LMFDB - Embedded newform 210.3.l.b.127.4

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			127.4
Root			$0.170157 + 0.170157i$ of defining polynomial
Character	$\chi$	$=$	210.127
Dual form			210.3.l.b.43.4

$q$-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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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
$5$	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	−0.938362	−	0.345654i	$-0.887657\pi$
$13$	−7.70521	+	7.70521i	−0.592708	+	0.592708i	0.345654	+	0.938362i	$0.387657\pi$
$14$		−	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	0.960123	+	0.279579i	$0.0901950\pi$
$17$	21.0749	+	21.0749i	1.23970	+	1.23970i	0.279579	+	0.960123i	$0.409805\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			24.1173i			1.26933i	0.772786	+	0.634666i	$0.218862\pi$
$19$			24.1173i			1.26933i	−0.772786	+	0.634666i	$0.781138\pi$
$20$	−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	0.392073	−	0.919934i	$-0.371758\pi$
$23$	30.1762	−	30.1762i	1.31201	−	1.31201i	0.919934	−	0.392073i	$-0.128242\pi$
$24$			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	$0.343608\pi$
$29$			51.1392i			1.76342i	−0.471790	+	0.881711i	$0.656392\pi$
$30$	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	0.582847	−	0.812582i	$-0.301939\pi$
$37$	−8.50020	−	8.50020i	−0.229735	−	0.229735i	−0.812582	+	0.582847i	$0.801939\pi$
$38$	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	−0.942388	−	0.334522i	$-0.891425\pi$
$43$	−26.1383	+	26.1383i	−0.607867	+	0.607867i	0.334522	+	0.942388i	$0.391425\pi$
$44$		−	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	0.997617	+	0.0690016i	$0.0219813\pi$
$47$	50.1311	+	50.1311i	1.06662	+	1.06662i	0.0690016	+	0.997617i	$0.478019\pi$
$48$	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	−0.637098	−	0.770783i	$-0.719865\pi$
$53$	7.08527	−	7.08527i	0.133684	−	0.133684i	0.770783	+	0.637098i	$0.219865\pi$
$54$		−	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	$-0.705063\pi$
$59$		−	94.3487i		−	1.59913i	0.600579	−	0.799565i	$-0.294937\pi$
$60$	−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	0.536034	−	0.844197i	$-0.319922\pi$
$67$	−20.6469	−	20.6469i	−0.308163	−	0.308163i	−0.844197	+	0.536034i	$0.819922\pi$
$68$	−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	−0.274170	−	0.961681i	$-0.588403\pi$
$73$	50.1883	−	50.1883i	0.687511	−	0.687511i	0.961681	+	0.274170i	$0.0884031\pi$
$74$			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	$0.00213796\pi$
$79$			1.06121i			0.0134331i	−0.999977	+	0.00671653i	$0.997862\pi$
$80$	−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	−0.305967	−	0.952042i	$-0.598980\pi$
$83$	53.6243	−	53.6243i	0.646075	−	0.646075i	0.952042	+	0.305967i	$0.0989796\pi$
$84$		−	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	$-0.696477\pi$
$89$		−	145.154i		−	1.63095i	0.578794	−	0.815473i	$-0.303523\pi$
$90$	−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	0.819009	−	0.573780i	$-0.194524\pi$
$97$	23.7872	+	23.7872i	0.245229	+	0.245229i	−0.573780	+	0.819009i	$0.694524\pi$
$98$	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	−0.378251	−	0.925703i	$-0.623474\pi$
$103$	56.3876	−	56.3876i	0.547453	−	0.547453i	0.925703	+	0.378251i	$0.123474\pi$
$104$			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	−0.948590	−	0.316506i	$-0.897490\pi$
$107$	−135.365	−	135.365i	−1.26510	−	1.26510i	−0.316506	−	0.948590i	$-0.602510\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	100.934i		−	0.926001i	−0.886358	−	0.463001i	$-0.846773\pi$
$109$		−	100.934i		−	0.926001i	0.886358	−	0.463001i	$-0.153227\pi$
$110$	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	−0.586153	−	0.810201i	$-0.699358\pi$
$113$	25.3174	−	25.3174i	0.224048	−	0.224048i	0.810201	+	0.586153i	$0.199358\pi$
$114$			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	0.996976	−	0.0777140i	$-0.0247621\pi$
$127$	116.746	+	116.746i	0.919262	+	0.919262i	−0.0777140	+	0.996976i	$0.524762\pi$
$128$	−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	0.999239	−	0.0390044i	$-0.0124186\pi$
$137$	131.552	+	131.552i	0.960235	+	0.960235i	−0.0390044	+	0.999239i	$0.512419\pi$
$138$	73.9162	−	73.9162i	0.535625	−	0.535625i
$139$			89.4407i			0.643458i	0.946832	+	0.321729i	$0.104264\pi$
$139$			89.4407i			0.643458i	−0.946832	+	0.321729i	$0.895736\pi$
$140$	−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	$-0.940108\pi$
$149$		−	55.7399i		−	0.374093i	0.982351	−	0.187047i	$-0.0598915\pi$
$150$	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	0.313839	−	0.949476i	$-0.398385\pi$
$157$	−99.7950	−	99.7950i	−0.635637	−	0.635637i	−0.949476	+	0.313839i	$0.898385\pi$
$158$	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	−0.832493	−	0.554036i	$-0.813087\pi$
$163$	−45.3884	+	45.3884i	−0.278457	+	0.278457i	0.554036	+	0.832493i	$0.313087\pi$
$164$			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	0.344481	−	0.938793i	$-0.388055\pi$
$167$	−99.2501	−	99.2501i	−0.594312	−	0.594312i	−0.938793	+	0.344481i	$0.888055\pi$
$168$	−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	−0.900470	−	0.434919i	$-0.856777\pi$
$173$	−80.5404	+	80.5404i	−0.465551	+	0.465551i	0.434919	+	0.900470i	$0.356777\pi$
$174$			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	$0.141808\pi$
$179$			154.267i			0.861824i	−0.902394	+	0.430912i	$0.858192\pi$
$180$	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	−0.747880	−	0.663833i	$-0.768928\pi$
$193$	−16.2211	+	16.2211i	−0.0840471	+	0.0840471i	0.663833	+	0.747880i	$0.268928\pi$
$194$		−	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	0.689946	−	0.723861i	$-0.257634\pi$
$197$	−6.68134	−	6.68134i	−0.0339154	−	0.0339154i	−0.723861	+	0.689946i	$0.757634\pi$
$198$	34.5235	−	34.5235i	0.174361	−	0.174361i
$199$		−	32.0712i		−	0.161162i	−0.996748	−	0.0805808i	$-0.974322\pi$
$199$		−	32.0712i		−	0.161162i	0.996748	−	0.0805808i	$-0.0256775\pi$
$200$	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	−0.866575	−	0.499046i	$-0.833684\pi$
$223$	−81.9590	+	81.9590i	−0.367529	+	0.367529i	0.499046	+	0.866575i	$0.333684\pi$
$224$			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	0.882565	−	0.470191i	$-0.155815\pi$
$227$	93.6089	+	93.6089i	0.412374	+	0.412374i	−0.470191	+	0.882565i	$0.655815\pi$
$228$	59.0751	−	59.0751i	0.259101	−	0.259101i
$229$		−	348.973i		−	1.52390i	−0.647635	−	0.761950i	$-0.724242\pi$
$229$		−	348.973i		−	1.52390i	0.647635	−	0.761950i	$-0.275758\pi$
$230$	−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	−0.100829	−	0.994904i	$-0.532150\pi$
$233$	208.319	−	208.319i	0.894074	−	0.894074i	0.994904	+	0.100829i	$0.0321496\pi$
$234$		−	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	$-0.756715\pi$
$239$		−	330.793i		−	1.38407i	0.721864	−	0.692035i	$-0.243285\pi$
$240$	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	0.481828	−	0.876266i	$-0.339973\pi$
$257$	−101.370	−	101.370i	−0.394437	−	0.394437i	−0.876266	+	0.481828i	$0.839973\pi$
$258$	−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	−0.321184	−	0.947017i	$-0.604081\pi$
$263$	164.594	−	164.594i	0.625833	−	0.625833i	0.947017	+	0.321184i	$0.104081\pi$
$264$		−	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	$0.156610\pi$
$269$			254.148i			0.944788i	−0.881387	+	0.472394i	$0.843390\pi$
$270$	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	0.787463	−	0.616362i	$-0.211394\pi$
$277$	47.3949	+	47.3949i	0.171101	+	0.171101i	−0.616362	+	0.787463i	$0.711394\pi$
$278$	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	−0.881486	−	0.472209i	$-0.843457\pi$
$283$	−115.825	+	115.825i	−0.409277	+	0.409277i	0.472209	+	0.881486i	$0.343457\pi$
$284$		−	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	−0.211364	−	0.977407i	$-0.567791\pi$
$293$	224.451	−	224.451i	0.766043	−	0.766043i	0.977407	+	0.211364i	$0.0677906\pi$
$294$			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	0.634471	−	0.772947i	$-0.281218\pi$
$307$	−42.5120	−	42.5120i	−0.138476	−	0.138476i	−0.772947	+	0.634471i	$0.781218\pi$
$308$	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	−0.841753	−	0.539863i	$-0.818476\pi$
$313$	−94.4913	+	94.4913i	−0.301889	+	0.301889i	0.539863	+	0.841753i	$0.318476\pi$
$314$			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	0.898996	−	0.437956i	$-0.144297\pi$
$317$	146.150	+	146.150i	0.461040	+	0.461040i	−0.437956	+	0.898996i	$0.644297\pi$
$318$	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	0.642454	−	0.766324i	$-0.277916\pi$
$337$	−41.7444	−	41.7444i	−0.123871	−	0.123871i	−0.766324	+	0.642454i	$0.777916\pi$
$338$	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	0.985530	−	0.169500i	$-0.0542152\pi$
$347$	283.163	+	283.163i	0.816031	+	0.816031i	−0.169500	+	0.985530i	$0.554215\pi$
$348$	125.265	−	125.265i	0.359957	−	0.359957i
$349$			73.8529i			0.211613i	0.994387	+	0.105807i	$0.0337424\pi$
$349$			73.8529i			0.211613i	−0.994387	+	0.105807i	$0.966258\pi$
$350$	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	−0.947576	−	0.319530i	$-0.896475\pi$
$353$	−221.700	+	221.700i	−0.628047	+	0.628047i	0.319530	+	0.947576i	$0.396475\pi$
$354$		−	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	$0.162960\pi$
$359$			351.735i			0.979764i	−0.871789	+	0.489882i	$0.837040\pi$
$360$	−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	0.719312	−	0.694687i	$-0.244457\pi$
$367$	9.03767	+	9.03767i	0.0246258	+	0.0246258i	−0.694687	+	0.719312i	$0.744457\pi$
$368$	−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	−0.880019	−	0.474939i	$-0.842470\pi$
$373$	−151.095	+	151.095i	−0.405079	+	0.405079i	0.474939	+	0.880019i	$0.342470\pi$
$374$			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	$0.115383\pi$
$379$			268.787i			0.709201i	−0.935018	+	0.354601i	$0.884617\pi$
$380$	−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	−0.187618	−	0.982242i	$-0.560077\pi$
$383$	304.341	−	304.341i	0.794625	−	0.794625i	0.982242	+	0.187618i	$0.0600766\pi$
$384$		−	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	$-0.979524\pi$
$389$		−	50.0127i		−	0.128567i	0.997932	−	0.0642837i	$-0.0204763\pi$
$390$	−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	0.167268	−	0.985912i	$-0.446506\pi$
$397$	−325.002	−	325.002i	−0.818644	−	0.818644i	−0.985912	+	0.167268i	$0.946506\pi$
$398$	−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	$0.0514451\pi$
$409$			131.630i			0.321834i	−0.986968	+	0.160917i	$0.948555\pi$
$410$	−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	$0.221114\pi$
$419$			536.418i			1.28023i	−0.768277	+	0.640117i	$0.778886\pi$
$420$	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	−0.840554	−	0.541729i	$-0.817770\pi$
$433$	−129.391	+	129.391i	−0.298825	+	0.298825i	0.541729	+	0.840554i	$0.317770\pi$
$434$			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	$-0.981216\pi$
$439$		−	51.7818i		−	0.117954i	0.998259	−	0.0589770i	$-0.0187839\pi$
$440$	−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	−0.177154	−	0.984183i	$-0.556689\pi$
$443$	357.514	−	357.514i	0.807029	−	0.807029i	0.984183	+	0.177154i	$0.0566891\pi$
$444$			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	$-0.759504\pi$
$449$		−	615.742i		−	1.37136i	0.727902	−	0.685681i	$-0.240496\pi$
$450$	−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	−0.994553	−	0.104230i	$-0.966762\pi$
$457$	−502.144	−	502.144i	−1.09878	−	1.09878i	−0.104230	−	0.994553i	$-0.533238\pi$
$458$	−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	−0.284347	−	0.958721i	$-0.591777\pi$
$463$	312.235	−	312.235i	0.674374	−	0.674374i	0.958721	+	0.284347i	$0.0917768\pi$
$464$		−	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	0.996849	+	0.0793198i	$0.0252748\pi$
$467$	502.571	+	502.571i	1.07617	+	1.07617i	0.0793198	+	0.996849i	$0.474725\pi$
$468$	−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	$0.0909899\pi$
$479$			270.133i			0.563952i	−0.959421	+	0.281976i	$0.909010\pi$
$480$	−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	0.433660	−	0.901077i	$-0.357222\pi$
$487$	−227.632	−	227.632i	−0.467417	−	0.467417i	−0.901077	+	0.433660i	$0.857222\pi$
$488$	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	$0.103588\pi$
$499$			319.077i			0.639433i	−0.947513	+	0.319717i	$0.896412\pi$
$500$	−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	0.180990	−	0.983485i	$-0.442070\pi$
$503$	585.731	−	585.731i	1.16448	−	1.16448i	0.983485	−	0.180990i	$-0.0579302\pi$
$504$		−	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	$0.0842009\pi$
$509$			266.157i			0.522902i	−0.965217	+	0.261451i	$0.915799\pi$
$510$	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	−0.413254	−	0.910616i	$-0.635608\pi$
$523$	260.120	−	260.120i	0.497362	−	0.497362i	0.910616	+	0.413254i	$0.135608\pi$
$524$			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	0.952966	−	0.303077i	$-0.0980138\pi$
$547$	355.490	+	355.490i	0.649890	+	0.649890i	−0.303077	+	0.952966i	$0.598014\pi$
$548$	−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	0.420802	−	0.907152i	$-0.361749\pi$
$557$	−270.897	−	270.897i	−0.486350	−	0.486350i	−0.907152	+	0.420802i	$0.861749\pi$
$558$	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	−0.639186	−	0.769052i	$-0.720729\pi$
$563$	73.1143	−	73.1143i	0.129866	−	0.129866i	0.769052	+	0.639186i	$0.220729\pi$
$564$		−	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	$-0.647149\pi$
$569$		−	1018.55i		−	1.79007i	0.445992	−	0.895037i	$-0.352851\pi$
$570$	−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	0.915608	+	0.402071i	$0.131710\pi$
$577$	760.301	+	760.301i	1.31768	+	1.31768i	0.402071	+	0.915608i	$0.368290\pi$
$578$	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	0.712153	−	0.702024i	$-0.247720\pi$
$587$	5.94607	+	5.94607i	0.0101296	+	0.0101296i	−0.702024	+	0.712153i	$0.747720\pi$
$588$	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	−0.980222	−	0.197902i	$-0.936587\pi$
$593$	−463.916	+	463.916i	−0.782320	+	0.782320i	0.197902	+	0.980222i	$0.436587\pi$
$594$			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	$0.185960\pi$
$599$			660.745i			1.10308i	−0.834148	+	0.551540i	$0.814040\pi$
$600$	−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	0.990650	−	0.136426i	$-0.0435615\pi$
$607$	518.514	+	518.514i	0.854224	+	0.854224i	−0.136426	+	0.990650i	$0.543562\pi$
$608$	−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	−0.985653	−	0.168786i	$-0.946015\pi$
$613$	−500.739	+	500.739i	−0.816867	+	0.816867i	0.168786	+	0.985653i	$0.446015\pi$
$614$			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	0.799195	−	0.601072i	$-0.205260\pi$
$617$	122.242	+	122.242i	0.198123	+	0.198123i	−0.601072	+	0.799195i	$0.705260\pi$
$618$	138.121	−	138.121i	0.223497	−	0.223497i
$619$		−	320.914i		−	0.518440i	−0.965818	−	0.259220i	$-0.916534\pi$
$619$		−	320.914i		−	0.518440i	0.965818	−	0.259220i	$-0.0834655\pi$
$620$	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	−0.711242	−	0.702948i	$-0.751867\pi$
$643$	−5.33298	+	5.33298i	−0.00829390	+	0.00829390i	0.702948	+	0.711242i	$0.251867\pi$
$644$			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	0.892661	−	0.450728i	$-0.148836\pi$
$647$	285.931	+	285.931i	0.441933	+	0.441933i	−0.450728	+	0.892661i	$0.648836\pi$
$648$	−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	−0.537689	−	0.843144i	$-0.680702\pi$
$653$	199.462	−	199.462i	0.305455	−	0.305455i	0.843144	+	0.537689i	$0.180702\pi$
$654$		−	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	$-0.950366\pi$
$659$		−	204.685i		−	0.310599i	0.987867	−	0.155300i	$-0.0496343\pi$
$660$	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	−0.902499	−	0.430691i	$-0.858270\pi$
$673$	−317.527	+	317.527i	−0.471808	+	0.471808i	0.430691	+	0.902499i	$0.358270\pi$
$674$			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	0.476450	−	0.879202i	$-0.341923\pi$
$677$	−272.663	−	272.663i	−0.402752	−	0.402752i	−0.879202	+	0.476450i	$0.841923\pi$
$678$	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	−0.954843	−	0.297111i	$-0.903977\pi$
$683$	−449.231	+	449.231i	−0.657732	+	0.657732i	0.297111	+	0.954843i	$0.403977\pi$
$684$			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	$-0.982100\pi$
$709$		−	79.6980i		−	0.112409i	0.998419	−	0.0562045i	$-0.0178999\pi$
$710$	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	$-0.729207\pi$
$719$		−	1081.03i		−	1.50351i	0.659440	−	0.751757i	$-0.270793\pi$
$720$	−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	0.873789	−	0.486305i	$-0.161656\pi$
$727$	281.701	+	281.701i	0.387484	+	0.387484i	−0.486305	+	0.873789i	$0.661656\pi$
$728$	−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	0.553858	−	0.832611i	$-0.313155\pi$
$733$	1016.28	−	1016.28i	1.38647	−	1.38647i	0.832611	−	0.553858i	$-0.186845\pi$
$734$		−	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	$-0.937325\pi$
$739$		−	289.140i		−	0.391258i	0.980678	−	0.195629i	$-0.0626749\pi$
$740$	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	−0.484054	−	0.875038i	$-0.660836\pi$
$743$	290.501	−	290.501i	0.390984	−	0.390984i	0.875038	+	0.484054i	$0.160836\pi$
$744$		−	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	0.816456	−	0.577408i	$-0.195936\pi$
$757$	180.960	+	180.960i	0.239049	+	0.239049i	−0.577408	+	0.816456i	$0.695936\pi$
$758$	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	$0.197075\pi$
$769$			892.540i			1.16065i	−0.814385	+	0.580325i	$0.802925\pi$
$770$	−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	0.0862244	−	0.996276i	$-0.472520\pi$
$773$	836.773	−	836.773i	1.08250	−	1.08250i	0.996276	−	0.0862244i	$-0.0274802\pi$
$774$		−	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	0.548420	−	0.836203i	$-0.315229\pi$
$787$	−226.485	−	226.485i	−0.287782	−	0.287782i	−0.836203	+	0.548420i	$0.815229\pi$
$788$	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	0.0820555	−	0.996628i	$-0.473852\pi$
$797$	−728.914	−	728.914i	−0.914572	−	0.914572i	−0.996628	+	0.0820555i	$0.973852\pi$
$798$	−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	$-0.735101\pi$
$809$		−	1196.38i		−	1.47884i	0.673247	−	0.739418i	$-0.264899\pi$
$810$	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	−0.379737	−	0.925094i	$-0.623986\pi$
$823$	448.829	−	448.829i	0.545357	−	0.545357i	0.925094	+	0.379737i	$0.123986\pi$
$824$		−	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	0.998214	+	0.0597373i	$0.0190263\pi$
$827$	874.926	+	874.926i	1.05795	+	1.05795i	0.0597373	+	0.998214i	$0.480974\pi$
$828$	181.057	−	181.057i	0.218668	−	0.218668i
$829$			934.022i			1.12669i	0.826223	+	0.563343i	$0.190485\pi$
$829$			934.022i			1.12669i	−0.826223	+	0.563343i	$0.809515\pi$
$830$	−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	$-0.998005\pi$
$839$		−	10.5147i		−	0.0125324i	0.999980	−	0.00626621i	$-0.00199461\pi$
$840$	−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	0.322603	−	0.946534i	$-0.395442\pi$
$853$	1082.57	−	1082.57i	1.26914	−	1.26914i	0.946534	−	0.322603i	$-0.104558\pi$
$854$		−	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	0.938014	−	0.346598i	$-0.112663\pi$
$857$	506.843	+	506.843i	0.591416	+	0.591416i	−0.346598	+	0.938014i	$0.612663\pi$
$858$	217.197	−	217.197i	0.253143	−	0.253143i
$859$		−	471.172i		−	0.548512i	−0.961657	−	0.274256i	$-0.911568\pi$
$859$		−	471.172i		−	0.548512i	0.961657	−	0.274256i	$-0.0884315\pi$
$860$	−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	−0.472689	−	0.881229i	$-0.656717\pi$
$863$	352.570	−	352.570i	0.408540	−	0.408540i	0.881229	+	0.472689i	$0.156717\pi$
$864$			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	−0.812137	−	0.583467i	$-0.801696\pi$
$877$	−1223.94	−	1223.94i	−1.39560	−	1.39560i	−0.583467	−	0.812137i	$-0.698304\pi$
$878$	−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	−0.825498	−	0.564405i	$-0.809106\pi$
$883$	−230.546	+	230.546i	−0.261094	+	0.261094i	0.564405	+	0.825498i	$0.309106\pi$
$884$		−	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	−0.843518	−	0.537101i	$-0.819520\pi$
$887$	−1224.61	−	1224.61i	−1.38062	−	1.38062i	−0.537101	−	0.843518i	$-0.680480\pi$
$888$	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	0.989546	−	0.144217i	$-0.0460664\pi$
$907$	766.713	+	766.713i	0.845329	+	0.845329i	−0.144217	+	0.989546i	$0.546066\pi$
$908$	−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	$-0.845380\pi$
$919$		−	858.117i		−	0.933750i	0.884323	−	0.466875i	$-0.154620\pi$
$920$	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	$-0.889605\pi$
$929$		−	631.542i		−	0.679809i	0.940460	−	0.339904i	$-0.110395\pi$
$930$	−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	0.957474	+	0.288519i	$0.0931630\pi$
$937$	1167.50	+	1167.50i	1.24599	+	1.24599i	0.288519	+	0.957474i	$0.406837\pi$
$938$	−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	0.287072	−	0.957909i	$-0.407318\pi$
$947$	−635.282	−	635.282i	−0.670837	−	0.670837i	−0.957909	+	0.287072i	$0.907318\pi$
$948$	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	−0.498872	−	0.866676i	$-0.666252\pi$
$953$	350.517	−	350.517i	0.367803	−	0.367803i	0.866676	+	0.498872i	$0.166252\pi$
$954$			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	0.895373	−	0.445317i	$-0.146909\pi$
$967$	435.204	+	435.204i	0.450056	+	0.450056i	−0.445317	+	0.895373i	$0.646909\pi$
$968$	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	0.999698	+	0.0245886i	$0.00782759\pi$
$977$	1000.73	+	1000.73i	1.02429	+	1.02429i	0.0245886	+	0.999698i	$0.492172\pi$
$978$	−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	−0.0663648	−	0.997795i	$-0.521140\pi$
$983$	915.596	−	915.596i	0.931431	−	0.931431i	0.997795	+	0.0663648i	$0.0211401\pi$
$984$			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	0.791919	−	0.610627i	$-0.209082\pi$
$997$	180.748	+	180.748i	0.181292	+	0.181292i	−0.610627	+	0.791919i	$0.709082\pi$
$998$	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.127.4	yes	16
3.2	odd	2		630.3.o.f.127.1		16
5.2	odd	4		1050.3.l.h.43.5		16
5.3	odd	4	inner	210.3.l.b.43.4	✓	16
5.4	even	2		1050.3.l.h.757.5		16
15.8	even	4		630.3.o.f.253.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.4	✓	16	5.3	odd	4	inner
210.3.l.b.127.4	yes	16	1.1	even	1	trivial
630.3.o.f.127.1		16	3.2	odd	2
630.3.o.f.253.1		16	15.8	even	4
1050.3.l.h.43.5		16	5.2	odd	4
1050.3.l.h.757.5		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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.80148 + 1.39490i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(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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