LMFDB - Embedded newform 230.3.f.a.93.2

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			93.2
Root			$-2.63948 - 2.63948i$ of defining polynomial
Character	$\chi$	$=$	230.93
Dual form			230.3.f.a.47.2

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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	0.113691	−	0.993516i	$-0.463733\pi$
$3$	−2.63948	−	2.63948i	−0.879825	−	0.879825i	−0.993516	+	0.113691i	$0.963733\pi$
$4$		−	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	−0.156863	−	0.987620i	$-0.550138\pi$
$7$	5.81530	−	5.81530i	0.830758	−	0.830758i	0.987620	+	0.156863i	$0.0501380\pi$
$8$	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	0.966110	−	0.258130i	$-0.0831062\pi$
$13$	9.20375	+	9.20375i	0.707981	+	0.707981i	−0.258130	+	0.966110i	$0.583106\pi$
$14$			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	−0.740559	−	0.671991i	$-0.765439\pi$
$17$	−1.16565	+	1.16565i	−0.0685676	+	0.0685676i	0.671991	+	0.740559i	$0.265439\pi$
$18$	−4.93366	−	4.93366i	−0.274092	−	0.274092i
$19$		−	28.2361i		−	1.48611i	−0.669231	−	0.743055i	$-0.733376\pi$
$19$		−	28.2361i		−	1.48611i	0.669231	−	0.743055i	$-0.266624\pi$
$20$	−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	$-0.976445\pi$
$29$		−	4.28812i		−	0.147866i	0.997263	−	0.0739330i	$-0.0235551\pi$
$30$	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	−0.750990	−	0.660313i	$-0.770424\pi$
$37$	−3.35506	+	3.35506i	−0.0906772	+	0.0906772i	0.660313	+	0.750990i	$0.270424\pi$
$38$	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	0.997557	−	0.0698563i	$-0.0222541\pi$
$43$	39.8911	+	39.8911i	0.927701	+	0.927701i	−0.0698563	+	0.997557i	$0.522254\pi$
$44$			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	−0.893514	−	0.449035i	$-0.851768\pi$
$47$	−20.8905	+	20.8905i	−0.444479	+	0.444479i	0.449035	+	0.893514i	$0.351768\pi$
$48$	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	0.592837	−	0.805323i	$-0.298008\pi$
$53$	−11.2617	−	11.2617i	−0.212486	−	0.212486i	−0.805323	+	0.592837i	$0.798008\pi$
$54$		−	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	$-0.881636\pi$
$59$		−	42.8744i		−	0.726685i	0.931656	−	0.363342i	$-0.118364\pi$
$60$	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	0.0199332	−	0.999801i	$-0.493655\pi$
$67$	68.3222	−	68.3222i	1.01973	−	1.01973i	0.999801	−	0.0199332i	$-0.00634537\pi$
$68$	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	0.971017	−	0.239012i	$-0.0768234\pi$
$73$	53.4364	+	53.4364i	0.732005	+	0.732005i	−0.239012	+	0.971017i	$0.576823\pi$
$74$		−	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	$-0.910698\pi$
$79$		−	43.7476i		−	0.553767i	0.960904	−	0.276883i	$-0.0893016\pi$
$80$	−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	0.121172	−	0.992632i	$-0.461335\pi$
$83$	−72.3311	−	72.3311i	−0.871459	−	0.871459i	−0.992632	+	0.121172i	$0.961335\pi$
$84$			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	$0.351353\pi$
$89$			158.941i			1.78586i	−0.450199	+	0.892928i	$0.648647\pi$
$90$	−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	−0.513259	−	0.858234i	$-0.671562\pi$
$97$	33.4626	−	33.4626i	0.344976	−	0.344976i	0.858234	+	0.513259i	$0.171562\pi$
$98$	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	−0.949933	−	0.312454i	$-0.898849\pi$
$103$	−130.026	−	130.026i	−1.26239	−	1.26239i	−0.312454	−	0.949933i	$-0.601151\pi$
$104$			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	0.466743	−	0.884393i	$-0.345427\pi$
$107$	144.572	−	144.572i	1.35114	−	1.35114i	0.884393	−	0.466743i	$-0.154573\pi$
$108$	21.4660	+	21.4660i	0.198759	+	0.198759i
$109$		−	134.634i		−	1.23518i	−0.786501	−	0.617589i	$-0.788109\pi$
$109$		−	134.634i		−	1.23518i	0.786501	−	0.617589i	$-0.211891\pi$
$110$	−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	0.996842	+	0.0794141i	$0.0253049\pi$
$113$	121.617	+	121.617i	1.07626	+	1.07626i	0.0794141	+	0.996842i	$0.474695\pi$
$114$		−	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	0.395381	−	0.918517i	$-0.370612\pi$
$127$	166.865	−	166.865i	1.31390	−	1.31390i	0.918517	−	0.395381i	$-0.129388\pi$
$128$	−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	−0.763591	−	0.645700i	$-0.776566\pi$
$137$	−16.1511	+	16.1511i	−0.117891	+	0.117891i	0.645700	+	0.763591i	$0.276566\pi$
$138$	−17.9018	−	17.9018i	−0.129723	−	0.129723i
$139$		−	84.0074i		−	0.604370i	−0.953249	−	0.302185i	$-0.902284\pi$
$139$		−	84.0074i		−	0.604370i	0.953249	−	0.302185i	$-0.0977160\pi$
$140$	−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	$-0.812922\pi$
$149$		−	165.231i		−	1.10894i	0.832205	−	0.554468i	$-0.187078\pi$
$150$	−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	−0.0391252	−	0.999234i	$-0.512457\pi$
$157$	150.737	−	150.737i	0.960109	−	0.960109i	0.999234	+	0.0391252i	$0.0124571\pi$
$158$	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	0.946647	+	0.322272i	$0.104446\pi$
$163$	206.834	+	206.834i	1.26892	+	1.26892i	0.322272	+	0.946647i	$0.395554\pi$
$164$			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	−0.978760	−	0.205007i	$-0.934278\pi$
$167$	−129.217	+	129.217i	−0.773753	+	0.773753i	0.205007	+	0.978760i	$0.434278\pi$
$168$	−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	0.608541	−	0.793522i	$-0.291755\pi$
$173$	−32.0017	−	32.0017i	−0.184981	−	0.184981i	−0.793522	+	0.608541i	$0.791755\pi$
$174$		−	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	$-0.729684\pi$
$179$		−	268.775i		−	1.50154i	0.660566	−	0.750768i	$-0.270316\pi$
$180$	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	−0.997264	−	0.0739166i	$-0.976450\pi$
$193$	−206.738	−	206.738i	−1.07118	−	1.07118i	−0.0739166	−	0.997264i	$-0.523550\pi$
$194$			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	−0.960042	−	0.279857i	$-0.909713\pi$
$197$	−133.996	+	133.996i	−0.680185	+	0.680185i	0.279857	+	0.960042i	$0.409713\pi$
$198$	62.0947	+	62.0947i	0.313610	+	0.313610i
$199$			325.203i			1.63418i	0.576508	+	0.817092i	$0.304415\pi$
$199$			325.203i			1.63418i	−0.576508	+	0.817092i	$0.695585\pi$
$200$	−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	0.984896	+	0.173150i	$0.0553944\pi$
$223$	258.244	+	258.244i	1.15805	+	1.15805i	0.173150	+	0.984896i	$0.444606\pi$
$224$		−	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	0.00557065	−	0.999984i	$-0.498227\pi$
$227$	228.261	−	228.261i	1.00556	−	1.00556i	0.999984	−	0.00557065i	$-0.00177320\pi$
$228$	149.057	+	149.057i	0.653758	+	0.653758i
$229$		−	153.864i		−	0.671897i	−0.941880	−	0.335949i	$-0.890943\pi$
$229$		−	153.864i		−	0.671897i	0.941880	−	0.335949i	$-0.109057\pi$
$230$	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	0.743350	−	0.668903i	$-0.233236\pi$
$233$	17.3460	+	17.3460i	0.0744465	+	0.0744465i	−0.668903	+	0.743350i	$0.733236\pi$
$234$		−	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	$0.238762\pi$
$239$			325.856i			1.36341i	−0.731626	+	0.681706i	$0.761238\pi$
$240$	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	0.0935464	−	0.995615i	$-0.470180\pi$
$257$	279.914	−	279.914i	1.08916	−	1.08916i	0.995615	−	0.0935464i	$-0.0298203\pi$
$258$	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	0.993270	−	0.115821i	$-0.0369499\pi$
$263$	230.769	+	230.769i	0.877449	+	0.877449i	−0.115821	+	0.993270i	$0.536950\pi$
$264$			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	$-0.715337\pi$
$269$		−	419.515i		−	1.55953i	0.626070	−	0.779767i	$-0.284663\pi$
$270$	−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	−0.932961	−	0.359977i	$-0.882784\pi$
$277$	−158.716	+	158.716i	−0.572984	+	0.572984i	0.359977	+	0.932961i	$0.382784\pi$
$278$	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	−0.987094	−	0.160141i	$-0.948805\pi$
$283$	−324.668	−	324.668i	−1.14724	−	1.14724i	−0.160141	−	0.987094i	$-0.551195\pi$
$284$			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	0.854765	−	0.519015i	$-0.173701\pi$
$293$	98.3747	+	98.3747i	0.335750	+	0.335750i	−0.519015	+	0.854765i	$0.673701\pi$
$294$		−	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	−0.956731	−	0.290972i	$-0.906021\pi$
$307$	−204.388	+	204.388i	−0.665759	+	0.665759i	0.290972	+	0.956731i	$0.406021\pi$
$308$	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	0.127334	−	0.991860i	$-0.459358\pi$
$313$	−270.597	−	270.597i	−0.864526	−	0.864526i	−0.991860	+	0.127334i	$0.959358\pi$
$314$			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	−0.794780	−	0.606897i	$-0.792414\pi$
$317$	−59.5591	+	59.5591i	−0.187883	+	0.187883i	0.606897	+	0.794780i	$0.292414\pi$
$318$	−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	−0.754596	−	0.656189i	$-0.772167\pi$
$337$	−33.1631	+	33.1631i	−0.0984068	+	0.0984068i	0.656189	+	0.754596i	$0.272167\pi$
$338$	−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	−0.921223	−	0.389035i	$-0.872809\pi$
$347$	−184.669	+	184.669i	−0.532188	+	0.532188i	0.389035	+	0.921223i	$0.372809\pi$
$348$	22.6368	+	22.6368i	0.0650482	+	0.0650482i
$349$		−	185.462i		−	0.531409i	−0.964055	−	0.265704i	$-0.914396\pi$
$349$		−	185.462i		−	0.531409i	0.964055	−	0.265704i	$-0.0856045\pi$
$350$	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	0.236704	−	0.971582i	$-0.423933\pi$
$353$	−259.412	−	259.412i	−0.734878	−	0.734878i	−0.971582	+	0.236704i	$0.923933\pi$
$354$		−	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	$-0.923684\pi$
$359$		−	170.499i		−	0.474929i	0.971396	−	0.237464i	$-0.0763163\pi$
$360$	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	−0.927919	−	0.372782i	$-0.878404\pi$
$367$	−203.735	+	203.735i	−0.555137	+	0.555137i	0.372782	+	0.927919i	$0.378404\pi$
$368$	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	0.764463	−	0.644667i	$-0.223004\pi$
$373$	44.6839	+	44.6839i	0.119796	+	0.119796i	−0.644667	+	0.764463i	$0.723004\pi$
$374$			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	$0.112032\pi$
$379$			261.312i			0.689477i	−0.938699	+	0.344739i	$0.887968\pi$
$380$	−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	0.672403	−	0.740186i	$-0.265262\pi$
$383$	−25.9608	−	25.9608i	−0.0677829	−	0.0677829i	−0.740186	+	0.672403i	$0.765262\pi$
$384$			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	$0.0361448\pi$
$389$			88.1539i			0.226617i	−0.993560	+	0.113308i	$0.963855\pi$
$390$	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	−0.930938	−	0.365178i	$-0.881008\pi$
$397$	−224.607	+	224.607i	−0.565760	+	0.565760i	0.365178	+	0.930938i	$0.381008\pi$
$398$	−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	$-0.833313\pi$
$409$		−	409.046i		−	1.00011i	0.865993	−	0.500056i	$-0.166687\pi$
$410$	−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	$0.0389260\pi$
$419$			102.223i			0.243970i	−0.992532	+	0.121985i	$0.961074\pi$
$420$	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	0.615042	−	0.788495i	$-0.289139\pi$
$433$	−75.1051	−	75.1051i	−0.173453	−	0.173453i	−0.788495	+	0.615042i	$0.789139\pi$
$434$		−	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	$-0.920283\pi$
$439$		−	217.593i		−	0.495656i	0.968804	−	0.247828i	$-0.0797168\pi$
$440$	−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	0.461905	−	0.886929i	$-0.347166\pi$
$443$	−188.286	−	188.286i	−0.425025	−	0.425025i	−0.886929	+	0.461905i	$0.847166\pi$
$444$		−	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	$-0.856893\pi$
$449$		−	390.262i		−	0.869181i	0.900628	−	0.434591i	$-0.143107\pi$
$450$	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	−0.848196	−	0.529683i	$-0.822311\pi$
$457$	−145.560	+	145.560i	−0.318513	+	0.318513i	0.529683	+	0.848196i	$0.322311\pi$
$458$	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	0.937862	−	0.347008i	$-0.112802\pi$
$463$	273.566	+	273.566i	0.590854	+	0.590854i	−0.347008	+	0.937862i	$0.612802\pi$
$464$			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	−0.426287	−	0.904588i	$-0.640179\pi$
$467$	223.366	−	223.366i	0.478300	−	0.478300i	0.904588	+	0.426287i	$0.140179\pi$
$468$	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	$-0.823676\pi$
$479$		−	503.948i		−	1.05208i	0.850459	−	0.526041i	$-0.176324\pi$
$480$	−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	−0.876152	−	0.482035i	$-0.839898\pi$
$487$	−191.935	+	191.935i	−0.394117	+	0.394117i	0.482035	+	0.876152i	$0.339898\pi$
$488$	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	$0.0629563\pi$
$499$			196.103i			0.392992i	−0.980505	+	0.196496i	$0.937044\pi$
$500$	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	0.599556	−	0.800332i	$-0.295344\pi$
$503$	−100.990	−	100.990i	−0.200776	−	0.200776i	−0.800332	+	0.599556i	$0.795344\pi$
$504$			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	$-0.748757\pi$
$509$		−	722.640i		−	1.41972i	0.704341	−	0.709862i	$-0.251243\pi$
$510$	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	0.940992	−	0.338428i	$-0.109895\pi$
$523$	315.141	+	315.141i	0.602564	+	0.602564i	−0.338428	+	0.940992i	$0.609895\pi$
$524$			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	−0.792458	−	0.609926i	$-0.791199\pi$
$547$	−99.8453	+	99.8453i	−0.182533	+	0.182533i	0.609926	+	0.792458i	$0.291199\pi$
$548$	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	−0.968727	−	0.248131i	$-0.920184\pi$
$557$	−401.372	+	401.372i	−0.720596	+	0.720596i	0.248131	+	0.968727i	$0.420184\pi$
$558$	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	0.900807	+	0.434221i	$0.142976\pi$
$563$	751.620	+	751.620i	1.33503	+	1.33503i	0.434221	+	0.900807i	$0.357024\pi$
$564$		−	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	$-0.855333\pi$
$569$		−	499.583i		−	0.878002i	0.898487	−	0.439001i	$-0.144667\pi$
$570$	−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	−0.235124	−	0.971965i	$-0.575550\pi$
$577$	425.157	−	425.157i	0.736841	−	0.736841i	0.971965	+	0.235124i	$0.0755497\pi$
$578$	−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	−0.388140	−	0.921600i	$-0.626882\pi$
$587$	313.141	−	313.141i	0.533460	−	0.533460i	0.921600	+	0.388140i	$0.126882\pi$
$588$	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	0.976809	−	0.214113i	$-0.0686861\pi$
$593$	452.279	+	452.279i	0.762696	+	0.762696i	−0.214113	+	0.976809i	$0.568686\pi$
$594$			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	$0.0650451\pi$
$599$			243.105i			0.405852i	−0.979194	+	0.202926i	$0.934955\pi$
$600$	−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	−0.334224	−	0.942494i	$-0.608474\pi$
$607$	369.220	−	369.220i	0.608270	−	0.608270i	0.942494	+	0.334224i	$0.108474\pi$
$608$	−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	0.964355	+	0.264611i	$0.0852434\pi$
$613$	753.356	+	753.356i	1.22897	+	1.22897i	0.264611	+	0.964355i	$0.414757\pi$
$614$		−	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	−0.745313	−	0.666715i	$-0.767700\pi$
$617$	−48.4951	+	48.4951i	−0.0785982	+	0.0785982i	0.666715	+	0.745313i	$0.267700\pi$
$618$	−686.400	−	686.400i	−1.11068	−	1.11068i
$619$			1115.83i			1.80264i	0.433153	+	0.901321i	$0.357401\pi$
$619$			1115.83i			1.80264i	−0.433153	+	0.901321i	$0.642599\pi$
$620$	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	0.768996	−	0.639253i	$-0.220757\pi$
$643$	83.4245	+	83.4245i	0.129743	+	0.129743i	−0.639253	+	0.768996i	$0.720757\pi$
$644$			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	−0.494832	−	0.868988i	$-0.664771\pi$
$647$	242.079	−	242.079i	0.374156	−	0.374156i	0.868988	+	0.494832i	$0.164771\pi$
$648$	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	0.996971	+	0.0777728i	$0.0247809\pi$
$653$	701.808	+	701.808i	1.07474	+	1.07474i	0.0777728	+	0.996971i	$0.475219\pi$
$654$		−	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	$0.319658\pi$
$659$			1112.06i			1.68750i	−0.536735	+	0.843751i	$0.680342\pi$
$660$	−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	0.415938	−	0.909393i	$-0.363453\pi$
$673$	−332.095	−	332.095i	−0.493454	−	0.493454i	−0.909393	+	0.415938i	$0.863453\pi$
$674$		−	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	−0.795536	−	0.605906i	$-0.792811\pi$
$677$	−128.380	+	128.380i	−0.189631	+	0.189631i	0.605906	+	0.795536i	$0.292811\pi$
$678$	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	0.888764	+	0.458365i	$0.151565\pi$
$683$	920.089	+	920.089i	1.34713	+	1.34713i	0.458365	+	0.888764i	$0.348435\pi$
$684$		−	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	$-0.954183\pi$
$709$		−	203.403i		−	0.286887i	0.989659	−	0.143443i	$-0.0458175\pi$
$710$	−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	$0.0537280\pi$
$719$			241.571i			0.335982i	−0.985788	+	0.167991i	$0.946272\pi$
$720$	−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	−0.990093	−	0.140412i	$-0.955157\pi$
$727$	−617.718	+	617.718i	−0.849681	+	0.849681i	0.140412	+	0.990093i	$0.455157\pi$
$728$	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	0.464012	−	0.885829i	$-0.346409\pi$
$733$	−309.192	−	309.192i	−0.421817	−	0.421817i	−0.885829	+	0.464012i	$0.846409\pi$
$734$		−	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	$-0.979204\pi$
$739$		−	96.4942i		−	0.130574i	0.997867	−	0.0652870i	$-0.0207963\pi$
$740$	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	0.199898	−	0.979817i	$-0.435939\pi$
$743$	−579.479	−	579.479i	−0.779918	−	0.779918i	−0.979817	+	0.199898i	$0.935939\pi$
$744$			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	0.134112	−	0.990966i	$-0.457182\pi$
$757$	851.684	−	851.684i	1.12508	−	1.12508i	0.990966	−	0.134112i	$-0.0428183\pi$
$758$	−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	$0.283073\pi$
$769$			1194.46i			1.55326i	−0.629956	+	0.776631i	$0.716927\pi$
$770$	−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	0.921442	−	0.388517i	$-0.127012\pi$
$773$	411.951	+	411.951i	0.532925	+	0.532925i	−0.388517	+	0.921442i	$0.627012\pi$
$774$		−	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	−0.978461	−	0.206431i	$-0.933815\pi$
$787$	−607.588	+	607.588i	−0.772030	+	0.772030i	0.206431	+	0.978461i	$0.433815\pi$
$788$	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	−0.757374	−	0.652981i	$-0.773518\pi$
$797$	−83.2010	+	83.2010i	−0.104393	+	0.104393i	0.652981	+	0.757374i	$0.273518\pi$
$798$	−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	$-0.782437\pi$
$809$		−	1021.78i		−	1.26301i	0.775371	−	0.631506i	$-0.217563\pi$
$810$	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	−0.900737	−	0.434364i	$-0.856973\pi$
$823$	−1098.79	−	1098.79i	−1.33510	−	1.33510i	−0.434364	−	0.900737i	$-0.643027\pi$
$824$		−	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	−0.950789	−	0.309839i	$-0.899725\pi$
$827$	−530.066	+	530.066i	−0.640950	+	0.640950i	0.309839	+	0.950789i	$0.399725\pi$
$828$	−33.4617	−	33.4617i	−0.0404127	−	0.0404127i
$829$			164.962i			0.198990i	0.995038	+	0.0994948i	$0.0317227\pi$
$829$			164.962i			0.198990i	−0.995038	+	0.0994948i	$0.968277\pi$
$830$	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	$-0.633843\pi$
$839$		−	1531.83i		−	1.82579i	0.408199	−	0.912893i	$-0.366157\pi$
$840$	−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	0.879749	−	0.475439i	$-0.157711\pi$
$853$	344.877	+	344.877i	0.404310	+	0.404310i	−0.475439	+	0.879749i	$0.657711\pi$
$854$			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	−0.731768	−	0.681554i	$-0.761304\pi$
$857$	−43.0332	+	43.0332i	−0.0502138	+	0.0502138i	0.681554	+	0.731768i	$0.261304\pi$
$858$	−611.501	−	611.501i	−0.712705	−	0.712705i
$859$			1083.34i			1.26116i	0.776124	+	0.630580i	$0.217183\pi$
$859$			1083.34i			1.26116i	−0.776124	+	0.630580i	$0.782817\pi$
$860$	−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	0.878404	+	0.477919i	$0.158609\pi$
$863$	1170.51	+	1170.51i	1.35632	+	1.35632i	0.477919	+	0.878404i	$0.341391\pi$
$864$			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	−0.849635	−	0.527371i	$-0.823178\pi$
$877$	−282.626	+	282.626i	−0.322264	+	0.322264i	0.527371	+	0.849635i	$0.323178\pi$
$878$	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	0.694849	−	0.719156i	$-0.255471\pi$
$883$	−21.4634	−	21.4634i	−0.0243074	−	0.0243074i	−0.719156	+	0.694849i	$0.755471\pi$
$884$			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	−0.826902	−	0.562346i	$-0.809899\pi$
$887$	−234.661	+	234.661i	−0.264556	+	0.264556i	0.562346	+	0.826902i	$0.309899\pi$
$888$	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	0.00126519	−	0.999999i	$-0.499597\pi$
$907$	908.147	−	908.147i	1.00126	−	1.00126i	0.999999	−	0.00126519i	$-0.000402724\pi$
$908$	−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	$0.255771\pi$
$919$			1323.01i			1.43962i	−0.694172	+	0.719809i	$0.744229\pi$
$920$	−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	$-0.743738\pi$
$929$		−	1339.40i		−	1.44176i	0.693059	−	0.720881i	$-0.256262\pi$
$930$	−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	−0.225505	+	0.974242i	$0.572403\pi$
$937$	−1124.16	+	1124.16i	−1.19975	+	1.19975i	−0.974242	+	0.225505i	$0.927597\pi$
$938$	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	−0.972278	−	0.233826i	$-0.924875\pi$
$947$	−699.314	+	699.314i	−0.738452	+	0.738452i	0.233826	+	0.972278i	$0.424875\pi$
$948$	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	0.962306	−	0.271968i	$-0.0876745\pi$
$953$	657.892	+	657.892i	0.690338	+	0.690338i	−0.271968	+	0.962306i	$0.587674\pi$
$954$			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	−0.301223	−	0.953554i	$-0.597395\pi$
$967$	630.803	−	630.803i	0.652330	−	0.652330i	0.953554	+	0.301223i	$0.0973950\pi$
$968$	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	−0.810483	−	0.585762i	$-0.800795\pi$
$977$	−219.553	+	219.553i	−0.224721	+	0.224721i	0.585762	+	0.810483i	$0.300795\pi$
$978$	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	0.803249	−	0.595643i	$-0.203103\pi$
$983$	204.077	+	204.077i	0.207607	+	0.207607i	−0.595643	+	0.803249i	$0.703103\pi$
$984$			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	−0.603587	−	0.797297i	$-0.706262\pi$
$997$	193.129	−	193.129i	0.193710	−	0.193710i	0.797297	+	0.603587i	$0.206262\pi$
$998$	−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.93.2	yes	20
5.2	odd	4	inner	230.3.f.a.47.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.2	✓	20	5.2	odd	4	inner
230.3.f.a.93.2	yes	20	1.1	even	1	trivial

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

Fields

Representations

Groups

Database

Properties

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