	−82.9665	+	82.9665i	−0.274724	+	0.274724i
$303$	−61.4169	−	61.4169i	−0.202696	−	0.202696i
$304$			96.4693i			0.317333i
$305$	38.8441	−	11.2848i	0.127358	−	0.0369993i
$306$	−126.450			−0.413234
$307$	−42.5120	+	42.5120i	−0.138476	+	0.138476i	−0.772947	−	0.634471i	$-0.781218\pi$
$307$	−42.5120	+	42.5120i	−0.138476	+	0.138476i	0.634471	+	0.772947i	$0.281218\pi$
$308$	43.0583	+	43.0583i	0.139800	+	0.139800i
$309$		−	138.121i		−	0.446993i
$310$	160.059	−	291.139i	0.516319	−	0.939157i
$311$	−97.1353			−0.312332			−0.156166	−	0.987731i	$-0.549914\pi$
$311$	−97.1353			−0.312332			−0.156166	+	0.987731i	$0.549914\pi$
$312$	−37.7477	+	37.7477i	−0.120986	+	0.120986i
$313$	−94.4913	−	94.4913i	−0.301889	−	0.301889i	0.539863	−	0.841753i	$-0.318476\pi$
$313$	−94.4913	−	94.4913i	−0.301889	−	0.301889i	−0.841753	+	0.539863i	$0.818476\pi$
$314$		−	199.590i		−	0.635637i
$315$	34.7771	+	19.1194i	0.110404	+	0.0606965i
$316$	−2.12242			−0.00671653
$317$	146.150	−	146.150i	0.461040	−	0.461040i	−0.437956	−	0.898996i	$-0.644297\pi$
$317$	146.150	−	146.150i	0.461040	−	0.461040i	0.898996	+	0.437956i	$0.144297\pi$
$318$	17.3553	+	17.3553i	0.0545764	+	0.0545764i
$319$			588.501i			1.84483i
$320$	11.1592	+	38.4119i	0.0348726	+	0.120037i
$321$	331.576			1.03295
$322$	−112.909	+	112.909i	−0.350649	+	0.350649i
$323$	−508.271	−	508.271i	−1.57359	−	1.57359i
$324$			18.0000i			0.0555556i
$325$	−265.858	−	59.4326i	−0.818025	−	0.182869i
$326$	90.7768			0.278457
$327$	123.619	−	123.619i	0.378039	−	0.378039i
$328$	37.2177	+	37.2177i	0.113469	+	0.113469i
$329$		−	187.573i		−	0.570131i
$330$	−135.346	+	39.3199i	−0.410138	+	0.119151i
$331$	223.981			0.676679			0.338339	−	0.941024i	$-0.390135\pi$
$331$	223.981			0.676679			0.338339	+	0.941024i	$0.390135\pi$
$332$	107.249	−	107.249i	0.323038	−	0.323038i
$333$	−25.5006	−	25.5006i	−0.0765784	−	0.0765784i
$334$		−	198.500i		−	0.594312i
$335$	−70.3354	+	127.936i	−0.209956	+	0.381899i
$336$	18.3303			0.0545545
$337$	−41.7444	+	41.7444i	−0.123871	+	0.123871i	−0.766324	−	0.642454i	$-0.777916\pi$
$337$	−41.7444	+	41.7444i	−0.123871	+	0.123871i	0.642454	+	0.766324i	$0.277916\pi$
$338$	50.2595	+	50.2595i	0.148697	+	0.148697i
$339$		−	62.0147i		−	0.182934i
$340$	−261.177	−	143.587i	−0.768167	−	0.422315i
$341$	540.697			1.58562
$342$	−72.3520	+	72.3520i	−0.211555	+	0.211555i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$		−	104.553i		−	0.303933i
$345$	−103.106	−	354.907i	−0.298858	−	1.02872i
$346$	161.081			0.465551
$347$	283.163	−	283.163i	0.816031	−	0.816031i	−0.169500	−	0.985530i	$-0.554215\pi$
$347$	283.163	−	283.163i	0.816031	−	0.816031i	0.985530	+	0.169500i	$0.0542152\pi$
$348$	125.265	+	125.265i	0.359957	+	0.359957i
$349$		−	73.8529i		−	0.211613i	−0.994387	−	0.105807i	$-0.966258\pi$
$349$		−	73.8529i		−	0.211613i	0.994387	−	0.105807i	$-0.0337424\pi$
$350$	50.1203	+	78.9808i	0.143201	+	0.225659i
$351$	−56.6215			−0.161315
$352$	−46.0313	+	46.0313i	−0.130771	+	0.130771i
$353$	−221.700	−	221.700i	−0.628047	−	0.628047i	0.319530	−	0.947576i	$-0.396475\pi$
$353$	−221.700	−	221.700i	−0.628047	−	0.628047i	−0.947576	+	0.319530i	$0.896475\pi$
$354$			231.106i			0.652842i
$355$	−306.140	+	88.9383i	−0.862367	+	0.250530i
$356$	290.309			0.815473
$357$	−96.5775	+	96.5775i	−0.270525	+	0.270525i
$358$	154.267	+	154.267i	0.430912	+	0.430912i
$359$		−	351.735i		−	0.979764i	−0.871789	−	0.489882i	$-0.837040\pi$
$359$		−	351.735i		−	0.979764i	0.871789	−	0.489882i	$-0.162960\pi$
$360$	−20.4395	+	37.1783i	−0.0567764	+	0.103273i
$361$	−220.645			−0.611205
$362$	−166.548	+	166.548i	−0.460078	+	0.460078i
$363$	−13.9988	−	13.9988i	−0.0385641	−	0.0385641i
$364$			57.6605i			0.158408i
$365$	310.986	+	170.971i	0.852017	+	0.468413i
$366$	19.8164			0.0541433
$367$	9.03767	−	9.03767i	0.0246258	−	0.0246258i	−0.694687	−	0.719312i	$-0.744457\pi$
$367$	9.03767	−	9.03767i	0.0246258	−	0.0246258i	0.719312	+	0.694687i	$0.244457\pi$
$368$	−120.705	−	120.705i	−0.328002	−	0.328002i
$369$			55.8266i			0.151292i
$370$	−23.7139	−	81.6271i	−0.0640916	−	0.220614i
$371$	26.5107			0.0714573
$372$	115.090	−	115.090i	0.309381	−	0.309381i
$373$	−151.095	−	151.095i	−0.405079	−	0.405079i	0.474939	−	0.880019i	$-0.342470\pi$
$373$	−151.095	−	151.095i	−0.405079	−	0.405079i	−0.880019	+	0.474939i	$0.842470\pi$
$374$		−	485.053i		−	1.29693i
$375$	−216.080	+	13.5873i	−0.576212	+	0.0362329i
$376$	200.524			0.533309
$377$	−394.039	+	394.039i	−1.04520	+	1.04520i
$378$	13.7477	+	13.7477i	0.0363696	+	0.0363696i
$379$		−	268.787i		−	0.709201i	−0.935018	−	0.354601i	$-0.884617\pi$
$379$		−	268.787i		−	0.709201i	0.935018	−	0.354601i	$-0.115383\pi$
$380$	−231.598	+	67.2826i	−0.609468	+	0.177059i
$381$	−285.969			−0.750574
$382$	235.646	−	235.646i	0.616873	−	0.616873i
$383$	304.341	+	304.341i	0.794625	+	0.794625i	0.982242	−	0.187618i	$-0.0600766\pi$
$383$	304.341	+	304.341i	0.794625	+	0.794625i	−0.187618	+	0.982242i	$0.560077\pi$
$384$			19.5959i			0.0510310i
$385$	−73.3408	+	133.403i	−0.190496	+	0.346501i
$386$	32.4422			0.0840471
$387$	78.4148	−	78.4148i	0.202622	−	0.202622i
$388$	−47.5744	−	47.5744i	−0.122614	−	0.122614i
$389$			50.0127i			0.128567i	0.997932	+	0.0642837i	$0.0204763\pi$
$389$			50.0127i			0.128567i	−0.997932	+	0.0642837i	$0.979524\pi$
$390$	−116.950	−	64.2952i	−0.299871	−	0.164860i
$391$	1271.92			3.25299
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$	−42.6216	−	42.6216i	−0.108452	−	0.108452i
$394$		−	13.3627i		−	0.0339154i
$395$	−1.48029	−	5.09539i	−0.00374756	−	0.0128997i
$396$	−69.0469			−0.174361
$397$	−325.002	+	325.002i	−0.818644	+	0.818644i	−0.985912	−	0.167268i	$-0.946506\pi$
$397$	−325.002	+	325.002i	−0.818644	+	0.818644i	0.167268	+	0.985912i	$0.446506\pi$
$398$	−32.0712	−	32.0712i	−0.0805808	−	0.0805808i
$399$			110.519i			0.276991i
$400$	−84.4340	+	53.5808i	−0.211085	+	0.133952i
$401$	−462.981			−1.15457			−0.577283	−	0.816544i	$-0.695887\pi$
$401$	−462.981			−1.15457			−0.577283	+	0.816544i	$0.695887\pi$
$402$	−50.5744	+	50.5744i	−0.125807	+	0.125807i
$403$	362.031	+	362.031i	0.898340	+	0.898340i
$404$		−	100.293i		−	0.248251i
$405$	−43.2134	+	12.5541i	−0.106700	+	0.0309978i
$406$	191.346			0.471294
$407$	97.8188	−	97.8188i	0.240341	−	0.240341i
$408$	−103.246	−	103.246i	−0.253053	−	0.253053i
$409$		−	131.630i		−	0.321834i	−0.986968	−	0.160917i	$-0.948555\pi$
$409$		−	131.630i		−	0.321834i	0.986968	−	0.160917i	$-0.0514451\pi$
$410$	−63.3926	+	115.308i	−0.154616	+	0.281238i
$411$	−322.236			−0.784028
$412$	112.775	−	112.775i	0.273726	−	0.273726i
$413$	176.510	+	176.510i	0.427386	+	0.427386i
$414$		−	181.057i		−	0.437336i
$415$	332.277	+	182.675i	0.800667	+	0.440182i
$416$	−61.6417			−0.148177
$417$	−109.542	+	109.542i	−0.262691	+	0.262691i
$418$	−277.538	−	277.538i	−0.663966	−	0.663966i
$419$		−	536.418i		−	1.28023i	−0.768277	−	0.640117i	$-0.778886\pi$
$419$		−	536.418i		−	1.28023i	0.768277	−	0.640117i	$-0.221114\pi$
$420$	12.7845	+	44.0063i	0.0304393	+	0.104777i
$421$	−508.770			−1.20848			−0.604240	−	0.796803i	$-0.706523\pi$
$421$	−508.770			−1.20848			−0.604240	+	0.796803i	$0.706523\pi$
$422$	−123.531	+	123.531i	−0.292728	+	0.292728i
$423$	150.393	+	150.393i	0.355539	+	0.355539i
$424$			28.3411i			0.0668422i
$425$	162.557	−	727.163i	0.382487	−	1.71097i
$426$	−156.178			−0.366616
$427$	15.1351	−	15.1351i	0.0354451	−	0.0354451i
$428$	270.731	+	270.731i	0.632548	+	0.632548i
$429$		−	217.197i		−	0.506286i
$430$	251.005	−	72.9206i	0.583732	−	0.169583i
$431$	467.561			1.08483			0.542414	−	0.840111i	$-0.317510\pi$
$431$	467.561			1.08483			0.542414	+	0.840111i	$0.317510\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	−129.391	−	129.391i	−0.298825	−	0.298825i	0.541729	−	0.840554i	$-0.317770\pi$
$433$	−129.391	−	129.391i	−0.298825	−	0.298825i	−0.840554	+	0.541729i	$0.817770\pi$
$434$		−	175.803i		−	0.405075i
$435$	−213.363	+	388.095i	−0.490489	+	0.892173i
$436$	201.868			0.463001
$437$	727.768	−	727.768i	1.66537	−	1.66537i
$438$	122.936	+	122.936i	0.280675	+	0.280675i
$439$			51.7818i			0.117954i	0.998259	+	0.0589770i	$0.0187839\pi$
$439$			51.7818i			0.117954i	−0.998259	+	0.0589770i	$0.981216\pi$
$440$	−142.614	−	78.4047i	−0.324122	−	0.178192i
$441$	21.0000			0.0476190
$442$	324.774	−	324.774i	0.734782	−	0.734782i
$443$	357.514	+	357.514i	0.807029	+	0.807029i	0.984183	−	0.177154i	$-0.0566891\pi$
$443$	357.514	+	357.514i	0.807029	+	0.807029i	−0.177154	+	0.984183i	$0.556689\pi$
$444$		−	41.6423i		−	0.0937890i
$445$	202.476	+	696.956i	0.455002	+	1.56619i
$446$	163.918			0.367529
$447$	68.2671	−	68.2671i	0.152723	−	0.152723i
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$			615.742i			1.37136i	0.727902	+	0.685681i	$0.240496\pi$
$449$			615.742i			1.37136i	−0.727902	+	0.685681i	$0.759504\pi$
$450$	−103.511	−	23.1399i	−0.230025	−	0.0514220i
$451$	−214.148			−0.474828
$452$	50.6348	−	50.6348i	0.112024	−	0.112024i
$453$	−101.613	−	101.613i	−0.224311	−	0.224311i
$454$			187.218i			0.412374i
$455$	−138.428	+	40.2154i	−0.304237	+	0.0883855i
$456$	−118.150			−0.259101
$457$	−502.144	+	502.144i	−1.09878	+	1.09878i	−0.104230	+	0.994553i	$0.533238\pi$
$457$	−502.144	+	502.144i	−1.09878	+	1.09878i	−0.994553	+	0.104230i	$0.966762\pi$
$458$	−348.973	−	348.973i	−0.761950	−	0.761950i
$459$		−	154.868i		−	0.337404i
$460$	205.595	−	373.966i	0.446946	−	0.812970i
$461$	100.965			0.219012			0.109506	−	0.993986i	$-0.465073\pi$
$461$	100.965			0.219012			0.109506	+	0.993986i	$0.465073\pi$
$462$	−52.7355	+	52.7355i	−0.114146	+	0.114146i
$463$	312.235	+	312.235i	0.674374	+	0.674374i	0.958721	−	0.284347i	$-0.0917768\pi$
$463$	312.235	+	312.235i	0.674374	+	0.674374i	−0.284347	+	0.958721i	$0.591777\pi$
$464$			204.557i			0.440856i
$465$	356.570	+	196.031i	0.766818	+	0.421573i
$466$	−416.639			−0.894074
$467$	502.571	−	502.571i	1.07617	−	1.07617i	0.0793198	−	0.996849i	$-0.474725\pi$
$467$	502.571	−	502.571i	1.07617	−	1.07617i	0.996849	−	0.0793198i	$-0.0252748\pi$
$468$	−46.2313	−	46.2313i	−0.0987847	−	0.0987847i
$469$			77.2537i			0.164720i
$470$	139.856	+	481.407i	0.297566	+	1.02427i
$471$	244.447			0.518995
$472$	−188.697	+	188.697i	−0.399783	+	0.399783i
$473$	300.794	+	300.794i	0.635929	+	0.635929i
$474$		−	2.59943i		−	0.00548403i
$475$	−323.056	−	509.080i	−0.680119	−	1.07175i
$476$	−157.710			−0.331324
$477$	−21.2558	+	21.2558i	−0.0445614	+	0.0445614i
$478$	−330.793	−	330.793i	−0.692035	−	0.692035i
$479$		−	270.133i		−	0.563952i	−0.959421	−	0.281976i	$-0.909010\pi$
$479$		−	270.133i		−	0.563952i	0.959421	−	0.281976i	$-0.0909899\pi$
$480$	−47.0447	+	13.6672i	−0.0980099	+	0.0284733i
$481$	130.992			0.272332
$482$	−375.584	+	375.584i	−0.779221	+	0.779221i
$483$	−138.285	−	138.285i	−0.286303	−	0.286303i
$484$		−	22.8599i		−	0.0472312i
$485$	81.0330	−	147.395i	0.167078	−	0.303906i
$486$	−22.0454			−0.0453609
$487$	−227.632	+	227.632i	−0.467417	+	0.467417i	−0.901077	−	0.433660i	$-0.857222\pi$
$487$	−227.632	+	227.632i	−0.467417	+	0.467417i	0.433660	+	0.901077i	$0.357222\pi$
$488$	16.1801	+	16.1801i	0.0331559	+	0.0331559i
$489$			111.178i			0.227359i
$490$	43.3747	+	23.8461i	0.0885198	+	0.0486655i
$491$	−23.2563			−0.0473652			−0.0236826	−	0.999720i	$-0.507539\pi$
$491$	−23.2563			−0.0473652			−0.0236826	+	0.999720i	$0.507539\pi$
$492$	−45.5822	+	45.5822i	−0.0926468	+	0.0926468i
$493$	−1077.76	−	1077.76i	−2.18612	−	2.18612i
$494$		−	371.658i		−	0.752344i
$495$	−48.1569	−	165.764i	−0.0972866	−	0.334876i
$496$	187.941			0.378913
$497$	−119.283	+	119.283i	−0.240006	+	0.240006i
$498$	131.352	+	131.352i	0.263759	+	0.263759i
$499$		−	319.077i		−	0.639433i	−0.947513	−	0.319717i	$-0.896412\pi$
$499$		−	319.077i		−	0.639433i	0.947513	−	0.319717i	$-0.103588\pi$
$500$	−187.522	−	165.334i	−0.375045	−	0.330668i
$501$	243.112			0.485254
$502$	−41.2876	+	41.2876i	−0.0822463	+	0.0822463i
$503$	585.731	+	585.731i	1.16448	+	1.16448i	0.983485	+	0.180990i	$0.0579302\pi$
$503$	585.731	+	585.731i	1.16448	+	1.16448i	0.180990	+	0.983485i	$0.442070\pi$
$504$			22.4499i			0.0445435i
$505$	240.779	−	69.9498i	0.476789	−	0.138514i
$506$	694.524			1.37258
$507$	−61.5551	+	61.5551i	−0.121410	+	0.121410i
$508$	−233.492	−	233.492i	−0.459631	−	0.459631i
$509$		−	266.157i		−	0.522902i	−0.965217	−	0.261451i	$-0.915799\pi$
$509$		−	266.157i		−	0.522902i	0.965217	−	0.261451i	$-0.0842009\pi$
$510$	175.857	−	319.875i	0.344818	−	0.627206i
$511$	187.787			0.367490
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−88.6127	−	88.6127i	−0.172734	−	0.172734i
$514$		−	202.741i		−	0.394437i
$515$	349.399	+	192.089i	0.678446	+	0.372988i
$516$	128.051			0.248161
$517$	−576.899	+	576.899i	−1.11586	+	1.11586i
$518$	−31.8048	−	31.8048i	−0.0613993	−	0.0613993i
$519$			197.283i			0.380121i
$520$	−42.9921	−	147.986i	−0.0826770	−	0.284588i
$521$	−1.52542			−0.00292786			−0.00146393	−	0.999999i	$-0.500466\pi$
$521$	−1.52542			−0.00292786			−0.00146393	+	0.999999i	$0.500466\pi$
$522$	−153.418	+	153.418i	−0.293904	+	0.293904i
$523$	260.120	+	260.120i	0.497362	+	0.497362i	0.910616	−	0.413254i	$-0.135608\pi$
$523$	260.120	+	260.120i	0.497362	+	0.497362i	−0.413254	+	0.910616i	$0.635608\pi$
$524$		−	69.6007i		−	0.132826i
$525$	−96.7313	+	61.3845i	−0.184250	+	0.116923i
$526$	−329.188			−0.625833
$527$	−990.210	+	990.210i	−1.87896	+	1.87896i
$528$	−56.3766	−	56.3766i	−0.106774	−	0.106774i
$529$			1292.20i			2.44272i
$530$	−68.0396	+	19.7665i	−0.128377	+	0.0372953i
$531$	−283.046			−0.533044
$532$	−90.2387	+	90.2387i	−0.169622	+	0.169622i
$533$	−143.385	−	143.385i	−0.269015	−	0.269015i
$534$			355.554i			0.665831i
$535$	−461.133	+	838.776i	−0.861931	+	1.56781i
$536$	−82.5877			−0.154081
$537$	−188.937	+	188.937i	−0.351838	+	0.351838i
$538$	254.148	+	254.148i	0.472394	+	0.472394i
$539$			80.5547i			0.149452i
$540$	−45.5340	−	25.0332i	−0.0843221	−	0.0463577i
$541$	−273.648			−0.505820			−0.252910	−	0.967490i	$-0.581388\pi$
$541$	−273.648			−0.505820			−0.252910	+	0.967490i	$0.581388\pi$
$542$	−22.4723	+	22.4723i	−0.0414619	+	0.0414619i
$543$	−203.979	−	203.979i	−0.375652	−	0.375652i
$544$		−	168.599i		−	0.309925i
$545$	140.793	+	484.634i	0.258336	+	0.889236i
$546$	−70.6194			−0.129340
$547$	355.490	−	355.490i	0.649890	−	0.649890i	−0.303077	−	0.952966i	$-0.598014\pi$
$547$	355.490	−	355.490i	0.649890	−	0.649890i	0.952966	+	0.303077i	$0.0980138\pi$
$548$	−263.104	−	263.104i	−0.480117	−	0.480117i
$549$			24.2701i			0.0442078i
$550$	88.7632	−	397.062i	0.161388	−	0.721932i
$551$	−1233.34			−2.23837
$552$	147.832	−	147.832i	0.267812	−	0.267812i
$553$	−1.98535	−	1.98535i	−0.00359014	−	0.00359014i
$554$			94.7898i			0.171101i
$555$	99.9724	−	29.0435i	0.180130	−	0.0523306i
$556$	−178.881			−0.321729
$557$	−270.897	+	270.897i	−0.486350	+	0.486350i	−0.907152	−	0.420802i	$-0.861749\pi$
$557$	−270.897	+	270.897i	−0.486350	+	0.486350i	0.420802	+	0.907152i	$0.361749\pi$
$558$	140.956	+	140.956i	0.252609	+	0.252609i
$559$			402.802i			0.720575i
$560$	−25.4925	+	46.3695i	−0.0455224	+	0.0828027i
$561$	594.066			1.05894
$562$	18.8810	−	18.8810i	0.0335960	−	0.0335960i
$563$	73.1143	+	73.1143i	0.129866	+	0.129866i	0.769052	−	0.639186i	$-0.220729\pi$
$563$	73.1143	+	73.1143i	0.129866	+	0.129866i	−0.639186	+	0.769052i	$0.720729\pi$
$564$			245.591i			0.435445i
$565$	156.876	+	86.2458i	0.277657	+	0.152647i
$566$	231.651			0.409277
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	−127.519	−	127.519i	−0.224505	−	0.224505i
$569$			1018.55i			1.79007i	0.445992	+	0.895037i	$0.352851\pi$
$569$			1018.55i			1.79007i	−0.445992	+	0.895037i	$0.647149\pi$
$570$	−82.4040	−	283.648i	−0.144568	−	0.497629i
$571$	−621.517			−1.08847			−0.544236	−	0.838932i	$-0.683180\pi$
$571$	−621.517			−1.08847			−0.544236	+	0.838932i	$0.683180\pi$
$572$	177.340	−	177.340i	0.310036	−	0.310036i
$573$	288.606	+	288.606i	0.503675	+	0.503675i
$574$			69.6280i			0.121303i
$575$	1041.19	+	232.758i	1.81076	+	0.404796i
$576$	−24.0000			−0.0416667
$577$	760.301	−	760.301i	1.31768	−	1.31768i	0.402071	−	0.915608i	$-0.368290\pi$
$577$	760.301	−	760.301i	1.31768	−	1.31768i	0.915608	−	0.402071i	$-0.131710\pi$
$578$	599.306	+	599.306i	1.03686	+	1.03686i
$579$			39.7334i			0.0686242i
$580$	−491.089	+	142.668i	−0.846704	+	0.245980i
$581$	200.644			0.345342
$582$	58.2665	−	58.2665i	0.100114	−	0.100114i
$583$	−81.5360	−	81.5360i	−0.139856	−	0.139856i
$584$			200.753i			0.343756i
$585$	78.7453	−	143.233i	0.134607	−	0.244843i
$586$	−448.901			−0.766043
$587$	5.94607	−	5.94607i	0.0101296	−	0.0101296i	−0.702024	−	0.712153i	$-0.747720\pi$
$587$	5.94607	−	5.94607i	0.0101296	−	0.0101296i	0.712153	+	0.702024i	$0.247720\pi$
$588$	17.1464	+	17.1464i	0.0291606	+	0.0291606i
$589$			1133.16i			1.92387i
$590$	−584.621	−	321.407i	−0.990883	−	0.544757i
$591$	16.3659			0.0276918
$592$	34.0008	−	34.0008i	0.0574338	−	0.0574338i
$593$	−463.916	−	463.916i	−0.782320	−	0.782320i	0.197902	−	0.980222i	$-0.436587\pi$
$593$	−463.916	−	463.916i	−0.782320	−	0.782320i	−0.980222	+	0.197902i	$0.936587\pi$
$594$		−	84.5649i		−	0.142365i
$595$	−109.995	−	378.622i	−0.184866	−	0.636339i
$596$	111.480			0.187047
$597$	39.2790	−	39.2790i	0.0657940	−	0.0657940i
$598$	465.027	+	465.027i	0.777638	+	0.777638i
$599$		−	660.745i		−	1.10308i	−0.834148	−	0.551540i	$-0.814040\pi$
$599$		−	660.745i		−	1.10308i	0.834148	−	0.551540i	$-0.185960\pi$
$600$	−65.6228	−	103.410i	−0.109371	−	0.172350i
$601$	−905.439			−1.50655			−0.753277	−	0.657704i	$-0.771528\pi$
$601$	−905.439			−1.50655			−0.753277	+	0.657704i	$0.771528\pi$
$602$	97.8004	−	97.8004i	0.162459	−	0.162459i
$603$	−61.9407	−	61.9407i	−0.102721	−	0.102721i
$604$		−	165.933i		−	0.274724i
$605$	54.8807	−	15.9436i	0.0907119	−	0.0263531i
$606$	122.834			0.202696
$607$	518.514	−	518.514i	0.854224	−	0.854224i	−0.136426	−	0.990650i	$-0.543562\pi$
$607$	518.514	−	518.514i	0.854224	−	0.854224i	0.990650	+	0.136426i	$0.0435615\pi$
$608$	−96.4693	−	96.4693i	−0.158667	−	0.158667i
$609$			234.349i			0.384810i
$610$	−27.5593	+	50.1289i	−0.0451792	+	0.0821786i
$611$	−772.541			−1.26439
$612$	126.450	−	126.450i	0.206617	−	0.206617i
$613$	−500.739	−	500.739i	−0.816867	−	0.816867i	0.168786	−	0.985653i	$-0.446015\pi$
$613$	−500.739	−	500.739i	−0.816867	−	0.816867i	−0.985653	+	0.168786i	$0.946015\pi$
$614$		−	85.0240i		−	0.138476i
$615$	−141.223	−	77.6398i	−0.229630	−	0.126244i
$616$	−86.1166			−0.139800
$617$	122.242	−	122.242i	0.198123	−	0.198123i	−0.601072	−	0.799195i	$-0.705260\pi$
$617$	122.242	−	122.242i	0.198123	−	0.198123i	0.799195	+	0.601072i	$0.205260\pi$
$618$	138.121	+	138.121i	0.223497	+	0.223497i
$619$			320.914i			0.518440i	0.965818	+	0.259220i	$0.0834655\pi$
$619$			320.914i			0.518440i	−0.965818	+	0.259220i	$0.916534\pi$
$620$	131.080	+	451.198i	0.211419	+	0.727738i
$621$	221.749			0.357083
$622$	97.1353	−	97.1353i	0.156166	−	0.156166i
$623$	271.559	+	271.559i	0.435889	+	0.435889i
$624$		−	75.4953i		−	0.120986i
$625$	266.137	−	565.505i	0.425820	−	0.904808i
$626$	188.983			0.301889
$627$	339.913	−	339.913i	0.542126	−	0.542126i
$628$	199.590	+	199.590i	0.317818	+	0.317818i
$629$			358.282i			0.569606i
$630$	−53.8965	+	15.6577i	−0.0855500	+	0.0248536i
$631$	−636.141			−1.00815			−0.504074	−	0.863661i	$-0.668166\pi$
$631$	−636.141			−1.00815			−0.504074	+	0.863661i	$0.668166\pi$
$632$	2.12242	−	2.12242i	0.00335827	−	0.00335827i
$633$	−151.294	−	151.294i	−0.239012	−	0.239012i
$634$			292.300i			0.461040i
$635$	397.706	−	723.405i	0.626308	−	1.13922i
$636$	−34.7106			−0.0545764
$637$	−53.9365	+	53.9365i	−0.0846726	+	0.0846726i
$638$	−588.501	−	588.501i	−0.922416	−	0.922416i
$639$		−	191.278i		−	0.299340i
$640$	−49.5711	−	27.2527i	−0.0774548	−	0.0425823i
$641$	−682.051			−1.06404			−0.532021	−	0.846731i	$-0.678567\pi$
$641$	−682.051			−1.06404			−0.532021	+	0.846731i	$0.678567\pi$
$642$	−331.576	+	331.576i	−0.516474	+	0.516474i
$643$	−5.33298	−	5.33298i	−0.00829390	−	0.00829390i	0.702948	−	0.711242i	$-0.251867\pi$
$643$	−5.33298	−	5.33298i	−0.00829390	−	0.00829390i	−0.711242	+	0.702948i	$0.751867\pi$
$644$		−	225.818i		−	0.350649i
$645$	89.3092	+	307.417i	0.138464	+	0.476615i
$646$	1016.54			1.57359
$647$	285.931	−	285.931i	0.441933	−	0.441933i	−0.450728	−	0.892661i	$-0.648836\pi$
$647$	285.931	−	285.931i	0.441933	−	0.441933i	0.892661	+	0.450728i	$0.148836\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	1085.75i		−	1.67296i
$650$	325.291	−	206.426i	0.500447	−	0.317578i
$651$	215.313			0.330742
$652$	−90.7768	+	90.7768i	−0.139228	+	0.139228i
$653$	199.462	+	199.462i	0.305455	+	0.305455i	0.843144	−	0.537689i	$-0.180702\pi$
$653$	199.462	+	199.462i	0.305455	+	0.305455i	−0.537689	+	0.843144i	$0.680702\pi$
$654$			247.237i			0.378039i
$655$	167.093	−	48.5431i	0.255104	−	0.0741116i
$656$	−74.4355			−0.113469
$657$	−150.565	+	150.565i	−0.229170	+	0.229170i
$658$	187.573	+	187.573i	0.285066	+	0.285066i
$659$			204.685i			0.310599i	0.987867	+	0.155300i	$0.0496343\pi$
$659$			204.685i			0.310599i	−0.987867	+	0.155300i	$0.950366\pi$
$660$	96.0257	−	174.666i	0.145494	−	0.264645i
$661$	143.044			0.216406			0.108203	−	0.994129i	$-0.465490\pi$
$661$	143.044			0.216406			0.108203	+	0.994129i	$0.465490\pi$
$662$	−223.981	+	223.981i	−0.338339	+	0.338339i
$663$	397.765	+	397.765i	0.599947	+	0.599947i
$664$			214.497i			0.323038i
$665$	−279.577	−	153.703i	−0.420417	−	0.231132i
$666$	51.0012			0.0765784
$667$	1543.19	−	1543.19i	2.31362	−	2.31362i
$668$	198.500	+	198.500i	0.297156	+	0.297156i
$669$			200.758i			0.300086i
$670$	−57.6008	−	198.272i	−0.0859714	−	0.295928i
$671$	−93.0986			−0.138746
$672$	−18.3303	+	18.3303i	−0.0272772	+	0.0272772i
$673$	−317.527	−	317.527i	−0.471808	−	0.471808i	0.430691	−	0.902499i	$-0.358270\pi$
$673$	−317.527	−	317.527i	−0.471808	−	0.471808i	−0.902499	+	0.430691i	$0.858270\pi$
$674$		−	83.4888i		−	0.123871i
$675$	28.3405	−	126.775i	0.0419859	−	0.187814i
$676$	−100.519			−0.148697
$677$	−272.663	+	272.663i	−0.402752	+	0.402752i	−0.879202	−	0.476450i	$-0.841923\pi$
$677$	−272.663	+	272.663i	−0.402752	+	0.402752i	0.476450	+	0.879202i	$0.341923\pi$
$678$	62.0147	+	62.0147i	0.0914671	+	0.0914671i
$679$		−	89.0035i		−	0.131080i
$680$	404.764	−	117.590i	0.595241	−	0.172926i
$681$	−229.294			−0.336702
$682$	−540.697	+	540.697i	−0.792812	+	0.792812i
$683$	−449.231	−	449.231i	−0.657732	−	0.657732i	0.297111	−	0.954843i	$-0.403977\pi$
$683$	−449.231	−	449.231i	−0.657732	−	0.657732i	−0.954843	+	0.297111i	$0.903977\pi$
$684$		−	144.704i		−	0.211555i
$685$	448.143	−	815.148i	0.654224	−	1.19000i
$686$	26.1916			0.0381802
$687$	427.403	−	427.403i	0.622130	−	0.622130i
$688$	104.553	+	104.553i	0.151967	+	0.151967i
$689$		−	109.187i		−	0.158472i
$690$	458.013	+	251.802i	0.663787	+	0.364930i
$691$	1004.13			1.45316			0.726578	−	0.687084i	$-0.241109\pi$
$691$	1004.13			1.45316			0.726578	+	0.687084i	$0.241109\pi$
$692$	−161.081	+	161.081i	−0.232776	+	0.232776i
$693$	−64.5875	−	64.5875i	−0.0931998	−	0.0931998i
$694$			566.325i			0.816031i
$695$	−124.761	−	429.448i	−0.179512	−	0.617911i
$696$	−250.530			−0.359957
$697$	392.181	−	392.181i	0.562669	−	0.562669i
$698$	73.8529	+	73.8529i	0.105807	+	0.105807i
$699$		−	510.276i		−	0.730009i
$700$	−129.101	−	28.8605i	−0.184430	−	0.0412293i
$701$	−869.248			−1.24001			−0.620006	−	0.784597i	$-0.712870\pi$
$701$	−869.248			−1.24001			−0.620006	+	0.784597i	$0.712870\pi$
$702$	56.6215	−	56.6215i	0.0806574	−	0.0806574i
$703$	205.002	+	205.002i	0.291610	+	0.291610i
$704$		−	92.0626i		−	0.130771i
$705$	−589.601	+	171.288i	−0.836313	+	0.242961i
$706$	443.401			0.628047
$707$	93.8159	−	93.8159i	0.132696	−	0.132696i
$708$	−231.106	−	231.106i	−0.326421	−	0.326421i
$709$			79.6980i			0.112409i	0.998419	+	0.0562045i	$0.0178999\pi$
$709$			79.6980i			0.112409i	−0.998419	+	0.0562045i	$0.982100\pi$
$710$	217.202	−	395.078i	0.305918	−	0.556449i
$711$	3.18364			0.00447769
$712$	−290.309	+	290.309i	−0.407737	+	0.407737i
$713$	−1417.83	−	1417.83i	−1.98855	−	1.98855i
$714$		−	193.155i		−	0.270525i
$715$	549.435	+	302.062i	0.768440	+	0.422465i
$716$	−308.533			−0.430912
$717$	405.136	−	405.136i	0.565044	−	0.565044i
$718$	351.735	+	351.735i	0.489882	+	0.489882i
$719$			1081.03i			1.50351i	0.659440	+	0.751757i	$0.270793\pi$
$719$			1081.03i			1.50351i	−0.659440	+	0.751757i	$0.729207\pi$
$720$	−16.7388	−	57.6178i	−0.0232484	−	0.0800247i
$721$	210.983			0.292626
$722$	220.645	−	220.645i	0.305603	−	0.305603i
$723$	−459.995	−	459.995i	−0.636231	−	0.636231i
$724$		−	333.096i		−	0.460078i
$725$	−685.020	−	1079.47i	−0.944856	−	1.48893i
$726$	27.9975			0.0385641
$727$	281.701	−	281.701i	0.387484	−	0.387484i	−0.486305	−	0.873789i	$-0.661656\pi$
$727$	281.701	−	281.701i	0.387484	−	0.387484i	0.873789	+	0.486305i	$0.161656\pi$
$728$	−57.6605	−	57.6605i	−0.0792040	−	0.0792040i
$729$		−	27.0000i		−	0.0370370i
$730$	−481.957	+	140.016i	−0.660215	+	0.191802i
$731$	−1101.72			−1.50715
$732$	−19.8164	+	19.8164i	−0.0270716	+	0.0270716i
$733$	1016.28	+	1016.28i	1.38647	+	1.38647i	0.832611	+	0.553858i	$0.186845\pi$
$733$	1016.28	+	1016.28i	1.38647	+	1.38647i	0.553858	+	0.832611i	$0.313155\pi$
$734$			18.0753i			0.0246258i
$735$	−29.2054	+	53.1229i	−0.0397352	+	0.0722761i
$736$	241.409			0.328002
$737$	237.601	−	237.601i	0.322389	−	0.322389i
$738$	−55.8266	−	55.8266i	−0.0756458	−	0.0756458i
$739$			289.140i			0.391258i	0.980678	+	0.195629i	$0.0626749\pi$
$739$			289.140i			0.391258i	−0.980678	+	0.195629i	$0.937325\pi$
$740$	105.341	+	57.9132i	0.142353	+	0.0782611i
$741$	455.186			0.614286
$742$	−26.5107	+	26.5107i	−0.0357286	+	0.0357286i
$743$	290.501	+	290.501i	0.390984	+	0.390984i	0.875038	−	0.484054i	$-0.160836\pi$
$743$	290.501	+	290.501i	0.390984	+	0.390984i	−0.484054	+	0.875038i	$0.660836\pi$
$744$			230.180i			0.309381i
$745$	77.7517	+	267.634i	0.104365	+	0.359240i
$746$	302.189			0.405079
$747$	−160.873	+	160.873i	−0.215358	+	0.215358i
$748$	485.053	+	485.053i	0.648467	+	0.648467i
$749$			506.491i			0.676223i
$750$	202.492	−	229.667i	0.269990	−	0.306223i
$751$	688.089			0.916231			0.458115	−	0.888893i	$-0.348525\pi$
$751$	688.089			0.916231			0.458115	+	0.888893i	$0.348525\pi$
$752$	−200.524	+	200.524i	−0.266655	+	0.266655i
$753$	−50.5668	−	50.5668i	−0.0671538	−	0.0671538i
$754$		−	788.077i		−	1.04520i
$755$	398.363	−	115.730i	0.527632	−	0.153285i
$756$	−27.4955			−0.0363696
$757$	180.960	−	180.960i	0.239049	−	0.239049i	−0.577408	−	0.816456i	$-0.695936\pi$
$757$	180.960	−	180.960i	0.239049	−	0.239049i	0.816456	+	0.577408i	$0.195936\pi$
$758$	268.787	+	268.787i	0.354601	+	0.354601i
$759$			850.614i			1.12070i
$760$	164.315	−	298.880i	0.216204	−	0.393264i
$761$	1096.09			1.44033			0.720163	−	0.693805i	$-0.244067\pi$
$761$	1096.09			1.44033			0.720163	+	0.693805i	$0.244067\pi$
$762$	285.969	−	285.969i	0.375287	−	0.375287i
$763$	188.831	+	188.831i	0.247484	+	0.247484i
$764$			471.291i			0.616873i
$765$	391.765	+	215.380i	0.512111	+	0.281543i
$766$	−608.682			−0.794625
$767$	726.977	−	726.977i	0.947818	−	0.947818i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$		−	892.540i		−	1.16065i	−0.814385	−	0.580325i	$-0.802925\pi$
$769$		−	892.540i		−	1.16065i	0.814385	−	0.580325i	$-0.197075\pi$
$770$	−60.0621	−	206.744i	−0.0780028	−	0.268499i
$771$	248.306			0.322057
$772$	−32.4422	+	32.4422i	−0.0420235	+	0.0420235i
$773$	836.773	+	836.773i	1.08250	+	1.08250i	0.996276	+	0.0862244i	$0.0274802\pi$
$773$	836.773	+	836.773i	1.08250	+	1.08250i	0.0862244	+	0.996276i	$0.472520\pi$
$774$			156.830i			0.202622i
$775$	−991.787	+	629.376i	−1.27973	+	0.812099i
$776$	95.1487			0.122614
$777$	38.9528	−	38.9528i	0.0501323	−	0.0501323i
$778$	−50.0127	−	50.0127i	−0.0642837	−	0.0642837i
$779$		−	448.796i		−	0.576118i
$780$	181.245	−	52.6543i	0.232365	−	0.0675055i
$781$	733.733			0.939479
$782$	−1271.92	+	1271.92i	−1.62650	+	1.62650i
$783$	−187.898	−	187.898i	−0.239971	−	0.239971i
$784$			28.0000i			0.0357143i
$785$	−339.960	+	618.368i	−0.433070	+	0.787730i
$786$	85.2431			0.108452
$787$	−226.485	+	226.485i	−0.287782	+	0.287782i	−0.836203	−	0.548420i	$-0.815229\pi$
$787$	−226.485	+	226.485i	−0.287782	+	0.287782i	0.548420	+	0.836203i	$0.315229\pi$
$788$	13.3627	+	13.3627i	0.0169577	+	0.0169577i
$789$		−	403.171i		−	0.510990i
$790$	6.57568	+	3.61511i	0.00832365	+	0.00457608i
$791$	94.7290			0.119759
$792$	69.0469	−	69.0469i	0.0871805	−	0.0871805i
$793$	−62.3354	−	62.3354i	−0.0786070	−	0.0786070i
$794$		−	650.003i		−	0.818644i
$795$	−24.2089	−	83.3312i	−0.0304515	−	0.104819i
$796$	64.1423			0.0805808
$797$	−728.914	+	728.914i	−0.914572	+	0.914572i	−0.996628	−	0.0820555i	$-0.973852\pi$
$797$	−728.914	+	728.914i	−0.914572	+	0.914572i	0.0820555	+	0.996628i	$0.473852\pi$
$798$	−110.519	−	110.519i	−0.138496	−	0.138496i
$799$		−	2113.02i		−	2.64458i
$800$	30.8532	−	138.015i	0.0385665	−	0.172518i
$801$	−435.463			−0.543649
$802$	462.981	−	462.981i	0.577283	−	0.577283i
$803$	−577.558	−	577.558i	−0.719250	−	0.719250i
$804$		−	101.149i		−	0.125807i
$805$	542.130	−	157.497i	0.673453	−	0.195648i
$806$	−724.062			−0.898340
$807$	−311.267	+	311.267i	−0.385708	+	0.385708i
$808$	100.293	+	100.293i	0.124126	+	0.124126i
$809$			1196.38i			1.47884i	0.673247	+	0.739418i	$0.264899\pi$
$809$			1196.38i			1.47884i	−0.673247	+	0.739418i	$0.735101\pi$
$810$	30.6592	−	55.7675i	0.0378509	−	0.0688487i
$811$	−1180.03			−1.45503			−0.727513	−	0.686094i	$-0.759324\pi$
$811$	−1180.03			−1.45503			−0.727513	+	0.686094i	$0.759324\pi$
$812$	−191.346	+	191.346i	−0.235647	+	0.235647i
$813$	−27.5229	−	27.5229i	−0.0338535	−	0.0338535i
$814$			195.638i			0.240341i
$815$	−281.244	−	154.619i	−0.345085	−	0.189717i
$816$	206.491			0.253053
$817$	−630.385	+	630.385i	−0.771585	+	0.771585i
$818$	131.630	+	131.630i	0.160917	+	0.160917i
$819$		−	86.4908i		−	0.105605i
$820$	−51.9151	−	178.700i	−0.0633111	−	0.217927i
$821$	35.8305			0.0436425			0.0218212	−	0.999762i	$-0.493054\pi$
$821$	35.8305			0.0436425			0.0218212	+	0.999762i	$0.493054\pi$
$822$	322.236	−	322.236i	0.392014	−	0.392014i
$823$	448.829	+	448.829i	0.545357	+	0.545357i	0.925094	−	0.379737i	$-0.123986\pi$
$823$	448.829	+	448.829i	0.545357	+	0.545357i	−0.379737	+	0.925094i	$0.623986\pi$
$824$			225.550i			0.273726i
$825$	486.300	+	108.712i	0.589455	+	0.131772i
$826$	−353.021			−0.427386
$827$	874.926	−	874.926i	1.05795	−	1.05795i	0.0597373	−	0.998214i	$-0.480974\pi$
$827$	874.926	−	874.926i	1.05795	−	1.05795i	0.998214	−	0.0597373i	$-0.0190263\pi$
$828$	181.057	+	181.057i	0.218668	+	0.218668i
$829$		−	934.022i		−	1.12669i	−0.826223	−	0.563343i	$-0.809515\pi$
$829$		−	934.022i		−	1.12669i	0.826223	−	0.563343i	$-0.190485\pi$
$830$	−514.952	+	149.601i	−0.620424	+	0.180242i
$831$	−116.093			−0.139703
$832$	61.6417	−	61.6417i	0.0740886	−	0.0740886i
$833$	−147.525	−	147.525i	−0.177100	−	0.177100i
$834$		−	219.084i		−	0.262691i
$835$	−338.104	+	614.992i	−0.404915	+	0.736517i
$836$	555.076			0.663966
$837$	−172.635	+	172.635i	−0.206254	+	0.206254i
$838$	536.418	+	536.418i	0.640117	+	0.640117i
$839$			10.5147i			0.0125324i	0.999980	+	0.00626621i	$0.00199461\pi$
$839$			10.5147i			0.0125324i	−0.999980	+	0.00626621i	$0.998005\pi$
$840$	−56.7908	−	31.2218i	−0.0676081	−	0.0371689i
$841$	−1774.22			−2.10966
$842$	508.770	−	508.770i	0.604240	−	0.604240i
$843$	23.1244	+	23.1244i	0.0274310	+	0.0274310i
$844$		−	247.063i		−	0.292728i
$845$	−70.1071	−	241.320i	−0.0829670	−	0.285586i
$846$	−300.786			−0.355539
$847$	21.3835	−	21.3835i	0.0252461	−	0.0252461i
$848$	−28.3411	−	28.3411i	−0.0334211	−	0.0334211i
$849$			283.713i			0.334173i
$850$	564.606	+	889.720i	0.664242	+	1.04673i
$851$	−513.007			−0.602828
$852$	156.178	−	156.178i	0.183308	−	0.183308i
$853$	1082.57	+	1082.57i	1.26914	+	1.26914i	0.946534	+	0.322603i	$0.104558\pi$
$853$	1082.57	+	1082.57i	1.26914	+	1.26914i	0.322603	+	0.946534i	$0.395442\pi$
$854$			30.2701i			0.0354451i
$855$	347.397	−	100.924i	0.406312	−	0.118040i
$856$	−541.461			−0.632548
$857$	506.843	−	506.843i	0.591416	−	0.591416i	−0.346598	−	0.938014i	$-0.612663\pi$
$857$	506.843	−	506.843i	0.591416	−	0.591416i	0.938014	+	0.346598i	$0.112663\pi$
$858$	217.197	+	217.197i	0.253143	+	0.253143i
$859$			471.172i			0.548512i	0.961657	+	0.274256i	$0.0884315\pi$
$859$			471.172i			0.548512i	−0.961657	+	0.274256i	$0.911568\pi$
$860$	−178.084	+	323.926i	−0.207075	+	0.376658i
$861$	−85.2765			−0.0990436
$862$	−467.561	+	467.561i	−0.542414	+	0.542414i
$863$	352.570	+	352.570i	0.408540	+	0.408540i	0.881229	−	0.472689i	$-0.156717\pi$
$863$	352.570	+	352.570i	0.408540	+	0.408540i	−0.472689	+	0.881229i	$0.656717\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−499.059	−	274.367i	−0.576947	−	0.317188i
$866$	258.782			0.298825
$867$	−733.996	+	733.996i	−0.846593	+	0.846593i
$868$	175.803	+	175.803i	0.202538	+	0.202538i
$869$			12.2122i			0.0140532i
$870$	−174.732	−	601.458i	−0.200842	−	0.691331i
$871$	318.178			0.365301
$872$	−201.868	+	201.868i	−0.231500	+	0.231500i
$873$	71.3616	+	71.3616i	0.0817429	+	0.0817429i
$874$			1455.54i			1.66537i
$875$	−20.7550	−	330.067i	−0.0237200	−	0.377219i
$876$	−245.872			−0.280675
$877$	−1223.94	+	1223.94i	−1.39560	+	1.39560i	−0.583467	+	0.812137i	$0.698304\pi$
$877$	−1223.94	+	1223.94i	−1.39560	+	1.39560i	−0.812137	+	0.583467i	$0.801696\pi$
$878$	−51.7818	−	51.7818i	−0.0589770	−	0.0589770i
$879$		−	549.790i		−	0.625472i
$880$	221.018	−	64.2091i	0.251157	−	0.0729649i
$881$	−635.103			−0.720889			−0.360444	−	0.932781i	$-0.617375\pi$
$881$	−635.103			−0.720889			−0.360444	+	0.932781i	$0.617375\pi$
$882$	−21.0000	+	21.0000i	−0.0238095	+	0.0238095i
$883$	−230.546	−	230.546i	−0.261094	−	0.261094i	0.564405	−	0.825498i	$-0.309106\pi$
$883$	−230.546	−	230.546i	−0.261094	−	0.261094i	−0.825498	+	0.564405i	$0.809106\pi$
$884$			649.547i			0.734782i
$885$	393.641	−	716.012i	0.444792	−	0.809053i
$886$	−715.028			−0.807029
$887$	−1224.61	+	1224.61i	−1.38062	+	1.38062i	−0.537101	+	0.843518i	$0.680480\pi$
$887$	−1224.61	+	1224.61i	−1.38062	+	1.38062i	−0.843518	+	0.537101i	$0.819520\pi$
$888$	41.6423	+	41.6423i	0.0468945	+	0.0468945i
$889$		−	436.824i		−	0.491366i
$890$	−899.432	−	494.480i	−1.01060	−	0.555595i
$891$	103.570			0.116241
$892$	−163.918	+	163.918i	−0.183765	+	0.183765i
$893$	−1209.03	−	1209.03i	−1.35389	−	1.35389i
$894$			136.534i			0.152723i
$895$	−215.187	−	740.708i	−0.240432	−	0.827607i
$896$	−29.9333			−0.0334077
$897$	−569.540	+	569.540i	−0.634938	+	0.634938i
$898$	−615.742	−	615.742i	−0.685681	−	0.685681i
$899$			2402.79i			2.67273i
$900$	126.651	−	80.3712i	0.140723	−	0.0893013i
$901$	298.643			0.331457
$902$	214.148	−	214.148i	0.237414	−	0.237414i
$903$	119.781	+	119.781i	0.132647	+	0.132647i
$904$			101.270i			0.112024i
$905$	799.678	−	232.318i	0.883622	−	0.256705i
$906$	203.226			0.224311
$907$	766.713	−	766.713i	0.845329	−	0.845329i	−0.144217	−	0.989546i	$-0.546066\pi$
$907$	766.713	−	766.713i	0.845329	−	0.845329i	0.989546	+	0.144217i	$0.0460664\pi$
$908$	−187.218	−	187.218i	−0.206187	−	0.206187i
$909$			150.440i			0.165501i
$910$	98.2126	−	178.643i	0.107926	−	0.196311i
$911$	−754.441			−0.828146			−0.414073	−	0.910244i	$-0.635894\pi$
$911$	−754.441			−0.828146			−0.414073	+	0.910244i	$0.635894\pi$
$912$	118.150	−	118.150i	0.129551	−	0.129551i
$913$	−617.098	−	617.098i	−0.675902	−	0.675902i
$914$		−	1004.29i		−	1.09878i
$915$	−61.3952	−	33.7532i	−0.0670985	−	0.0368887i
$916$	697.947			0.761950
$917$	65.1055	−	65.1055i	0.0709984	−	0.0709984i
$918$	154.868	+	154.868i	0.168702	+	0.168702i
$919$			858.117i			0.933750i	0.884323	+	0.466875i	$0.154620\pi$
$919$			858.117i			0.933750i	−0.884323	+	0.466875i	$0.845380\pi$
$920$	168.371	+	579.561i	0.183012	+	0.629958i
$921$	104.133			0.113065
$922$	−100.965	+	100.965i	−0.109506	+	0.109506i
$923$	491.280	+	491.280i	0.532265	+	0.532265i
$924$		−	105.471i		−	0.114146i
$925$	−65.5645	+	293.288i	−0.0708806	+	0.317068i
$926$	−624.471			−0.674374
$927$	−169.163	+	169.163i	−0.182484	+	0.182484i
$928$	−204.557	−	204.557i	−0.220428	−	0.220428i
$929$			631.542i			0.679809i	0.940460	+	0.339904i	$0.110395\pi$
$929$			631.542i			0.679809i	−0.940460	+	0.339904i	$0.889605\pi$
$930$	−552.602	+	160.539i	−0.594196	+	0.172623i
$931$	−168.821			−0.181333
$932$	416.639	−	416.639i	0.447037	−	0.447037i
$933$	118.966	+	118.966i	0.127509	+	0.127509i
$934$			1005.14i			1.07617i
$935$	−826.186	+	1502.79i	−0.883622	+	1.60726i
$936$	92.4625			0.0987847
$937$	1167.50	−	1167.50i	1.24599	−	1.24599i	0.288519	−	0.957474i	$-0.406837\pi$
$937$	1167.50	−	1167.50i	1.24599	−	1.24599i	0.957474	−	0.288519i	$-0.0931630\pi$
$938$	−77.2537	−	77.2537i	−0.0823600	−	0.0823600i
$939$			231.455i			0.246491i
$940$	−621.263	−	341.551i	−0.660918	−	0.363352i
$941$	−614.550			−0.653082			−0.326541	−	0.945183i	$-0.605883\pi$
$941$	−614.550			−0.653082			−0.326541	+	0.945183i	$0.605883\pi$
$942$	−244.447	+	244.447i	−0.259498	+	0.259498i
$943$	561.544	+	561.544i	0.595487	+	0.595487i
$944$		−	377.395i		−	0.399783i
$945$	−19.1767	−	66.0095i	−0.0202928	−	0.0698513i
$946$	−601.589			−0.635929
$947$	−635.282	+	635.282i	−0.670837	+	0.670837i	−0.957909	−	0.287072i	$-0.907318\pi$
$947$	−635.282	+	635.282i	−0.670837	+	0.670837i	0.287072	+	0.957909i	$0.407318\pi$
$948$	2.59943	+	2.59943i	0.00274201	+	0.00274201i
$949$		−	773.423i		−	0.814987i
$950$	832.137	+	186.024i	0.875933	+	0.195815i
$951$	−357.992			−0.376438
$952$	157.710	−	157.710i	0.165662	−	0.165662i
$953$	350.517	+	350.517i	0.367803	+	0.367803i	0.866676	−	0.498872i	$-0.166252\pi$
$953$	350.517	+	350.517i	0.367803	+	0.367803i	−0.498872	+	0.866676i	$0.666252\pi$
$954$		−	42.5116i		−	0.0445614i
$955$	−1131.45	+	328.703i	−1.18476	+	0.344191i
$956$	661.585			0.692035
$957$	720.764	−	720.764i	0.753149	−	0.753149i
$958$	270.133	+	270.133i	0.281976	+	0.281976i
$959$		−	492.223i		−	0.513267i
$960$	33.3775	−	60.7119i	0.0347683	−	0.0632416i
$961$	1246.61			1.29720
$962$	−130.992	+	130.992i	−0.136166	+	0.136166i
$963$	−406.096	−	406.096i	−0.421699	−	0.421699i
$964$		−	751.169i		−	0.779221i
$965$	−100.512	−	55.2585i	−0.104158	−	0.0572627i
$966$	276.569			0.286303
$967$	435.204	−	435.204i	0.450056	−	0.450056i	−0.445317	−	0.895373i	$-0.646909\pi$
$967$	435.204	−	435.204i	0.450056	−	0.450056i	0.895373	+	0.445317i	$0.146909\pi$
$968$	22.8599	+	22.8599i	0.0236156	+	0.0236156i
$969$			1245.00i			1.28483i
$970$	66.3616	+	228.428i	0.0684140	+	0.235492i
$971$	218.866			0.225403			0.112701	−	0.993629i	$-0.464050\pi$
$971$	218.866			0.225403			0.112701	+	0.993629i	$0.464050\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−167.328	−	167.328i	−0.171971	−	0.171971i
$974$		−	455.264i		−	0.467417i
$975$	252.819	+	398.398i	0.259301	+	0.408614i
$976$	−32.3601			−0.0331559
$977$	1000.73	−	1000.73i	1.02429	−	1.02429i	0.0245886	−	0.999698i	$-0.492172\pi$
$977$	1000.73	−	1000.73i	1.02429	−	1.02429i	0.999698	−	0.0245886i	$-0.00782759\pi$
$978$	−111.178	−	111.178i	−0.113679	−	0.113679i
$979$		−	1670.41i		−	1.70624i
$980$	−67.2208	+	19.5286i	−0.0685926	+	0.0199272i
$981$	−302.802			−0.308667
$982$	23.2563	−	23.2563i	0.0236826	−	0.0236826i
$983$	915.596	+	915.596i	0.931431	+	0.931431i	0.997795	−	0.0663648i	$-0.0211401\pi$
$983$	915.596	+	915.596i	0.931431	+	0.931431i	−0.0663648	+	0.997795i	$0.521140\pi$
$984$		−	91.1645i		−	0.0926468i
$985$	−22.7605	+	41.4001i	−0.0231071	+	0.0420306i
$986$	2155.51			2.18612
$987$	−229.729	+	229.729i	−0.232755	+	0.232755i
$988$	371.658	+	371.658i	0.376172	+	0.376172i
$989$		−	1577.50i		−	1.59505i
$990$	213.921	+	117.607i	0.216082	+	0.118795i
$991$	−437.633			−0.441608			−0.220804	−	0.975318i	$-0.570868\pi$
$991$	−437.633			−0.441608			−0.220804	+	0.975318i	$0.570868\pi$
$992$	−187.941	+	187.941i	−0.189457	+	0.189457i
$993$	−274.319	−	274.319i	−0.276253	−	0.276253i
$994$		−	238.566i		−	0.240006i
$995$	44.7361	+	153.989i	0.0449609	+	0.154763i
$996$	−262.704			−0.263759
$997$	180.748	−	180.748i	0.181292	−	0.181292i	−0.610627	−	0.791919i	$-0.709082\pi$
$997$	180.748	−	180.748i	0.181292	−	0.181292i	0.791919	+	0.610627i	$0.209082\pi$
$998$	319.077	+	319.077i	0.319717	+	0.319717i
$999$			62.4634i			0.0625260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.b.43.4	✓	16
3.2	odd	2		630.3.o.f.253.1		16
5.2	odd	4	inner	210.3.l.b.127.4	yes	16
5.3	odd	4		1050.3.l.h.757.5		16
5.4	even	2		1050.3.l.h.43.5		16
15.2	even	4		630.3.o.f.127.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.4	✓	16	1.1	even	1	trivial
210.3.l.b.127.4	yes	16	5.2	odd	4	inner
630.3.o.f.127.1		16	15.2	even	4
630.3.o.f.253.1		16	3.2	odd	2
1050.3.l.h.43.5		16	5.4	even	2
1050.3.l.h.757.5		16	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(4.80148 - 1.39490i) q^{5} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(4.80148 - 1.39490i) q^{5} +2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-3.40658 + 6.19639i) q^{10} -11.5078 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-7.70521 - 7.70521i) q^{13} +3.74166i q^{14} +(-7.58899 - 4.17219i) q^{15} -4.00000 q^{16} +(21.0749 - 21.0749i) q^{17} +(-3.00000 - 3.00000i) q^{18} -24.1173i q^{19} +(-2.78980 - 9.60297i) q^{20} -4.58258 q^{21} +(11.5078 - 11.5078i) q^{22} +(30.1762 + 30.1762i) q^{23} -4.89898i q^{24} +(21.1085 - 13.3952i) q^{25} +15.4104 q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -51.1392i q^{29} +(11.7612 - 3.41680i) q^{30} -46.9852 q^{31} +(4.00000 - 4.00000i) q^{32} +(14.0941 + 14.0941i) q^{33} +42.1499i q^{34} +(6.37313 - 11.5924i) q^{35} +6.00000 q^{36} +(-8.50020 + 8.50020i) q^{37} +(24.1173 + 24.1173i) q^{38} +18.8738i q^{39} +(12.3928 + 6.81316i) q^{40} +18.6089 q^{41} +(4.58258 - 4.58258i) q^{42} +(-26.1383 - 26.1383i) q^{43} +23.0156i q^{44} +(4.18471 + 14.4045i) q^{45} -60.3523 q^{46} +(50.1311 - 50.1311i) q^{47} +(4.89898 + 4.89898i) q^{48} -7.00000i q^{49} +(-7.71330 + 34.5037i) q^{50} -51.6228 q^{51} +(-15.4104 + 15.4104i) q^{52} +(7.08527 + 7.08527i) q^{53} +7.34847i q^{54} +(-55.2546 + 16.0523i) q^{55} +7.48331 q^{56} +(-29.5376 + 29.5376i) q^{57} +(51.1392 + 51.1392i) q^{58} +94.3487i q^{59} +(-8.34439 + 15.1780i) q^{60} +8.09003 q^{61} +(46.9852 - 46.9852i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} +(-47.7445 - 26.2484i) q^{65} -28.1883 q^{66} +(-20.6469 + 20.6469i) q^{67} +(-42.1499 - 42.1499i) q^{68} -73.9162i q^{69} +(5.21925 + 17.9655i) q^{70} -63.7595 q^{71} +(-6.00000 + 6.00000i) q^{72} +(50.1883 + 50.1883i) q^{73} -17.0004i q^{74} +(-42.2582 - 9.44682i) q^{75} -48.2346 q^{76} +(-21.5292 + 21.5292i) q^{77} +(-18.8738 - 18.8738i) q^{78} -1.06121i q^{79} +(-19.2059 + 5.57961i) q^{80} -9.00000 q^{81} +(-18.6089 + 18.6089i) q^{82} +(53.6243 + 53.6243i) q^{83} +9.16515i q^{84} +(71.7935 - 130.588i) q^{85} +52.2765 q^{86} +(-62.6325 + 62.6325i) q^{87} +(-23.0156 - 23.0156i) q^{88} +145.154i q^{89} +(-18.5892 - 10.2197i) q^{90} -28.8303 q^{91} +(60.3523 - 60.3523i) q^{92} +(57.5449 + 57.5449i) q^{93} +100.262i q^{94} +(-33.6413 - 115.799i) q^{95} -9.79796 q^{96} +(23.7872 - 23.7872i) q^{97} +(7.00000 + 7.00000i) q^{98} -34.5235i 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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