LMFDB - Embedded newform 230.3.f.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 $ x^20 - 52x^17 + 1020x^16 - 1316x^15 + 1352x^14 - 18724x^13 + 250686x^12 - 439644x^11 + 460536x^10 - 1833716x^9 + 16970128x^8 - 36894604x^7 + 40544632x^6 - 4380588x^5 + 34721x^4 - 4419956x^3 + 9945800x^2 + 1329080*x + 88804
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.2
Root			$-2.63948 + 2.63948i$ of defining polynomial
Character	$\chi$	$=$	230.47
Dual form			230.3.f.a.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-2.63948 + 2.63948i) q^{3} +2.00000i q^{4} +(1.86266 + 4.64010i) q^{5} +5.27895 q^{6} +(5.81530 + 5.81530i) q^{7} +(2.00000 - 2.00000i) q^{8} -4.93366i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.63948 + 2.63948i) q^{3} +2.00000i q^{4} +(1.86266 + 4.64010i) q^{5} +5.27895 q^{6} +(5.81530 + 5.81530i) q^{7} +(2.00000 - 2.00000i) q^{8} -4.93366i q^{9} +(2.77744 - 6.50275i) q^{10} -12.5859 q^{11} +(-5.27895 - 5.27895i) q^{12} +(9.20375 - 9.20375i) q^{13} -11.6306i q^{14} +(-17.1639 - 7.33099i) q^{15} -4.00000 q^{16} +(-1.16565 - 1.16565i) q^{17} +(-4.93366 + 4.93366i) q^{18} +28.2361i q^{19} +(-9.28020 + 3.72531i) q^{20} -30.6987 q^{21} +(12.5859 + 12.5859i) q^{22} +(-3.39116 + 3.39116i) q^{23} +10.5579i q^{24} +(-18.0610 + 17.2858i) q^{25} -18.4075 q^{26} +(-10.7330 - 10.7330i) q^{27} +(-11.6306 + 11.6306i) q^{28} +4.28812i q^{29} +(9.83287 + 24.4949i) q^{30} -33.8299 q^{31} +(4.00000 + 4.00000i) q^{32} +(33.2202 - 33.2202i) q^{33} +2.33130i q^{34} +(-16.1517 + 37.8155i) q^{35} +9.86733 q^{36} +(-3.35506 - 3.35506i) q^{37} +(28.2361 - 28.2361i) q^{38} +48.5861i q^{39} +(13.0055 + 5.55489i) q^{40} -30.6884 q^{41} +(30.6987 + 30.6987i) q^{42} +(39.8911 - 39.8911i) q^{43} -25.1718i q^{44} +(22.8927 - 9.18972i) q^{45} +6.78233 q^{46} +(-20.8905 - 20.8905i) q^{47} +(10.5579 - 10.5579i) q^{48} +18.6355i q^{49} +(35.3468 + 0.775219i) q^{50} +6.15341 q^{51} +(18.4075 + 18.4075i) q^{52} +(-11.2617 + 11.2617i) q^{53} +21.4660i q^{54} +(-23.4432 - 58.3999i) q^{55} +23.2612 q^{56} +(-74.5285 - 74.5285i) q^{57} +(4.28812 - 4.28812i) q^{58} +42.8744i q^{59} +(14.6620 - 34.3277i) q^{60} +25.6581 q^{61} +(33.8299 + 33.8299i) q^{62} +(28.6908 - 28.6908i) q^{63} -8.00000i q^{64} +(59.8497 + 25.5629i) q^{65} -66.4404 q^{66} +(68.3222 + 68.3222i) q^{67} +(2.33130 - 2.33130i) q^{68} -17.9018i q^{69} +(53.9672 - 21.6638i) q^{70} -33.1444 q^{71} +(-9.86733 - 9.86733i) q^{72} +(53.4364 - 53.4364i) q^{73} +6.71011i q^{74} +(2.04617 - 93.2971i) q^{75} -56.4722 q^{76} +(-73.1909 - 73.1909i) q^{77} +(48.5861 - 48.5861i) q^{78} +43.7476i q^{79} +(-7.45062 - 18.5604i) q^{80} +101.062 q^{81} +(30.6884 + 30.6884i) q^{82} +(-72.3311 + 72.3311i) q^{83} -61.3974i q^{84} +(3.23753 - 7.57994i) q^{85} -79.7823 q^{86} +(-11.3184 - 11.3184i) q^{87} +(-25.1718 + 25.1718i) q^{88} -158.941i q^{89} +(-32.0824 - 13.7030i) q^{90} +107.045 q^{91} +(-6.78233 - 6.78233i) q^{92} +(89.2933 - 89.2933i) q^{93} +41.7810i q^{94} +(-131.018 + 52.5941i) q^{95} -21.1158 q^{96} +(33.4626 + 33.4626i) q^{97} +(18.6355 - 18.6355i) q^{98} +62.0947i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−2.63948	+	2.63948i	−0.879825	+	0.879825i	−0.993516	−	0.113691i	$-0.963733\pi$
$3$	−2.63948	+	2.63948i	−0.879825	+	0.879825i	0.113691	+	0.993516i	$0.463733\pi$
$4$			2.00000i			0.500000i
$5$	1.86266	+	4.64010i	0.372531	+	0.928020i
$5$	1.86266	+	4.64010i	0.372531	+	0.928020i
$6$	5.27895			0.879825
$7$	5.81530	+	5.81530i	0.830758	+	0.830758i	0.987620	−	0.156863i	$-0.0501380\pi$
$7$	5.81530	+	5.81530i	0.830758	+	0.830758i	−0.156863	+	0.987620i	$0.550138\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	4.93366i		−	0.548185i
$10$	2.77744	−	6.50275i	0.277744	−	0.650275i
$11$	−12.5859			−1.14417			−0.572087	−	0.820193i	$-0.693866\pi$
$11$	−12.5859			−1.14417			−0.572087	+	0.820193i	$0.693866\pi$
$12$	−5.27895	−	5.27895i	−0.439913	−	0.439913i
$13$	9.20375	−	9.20375i	0.707981	−	0.707981i	−0.258130	−	0.966110i	$-0.583106\pi$
$13$	9.20375	−	9.20375i	0.707981	−	0.707981i	0.966110	+	0.258130i	$0.0831062\pi$
$14$		−	11.6306i		−	0.830758i
$15$	−17.1639	−	7.33099i	−1.14426	−	0.488733i
$16$	−4.00000			−0.250000
$17$	−1.16565	−	1.16565i	−0.0685676	−	0.0685676i	0.671991	−	0.740559i	$-0.265439\pi$
$17$	−1.16565	−	1.16565i	−0.0685676	−	0.0685676i	−0.740559	+	0.671991i	$0.765439\pi$
$18$	−4.93366	+	4.93366i	−0.274092	+	0.274092i
$19$			28.2361i			1.48611i	0.669231	+	0.743055i	$0.266624\pi$
$19$			28.2361i			1.48611i	−0.669231	+	0.743055i	$0.733376\pi$
$20$	−9.28020	+	3.72531i	−0.464010	+	0.186266i
$21$	−30.6987			−1.46184
$22$	12.5859	+	12.5859i	0.572087	+	0.572087i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			10.5579i			0.439913i
$25$	−18.0610	+	17.2858i	−0.722441	+	0.691432i
$26$	−18.4075			−0.707981
$27$	−10.7330	−	10.7330i	−0.397518	−	0.397518i
$28$	−11.6306	+	11.6306i	−0.415379	+	0.415379i
$29$			4.28812i			0.147866i	0.997263	+	0.0739330i	$0.0235551\pi$
$29$			4.28812i			0.147866i	−0.997263	+	0.0739330i	$0.976445\pi$
$30$	9.83287	+	24.4949i	0.327762	+	0.816495i
$31$	−33.8299			−1.09129			−0.545644	−	0.838017i	$-0.683715\pi$
$31$	−33.8299			−1.09129			−0.545644	+	0.838017i	$0.683715\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	33.2202	−	33.2202i	1.00667	−	1.00667i
$34$			2.33130i			0.0685676i
$35$	−16.1517	+	37.8155i	−0.461476	+	1.08044i
$36$	9.86733			0.274092
$37$	−3.35506	−	3.35506i	−0.0906772	−	0.0906772i	0.660313	−	0.750990i	$-0.270424\pi$
$37$	−3.35506	−	3.35506i	−0.0906772	−	0.0906772i	−0.750990	+	0.660313i	$0.770424\pi$
$38$	28.2361	−	28.2361i	0.743055	−	0.743055i
$39$			48.5861i			1.24580i
$40$	13.0055	+	5.55489i	0.325138	+	0.138872i
$41$	−30.6884			−0.748499			−0.374249	−	0.927328i	$-0.622100\pi$
$41$	−30.6884			−0.748499			−0.374249	+	0.927328i	$0.622100\pi$
$42$	30.6987	+	30.6987i	0.730922	+	0.730922i
$43$	39.8911	−	39.8911i	0.927701	−	0.927701i	−0.0698563	−	0.997557i	$-0.522254\pi$
$43$	39.8911	−	39.8911i	0.927701	−	0.927701i	0.997557	+	0.0698563i	$0.0222541\pi$
$44$		−	25.1718i		−	0.572087i
$45$	22.8927	−	9.18972i	0.508726	−	0.204216i
$46$	6.78233			0.147442
$47$	−20.8905	−	20.8905i	−0.444479	−	0.444479i	0.449035	−	0.893514i	$-0.351768\pi$
$47$	−20.8905	−	20.8905i	−0.444479	−	0.444479i	−0.893514	+	0.449035i	$0.851768\pi$
$48$	10.5579	−	10.5579i	0.219956	−	0.219956i
$49$			18.6355i			0.380317i
$50$	35.3468	+	0.775219i	0.706937	+	0.0155044i
$51$	6.15341			0.120655
$52$	18.4075	+	18.4075i	0.353990	+	0.353990i
$53$	−11.2617	+	11.2617i	−0.212486	+	0.212486i	−0.805323	−	0.592837i	$-0.798008\pi$
$53$	−11.2617	+	11.2617i	−0.212486	+	0.212486i	0.592837	+	0.805323i	$0.298008\pi$
$54$			21.4660i			0.397518i
$55$	−23.4432	−	58.3999i	−0.426241	−	1.06182i
$56$	23.2612			0.415379
$57$	−74.5285	−	74.5285i	−1.30752	−	1.30752i
$58$	4.28812	−	4.28812i	0.0739330	−	0.0739330i
$59$			42.8744i			0.726685i	0.931656	+	0.363342i	$0.118364\pi$
$59$			42.8744i			0.726685i	−0.931656	+	0.363342i	$0.881636\pi$
$60$	14.6620	−	34.3277i	0.244366	−	0.572129i
$61$	25.6581			0.420625			0.210312	−	0.977634i	$-0.432552\pi$
$61$	25.6581			0.420625			0.210312	+	0.977634i	$0.432552\pi$
$62$	33.8299	+	33.8299i	0.545644	+	0.545644i
$63$	28.6908	−	28.6908i	0.455409	−	0.455409i
$64$		−	8.00000i		−	0.125000i
$65$	59.8497	+	25.5629i	0.920765	+	0.393275i
$66$	−66.4404			−1.00667
$67$	68.3222	+	68.3222i	1.01973	+	1.01973i	0.999801	+	0.0199332i	$0.00634537\pi$
$67$	68.3222	+	68.3222i	1.01973	+	1.01973i	0.0199332	+	0.999801i	$0.493655\pi$
$68$	2.33130	−	2.33130i	0.0342838	−	0.0342838i
$69$		−	17.9018i		−	0.259446i
$70$	53.9672	−	21.6638i	0.770959	−	0.309483i
$71$	−33.1444			−0.466823			−0.233411	−	0.972378i	$-0.574989\pi$
$71$	−33.1444			−0.466823			−0.233411	+	0.972378i	$0.574989\pi$
$72$	−9.86733	−	9.86733i	−0.137046	−	0.137046i
$73$	53.4364	−	53.4364i	0.732005	−	0.732005i	−0.239012	−	0.971017i	$-0.576823\pi$
$73$	53.4364	−	53.4364i	0.732005	−	0.732005i	0.971017	+	0.239012i	$0.0768234\pi$
$74$			6.71011i			0.0906772i
$75$	2.04617	−	93.2971i	0.0272823	−	1.24396i
$76$	−56.4722			−0.743055
$77$	−73.1909	−	73.1909i	−0.950532	−	0.950532i
$78$	48.5861	−	48.5861i	0.622899	−	0.622899i
$79$			43.7476i			0.553767i	0.960904	+	0.276883i	$0.0893016\pi$
$79$			43.7476i			0.553767i	−0.960904	+	0.276883i	$0.910698\pi$
$80$	−7.45062	−	18.5604i	−0.0931328	−	0.232005i
$81$	101.062			1.24768
$82$	30.6884	+	30.6884i	0.374249	+	0.374249i
$83$	−72.3311	+	72.3311i	−0.871459	+	0.871459i	−0.992632	−	0.121172i	$-0.961335\pi$
$83$	−72.3311	+	72.3311i	−0.871459	+	0.871459i	0.121172	+	0.992632i	$0.461335\pi$
$84$		−	61.3974i		−	0.730922i
$85$	3.23753	−	7.57994i	0.0380885	−	0.0891757i
$86$	−79.7823			−0.927701
$87$	−11.3184	−	11.3184i	−0.130096	−	0.130096i
$88$	−25.1718	+	25.1718i	−0.286044	+	0.286044i
$89$		−	158.941i		−	1.78586i	−0.450199	−	0.892928i	$-0.648647\pi$
$89$		−	158.941i		−	1.78586i	0.450199	−	0.892928i	$-0.351353\pi$
$90$	−32.0824	−	13.7030i	−0.356471	−	0.152255i
$91$	107.045			1.17632
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	89.2933	−	89.2933i	0.960143	−	0.960143i
$94$			41.7810i			0.444479i
$95$	−131.018	+	52.5941i	−1.37914	+	0.553622i
$96$	−21.1158			−0.219956
$97$	33.4626	+	33.4626i	0.344976	+	0.344976i	0.858234	−	0.513259i	$-0.171562\pi$
$97$	33.4626	+	33.4626i	0.344976	+	0.344976i	−0.513259	+	0.858234i	$0.671562\pi$
$98$	18.6355	−	18.6355i	0.190158	−	0.190158i
$99$			62.0947i			0.627219i
$100$	−34.5716	−	36.1221i	−0.345716	−	0.361221i
$101$	78.2123			0.774379			0.387190	−	0.922000i	$-0.373446\pi$
$101$	78.2123			0.774379			0.387190	+	0.922000i	$0.373446\pi$
$102$	−6.15341	−	6.15341i	−0.0603275	−	0.0603275i
$103$	−130.026	+	130.026i	−1.26239	+	1.26239i	−0.312454	+	0.949933i	$0.601151\pi$
$103$	−130.026	+	130.026i	−1.26239	+	1.26239i	−0.949933	+	0.312454i	$0.898849\pi$
$104$		−	36.8150i		−	0.353990i
$105$	−57.1811	−	142.445i	−0.544582	−	1.35662i
$106$	22.5235			0.212486
$107$	144.572	+	144.572i	1.35114	+	1.35114i	0.884393	+	0.466743i	$0.154573\pi$
$107$	144.572	+	144.572i	1.35114	+	1.35114i	0.466743	+	0.884393i	$0.345427\pi$
$108$	21.4660	−	21.4660i	0.198759	−	0.198759i
$109$			134.634i			1.23518i	0.786501	+	0.617589i	$0.211891\pi$
$109$			134.634i			1.23518i	−0.786501	+	0.617589i	$0.788109\pi$
$110$	−34.9567	+	81.8431i	−0.317788	+	0.744028i
$111$	17.7112			0.159560
$112$	−23.2612	−	23.2612i	−0.207689	−	0.207689i
$113$	121.617	−	121.617i	1.07626	−	1.07626i	0.0794141	−	0.996842i	$-0.474695\pi$
$113$	121.617	−	121.617i	1.07626	−	1.07626i	0.996842	−	0.0794141i	$-0.0253049\pi$
$114$			149.057i			1.30752i
$115$	−22.0519	−	9.41877i	−0.191756	−	0.0819023i
$116$	−8.57623			−0.0739330
$117$	−45.4082	−	45.4082i	−0.388104	−	0.388104i
$118$	42.8744	−	42.8744i	0.363342	−	0.363342i
$119$		−	13.5572i		−	0.113926i
$120$	−48.9897	+	19.6657i	−0.408248	+	0.163881i
$121$	37.4053			0.309135
$122$	−25.6581	−	25.6581i	−0.210312	−	0.210312i
$123$	81.0014	−	81.0014i	0.658548	−	0.658548i
$124$		−	67.6599i		−	0.545644i
$125$	−113.849	−	51.6074i	−0.910795	−	0.412860i
$126$	−57.3815			−0.455409
$127$	166.865	+	166.865i	1.31390	+	1.31390i	0.918517	+	0.395381i	$0.129388\pi$
$127$	166.865	+	166.865i	1.31390	+	1.31390i	0.395381	+	0.918517i	$0.370612\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			210.583i			1.63243i
$130$	−34.2868	−	85.4126i	−0.263745	−	0.657020i
$131$	−79.3875			−0.606011			−0.303006	−	0.952989i	$-0.597990\pi$
$131$	−79.3875			−0.606011			−0.303006	+	0.952989i	$0.597990\pi$
$132$	66.4404	+	66.4404i	0.503337	+	0.503337i
$133$	−164.201	+	164.201i	−1.23460	+	1.23460i
$134$		−	136.644i		−	1.01973i
$135$	29.8103	−	69.7940i	0.220817	−	0.516993i
$136$	−4.66260			−0.0342838
$137$	−16.1511	−	16.1511i	−0.117891	−	0.117891i	0.645700	−	0.763591i	$-0.276566\pi$
$137$	−16.1511	−	16.1511i	−0.117891	−	0.117891i	−0.763591	+	0.645700i	$0.776566\pi$
$138$	−17.9018	+	17.9018i	−0.129723	+	0.129723i
$139$			84.0074i			0.604370i	0.953249	+	0.302185i	$0.0977160\pi$
$139$			84.0074i			0.604370i	−0.953249	+	0.302185i	$0.902284\pi$
$140$	−75.6310	−	32.3033i	−0.540221	−	0.230738i
$141$	110.280			0.782127
$142$	33.1444	+	33.1444i	0.233411	+	0.233411i
$143$	−115.838	+	115.838i	−0.810053	+	0.810053i
$144$			19.7347i			0.137046i
$145$	−19.8973	+	7.98728i	−0.137223	+	0.0550847i
$146$	−106.873			−0.732005
$147$	−49.1880	−	49.1880i	−0.334612	−	0.334612i
$148$	6.71011	−	6.71011i	0.0453386	−	0.0453386i
$149$			165.231i			1.10894i	0.832205	+	0.554468i	$0.187078\pi$
$149$			165.231i			1.10894i	−0.832205	+	0.554468i	$0.812922\pi$
$150$	−95.3433	+	91.2510i	−0.635622	+	0.608340i
$151$	10.4015			0.0688841			0.0344421	−	0.999407i	$-0.489035\pi$
$151$	10.4015			0.0688841			0.0344421	+	0.999407i	$0.489035\pi$
$152$	56.4722	+	56.4722i	0.371527	+	0.371527i
$153$	−5.75093	+	5.75093i	−0.0375877	+	0.0375877i
$154$			146.382i			0.950532i
$155$	−63.0135	−	156.974i	−0.406539	−	1.01274i
$156$	−97.1723			−0.622899
$157$	150.737	+	150.737i	0.960109	+	0.960109i	0.999234	−	0.0391252i	$-0.0124571\pi$
$157$	150.737	+	150.737i	0.960109	+	0.960109i	−0.0391252	+	0.999234i	$0.512457\pi$
$158$	43.7476	−	43.7476i	0.276883	−	0.276883i
$159$		−	59.4502i		−	0.373900i
$160$	−11.1098	+	26.0110i	−0.0694361	+	0.162569i
$161$	−39.4413			−0.244977
$162$	−101.062	−	101.062i	−0.623839	−	0.623839i
$163$	206.834	−	206.834i	1.26892	−	1.26892i	0.322272	−	0.946647i	$-0.395554\pi$
$163$	206.834	−	206.834i	1.26892	−	1.26892i	0.946647	−	0.322272i	$-0.104446\pi$
$164$		−	61.3769i		−	0.374249i
$165$	216.023	+	92.2673i	1.30923	+	0.559196i
$166$	144.662			0.871459
$167$	−129.217	−	129.217i	−0.773753	−	0.773753i	0.205007	−	0.978760i	$-0.434278\pi$
$167$	−129.217	−	129.217i	−0.773753	−	0.773753i	−0.978760	+	0.205007i	$0.934278\pi$
$168$	−61.3974	+	61.3974i	−0.365461	+	0.365461i
$169$		−	0.417979i		−	0.00247325i
$170$	−10.8175	+	4.34241i	−0.0636321	+	0.0255436i
$171$	139.307			0.814663
$172$	79.7823	+	79.7823i	0.463850	+	0.463850i
$173$	−32.0017	+	32.0017i	−0.184981	+	0.184981i	−0.793522	−	0.608541i	$-0.791755\pi$
$173$	−32.0017	+	32.0017i	−0.184981	+	0.184981i	0.608541	+	0.793522i	$0.291755\pi$
$174$			22.6368i			0.130096i
$175$	−205.553	−	4.50813i	−1.17459	−	0.0257608i
$176$	50.3437			0.286044
$177$	−113.166	−	113.166i	−0.639356	−	0.639356i
$178$	−158.941	+	158.941i	−0.892928	+	0.892928i
$179$			268.775i			1.50154i	0.660566	+	0.750768i	$0.270316\pi$
$179$			268.775i			1.50154i	−0.660566	+	0.750768i	$0.729684\pi$
$180$	18.3794	+	45.7854i	0.102108	+	0.254363i
$181$	161.189			0.890545			0.445273	−	0.895395i	$-0.353107\pi$
$181$	161.189			0.890545			0.445273	+	0.895395i	$0.353107\pi$
$182$	−107.045	−	107.045i	−0.588160	−	0.588160i
$183$	−67.7239	+	67.7239i	−0.370076	+	0.370076i
$184$			13.5647i			0.0737210i
$185$	9.31848	−	21.8171i	0.0503702	−	0.117930i
$186$	−178.587			−0.960143
$187$	14.6708	+	14.6708i	0.0784533	+	0.0784533i
$188$	41.7810	−	41.7810i	0.222239	−	0.222239i
$189$		−	124.831i		−	0.660483i
$190$	183.612	+	78.4241i	0.966381	+	0.412759i
$191$	−264.125			−1.38285			−0.691426	−	0.722448i	$-0.743017\pi$
$191$	−264.125			−1.38285			−0.691426	+	0.722448i	$0.743017\pi$
$192$	21.1158	+	21.1158i	0.109978	+	0.109978i
$193$	−206.738	+	206.738i	−1.07118	+	1.07118i	−0.0739166	+	0.997264i	$0.523550\pi$
$193$	−206.738	+	206.738i	−1.07118	+	1.07118i	−0.997264	+	0.0739166i	$0.976450\pi$
$194$		−	66.9253i		−	0.344976i
$195$	−225.444	+	90.4992i	−1.15613	+	0.464099i
$196$	−37.2710			−0.190158
$197$	−133.996	−	133.996i	−0.680185	−	0.680185i	0.279857	−	0.960042i	$-0.409713\pi$
$197$	−133.996	−	133.996i	−0.680185	−	0.680185i	−0.960042	+	0.279857i	$0.909713\pi$
$198$	62.0947	−	62.0947i	0.313610	−	0.313610i
$199$		−	325.203i		−	1.63418i	−0.576508	−	0.817092i	$-0.695585\pi$
$199$		−	325.203i		−	1.63418i	0.576508	−	0.817092i	$-0.304415\pi$
$200$	−1.55044	+	70.6937i	−0.00775219	+	0.353468i
$201$	−360.670			−1.79438
$202$	−78.2123	−	78.2123i	−0.387190	−	0.387190i
$203$	−24.9367	+	24.9367i	−0.122841	+	0.122841i
$204$			12.3068i			0.0603275i
$205$	−57.1620	−	142.397i	−0.278839	−	0.694621i
$206$	260.052			1.26239
$207$	16.7309	+	16.7309i	0.0808255	+	0.0808255i
$208$	−36.8150	+	36.8150i	−0.176995	+	0.176995i
$209$		−	355.377i		−	1.70037i
$210$	−85.2639	+	199.626i	−0.406019	+	0.950601i
$211$	189.976			0.900362			0.450181	−	0.892937i	$-0.351359\pi$
$211$	189.976			0.900362			0.450181	+	0.892937i	$0.351359\pi$
$212$	−22.5235	−	22.5235i	−0.106243	−	0.106243i
$213$	87.4839	−	87.4839i	0.410722	−	0.410722i
$214$		−	289.143i		−	1.35114i
$215$	259.402	+	110.795i	1.20652	+	0.515327i
$216$	−42.9320			−0.198759
$217$	−196.731	−	196.731i	−0.906596	−	0.906596i
$218$	134.634	−	134.634i	0.617589	−	0.617589i
$219$			282.088i			1.28807i
$220$	116.800	−	46.8865i	0.530908	−	0.213120i
$221$	−21.4567			−0.0970891
$222$	−17.7112	−	17.7112i	−0.0797801	−	0.0797801i
$223$	258.244	−	258.244i	1.15805	−	1.15805i	0.173150	−	0.984896i	$-0.444606\pi$
$223$	258.244	−	258.244i	1.15805	−	1.15805i	0.984896	−	0.173150i	$-0.0553944\pi$
$224$			46.5224i			0.207689i
$225$	85.2824	+	89.1070i	0.379033	+	0.396031i
$226$	−243.234			−1.07626
$227$	228.261	+	228.261i	1.00556	+	1.00556i	0.999984	+	0.00557065i	$0.00177320\pi$
$227$	228.261	+	228.261i	1.00556	+	1.00556i	0.00557065	+	0.999984i	$0.498227\pi$
$228$	149.057	−	149.057i	0.653758	−	0.653758i
$229$			153.864i			0.671897i	0.941880	+	0.335949i	$0.109057\pi$
$229$			153.864i			0.671897i	−0.941880	+	0.335949i	$0.890943\pi$
$230$	12.6331	+	31.4707i	0.0549267	+	0.136829i
$231$	386.371			1.67260
$232$	8.57623	+	8.57623i	0.0369665	+	0.0369665i
$233$	17.3460	−	17.3460i	0.0744465	−	0.0744465i	−0.668903	−	0.743350i	$-0.733236\pi$
$233$	17.3460	−	17.3460i	0.0744465	−	0.0744465i	0.743350	+	0.668903i	$0.233236\pi$
$234$			90.8164i			0.388104i
$235$	58.0221	−	135.846i	0.246903	−	0.578067i
$236$	−85.7488			−0.363342
$237$	−115.471	−	115.471i	−0.487218	−	0.487218i
$238$	−13.5572	+	13.5572i	−0.0569631	+	0.0569631i
$239$		−	325.856i		−	1.36341i	−0.731626	−	0.681706i	$-0.761238\pi$
$239$		−	325.856i		−	1.36341i	0.731626	−	0.681706i	$-0.238762\pi$
$240$	68.6554	+	29.3240i	0.286064	+	0.122183i
$241$	238.544			0.989811			0.494906	−	0.868947i	$-0.335203\pi$
$241$	238.544			0.989811			0.494906	+	0.868947i	$0.335203\pi$
$242$	−37.4053	−	37.4053i	−0.154567	−	0.154567i
$243$	−170.154	+	170.154i	−0.700220	+	0.700220i
$244$			51.3162i			0.210312i
$245$	−86.4706	+	34.7115i	−0.352941	+	0.141680i
$246$	−162.003			−0.658548
$247$	259.878	+	259.878i	1.05214	+	1.05214i
$248$	−67.6599	+	67.6599i	−0.272822	+	0.272822i
$249$		−	381.833i		−	1.53346i
$250$	62.2419	+	165.457i	0.248968	+	0.661827i
$251$	−218.536			−0.870661			−0.435331	−	0.900271i	$-0.643368\pi$
$251$	−218.536			−0.870661			−0.435331	+	0.900271i	$0.643368\pi$
$252$	57.3815	+	57.3815i	0.227704	+	0.227704i
$253$	42.6809	−	42.6809i	0.168699	−	0.168699i
$254$		−	333.730i		−	1.31390i
$255$	11.4617	+	28.5524i	0.0449478	+	0.111970i
$256$	16.0000			0.0625000
$257$	279.914	+	279.914i	1.08916	+	1.08916i	0.995615	+	0.0935464i	$0.0298203\pi$
$257$	279.914	+	279.914i	1.08916	+	1.08916i	0.0935464	+	0.995615i	$0.470180\pi$
$258$	210.583	−	210.583i	0.816215	−	0.816215i
$259$		−	39.0213i		−	0.150662i
$260$	−51.1258	+	119.699i	−0.196638	+	0.460382i
$261$	21.1561			0.0810580
$262$	79.3875	+	79.3875i	0.303006	+	0.303006i
$263$	230.769	−	230.769i	0.877449	−	0.877449i	−0.115821	−	0.993270i	$-0.536950\pi$
$263$	230.769	−	230.769i	0.877449	−	0.877449i	0.993270	+	0.115821i	$0.0369499\pi$
$264$		−	132.881i		−	0.503337i
$265$	−73.2323	−	31.2788i	−0.276348	−	0.118033i
$266$	328.403			1.23460
$267$	419.522	+	419.522i	1.57124	+	1.57124i
$268$	−136.644	+	136.644i	−0.509867	+	0.509867i
$269$			419.515i			1.55953i	0.626070	+	0.779767i	$0.284663\pi$
$269$			419.515i			1.55953i	−0.626070	+	0.779767i	$0.715337\pi$
$270$	−99.6043	+	39.9837i	−0.368905	+	0.148088i
$271$	31.7902			0.117307			0.0586535	−	0.998278i	$-0.481319\pi$
$271$	31.7902			0.117307			0.0586535	+	0.998278i	$0.481319\pi$
$272$	4.66260	+	4.66260i	0.0171419	+	0.0171419i
$273$	−282.543	+	282.543i	−1.03496	+	1.03496i
$274$			32.3023i			0.117891i
$275$	227.315	−	217.558i	0.826599	−	0.791119i
$276$	35.8036			0.129723
$277$	−158.716	−	158.716i	−0.572984	−	0.572984i	0.359977	−	0.932961i	$-0.382784\pi$
$277$	−158.716	−	158.716i	−0.572984	−	0.572984i	−0.932961	+	0.359977i	$0.882784\pi$
$278$	84.0074	−	84.0074i	0.302185	−	0.302185i
$279$			166.906i			0.598228i
$280$	43.3276	+	107.934i	0.154742	+	0.385480i
$281$	11.9011			0.0423528			0.0211764	−	0.999776i	$-0.493259\pi$
$281$	11.9011			0.0423528			0.0211764	+	0.999776i	$0.493259\pi$
$282$	−110.280	−	110.280i	−0.391063	−	0.391063i
$283$	−324.668	+	324.668i	−1.14724	+	1.14724i	−0.160141	+	0.987094i	$0.551195\pi$
$283$	−324.668	+	324.668i	−1.14724	+	1.14724i	−0.987094	+	0.160141i	$0.948805\pi$
$284$		−	66.2888i		−	0.233411i
$285$	206.999	−	484.640i	0.726311	−	1.70049i
$286$	231.675			0.810053
$287$	−178.463	−	178.463i	−0.621821	−	0.621821i
$288$	19.7347	−	19.7347i	0.0685231	−	0.0685231i
$289$		−	286.283i		−	0.990597i
$290$	27.8846	+	11.9100i	0.0961537	+	0.0410690i
$291$	−176.648			−0.607036
$292$	106.873	+	106.873i	0.366002	+	0.366002i
$293$	98.3747	−	98.3747i	0.335750	−	0.335750i	−0.519015	−	0.854765i	$-0.673701\pi$
$293$	98.3747	−	98.3747i	0.335750	−	0.335750i	0.854765	+	0.519015i	$0.173701\pi$
$294$			98.3760i			0.334612i
$295$	−198.941	+	79.8602i	−0.674378	+	0.270713i
$296$	−13.4202			−0.0453386
$297$	135.085	+	135.085i	0.454830	+	0.454830i
$298$	165.231	−	165.231i	0.554468	−	0.554468i
$299$			62.4229i			0.208772i
$300$	186.594	+	4.09234i	0.621981	+	0.0136411i
$301$	463.958			1.54139
$302$	−10.4015	−	10.4015i	−0.0344421	−	0.0344421i
$303$	−206.439	+	206.439i	−0.681318	+	0.681318i
$304$		−	112.944i		−	0.371527i
$305$	47.7922	+	119.056i	0.156696	+	0.390348i
$306$	11.5019			0.0375877
$307$	−204.388	−	204.388i	−0.665759	−	0.665759i	0.290972	−	0.956731i	$-0.406021\pi$
$307$	−204.388	−	204.388i	−0.665759	−	0.665759i	−0.956731	+	0.290972i	$0.906021\pi$
$308$	146.382	−	146.382i	0.475266	−	0.475266i
$309$		−	686.400i		−	2.22136i
$310$	−93.9607	+	219.988i	−0.303099	+	0.709638i
$311$	359.232			1.15509			0.577544	−	0.816360i	$-0.304011\pi$
$311$	359.232			1.15509			0.577544	+	0.816360i	$0.304011\pi$
$312$	97.1723	+	97.1723i	0.311450	+	0.311450i
$313$	−270.597	+	270.597i	−0.864526	+	0.864526i	−0.991860	−	0.127334i	$-0.959358\pi$
$313$	−270.597	+	270.597i	−0.864526	+	0.864526i	0.127334	+	0.991860i	$0.459358\pi$
$314$		−	301.474i		−	0.960109i
$315$	186.569	+	79.6869i	0.592282	+	0.252974i
$316$	−87.4952			−0.276883
$317$	−59.5591	−	59.5591i	−0.187883	−	0.187883i	0.606897	−	0.794780i	$-0.292414\pi$
$317$	−59.5591	−	59.5591i	−0.187883	−	0.187883i	−0.794780	+	0.606897i	$0.792414\pi$
$318$	−59.4502	+	59.4502i	−0.186950	+	0.186950i
$319$		−	53.9699i		−	0.169185i
$320$	37.1208	−	14.9012i	0.116002	−	0.0465664i
$321$	−763.186			−2.37753
$322$	39.4413	+	39.4413i	0.122489	+	0.122489i
$323$	32.9134	−	32.9134i	0.101899	−	0.101899i
$324$			202.124i			0.623839i
$325$	−7.13492	+	325.323i	−0.0219536	+	1.00100i
$326$	−413.668			−1.26892
$327$	−355.364	−	355.364i	−1.08674	−	1.08674i
$328$	−61.3769	+	61.3769i	−0.187125	+	0.187125i
$329$		−	242.969i		−	0.738508i
$330$	−123.756	−	308.290i	−0.375017	−	0.934213i
$331$	−341.218			−1.03087			−0.515436	−	0.856928i	$-0.672370\pi$
$331$	−341.218			−1.03087			−0.515436	+	0.856928i	$0.672370\pi$
$332$	−144.662	−	144.662i	−0.435730	−	0.435730i
$333$	−16.5527	+	16.5527i	−0.0497079	+	0.0497079i
$334$			258.434i			0.773753i
$335$	−189.761	+	444.283i	−0.566451	+	1.32622i
$336$	122.795			0.365461
$337$	−33.1631	−	33.1631i	−0.0984068	−	0.0984068i	0.656189	−	0.754596i	$-0.272167\pi$
$337$	−33.1631	−	33.1631i	−0.0984068	−	0.0984068i	−0.754596	+	0.656189i	$0.772167\pi$
$338$	−0.417979	+	0.417979i	−0.00123662	+	0.00123662i
$339$			642.010i			1.89383i
$340$	15.1599	+	6.47505i	0.0445879	+	0.0190443i
$341$	425.781			1.24862
$342$	−139.307	−	139.307i	−0.407331	−	0.407331i
$343$	176.579	−	176.579i	0.514807	−	0.514807i
$344$		−	159.565i		−	0.463850i
$345$	83.0661	−	33.3449i	0.240771	−	0.0966518i
$346$	64.0033			0.184981
$347$	−184.669	−	184.669i	−0.532188	−	0.532188i	0.389035	−	0.921223i	$-0.372809\pi$
$347$	−184.669	−	184.669i	−0.532188	−	0.532188i	−0.921223	+	0.389035i	$0.872809\pi$
$348$	22.6368	−	22.6368i	0.0650482	−	0.0650482i
$349$			185.462i			0.531409i	0.964055	+	0.265704i	$0.0856045\pi$
$349$			185.462i			0.531409i	−0.964055	+	0.265704i	$0.914396\pi$
$350$	201.044	+	210.061i	0.574413	+	0.600174i
$351$	−197.568			−0.562871
$352$	−50.3437	−	50.3437i	−0.143022	−	0.143022i
$353$	−259.412	+	259.412i	−0.734878	+	0.734878i	−0.971582	−	0.236704i	$-0.923933\pi$
$353$	−259.412	+	259.412i	−0.734878	+	0.734878i	0.236704	+	0.971582i	$0.423933\pi$
$354$			226.332i			0.639356i
$355$	−61.7366	−	153.793i	−0.173906	−	0.433221i
$356$	317.883			0.892928
$357$	35.7839	+	35.7839i	0.100235	+	0.100235i
$358$	268.775	−	268.775i	0.750768	−	0.750768i
$359$			170.499i			0.474929i	0.971396	+	0.237464i	$0.0763163\pi$
$359$			170.499i			0.474929i	−0.971396	+	0.237464i	$0.923684\pi$
$360$	27.4059	−	64.1648i	0.0761276	−	0.178236i
$361$	−436.276			−1.20852
$362$	−161.189	−	161.189i	−0.445273	−	0.445273i
$363$	−98.7304	+	98.7304i	−0.271985	+	0.271985i
$364$			214.090i			0.588160i
$365$	347.484	+	148.416i	0.952010	+	0.406620i
$366$	135.448			0.370076
$367$	−203.735	−	203.735i	−0.555137	−	0.555137i	0.372782	−	0.927919i	$-0.378404\pi$
$367$	−203.735	−	203.735i	−0.555137	−	0.555137i	−0.927919	+	0.372782i	$0.878404\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$			151.406i			0.410316i
$370$	−31.1356	+	12.4986i	−0.0841502	+	0.0337801i
$371$	−130.981			−0.353048
$372$	178.587	+	178.587i	0.480072	+	0.480072i
$373$	44.6839	−	44.6839i	0.119796	−	0.119796i	−0.644667	−	0.764463i	$-0.723004\pi$
$373$	44.6839	−	44.6839i	0.119796	−	0.119796i	0.764463	+	0.644667i	$0.223004\pi$
$374$		−	29.3415i		−	0.0784533i
$375$	436.719	−	164.286i	1.16458	−	0.438096i
$376$	−83.5620			−0.222239
$377$	39.4667	+	39.4667i	0.104686	+	0.104686i
$378$	−124.831	+	124.831i	−0.330241	+	0.330241i
$379$		−	261.312i		−	0.689477i	−0.938699	−	0.344739i	$-0.887968\pi$
$379$		−	261.312i		−	0.689477i	0.938699	−	0.344739i	$-0.112032\pi$
$380$	−105.188	−	262.036i	−0.276811	−	0.689570i
$381$	−880.873			−2.31200
$382$	264.125	+	264.125i	0.691426	+	0.691426i
$383$	−25.9608	+	25.9608i	−0.0677829	+	0.0677829i	−0.740186	−	0.672403i	$-0.765262\pi$
$383$	−25.9608	+	25.9608i	−0.0677829	+	0.0677829i	0.672403	+	0.740186i	$0.265262\pi$
$384$		−	42.2316i		−	0.109978i
$385$	203.284	−	475.943i	0.528009	−	1.23621i
$386$	413.476			1.07118
$387$	−196.809	−	196.809i	−0.508552	−	0.508552i
$388$	−66.9253	+	66.9253i	−0.172488	+	0.172488i
$389$		−	88.1539i		−	0.226617i	−0.993560	−	0.113308i	$-0.963855\pi$
$389$		−	88.1539i		−	0.226617i	0.993560	−	0.113308i	$-0.0361448\pi$
$390$	315.944	+	134.945i	0.810112	+	0.346013i
$391$	7.90582			0.0202195
$392$	37.2710	+	37.2710i	0.0950792	+	0.0950792i
$393$	209.541	−	209.541i	0.533184	−	0.533184i
$394$			267.993i			0.680185i
$395$	−202.993	+	81.4867i	−0.513907	+	0.206295i
$396$	−124.189			−0.313610
$397$	−224.607	−	224.607i	−0.565760	−	0.565760i	0.365178	−	0.930938i	$-0.381008\pi$
$397$	−224.607	−	224.607i	−0.565760	−	0.565760i	−0.930938	+	0.365178i	$0.881008\pi$
$398$	−325.203	+	325.203i	−0.817092	+	0.817092i
$399$		−	866.811i		−	2.17246i
$400$	72.2441	−	69.1432i	0.180610	−	0.172858i
$401$	487.984			1.21692			0.608459	−	0.793585i	$-0.291788\pi$
$401$	487.984			1.21692			0.608459	+	0.793585i	$0.291788\pi$
$402$	360.670	+	360.670i	0.897188	+	0.897188i
$403$	−311.362	+	311.362i	−0.772611	+	0.772611i
$404$			156.425i			0.387190i
$405$	188.244	+	468.937i	0.464799	+	1.15787i
$406$	49.8734			0.122841
$407$	42.2265	+	42.2265i	0.103751	+	0.103751i
$408$	12.3068	−	12.3068i	0.0301638	−	0.0301638i
$409$			409.046i			1.00011i	0.865993	+	0.500056i	$0.166687\pi$
$409$			409.046i			1.00011i	−0.865993	+	0.500056i	$0.833313\pi$
$410$	−85.2354	+	199.559i	−0.207891	+	0.486730i
$411$	85.2610			0.207448
$412$	−260.052	−	260.052i	−0.631193	−	0.631193i
$413$	−249.328	+	249.328i	−0.603699	+	0.603699i
$414$		−	33.4617i		−	0.0808255i
$415$	−470.352	−	200.896i	−1.13338	−	0.484086i
$416$	73.6300			0.176995
$417$	−221.735	−	221.735i	−0.531740	−	0.531740i
$418$	−355.377	+	355.377i	−0.850184	+	0.850184i
$419$		−	102.223i		−	0.243970i	−0.992532	−	0.121985i	$-0.961074\pi$
$419$		−	102.223i		−	0.243970i	0.992532	−	0.121985i	$-0.0389260\pi$
$420$	284.890	−	114.362i	0.678310	−	0.272291i
$421$	522.208			1.24040			0.620199	−	0.784445i	$-0.287052\pi$
$421$	522.208			1.24040			0.620199	+	0.784445i	$0.287052\pi$
$422$	−189.976	−	189.976i	−0.450181	−	0.450181i
$423$	−103.067	+	103.067i	−0.243656	+	0.243656i
$424$			45.0470i			0.106243i
$425$	41.2020	+	0.903634i	0.0969460	+	0.00212620i
$426$	−174.968			−0.410722
$427$	149.210	+	149.210i	0.349437	+	0.349437i
$428$	−289.143	+	289.143i	−0.675568	+	0.675568i
$429$		−	611.501i		−	1.42541i
$430$	−148.607	−	370.198i	−0.345597	−	0.860925i
$431$	184.845			0.428874			0.214437	−	0.976738i	$-0.431208\pi$
$431$	184.845			0.428874			0.214437	+	0.976738i	$0.431208\pi$
$432$	42.9320	+	42.9320i	0.0993796	+	0.0993796i
$433$	−75.1051	+	75.1051i	−0.173453	+	0.173453i	−0.788495	−	0.615042i	$-0.789139\pi$
$433$	−75.1051	+	75.1051i	−0.173453	+	0.173453i	0.615042	+	0.788495i	$0.289139\pi$
$434$			393.463i			0.906596i
$435$	31.4362	−	73.6006i	0.0722670	−	0.169197i
$436$	−269.269			−0.617589
$437$	−95.7532	−	95.7532i	−0.219115	−	0.219115i
$438$	282.088	−	282.088i	0.644036	−	0.644036i
$439$			217.593i			0.495656i	0.968804	+	0.247828i	$0.0797168\pi$
$439$			217.593i			0.495656i	−0.968804	+	0.247828i	$0.920283\pi$
$440$	−163.686	−	69.9133i	−0.372014	−	0.158894i
$441$	91.9414			0.208484
$442$	21.4567	+	21.4567i	0.0485446	+	0.0485446i
$443$	−188.286	+	188.286i	−0.425025	+	0.425025i	−0.886929	−	0.461905i	$-0.847166\pi$
$443$	−188.286	+	188.286i	−0.425025	+	0.425025i	0.461905	+	0.886929i	$0.347166\pi$
$444$			35.4224i			0.0797801i
$445$	737.503	−	296.053i	1.65731	−	0.665287i
$446$	−516.488			−1.15805
$447$	−436.124	−	436.124i	−0.975669	−	0.975669i
$448$	46.5224	−	46.5224i	0.103845	−	0.103845i
$449$			390.262i			0.869181i	0.900628	+	0.434591i	$0.143107\pi$
$449$			390.262i			0.869181i	−0.900628	+	0.434591i	$0.856893\pi$
$450$	3.82467	−	174.389i	0.00849926	−	0.387532i
$451$	386.242			0.856413
$452$	243.234	+	243.234i	0.538128	+	0.538128i
$453$	−27.4545	+	27.4545i	−0.0606060	+	0.0606060i
$454$		−	456.522i		−	1.00556i
$455$	199.388	+	496.700i	0.438216	+	1.09165i
$456$	−298.114			−0.653758
$457$	−145.560	−	145.560i	−0.318513	−	0.318513i	0.529683	−	0.848196i	$-0.322311\pi$
$457$	−145.560	−	145.560i	−0.318513	−	0.318513i	−0.848196	+	0.529683i	$0.822311\pi$
$458$	153.864	−	153.864i	0.335949	−	0.335949i
$459$			25.0218i			0.0545138i
$460$	18.8375	−	44.1038i	0.0409512	−	0.0958779i
$461$	604.045			1.31029			0.655147	−	0.755502i	$-0.272607\pi$
$461$	604.045			1.31029			0.655147	+	0.755502i	$0.272607\pi$
$462$	−386.371	−	386.371i	−0.836302	−	0.836302i
$463$	273.566	−	273.566i	0.590854	−	0.590854i	−0.347008	−	0.937862i	$-0.612802\pi$
$463$	273.566	−	273.566i	0.590854	−	0.590854i	0.937862	+	0.347008i	$0.112802\pi$
$464$		−	17.1525i		−	0.0369665i
$465$	580.652	+	248.007i	1.24871	+	0.533349i
$466$	−34.6921			−0.0744465
$467$	223.366	+	223.366i	0.478300	+	0.478300i	0.904588	−	0.426287i	$-0.140179\pi$
$467$	223.366	+	223.366i	0.478300	+	0.478300i	−0.426287	+	0.904588i	$0.640179\pi$
$468$	90.8164	−	90.8164i	0.194052	−	0.194052i
$469$			794.629i			1.69430i
$470$	−193.868	+	77.8236i	−0.412485	+	0.165582i
$471$	−795.734			−1.68946
$472$	85.7488	+	85.7488i	0.181671	+	0.181671i
$473$	−502.066	+	502.066i	−1.06145	+	1.06145i
$474$			230.941i			0.487218i
$475$	−488.084	−	509.973i	−1.02754	−	1.07363i
$476$	27.1144			0.0569631
$477$	55.5616	+	55.5616i	0.116481	+	0.116481i
$478$	−325.856	+	325.856i	−0.681706	+	0.681706i
$479$			503.948i			1.05208i	0.850459	+	0.526041i	$0.176324\pi$
$479$			503.948i			1.05208i	−0.850459	+	0.526041i	$0.823676\pi$
$480$	−39.3315	−	97.9794i	−0.0819406	−	0.204124i
$481$	−61.7582			−0.128395
$482$	−238.544	−	238.544i	−0.494906	−	0.494906i
$483$	104.104	−	104.104i	0.215537	−	0.215537i
$484$			74.8106i			0.154567i
$485$	−92.9405	+	217.599i	−0.191630	+	0.448658i
$486$	340.307			0.700220
$487$	−191.935	−	191.935i	−0.394117	−	0.394117i	0.482035	−	0.876152i	$-0.339898\pi$
$487$	−191.935	−	191.935i	−0.394117	−	0.394117i	−0.876152	+	0.482035i	$0.839898\pi$
$488$	51.3162	−	51.3162i	0.105156	−	0.105156i
$489$			1091.87i			2.23285i
$490$	121.182	+	51.7591i	0.247311	+	0.105631i
$491$	858.461			1.74839			0.874196	−	0.485573i	$-0.161389\pi$
$491$	858.461			1.74839			0.874196	+	0.485573i	$0.161389\pi$
$492$	162.003	+	162.003i	0.329274	+	0.329274i
$493$	4.99844	−	4.99844i	0.0101388	−	0.0101388i
$494$		−	519.756i		−	1.05214i
$495$	−288.125	+	115.661i	−0.582072	+	0.233659i
$496$	135.320			0.272822
$497$	−192.745	−	192.745i	−0.387816	−	0.387816i
$498$	−381.833	+	381.833i	−0.766732	+	0.766732i
$499$		−	196.103i		−	0.392992i	−0.980505	−	0.196496i	$-0.937044\pi$
$499$		−	196.103i		−	0.392992i	0.980505	−	0.196496i	$-0.0629563\pi$
$500$	103.215	−	227.699i	0.206430	−	0.455397i
$501$	682.129			1.36154
$502$	218.536	+	218.536i	0.435331	+	0.435331i
$503$	−100.990	+	100.990i	−0.200776	+	0.200776i	−0.800332	−	0.599556i	$-0.795344\pi$
$503$	−100.990	+	100.990i	−0.200776	+	0.200776i	0.599556	+	0.800332i	$0.295344\pi$
$504$		−	114.763i		−	0.227704i
$505$	145.683	+	362.913i	0.288480	+	0.718639i
$506$	−85.3618			−0.168699
$507$	1.10325	+	1.10325i	0.00217603	+	0.00217603i
$508$	−333.730	+	333.730i	−0.656949	+	0.656949i
$509$			722.640i			1.41972i	0.704341	+	0.709862i	$0.251243\pi$
$509$			722.640i			1.41972i	−0.704341	+	0.709862i	$0.748757\pi$
$510$	17.0907	−	40.0141i	0.0335113	−	0.0784590i
$511$	621.497			1.21624
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	303.058	−	303.058i	0.590756	−	0.590756i
$514$		−	559.829i		−	1.08916i
$515$	−845.526	−	361.139i	−1.64180	−	0.701242i
$516$	−421.167			−0.816215
$517$	262.926	+	262.926i	0.508561	+	0.508561i
$518$	−39.0213	+	39.0213i	−0.0753308	+	0.0753308i
$519$		−	168.935i		−	0.325501i
$520$	170.825	−	68.5737i	0.328510	−	0.131872i
$521$	−19.1648			−0.0367847			−0.0183923	−	0.999831i	$-0.505855\pi$
$521$	−19.1648			−0.0367847			−0.0183923	+	0.999831i	$0.505855\pi$
$522$	−21.1561	−	21.1561i	−0.0405290	−	0.0405290i
$523$	315.141	−	315.141i	0.602564	−	0.602564i	−0.338428	−	0.940992i	$-0.609895\pi$
$523$	315.141	−	315.141i	0.602564	−	0.602564i	0.940992	+	0.338428i	$0.109895\pi$
$524$		−	158.775i		−	0.303006i
$525$	554.450	−	530.652i	1.05610	−	1.01077i
$526$	−461.538			−0.877449
$527$	39.4339	+	39.4339i	0.0748271	+	0.0748271i
$528$	−132.881	+	132.881i	−0.251668	+	0.251668i
$529$		−	23.0000i		−	0.0434783i
$530$	41.9535	+	104.511i	0.0791575	+	0.197191i
$531$	211.528			0.398358
$532$	−328.403	−	328.403i	−0.617299	−	0.617299i
$533$	−282.449	+	282.449i	−0.529923	+	0.529923i
$534$		−	839.043i		−	1.57124i
$535$	−401.539	+	940.113i	−0.750541	+	1.75722i
$536$	273.289			0.509867
$537$	−709.425	−	709.425i	−1.32109	−	1.32109i
$538$	419.515	−	419.515i	0.779767	−	0.779767i
$539$		−	234.545i		−	0.435149i
$540$	139.588	+	59.6206i	0.258496	+	0.110408i
$541$	−120.782			−0.223257			−0.111628	−	0.993750i	$-0.535607\pi$
$541$	−120.782			−0.223257			−0.111628	+	0.993750i	$0.535607\pi$
$542$	−31.7902	−	31.7902i	−0.0586535	−	0.0586535i
$543$	−425.454	+	425.454i	−0.783524	+	0.783524i
$544$		−	9.32520i		−	0.0171419i
$545$	−624.717	+	250.778i	−1.14627	+	0.460142i
$546$	565.086			1.03496
$547$	−99.8453	−	99.8453i	−0.182533	−	0.182533i	0.609926	−	0.792458i	$-0.291199\pi$
$547$	−99.8453	−	99.8453i	−0.182533	−	0.182533i	−0.792458	+	0.609926i	$0.791199\pi$
$548$	32.3023	−	32.3023i	0.0589457	−	0.0589457i
$549$		−	126.588i		−	0.230580i
$550$	−444.872	−	9.75684i	−0.808859	−	0.0177397i
$551$	−121.080			−0.219745
$552$	−35.8036	−	35.8036i	−0.0648616	−	0.0648616i
$553$	−254.406	+	254.406i	−0.460046	+	0.460046i
$554$			317.433i			0.572984i
$555$	32.9898	+	82.1816i	0.0594411	+	0.148075i
$556$	−168.015			−0.302185
$557$	−401.372	−	401.372i	−0.720596	−	0.720596i	0.248131	−	0.968727i	$-0.420184\pi$
$557$	−401.372	−	401.372i	−0.720596	−	0.720596i	−0.968727	+	0.248131i	$0.920184\pi$
$558$	166.906	−	166.906i	0.299114	−	0.299114i
$559$		−	734.296i		−	1.31359i
$560$	64.6067	−	151.262i	0.115369	−	0.270111i
$561$	−77.4463			−0.138050
$562$	−11.9011	−	11.9011i	−0.0211764	−	0.0211764i
$563$	751.620	−	751.620i	1.33503	−	1.33503i	0.434221	−	0.900807i	$-0.357024\pi$
$563$	751.620	−	751.620i	1.33503	−	1.33503i	0.900807	−	0.434221i	$-0.142976\pi$
$564$			220.560i			0.391063i
$565$	790.845	+	337.784i	1.39973	+	0.597848i
$566$	649.335			1.14724
$567$	587.706	+	587.706i	1.03652	+	1.03652i
$568$	−66.2888	+	66.2888i	−0.116706	+	0.116706i
$569$			499.583i			0.878002i	0.898487	+	0.439001i	$0.144667\pi$
$569$			499.583i			0.878002i	−0.898487	+	0.439001i	$0.855333\pi$
$570$	−691.639	+	277.642i	−1.21340	+	0.487091i
$571$	336.391			0.589126			0.294563	−	0.955632i	$-0.404826\pi$
$571$	336.391			0.589126			0.294563	+	0.955632i	$0.404826\pi$
$572$	−231.675	−	231.675i	−0.405027	−	0.405027i
$573$	697.150	−	697.150i	1.21667	−	1.21667i
$574$			356.925i			0.621821i
$575$	2.62889	−	119.867i	0.00457199	−	0.208464i
$576$	−39.4693			−0.0685231
$577$	425.157	+	425.157i	0.736841	+	0.736841i	0.971965	−	0.235124i	$-0.0755497\pi$
$577$	425.157	+	425.157i	0.736841	+	0.736841i	−0.235124	+	0.971965i	$0.575550\pi$
$578$	−286.283	+	286.283i	−0.495298	+	0.495298i
$579$		−	1091.36i		−	1.88490i
$580$	−15.9746	−	39.7946i	−0.0275424	−	0.0686113i
$581$	−841.255			−1.44794
$582$	176.648	+	176.648i	0.303518	+	0.303518i
$583$	141.739	−	141.739i	0.243121	−	0.243121i
$584$		−	213.745i		−	0.366002i
$585$	126.119	−	295.278i	0.215588	−	0.504749i
$586$	−196.749			−0.335750
$587$	313.141	+	313.141i	0.533460	+	0.533460i	0.921600	−	0.388140i	$-0.126882\pi$
$587$	313.141	+	313.141i	0.533460	+	0.533460i	−0.388140	+	0.921600i	$0.626882\pi$
$588$	98.3760	−	98.3760i	0.167306	−	0.167306i
$589$		−	955.225i		−	1.62177i
$590$	278.802	+	119.081i	0.472545	+	0.201833i
$591$	707.361			1.19689
$592$	13.4202	+	13.4202i	0.0226693	+	0.0226693i
$593$	452.279	−	452.279i	0.762696	−	0.762696i	−0.214113	−	0.976809i	$-0.568686\pi$
$593$	452.279	−	452.279i	0.762696	−	0.762696i	0.976809	+	0.214113i	$0.0686861\pi$
$594$		−	270.169i		−	0.454830i
$595$	62.9068	−	25.2524i	0.105726	−	0.0424411i
$596$	−330.463			−0.554468
$597$	858.364	+	858.364i	1.43780	+	1.43780i
$598$	62.4229	−	62.4229i	0.104386	−	0.104386i
$599$		−	243.105i		−	0.405852i	−0.979194	−	0.202926i	$-0.934955\pi$
$599$		−	243.105i		−	0.405852i	0.979194	−	0.202926i	$-0.0650451\pi$
$600$	−182.502	−	190.687i	−0.304170	−	0.317811i
$601$	−443.771			−0.738387			−0.369194	−	0.929352i	$-0.620366\pi$
$601$	−443.771			−0.738387			−0.369194	+	0.929352i	$0.620366\pi$
$602$	−463.958	−	463.958i	−0.770695	−	0.770695i
$603$	337.079	−	337.079i	0.559003	−	0.559003i
$604$			20.8030i			0.0344421i
$605$	69.6732	+	173.564i	0.115162	+	0.286883i
$606$	412.879			0.681318
$607$	369.220	+	369.220i	0.608270	+	0.608270i	0.942494	−	0.334224i	$-0.108474\pi$
$607$	369.220	+	369.220i	0.608270	+	0.608270i	−0.334224	+	0.942494i	$0.608474\pi$
$608$	−112.944	+	112.944i	−0.185764	+	0.185764i
$609$		−	131.640i		−	0.216157i
$610$	71.2639	−	166.848i	0.116826	−	0.273522i
$611$	−384.542			−0.629364
$612$	−11.5019	−	11.5019i	−0.0187939	−	0.0187939i
$613$	753.356	−	753.356i	1.22897	−	1.22897i	0.264611	−	0.964355i	$-0.414757\pi$
$613$	753.356	−	753.356i	1.22897	−	1.22897i	0.964355	−	0.264611i	$-0.0852434\pi$
$614$			408.776i			0.665759i
$615$	526.732	+	224.977i	0.856475	+	0.365816i
$616$	−292.764			−0.475266
$617$	−48.4951	−	48.4951i	−0.0785982	−	0.0785982i	0.666715	−	0.745313i	$-0.267700\pi$
$617$	−48.4951	−	48.4951i	−0.0785982	−	0.0785982i	−0.745313	+	0.666715i	$0.767700\pi$
$618$	−686.400	+	686.400i	−1.11068	+	1.11068i
$619$		−	1115.83i		−	1.80264i	−0.433153	−	0.901321i	$-0.642599\pi$
$619$		−	1115.83i		−	1.80264i	0.433153	−	0.901321i	$-0.357401\pi$
$620$	313.949	−	126.027i	0.506369	−	0.203269i
$621$	72.7947			0.117222
$622$	−359.232	−	359.232i	−0.577544	−	0.577544i
$623$	924.292	−	924.292i	1.48361	−	1.48361i
$624$		−	194.345i		−	0.311450i
$625$	27.4015	−	624.399i	0.0438424	−	0.999038i
$626$	541.193			0.864526
$627$	938.009	+	938.009i	1.49603	+	1.49603i
$628$	−301.474	+	301.474i	−0.480055	+	0.480055i
$629$			7.82164i			0.0124350i
$630$	−106.882	−	266.256i	−0.169654	−	0.422628i
$631$	241.999			0.383516			0.191758	−	0.981442i	$-0.438581\pi$
$631$	241.999			0.383516			0.191758	+	0.981442i	$0.438581\pi$
$632$	87.4952	+	87.4952i	0.138442	+	0.138442i
$633$	−501.438	+	501.438i	−0.792161	+	0.792161i
$634$			119.118i			0.187883i
$635$	−463.458	+	1085.08i	−0.729856	+	1.70879i
$636$	118.900			0.186950
$637$	171.517	+	171.517i	0.269257	+	0.269257i
$638$	−53.9699	+	53.9699i	−0.0845923	+	0.0845923i
$639$			163.523i			0.255905i
$640$	−52.0220	−	22.2195i	−0.0812844	−	0.0347180i
$641$	61.3167			0.0956579			0.0478290	−	0.998856i	$-0.484770\pi$
$641$	61.3167			0.0956579			0.0478290	+	0.998856i	$0.484770\pi$
$642$	763.186	+	763.186i	1.18876	+	1.18876i
$643$	83.4245	−	83.4245i	0.129743	−	0.129743i	−0.639253	−	0.768996i	$-0.720757\pi$
$643$	83.4245	−	83.4245i	0.129743	−	0.129743i	0.768996	+	0.639253i	$0.220757\pi$
$644$		−	78.8826i		−	0.122489i
$645$	−977.128	+	392.244i	−1.51493	+	0.608131i
$646$	−65.8268			−0.101899
$647$	242.079	+	242.079i	0.374156	+	0.374156i	0.868988	−	0.494832i	$-0.164771\pi$
$647$	242.079	+	242.079i	0.374156	+	0.374156i	−0.494832	+	0.868988i	$0.664771\pi$
$648$	202.124	−	202.124i	0.311920	−	0.311920i
$649$		−	539.614i		−	0.831454i
$650$	332.458	−	318.189i	0.511474	−	0.489521i
$651$	1038.54			1.59529
$652$	413.668	+	413.668i	0.634459	+	0.634459i
$653$	701.808	−	701.808i	1.07474	−	1.07474i	0.0777728	−	0.996971i	$-0.475219\pi$
$653$	701.808	−	701.808i	1.07474	−	1.07474i	0.996971	−	0.0777728i	$-0.0247809\pi$
$654$			710.729i			1.08674i
$655$	−147.871	−	368.366i	−0.225758	−	0.562390i
$656$	122.754			0.187125
$657$	−263.637	−	263.637i	−0.401274	−	0.401274i
$658$	−242.969	+	242.969i	−0.369254	+	0.369254i
$659$		−	1112.06i		−	1.68750i	−0.536735	−	0.843751i	$-0.680342\pi$
$659$		−	1112.06i		−	1.68750i	0.536735	−	0.843751i	$-0.319658\pi$
$660$	−184.535	+	432.046i	−0.279598	+	0.654615i
$661$	−969.643			−1.46693			−0.733467	−	0.679725i	$-0.762099\pi$
$661$	−969.643			−1.46693			−0.733467	+	0.679725i	$0.762099\pi$
$662$	341.218	+	341.218i	0.515436	+	0.515436i
$663$	56.6344	−	56.6344i	0.0854215	−	0.0854215i
$664$			289.325i			0.435730i
$665$	−1067.76	−	456.060i	−1.60566	−	0.685805i
$666$	33.1054			0.0497079
$667$	−14.5417	−	14.5417i	−0.0218017	−	0.0218017i
$668$	258.434	−	258.434i	0.386877	−	0.386877i
$669$			1363.26i			2.03775i
$670$	634.044	−	254.522i	0.946334	−	0.379883i
$671$	−322.931			−0.481268
$672$	−122.795	−	122.795i	−0.182730	−	0.182730i
$673$	−332.095	+	332.095i	−0.493454	+	0.493454i	−0.909393	−	0.415938i	$-0.863453\pi$
$673$	−332.095	+	332.095i	−0.493454	+	0.493454i	0.415938	+	0.909393i	$0.363453\pi$
$674$			66.3262i			0.0984068i
$675$	379.377	+	8.32042i	0.562041	+	0.0123265i
$676$	0.835958			0.00123662
$677$	−128.380	−	128.380i	−0.189631	−	0.189631i	0.605906	−	0.795536i	$-0.292811\pi$
$677$	−128.380	−	128.380i	−0.189631	−	0.189631i	−0.795536	+	0.605906i	$0.792811\pi$
$678$	642.010	−	642.010i	0.946917	−	0.946917i
$679$			389.191i			0.573182i
$680$	−8.68482	−	21.6349i	−0.0127718	−	0.0318161i
$681$	−1204.98			−1.76943
$682$	−425.781	−	425.781i	−0.624312	−	0.624312i
$683$	920.089	−	920.089i	1.34713	−	1.34713i	0.458365	−	0.888764i	$-0.348435\pi$
$683$	920.089	−	920.089i	1.34713	−	1.34713i	0.888764	−	0.458365i	$-0.151565\pi$
$684$			278.615i			0.407331i
$685$	44.8588	−	105.027i	0.0654873	−	0.153324i
$686$	−353.157			−0.514807
$687$	−406.121	−	406.121i	−0.591152	−	0.591152i
$688$	−159.565	+	159.565i	−0.231925	+	0.231925i
$689$			207.300i			0.300871i
$690$	−116.411	−	49.7212i	−0.168712	−	0.0720597i
$691$	−1318.09			−1.90751			−0.953755	−	0.300585i	$-0.902818\pi$
$691$	−1318.09			−1.90751			−0.953755	+	0.300585i	$0.902818\pi$
$692$	−64.0033	−	64.0033i	−0.0924904	−	0.0924904i
$693$	−361.099	+	361.099i	−0.521067	+	0.521067i
$694$			369.339i			0.532188i
$695$	−389.803	+	156.477i	−0.560867	+	0.225147i
$696$	−45.2735			−0.0650482
$697$	35.7720	+	35.7720i	0.0513228	+	0.0513228i
$698$	185.462	−	185.462i	0.265704	−	0.265704i
$699$			91.5689i			0.131000i
$700$	9.01626	−	411.105i	0.0128804	−	0.587293i
$701$	400.987			0.572021			0.286010	−	0.958227i	$-0.407671\pi$
$701$	400.987			0.572021			0.286010	+	0.958227i	$0.407671\pi$
$702$	197.568	+	197.568i	0.281435	+	0.281435i
$703$	94.7337	−	94.7337i	0.134756	−	0.134756i
$704$			100.687i			0.143022i
$705$	205.413	+	511.710i	0.291367	+	0.725829i
$706$	518.824			0.734878
$707$	454.828	+	454.828i	0.643321	+	0.643321i
$708$	226.332	−	226.332i	0.319678	−	0.319678i
$709$			203.403i			0.286887i	0.989659	+	0.143443i	$0.0458175\pi$
$709$			203.403i			0.286887i	−0.989659	+	0.143443i	$0.954183\pi$
$710$	−92.0567	+	215.530i	−0.129657	+	0.303563i
$711$	215.836			0.303567
$712$	−317.883	−	317.883i	−0.446464	−	0.446464i
$713$	114.723	−	114.723i	0.160902	−	0.160902i
$714$		−	71.5679i		−	0.100235i
$715$	−753.264	−	321.732i	−1.05352	−	0.449975i
$716$	−537.550			−0.750768
$717$	860.088	+	860.088i	1.19956	+	1.19956i
$718$	170.499	−	170.499i	0.237464	−	0.237464i
$719$		−	241.571i		−	0.335982i	−0.985788	−	0.167991i	$-0.946272\pi$
$719$		−	241.571i		−	0.335982i	0.985788	−	0.167991i	$-0.0537280\pi$
$720$	−91.5707	+	36.7589i	−0.127182	+	0.0510540i
$721$	−1512.28			−2.09748
$722$	436.276	+	436.276i	0.604261	+	0.604261i
$723$	−629.632	+	629.632i	−0.870861	+	0.870861i
$724$			322.377i			0.445273i
$725$	−74.1236	−	77.4478i	−0.102239	−	0.106825i
$726$	197.461			0.271985
$727$	−617.718	−	617.718i	−0.849681	−	0.849681i	0.140412	−	0.990093i	$-0.455157\pi$
$727$	−617.718	−	617.718i	−0.849681	−	0.849681i	−0.990093	+	0.140412i	$0.955157\pi$
$728$	214.090	−	214.090i	0.294080	−	0.294080i
$729$			11.3250i			0.0155350i
$730$	−199.067	−	495.900i	−0.272695	−	0.679315i
$731$	−92.9982			−0.127221
$732$	−135.448	−	135.448i	−0.185038	−	0.185038i
$733$	−309.192	+	309.192i	−0.421817	+	0.421817i	−0.885829	−	0.464012i	$-0.846409\pi$
$733$	−309.192	+	309.192i	−0.421817	+	0.421817i	0.464012	+	0.885829i	$0.346409\pi$
$734$			407.470i			0.555137i
$735$	136.617	−	319.857i	0.185873	−	0.435180i
$736$	−27.1293			−0.0368605
$737$	−859.898	−	859.898i	−1.16675	−	1.16675i
$738$	151.406	−	151.406i	0.205158	−	0.205158i
$739$			96.4942i			0.130574i	0.997867	+	0.0652870i	$0.0207963\pi$
$739$			96.4942i			0.130574i	−0.997867	+	0.0652870i	$0.979204\pi$
$740$	43.6342	+	18.6370i	0.0589652	+	0.0251851i
$741$	−1371.88			−1.85139
$742$	130.981	+	130.981i	0.176524	+	0.176524i
$743$	−579.479	+	579.479i	−0.779918	+	0.779918i	−0.979817	−	0.199898i	$-0.935939\pi$
$743$	−579.479	+	579.479i	−0.779918	+	0.779918i	0.199898	+	0.979817i	$0.435939\pi$
$744$		−	357.173i		−	0.480072i
$745$	−766.690	+	307.769i	−1.02911	+	0.413113i
$746$	−89.3678			−0.119796
$747$	356.858	+	356.858i	0.477721	+	0.477721i
$748$	−29.3415	+	29.3415i	−0.0392267	+	0.0392267i
$749$			1681.46i			2.24493i
$750$	−601.005	−	272.433i	−0.801340	−	0.363244i
$751$	−863.952			−1.15040			−0.575201	−	0.818012i	$-0.695076\pi$
$751$	−863.952			−1.15040			−0.575201	+	0.818012i	$0.695076\pi$
$752$	83.5620	+	83.5620i	0.111120	+	0.111120i
$753$	576.820	−	576.820i	0.766030	−	0.766030i
$754$		−	78.9335i		−	0.104686i
$755$	19.3744	+	48.2640i	0.0256615	+	0.0639258i
$756$	249.663			0.330241
$757$	851.684	+	851.684i	1.12508	+	1.12508i	0.990966	+	0.134112i	$0.0428183\pi$
$757$	851.684	+	851.684i	1.12508	+	1.12508i	0.134112	+	0.990966i	$0.457182\pi$
$758$	−261.312	+	261.312i	−0.344739	+	0.344739i
$759$			225.311i			0.296852i
$760$	−156.848	+	367.225i	−0.206379	+	0.483190i
$761$	−692.231			−0.909634			−0.454817	−	0.890585i	$-0.650295\pi$
$761$	−692.231			−0.909634			−0.454817	+	0.890585i	$0.650295\pi$
$762$	880.873	+	880.873i	1.15600	+	1.15600i
$763$	−782.940	+	782.940i	−1.02613	+	1.02613i
$764$		−	528.249i		−	0.691426i
$765$	−37.3969	−	15.9729i	−0.0488848	−	0.0208796i
$766$	51.9217			0.0677829
$767$	394.605	+	394.605i	0.514479	+	0.514479i
$768$	−42.2316	+	42.2316i	−0.0549891	+	0.0549891i
$769$		−	1194.46i		−	1.55326i	−0.629956	−	0.776631i	$-0.716927\pi$
$769$		−	1194.46i		−	1.55326i	0.629956	−	0.776631i	$-0.283073\pi$
$770$	−679.226	+	272.659i	−0.882112	+	0.354103i
$771$	−1477.65			−1.91654
$772$	−413.476	−	413.476i	−0.535591	−	0.535591i
$773$	411.951	−	411.951i	0.532925	−	0.532925i	−0.388517	−	0.921442i	$-0.627012\pi$
$773$	411.951	−	411.951i	0.532925	−	0.532925i	0.921442	+	0.388517i	$0.127012\pi$
$774$			393.619i			0.508552i
$775$	611.004	−	584.778i	0.788392	−	0.754552i
$776$	133.851			0.172488
$777$	102.996	+	102.996i	0.132556	+	0.132556i
$778$	−88.1539	+	88.1539i	−0.113308	+	0.113308i
$779$		−	866.521i		−	1.11235i
$780$	−180.998	−	450.889i	−0.232049	−	0.578063i
$781$	417.153			0.534126
$782$	−7.90582	−	7.90582i	−0.0101097	−	0.0101097i
$783$	46.0243	−	46.0243i	0.0587795	−	0.0587795i
$784$		−	74.5421i		−	0.0950792i
$785$	−418.664	+	980.207i	−0.533330	+	1.24867i
$786$	−419.083			−0.533184
$787$	−607.588	−	607.588i	−0.772030	−	0.772030i	0.206431	−	0.978461i	$-0.433815\pi$
$787$	−607.588	−	607.588i	−0.772030	−	0.772030i	−0.978461	+	0.206431i	$0.933815\pi$
$788$	267.993	−	267.993i	0.340093	−	0.340093i
$789$			1218.22i			1.54400i
$790$	284.480	+	121.506i	0.360101	+	0.153806i
$791$	1414.48			1.78822
$792$	124.189	+	124.189i	0.156805	+	0.156805i
$793$	236.151	−	236.151i	0.297794	−	0.297794i
$794$			449.213i			0.565760i
$795$	275.855	−	110.735i	0.346987	−	0.139290i
$796$	650.405			0.817092
$797$	−83.2010	−	83.2010i	−0.104393	−	0.104393i	0.652981	−	0.757374i	$-0.273518\pi$
$797$	−83.2010	−	83.2010i	−0.104393	−	0.104393i	−0.757374	+	0.652981i	$0.773518\pi$
$798$	−866.811	+	866.811i	−1.08623	+	1.08623i
$799$			48.7020i			0.0609537i
$800$	−141.387	−	3.10087i	−0.176734	−	0.00387609i
$801$	−784.163			−0.978980
$802$	−487.984	−	487.984i	−0.608459	−	0.608459i
$803$	−672.546	+	672.546i	−0.837541	+	0.837541i
$804$		−	721.339i		−	0.897188i
$805$	−73.4656	−	183.012i	−0.0912616	−	0.227344i
$806$	622.725			0.772611
$807$	−1107.30	−	1107.30i	−1.37212	−	1.37212i
$808$	156.425	−	156.425i	0.193595	−	0.193595i
$809$			1021.78i			1.26301i	0.775371	+	0.631506i	$0.217563\pi$
$809$			1021.78i			1.26301i	−0.775371	+	0.631506i	$0.782437\pi$
$810$	280.694	−	657.181i	0.346536	−	0.811334i
$811$	−571.526			−0.704717			−0.352359	−	0.935865i	$-0.614620\pi$
$811$	−571.526			−0.704717			−0.352359	+	0.935865i	$0.614620\pi$
$812$	−49.8734	−	49.8734i	−0.0614204	−	0.0614204i
$813$	−83.9094	+	83.9094i	−0.103210	+	0.103210i
$814$		−	84.4529i		−	0.103751i
$815$	1344.99	+	574.469i	1.65029	+	0.704870i
$816$	−24.6136			−0.0301638
$817$	1126.37	+	1126.37i	1.37867	+	1.37867i
$818$	409.046	−	409.046i	0.500056	−	0.500056i
$819$		−	528.125i		−	0.644841i
$820$	284.795	−	114.324i	0.347311	−	0.139420i
$821$	−701.538			−0.854493			−0.427246	−	0.904135i	$-0.640516\pi$
$821$	−701.538			−0.854493			−0.427246	+	0.904135i	$0.640516\pi$
$822$	−85.2610	−	85.2610i	−0.103724	−	0.103724i
$823$	−1098.79	+	1098.79i	−1.33510	+	1.33510i	−0.434364	+	0.900737i	$0.643027\pi$
$823$	−1098.79	+	1098.79i	−1.33510	+	1.33510i	−0.900737	+	0.434364i	$0.856973\pi$
$824$			520.103i			0.631193i
$825$	−25.7529	+	1174.23i	−0.0312157	+	1.42331i
$826$	498.655			0.603699
$827$	−530.066	−	530.066i	−0.640950	−	0.640950i	0.309839	−	0.950789i	$-0.399725\pi$
$827$	−530.066	−	530.066i	−0.640950	−	0.640950i	−0.950789	+	0.309839i	$0.899725\pi$
$828$	−33.4617	+	33.4617i	−0.0404127	+	0.0404127i
$829$		−	164.962i		−	0.198990i	−0.995038	−	0.0994948i	$-0.968277\pi$
$829$		−	164.962i		−	0.198990i	0.995038	−	0.0994948i	$-0.0317227\pi$
$830$	269.456	+	671.247i	0.324646	+	0.808732i
$831$	837.856			1.00825
$832$	−73.6300	−	73.6300i	−0.0884976	−	0.0884976i
$833$	21.7225	−	21.7225i	0.0260774	−	0.0260774i
$834$			443.471i			0.531740i
$835$	358.892	−	840.265i	0.429811	−	1.00631i
$836$	710.754			0.850184
$837$	363.097	+	363.097i	0.433807	+	0.433807i
$838$	−102.223	+	102.223i	−0.121985	+	0.121985i
$839$			1531.83i			1.82579i	0.408199	+	0.912893i	$0.366157\pi$
$839$			1531.83i			1.82579i	−0.408199	+	0.912893i	$0.633843\pi$
$840$	−399.252	−	170.528i	−0.475300	−	0.203009i
$841$	822.612			0.978136
$842$	−522.208	−	522.208i	−0.620199	−	0.620199i
$843$	−31.4128	+	31.4128i	−0.0372631	+	0.0372631i
$844$			379.953i			0.450181i
$845$	1.93946	−	0.778551i	0.00229522	−	0.000921362i
$846$	206.133			0.243656
$847$	217.523	+	217.523i	0.256816	+	0.256816i
$848$	45.0470	−	45.0470i	0.0531214	−	0.0531214i
$849$		−	1713.90i		−	2.01873i
$850$	−40.2984	−	42.1057i	−0.0474099	−	0.0495361i
$851$	22.7551			0.0267392
$852$	174.968	+	174.968i	0.205361	+	0.205361i
$853$	344.877	−	344.877i	0.404310	−	0.404310i	−0.475439	−	0.879749i	$-0.657711\pi$
$853$	344.877	−	344.877i	0.404310	−	0.404310i	0.879749	+	0.475439i	$0.157711\pi$
$854$		−	298.419i		−	0.349437i
$855$	259.482	+	646.400i	0.303487	+	0.756023i
$856$	578.286			0.675568
$857$	−43.0332	−	43.0332i	−0.0502138	−	0.0502138i	0.681554	−	0.731768i	$-0.261304\pi$
$857$	−43.0332	−	43.0332i	−0.0502138	−	0.0502138i	−0.731768	+	0.681554i	$0.761304\pi$
$858$	−611.501	+	611.501i	−0.712705	+	0.712705i
$859$		−	1083.34i		−	1.26116i	−0.776124	−	0.630580i	$-0.782817\pi$
$859$		−	1083.34i		−	1.26116i	0.776124	−	0.630580i	$-0.217183\pi$
$860$	−221.591	+	518.804i	−0.257664	+	0.603261i
$861$	942.095			1.09419
$862$	−184.845	−	184.845i	−0.214437	−	0.214437i
$863$	1170.51	−	1170.51i	1.35632	−	1.35632i	0.477919	−	0.878404i	$-0.341391\pi$
$863$	1170.51	−	1170.51i	1.35632	−	1.35632i	0.878404	−	0.477919i	$-0.158609\pi$
$864$		−	85.8640i		−	0.0993796i
$865$	−208.099	−	88.8828i	−0.240577	−	0.102755i
$866$	150.210			0.173453
$867$	755.636	+	755.636i	0.871552	+	0.871552i
$868$	393.463	−	393.463i	0.453298	−	0.453298i
$869$		−	550.604i		−	0.633606i
$870$	−105.037	+	42.1645i	−0.120732	+	0.0484649i
$871$	1257.64			1.44390
$872$	269.269	+	269.269i	0.308795	+	0.308795i
$873$	165.093	−	165.093i	0.189110	−	0.189110i
$874$			191.506i			0.219115i
$875$	−361.956	−	962.181i	−0.413663	−	1.09964i
$876$	−564.176			−0.644036
$877$	−282.626	−	282.626i	−0.322264	−	0.322264i	0.527371	−	0.849635i	$-0.323178\pi$
$877$	−282.626	−	282.626i	−0.322264	−	0.322264i	−0.849635	+	0.527371i	$0.823178\pi$
$878$	217.593	−	217.593i	0.247828	−	0.247828i
$879$			519.315i			0.590802i
$880$	93.7729	+	233.600i	0.106560	+	0.265454i
$881$	−119.247			−0.135355			−0.0676773	−	0.997707i	$-0.521559\pi$
$881$	−119.247			−0.135355			−0.0676773	+	0.997707i	$0.521559\pi$
$882$	−91.9414	−	91.9414i	−0.104242	−	0.104242i
$883$	−21.4634	+	21.4634i	−0.0243074	+	0.0243074i	−0.719156	−	0.694849i	$-0.755471\pi$
$883$	−21.4634	+	21.4634i	−0.0243074	+	0.0243074i	0.694849	+	0.719156i	$0.255471\pi$
$884$		−	42.9134i		−	0.0485446i
$885$	314.312	−	735.890i	0.355155	−	0.831514i
$886$	376.572			0.425025
$887$	−234.661	−	234.661i	−0.264556	−	0.264556i	0.562346	−	0.826902i	$-0.309899\pi$
$887$	−234.661	−	234.661i	−0.264556	−	0.264556i	−0.826902	+	0.562346i	$0.809899\pi$
$888$	35.4224	−	35.4224i	0.0398900	−	0.0398900i
$889$			1940.74i			2.18306i
$890$	−1033.56	−	441.450i	−1.16130	−	0.496012i
$891$	−1271.96			−1.42756
$892$	516.488	+	516.488i	0.579023	+	0.579023i
$893$	589.866	−	589.866i	0.660544	−	0.660544i
$894$			872.248i			0.975669i
$895$	−1247.14	+	500.635i	−1.39345	+	0.559369i
$896$	−93.0449			−0.103845
$897$	−164.764	−	164.764i	−0.183683	−	0.183683i
$898$	390.262	−	390.262i	0.434591	−	0.434591i
$899$		−	145.067i		−	0.161365i
$900$	−178.214	+	170.565i	−0.198016	+	0.189516i
$901$	26.2545			0.0291393
$902$	−386.242	−	386.242i	−0.428206	−	0.428206i
$903$	−1224.61	+	1224.61i	−1.35615	+	1.35615i
$904$		−	486.468i		−	0.538128i
$905$	300.239	+	747.931i	0.331756	+	0.826443i
$906$	54.9090			0.0606060
$907$	908.147	+	908.147i	1.00126	+	1.00126i	0.999999	+	0.00126519i	$0.000402724\pi$
$907$	908.147	+	908.147i	1.00126	+	1.00126i	0.00126519	+	0.999999i	$0.499597\pi$
$908$	−456.522	+	456.522i	−0.502778	+	0.502778i
$909$		−	385.873i		−	0.424503i
$910$	297.312	−	696.089i	0.326716	−	0.764932i
$911$	457.493			0.502187			0.251094	−	0.967963i	$-0.419210\pi$
$911$	457.493			0.502187			0.251094	+	0.967963i	$0.419210\pi$
$912$	298.114	+	298.114i	0.326879	+	0.326879i
$913$	910.354	−	910.354i	0.997102	−	0.997102i
$914$			291.121i			0.318513i
$915$	−440.392	−	188.099i	−0.481303	−	0.205573i
$916$	−307.729			−0.335949
$917$	−461.662	−	461.662i	−0.503448	−	0.503448i
$918$	25.0218	−	25.0218i	0.0272569	−	0.0272569i
$919$		−	1323.01i		−	1.43962i	−0.694172	−	0.719809i	$-0.744229\pi$
$919$		−	1323.01i		−	1.43962i	0.694172	−	0.719809i	$-0.255771\pi$
$920$	−62.9414	+	25.2663i	−0.0684145	+	0.0274634i
$921$	1078.95			1.17150
$922$	−604.045	−	604.045i	−0.655147	−	0.655147i
$923$	−305.053	+	305.053i	−0.330501	+	0.330501i
$924$			772.743i			0.836302i
$925$	118.591	+	2.60090i	0.128206	+	0.00281179i
$926$	−547.131			−0.590854
$927$	641.504	+	641.504i	0.692021	+	0.692021i
$928$	−17.1525	+	17.1525i	−0.0184833	+	0.0184833i
$929$			1339.40i			1.44176i	0.693059	+	0.720881i	$0.256262\pi$
$929$			1339.40i			1.44176i	−0.693059	+	0.720881i	$0.743738\pi$
$930$	−332.645	−	828.660i	−0.357683	−	0.891032i
$931$	−526.194			−0.565192
$932$	34.6921	+	34.6921i	0.0372233	+	0.0372233i
$933$	−948.185	+	948.185i	−1.01628	+	1.01628i
$934$		−	446.732i		−	0.478300i
$935$	−40.7472	+	95.4004i	−0.0435799	+	0.102033i
$936$	−181.633			−0.194052
$937$	−1124.16	−	1124.16i	−1.19975	−	1.19975i	−0.974242	−	0.225505i	$-0.927597\pi$
$937$	−1124.16	−	1124.16i	−1.19975	−	1.19975i	−0.225505	−	0.974242i	$-0.572403\pi$
$938$	794.629	−	794.629i	0.847152	−	0.847152i
$939$		−	1428.47i		−	1.52126i
$940$	271.691	+	116.044i	0.289033	+	0.123451i
$941$	−746.721			−0.793539			−0.396770	−	0.917918i	$-0.629869\pi$
$941$	−746.721			−0.793539			−0.396770	+	0.917918i	$0.629869\pi$
$942$	795.734	+	795.734i	0.844728	+	0.844728i
$943$	104.070	−	104.070i	0.110360	−	0.110360i
$944$		−	171.498i		−	0.181671i
$945$	579.229	−	232.518i	0.612941	−	0.246050i
$946$	1004.13			1.06145
$947$	−699.314	−	699.314i	−0.738452	−	0.738452i	0.233826	−	0.972278i	$-0.424875\pi$
$947$	−699.314	−	699.314i	−0.738452	−	0.738452i	−0.972278	+	0.233826i	$0.924875\pi$
$948$	230.941	−	230.941i	0.243609	−	0.243609i
$949$		−	983.630i		−	1.03649i
$950$	−21.8891	+	998.056i	−0.0230412	+	1.05059i
$951$	314.409			0.330609
$952$	−27.1144	−	27.1144i	−0.0284815	−	0.0284815i
$953$	657.892	−	657.892i	0.690338	−	0.690338i	−0.271968	−	0.962306i	$-0.587674\pi$
$953$	657.892	−	657.892i	0.690338	−	0.690338i	0.962306	+	0.271968i	$0.0876745\pi$
$954$		−	111.123i		−	0.116481i
$955$	−491.973	−	1225.56i	−0.515155	−	1.28331i
$956$	651.711			0.681706
$957$	142.452	+	142.452i	0.148853	+	0.148853i
$958$	503.948	−	503.948i	0.526041	−	0.526041i
$959$		−	187.847i		−	0.195878i
$960$	−58.6479	+	137.311i	−0.0610916	+	0.143032i
$961$	183.465			0.190911
$962$	61.7582	+	61.7582i	0.0641977	+	0.0641977i
$963$	713.267	−	713.267i	0.740672	−	0.740672i
$964$			477.089i			0.494906i
$965$	−1344.37	−	574.203i	−1.39313	−	0.595029i
$966$	−208.209			−0.215537
$967$	630.803	+	630.803i	0.652330	+	0.652330i	0.953554	−	0.301223i	$-0.0973950\pi$
$967$	630.803	+	630.803i	0.652330	+	0.652330i	−0.301223	+	0.953554i	$0.597395\pi$
$968$	74.8106	−	74.8106i	0.0772837	−	0.0772837i
$969$			173.748i			0.179307i
$970$	310.540	−	124.659i	0.320144	−	0.128514i
$971$	−788.313			−0.811857			−0.405929	−	0.913905i	$-0.633052\pi$
$971$	−788.313			−0.811857			−0.405929	+	0.913905i	$0.633052\pi$
$972$	−340.307	−	340.307i	−0.350110	−	0.350110i
$973$	−488.529	+	488.529i	−0.502085	+	0.502085i
$974$			383.870i			0.394117i
$975$	−839.851	−	877.516i	−0.861385	−	0.900016i
$976$	−102.632			−0.105156
$977$	−219.553	−	219.553i	−0.224721	−	0.224721i	0.585762	−	0.810483i	$-0.300795\pi$
$977$	−219.553	−	219.553i	−0.224721	−	0.224721i	−0.810483	+	0.585762i	$0.800795\pi$
$978$	1091.87	−	1091.87i	1.11643	−	1.11643i
$979$			2000.42i			2.04333i
$980$	−69.4231	−	172.941i	−0.0708399	−	0.176471i
$981$	664.241			0.677106
$982$	−858.461	−	858.461i	−0.874196	−	0.874196i
$983$	204.077	−	204.077i	0.207607	−	0.207607i	−0.595643	−	0.803249i	$-0.703103\pi$
$983$	204.077	−	204.077i	0.207607	−	0.207607i	0.803249	+	0.595643i	$0.203103\pi$
$984$		−	324.006i		−	0.329274i
$985$	372.168	−	871.346i	0.377835	−	0.884615i
$986$	−9.99689			−0.0101388
$987$	641.311	+	641.311i	0.649758	+	0.649758i
$988$	−519.756	+	519.756i	−0.526068	+	0.526068i
$989$			270.555i			0.273564i
$990$	403.786	+	172.464i	0.407865	+	0.174207i
$991$	−587.640			−0.592976			−0.296488	−	0.955037i	$-0.595816\pi$
$991$	−587.640			−0.592976			−0.296488	+	0.955037i	$0.595816\pi$
$992$	−135.320	−	135.320i	−0.136411	−	0.136411i
$993$	900.638	−	900.638i	0.906987	−	0.906987i
$994$			385.490i			0.387816i
$995$	1508.97	−	605.740i	1.51655	−	0.608784i
$996$	763.665			0.766732
$997$	193.129	+	193.129i	0.193710	+	0.193710i	0.797297	−	0.603587i	$-0.206262\pi$
$997$	193.129	+	193.129i	0.193710	+	0.193710i	−0.603587	+	0.797297i	$0.706262\pi$
$998$	−196.103	+	196.103i	−0.196496	+	0.196496i
$999$			72.0196i			0.0720917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.47.2	✓	20
5.3	odd	4	inner	230.3.f.a.93.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.2	✓	20	1.1	even	1	trivial
230.3.f.a.93.2	yes	20	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.63948 + 2.63948i) q^{3} +2.00000i q^{4} +(1.86266 + 4.64010i) q^{5} +5.27895 q^{6} +(5.81530 + 5.81530i) q^{7} +(2.00000 - 2.00000i) q^{8} -4.93366i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.63948 + 2.63948i) q^{3} +2.00000i q^{4} +(1.86266 + 4.64010i) q^{5} +5.27895 q^{6} +(5.81530 + 5.81530i) q^{7} +(2.00000 - 2.00000i) q^{8} -4.93366i q^{9} +(2.77744 - 6.50275i) q^{10} -12.5859 q^{11} +(-5.27895 - 5.27895i) q^{12} +(9.20375 - 9.20375i) q^{13} -11.6306i q^{14} +(-17.1639 - 7.33099i) q^{15} -4.00000 q^{16} +(-1.16565 - 1.16565i) q^{17} +(-4.93366 + 4.93366i) q^{18} +28.2361i q^{19} +(-9.28020 + 3.72531i) q^{20} -30.6987 q^{21} +(12.5859 + 12.5859i) q^{22} +(-3.39116 + 3.39116i) q^{23} +10.5579i q^{24} +(-18.0610 + 17.2858i) q^{25} -18.4075 q^{26} +(-10.7330 - 10.7330i) q^{27} +(-11.6306 + 11.6306i) q^{28} +4.28812i q^{29} +(9.83287 + 24.4949i) q^{30} -33.8299 q^{31} +(4.00000 + 4.00000i) q^{32} +(33.2202 - 33.2202i) q^{33} +2.33130i q^{34} +(-16.1517 + 37.8155i) q^{35} +9.86733 q^{36} +(-3.35506 - 3.35506i) q^{37} +(28.2361 - 28.2361i) q^{38} +48.5861i q^{39} +(13.0055 + 5.55489i) q^{40} -30.6884 q^{41} +(30.6987 + 30.6987i) q^{42} +(39.8911 - 39.8911i) q^{43} -25.1718i q^{44} +(22.8927 - 9.18972i) q^{45} +6.78233 q^{46} +(-20.8905 - 20.8905i) q^{47} +(10.5579 - 10.5579i) q^{48} +18.6355i q^{49} +(35.3468 + 0.775219i) q^{50} +6.15341 q^{51} +(18.4075 + 18.4075i) q^{52} +(-11.2617 + 11.2617i) q^{53} +21.4660i q^{54} +(-23.4432 - 58.3999i) q^{55} +23.2612 q^{56} +(-74.5285 - 74.5285i) q^{57} +(4.28812 - 4.28812i) q^{58} +42.8744i q^{59} +(14.6620 - 34.3277i) q^{60} +25.6581 q^{61} +(33.8299 + 33.8299i) q^{62} +(28.6908 - 28.6908i) q^{63} -8.00000i q^{64} +(59.8497 + 25.5629i) q^{65} -66.4404 q^{66} +(68.3222 + 68.3222i) q^{67} +(2.33130 - 2.33130i) q^{68} -17.9018i q^{69} +(53.9672 - 21.6638i) q^{70} -33.1444 q^{71} +(-9.86733 - 9.86733i) q^{72} +(53.4364 - 53.4364i) q^{73} +6.71011i q^{74} +(2.04617 - 93.2971i) q^{75} -56.4722 q^{76} +(-73.1909 - 73.1909i) q^{77} +(48.5861 - 48.5861i) q^{78} +43.7476i q^{79} +(-7.45062 - 18.5604i) q^{80} +101.062 q^{81} +(30.6884 + 30.6884i) q^{82} +(-72.3311 + 72.3311i) q^{83} -61.3974i q^{84} +(3.23753 - 7.57994i) q^{85} -79.7823 q^{86} +(-11.3184 - 11.3184i) q^{87} +(-25.1718 + 25.1718i) q^{88} -158.941i q^{89} +(-32.0824 - 13.7030i) q^{90} +107.045 q^{91} +(-6.78233 - 6.78233i) q^{92} +(89.2933 - 89.2933i) q^{93} +41.7810i q^{94} +(-131.018 + 52.5941i) q^{95} -21.1158 q^{96} +(33.4626 + 33.4626i) q^{97} +(18.6355 - 18.6355i) q^{98} +62.0947i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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