LMFDB - Embedded newform 210.3.l.b.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("210.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.7
Root			$-3.48873 + 3.48873i$ of defining polynomial
Character	$\chi$	$=$	210.43
Dual form			210.3.l.b.127.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-1.66827 + 4.71348i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-1.66827 + 4.71348i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-3.04521 - 6.38175i) q^{10} -5.03576 q^{11} +(2.44949 - 2.44949i) q^{12} +(-2.44923 - 2.44923i) q^{13} -3.74166i q^{14} +(-7.81601 + 3.72961i) q^{15} -4.00000 q^{16} +(-18.2815 + 18.2815i) q^{17} +(-3.00000 - 3.00000i) q^{18} -9.56449i q^{19} +(9.42696 + 3.33654i) q^{20} -4.58258 q^{21} +(5.03576 - 5.03576i) q^{22} +(16.4256 + 16.4256i) q^{23} +4.89898i q^{24} +(-19.4338 - 15.7267i) q^{25} +4.89847 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} +4.18550i q^{29} +(4.08641 - 11.5456i) q^{30} -55.1410 q^{31} +(4.00000 - 4.00000i) q^{32} +(-6.16752 - 6.16752i) q^{33} -36.5631i q^{34} +(-5.69707 - 11.9392i) q^{35} +6.00000 q^{36} +(-1.23603 + 1.23603i) q^{37} +(9.56449 + 9.56449i) q^{38} -5.99937i q^{39} +(-12.7635 + 6.09042i) q^{40} -12.2171 q^{41} +(4.58258 - 4.58258i) q^{42} +(36.1249 + 36.1249i) q^{43} +10.0715i q^{44} +(-14.1404 - 5.00481i) q^{45} -32.8512 q^{46} +(18.6917 - 18.6917i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +(35.1605 - 3.70706i) q^{50} -44.7804 q^{51} +(-4.89847 + 4.89847i) q^{52} +(37.8979 + 37.8979i) q^{53} -7.34847i q^{54} +(8.40100 - 23.7359i) q^{55} -7.48331 q^{56} +(11.7141 - 11.7141i) q^{57} +(-4.18550 - 4.18550i) q^{58} +71.7488i q^{59} +(7.45921 + 15.6320i) q^{60} +60.8100 q^{61} +(55.1410 - 55.1410i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} +(15.6304 - 7.45843i) q^{65} +12.3350 q^{66} +(30.4868 - 30.4868i) q^{67} +(36.5631 + 36.5631i) q^{68} +40.2344i q^{69} +(17.6362 + 6.24209i) q^{70} +115.195 q^{71} +(-6.00000 + 6.00000i) q^{72} +(54.8705 + 54.8705i) q^{73} -2.47206i q^{74} +(-4.54020 - 43.0626i) q^{75} -19.1290 q^{76} +(9.42104 - 9.42104i) q^{77} +(5.99937 + 5.99937i) q^{78} +62.5991i q^{79} +(6.67307 - 18.8539i) q^{80} -9.00000 q^{81} +(12.2171 - 12.2171i) q^{82} +(52.8767 + 52.8767i) q^{83} +9.16515i q^{84} +(-55.6711 - 116.668i) q^{85} -72.2499 q^{86} +(-5.12617 + 5.12617i) q^{87} +(-10.0715 - 10.0715i) q^{88} +16.5994i q^{89} +(19.1452 - 9.13563i) q^{90} +9.16419 q^{91} +(32.8512 - 32.8512i) q^{92} +(-67.5336 - 67.5336i) q^{93} +37.3834i q^{94} +(45.0820 + 15.9561i) q^{95} +9.79796 q^{96} +(71.1722 - 71.1722i) q^{97} +(7.00000 + 7.00000i) q^{98} -15.1073i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	$ 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	−1.66827	+	4.71348i	−0.333654	+	0.942696i
$5$	−1.66827	+	4.71348i	−0.333654	+	0.942696i
$6$	−2.44949			−0.408248
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	−3.04521	−	6.38175i	−0.304521	−	0.638175i
$11$	−5.03576			−0.457796			−0.228898	−	0.973450i	$-0.573512\pi$
$11$	−5.03576			−0.457796			−0.228898	+	0.973450i	$0.573512\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−2.44923	−	2.44923i	−0.188403	−	0.188403i	0.606603	−	0.795005i	$-0.292532\pi$
$13$	−2.44923	−	2.44923i	−0.188403	−	0.188403i	−0.795005	+	0.606603i	$0.792532\pi$
$14$		−	3.74166i		−	0.267261i
$15$	−7.81601	+	3.72961i	−0.521067	+	0.248640i
$16$	−4.00000			−0.250000
$17$	−18.2815	+	18.2815i	−1.07538	+	1.07538i	−0.0784682	+	0.996917i	$0.525003\pi$
$17$	−18.2815	+	18.2815i	−1.07538	+	1.07538i	−0.996917	+	0.0784682i	$0.974997\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	9.56449i		−	0.503394i	−0.967806	−	0.251697i	$-0.919011\pi$
$19$		−	9.56449i		−	0.503394i	0.967806	−	0.251697i	$-0.0809887\pi$
$20$	9.42696	+	3.33654i	0.471348	+	0.166827i
$21$	−4.58258			−0.218218
$22$	5.03576	−	5.03576i	0.228898	−	0.228898i
$23$	16.4256	+	16.4256i	0.714157	+	0.714157i	0.967402	−	0.253245i	$-0.0814979\pi$
$23$	16.4256	+	16.4256i	0.714157	+	0.714157i	−0.253245	+	0.967402i	$0.581498\pi$
$24$			4.89898i			0.204124i
$25$	−19.4338	−	15.7267i	−0.777350	−	0.629068i
$26$	4.89847			0.188403
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	3.74166	+	3.74166i	0.133631	+	0.133631i
$29$			4.18550i			0.144328i	0.997393	+	0.0721639i	$0.0229905\pi$
$29$			4.18550i			0.144328i	−0.997393	+	0.0721639i	$0.977010\pi$
$30$	4.08641	−	11.5456i	0.136214	−	0.384854i
$31$	−55.1410			−1.77874			−0.889370	−	0.457188i	$-0.848857\pi$
$31$	−55.1410			−1.77874			−0.889370	+	0.457188i	$0.848857\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−6.16752	−	6.16752i	−0.186894	−	0.186894i
$34$		−	36.5631i		−	1.07538i
$35$	−5.69707	−	11.9392i	−0.162773	−	0.341119i
$36$	6.00000			0.166667
$37$	−1.23603	+	1.23603i	−0.0334062	+	0.0334062i	−0.723613	−	0.690206i	$-0.757520\pi$
$37$	−1.23603	+	1.23603i	−0.0334062	+	0.0334062i	0.690206	+	0.723613i	$0.257520\pi$
$38$	9.56449	+	9.56449i	0.251697	+	0.251697i
$39$		−	5.99937i		−	0.153830i
$40$	−12.7635	+	6.09042i	−0.319087	+	0.152260i
$41$	−12.2171			−0.297979			−0.148989	−	0.988839i	$-0.547602\pi$
$41$	−12.2171			−0.297979			−0.148989	+	0.988839i	$0.547602\pi$
$42$	4.58258	−	4.58258i	0.109109	−	0.109109i
$43$	36.1249	+	36.1249i	0.840115	+	0.840115i	0.988874	−	0.148759i	$-0.0475278\pi$
$43$	36.1249	+	36.1249i	0.840115	+	0.840115i	−0.148759	+	0.988874i	$0.547528\pi$
$44$			10.0715i			0.228898i
$45$	−14.1404	−	5.00481i	−0.314232	−	0.111218i
$46$	−32.8512			−0.714157
$47$	18.6917	−	18.6917i	0.397696	−	0.397696i	−0.479724	−	0.877419i	$-0.659263\pi$
$47$	18.6917	−	18.6917i	0.397696	−	0.397696i	0.877419	+	0.479724i	$0.159263\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$	35.1605	−	3.70706i	0.703209	−	0.0741412i
$51$	−44.7804			−0.878048
$52$	−4.89847	+	4.89847i	−0.0942013	+	0.0942013i
$53$	37.8979	+	37.8979i	0.715056	+	0.715056i	0.967588	−	0.252533i	$-0.0812636\pi$
$53$	37.8979	+	37.8979i	0.715056	+	0.715056i	−0.252533	+	0.967588i	$0.581264\pi$
$54$		−	7.34847i		−	0.136083i
$55$	8.40100	−	23.7359i	0.152745	−	0.431562i
$56$	−7.48331			−0.133631
$57$	11.7141	−	11.7141i	0.205510	−	0.205510i
$58$	−4.18550	−	4.18550i	−0.0721639	−	0.0721639i
$59$			71.7488i			1.21608i	0.793906	+	0.608041i	$0.208044\pi$
$59$			71.7488i			1.21608i	−0.793906	+	0.608041i	$0.791956\pi$
$60$	7.45921	+	15.6320i	0.124320	+	0.260534i
$61$	60.8100			0.996885			0.498442	−	0.866923i	$-0.333906\pi$
$61$	60.8100			0.996885			0.498442	+	0.866923i	$0.333906\pi$
$62$	55.1410	−	55.1410i	0.889370	−	0.889370i
$63$	−5.61249	−	5.61249i	−0.0890871	−	0.0890871i
$64$			8.00000i			0.125000i
$65$	15.6304	−	7.45843i	0.240467	−	0.114745i
$66$	12.3350			0.186894
$67$	30.4868	−	30.4868i	0.455027	−	0.455027i	−0.441992	−	0.897019i	$-0.645728\pi$
$67$	30.4868	−	30.4868i	0.455027	−	0.455027i	0.897019	+	0.441992i	$0.145728\pi$
$68$	36.5631	+	36.5631i	0.537692	+	0.537692i
$69$			40.2344i			0.583107i
$70$	17.6362	+	6.24209i	0.251946	+	0.0891727i
$71$	115.195			1.62246			0.811229	−	0.584728i	$-0.198799\pi$
$71$	115.195			1.62246			0.811229	+	0.584728i	$0.198799\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	54.8705	+	54.8705i	0.751651	+	0.751651i	0.974787	−	0.223136i	$-0.0716294\pi$
$73$	54.8705	+	54.8705i	0.751651	+	0.751651i	−0.223136	+	0.974787i	$0.571629\pi$
$74$		−	2.47206i		−	0.0334062i
$75$	−4.54020	−	43.0626i	−0.0605361	−	0.574168i
$76$	−19.1290			−0.251697
$77$	9.42104	−	9.42104i	0.122351	−	0.122351i
$78$	5.99937	+	5.99937i	0.0769150	+	0.0769150i
$79$			62.5991i			0.792394i	0.918165	+	0.396197i	$0.129670\pi$
$79$			62.5991i			0.792394i	−0.918165	+	0.396197i	$0.870330\pi$
$80$	6.67307	−	18.8539i	0.0834134	−	0.235674i
$81$	−9.00000			−0.111111
$82$	12.2171	−	12.2171i	0.148989	−	0.148989i
$83$	52.8767	+	52.8767i	0.637069	+	0.637069i	0.949831	−	0.312762i	$-0.101254\pi$
$83$	52.8767	+	52.8767i	0.637069	+	0.637069i	−0.312762	+	0.949831i	$0.601254\pi$
$84$			9.16515i			0.109109i
$85$	−55.6711	−	116.668i	−0.654954	−	1.37257i
$86$	−72.2499			−0.840115
$87$	−5.12617	+	5.12617i	−0.0589215	+	0.0589215i
$88$	−10.0715	−	10.0715i	−0.114449	−	0.114449i
$89$			16.5994i			0.186511i	0.995642	+	0.0932553i	$0.0297273\pi$
$89$			16.5994i			0.186511i	−0.995642	+	0.0932553i	$0.970273\pi$
$90$	19.1452	−	9.13563i	0.212725	−	0.101507i
$91$	9.16419			0.100705
$92$	32.8512	−	32.8512i	0.357079	−	0.357079i
$93$	−67.5336	−	67.5336i	−0.726168	−	0.726168i
$94$			37.3834i			0.397696i
$95$	45.0820	+	15.9561i	0.474548	+	0.167959i
$96$	9.79796			0.102062
$97$	71.1722	−	71.1722i	0.733734	−	0.733734i	−0.237623	−	0.971357i	$-0.576368\pi$
$97$	71.1722	−	71.1722i	0.733734	−	0.733734i	0.971357	+	0.237623i	$0.0763684\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$		−	15.1073i		−	0.152599i
$100$	−31.4534	+	38.8675i	−0.314534	+	0.388675i
$101$	−145.577			−1.44136			−0.720679	−	0.693269i	$-0.756170\pi$
$101$	−145.577			−1.44136			−0.720679	+	0.693269i	$0.756170\pi$
$102$	44.7804	−	44.7804i	0.439024	−	0.439024i
$103$	105.102	+	105.102i	1.02041	+	1.02041i	0.999787	+	0.0206221i	$0.00656470\pi$
$103$	105.102	+	105.102i	1.02041	+	1.02041i	0.0206221	+	0.999787i	$0.493435\pi$
$104$		−	9.79693i		−	0.0942013i
$105$	7.64497	−	21.5999i	0.0728092	−	0.205713i
$106$	−75.7959			−0.715056
$107$	−45.6173	+	45.6173i	−0.426330	+	0.426330i	−0.887376	−	0.461046i	$-0.847474\pi$
$107$	−45.6173	+	45.6173i	−0.426330	+	0.426330i	0.461046	+	0.887376i	$0.347474\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$		−	156.303i		−	1.43397i	−0.697087	−	0.716987i	$-0.745521\pi$
$109$		−	156.303i		−	1.43397i	0.697087	−	0.716987i	$-0.254479\pi$
$110$	15.3349	+	32.1369i	0.139409	+	0.292154i
$111$	−3.02764			−0.0272760
$112$	7.48331	−	7.48331i	0.0668153	−	0.0668153i
$113$	−78.3428	−	78.3428i	−0.693299	−	0.693299i	0.269657	−	0.962956i	$-0.413090\pi$
$113$	−78.3428	−	78.3428i	−0.693299	−	0.693299i	−0.962956	+	0.269657i	$0.913090\pi$
$114$			23.4281i			0.205510i
$115$	−104.824	+	50.0194i	−0.911514	+	0.434952i
$116$	8.37101			0.0721639
$117$	7.34770	−	7.34770i	0.0628009	−	0.0628009i
$118$	−71.7488	−	71.7488i	−0.608041	−	0.608041i
$119$		−	68.4033i		−	0.574817i
$120$	−23.0912	−	8.17281i	−0.192427	−	0.0681068i
$121$	−95.6411			−0.790423
$122$	−60.8100	+	60.8100i	−0.498442	+	0.498442i
$123$	−14.9629	−	14.9629i	−0.121649	−	0.121649i
$124$			110.282i			0.889370i
$125$	106.548	−	65.3642i	0.852385	−	0.522914i
$126$	11.2250			0.0890871
$127$	84.9960	−	84.9960i	0.669260	−	0.669260i	−0.288285	−	0.957545i	$-0.593085\pi$
$127$	84.9960	−	84.9960i	0.669260	−	0.669260i	0.957545	+	0.288285i	$0.0930851\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			88.4877i			0.685951i
$130$	−8.17196	+	23.0888i	−0.0628612	+	0.177606i
$131$	−220.554			−1.68362			−0.841808	−	0.539776i	$-0.818509\pi$
$131$	−220.554			−1.68362			−0.841808	+	0.539776i	$0.818509\pi$
$132$	−12.3350	+	12.3350i	−0.0934472	+	0.0934472i
$133$	17.8935	+	17.8935i	0.134538	+	0.134538i
$134$			60.9737i			0.455027i
$135$	−11.1888	−	23.4480i	−0.0828801	−	0.173689i
$136$	−73.1262			−0.537692
$137$	−116.039	+	116.039i	−0.846999	+	0.846999i	−0.989758	−	0.142759i	$-0.954403\pi$
$137$	−116.039	+	116.039i	−0.846999	+	0.846999i	0.142759	+	0.989758i	$0.454403\pi$
$138$	−40.2344	−	40.2344i	−0.291553	−	0.291553i
$139$			270.544i			1.94636i	0.230046	+	0.973180i	$0.426112\pi$
$139$			270.544i			1.94636i	−0.230046	+	0.973180i	$0.573888\pi$
$140$	−23.8783	+	11.3941i	−0.170559	+	0.0813867i
$141$	45.7851			0.324717
$142$	−115.195	+	115.195i	−0.811229	+	0.811229i
$143$	12.3337	+	12.3337i	0.0862500	+	0.0862500i
$144$		−	12.0000i		−	0.0833333i
$145$	−19.7283	−	6.98255i	−0.136057	−	0.0481555i
$146$	−109.741			−0.751651
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	2.47206	+	2.47206i	0.0167031	+	0.0167031i
$149$		−	101.794i		−	0.683184i	−0.939848	−	0.341592i	$-0.889034\pi$
$149$		−	101.794i		−	0.683184i	0.939848	−	0.341592i	$-0.110966\pi$
$150$	47.6028	+	38.5224i	0.317352	+	0.256816i
$151$	166.350			1.10165			0.550826	−	0.834620i	$-0.314313\pi$
$151$	166.350			1.10165			0.550826	+	0.834620i	$0.314313\pi$
$152$	19.1290	−	19.1290i	0.125849	−	0.125849i
$153$	−54.8446	−	54.8446i	−0.358462	−	0.358462i
$154$			18.8421i			0.122351i
$155$	91.9899	−	259.906i	0.593483	−	1.67681i
$156$	−11.9987			−0.0769150
$157$	−106.083	+	106.083i	−0.675686	+	0.675686i	−0.959021	−	0.283335i	$-0.908559\pi$
$157$	−106.083	+	106.083i	−0.675686	+	0.675686i	0.283335	+	0.959021i	$0.408559\pi$
$158$	−62.5991	−	62.5991i	−0.396197	−	0.396197i
$159$			92.8306i			0.583840i
$160$	12.1808	+	25.5270i	0.0761302	+	0.159544i
$161$	−61.4590			−0.381733
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	54.7674	+	54.7674i	0.335996	+	0.335996i	0.854858	−	0.518862i	$-0.173644\pi$
$163$	54.7674	+	54.7674i	0.335996	+	0.335996i	−0.518862	+	0.854858i	$0.673644\pi$
$164$			24.4342i			0.148989i
$165$	39.3595	−	18.7814i	0.238543	−	0.113827i
$166$	−105.753			−0.637069
$167$	12.2483	−	12.2483i	0.0733432	−	0.0733432i	−0.669484	−	0.742827i	$-0.733485\pi$
$167$	12.2483	−	12.2483i	0.0733432	−	0.0733432i	0.742827	+	0.669484i	$0.233485\pi$
$168$	−9.16515	−	9.16515i	−0.0545545	−	0.0545545i
$169$		−	157.003i		−	0.929009i
$170$	172.339	+	60.9970i	1.01376	+	0.358806i
$171$	28.6935			0.167798
$172$	72.2499	−	72.2499i	0.420057	−	0.420057i
$173$	−210.627	−	210.627i	−1.21750	−	1.21750i	−0.968506	−	0.248992i	$-0.919901\pi$
$173$	−210.627	−	210.627i	−1.21750	−	1.21750i	−0.248992	−	0.968506i	$-0.580099\pi$
$174$		−	10.2523i		−	0.0589215i
$175$	65.7792	−	6.93528i	0.375881	−	0.0396302i
$176$	20.1430			0.114449
$177$	−87.8740	+	87.8740i	−0.496463	+	0.496463i
$178$	−16.5994	−	16.5994i	−0.0932553	−	0.0932553i
$179$		−	141.089i		−	0.788208i	−0.919066	−	0.394104i	$-0.871055\pi$
$179$		−	141.089i		−	0.788208i	0.919066	−	0.394104i	$-0.128945\pi$
$180$	−10.0096	+	28.2809i	−0.0556090	+	0.157116i
$181$	−14.5190			−0.0802153			−0.0401077	−	0.999195i	$-0.512770\pi$
$181$	−14.5190			−0.0802153			−0.0401077	+	0.999195i	$0.512770\pi$
$182$	−9.16419	+	9.16419i	−0.0503527	+	0.0503527i
$183$	74.4767	+	74.4767i	0.406976	+	0.406976i
$184$			65.7025i			0.357079i
$185$	−3.76396	−	7.88802i	−0.0203458	−	0.0426379i
$186$	135.067			0.726168
$187$	92.0614	−	92.0614i	0.492307	−	0.492307i
$188$	−37.3834	−	37.3834i	−0.198848	−	0.198848i
$189$		−	13.7477i		−	0.0727393i
$190$	−61.0382	+	29.1259i	−0.321254	+	0.153294i
$191$	336.312			1.76080			0.880398	−	0.474235i	$-0.157275\pi$
$191$	336.312			1.76080			0.880398	+	0.474235i	$0.157275\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	15.7585	+	15.7585i	0.0816500	+	0.0816500i	0.746752	−	0.665102i	$-0.231612\pi$
$193$	15.7585	+	15.7585i	0.0816500	+	0.0816500i	−0.665102	+	0.746752i	$0.731612\pi$
$194$			142.344i			0.733734i
$195$	28.2779	+	10.0086i	0.145015	+	0.0513260i
$196$	−14.0000			−0.0714286
$197$	−160.208	+	160.208i	−0.813239	+	0.813239i	−0.985118	−	0.171879i	$-0.945016\pi$
$197$	−160.208	+	160.208i	−0.813239	+	0.813239i	0.171879	+	0.985118i	$0.445016\pi$
$198$	15.1073	+	15.1073i	0.0762994	+	0.0762994i
$199$		−	161.286i		−	0.810483i	−0.914210	−	0.405242i	$-0.867187\pi$
$199$		−	161.286i		−	0.810483i	0.914210	−	0.405242i	$-0.132813\pi$
$200$	−7.41412	−	70.3209i	−0.0370706	−	0.351605i
$201$	74.6772			0.371528
$202$	145.577	−	145.577i	0.720679	−	0.720679i
$203$	−7.83036	−	7.83036i	−0.0385732	−	0.0385732i
$204$			89.5609i			0.439024i
$205$	20.3814	−	57.5852i	0.0994217	−	0.280903i
$206$	−210.204			−1.02041
$207$	−49.2768	+	49.2768i	−0.238052	+	0.238052i
$208$	9.79693	+	9.79693i	0.0471006	+	0.0471006i
$209$			48.1645i			0.230452i
$210$	13.9549	+	29.2448i	0.0664519	+	0.139261i
$211$	−76.5522			−0.362806			−0.181403	−	0.983409i	$-0.558064\pi$
$211$	−76.5522			−0.362806			−0.181403	+	0.983409i	$0.558064\pi$
$212$	75.7959	−	75.7959i	0.357528	−	0.357528i
$213$	141.084	+	141.084i	0.662366	+	0.662366i
$214$		−	91.2347i		−	0.426330i
$215$	−230.540	+	110.008i	−1.07228	+	0.511665i
$216$	−14.6969			−0.0680414
$217$	103.159	−	103.159i	0.475388	−	0.475388i
$218$	156.303	+	156.303i	0.716987	+	0.716987i
$219$			134.405i			0.613721i
$220$	−47.4719	−	16.8020i	−0.215781	−	0.0763727i
$221$	89.5515			0.405210
$222$	3.02764	−	3.02764i	0.0136380	−	0.0136380i
$223$	247.136	+	247.136i	1.10823	+	1.10823i	0.993383	+	0.114852i	$0.0366394\pi$
$223$	247.136	+	247.136i	1.10823	+	1.10823i	0.114852	+	0.993383i	$0.463361\pi$
$224$			14.9666i			0.0668153i
$225$	47.1801	−	58.3013i	0.209689	−	0.259117i
$226$	156.686			0.693299
$227$	−195.992	+	195.992i	−0.863402	+	0.863402i	−0.991732	−	0.128330i	$-0.959038\pi$
$227$	−195.992	+	195.992i	−0.863402	+	0.863402i	0.128330	+	0.991732i	$0.459038\pi$
$228$	−23.4281	−	23.4281i	−0.102755	−	0.102755i
$229$		−	70.9486i		−	0.309819i	−0.987929	−	0.154910i	$-0.950491\pi$
$229$		−	70.9486i		−	0.309819i	0.987929	−	0.154910i	$-0.0495086\pi$
$230$	54.8047	−	154.844i	0.238281	−	0.673233i
$231$	23.0767			0.0998993
$232$	−8.37101	+	8.37101i	−0.0360819	+	0.0360819i
$233$	−13.5120	−	13.5120i	−0.0579912	−	0.0579912i	0.677516	−	0.735508i	$-0.263056\pi$
$233$	−13.5120	−	13.5120i	−0.0579912	−	0.0579912i	−0.735508	+	0.677516i	$0.763056\pi$
$234$			14.6954i			0.0628009i
$235$	56.9201	+	119.286i	0.242213	+	0.507599i
$236$	143.498			0.608041
$237$	−76.6680	+	76.6680i	−0.323494	+	0.323494i
$238$	68.4033	+	68.4033i	0.287409	+	0.287409i
$239$		−	157.888i		−	0.660617i	−0.943873	−	0.330309i	$-0.892847\pi$
$239$		−	157.888i		−	0.660617i	0.943873	−	0.330309i	$-0.107153\pi$
$240$	31.2640	−	14.9184i	0.130267	−	0.0621601i
$241$	142.701			0.592119			0.296060	−	0.955169i	$-0.404327\pi$
$241$	142.701			0.592119			0.296060	+	0.955169i	$0.404327\pi$
$242$	95.6411	−	95.6411i	0.395211	−	0.395211i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	121.620i		−	0.498442i
$245$	32.9943	+	11.6779i	0.134671	+	0.0476648i
$246$	29.9257			0.121649
$247$	−23.4257	+	23.4257i	−0.0948408	+	0.0948408i
$248$	−110.282	−	110.282i	−0.444685	−	0.444685i
$249$			129.521i			0.520165i
$250$	−41.1839	+	171.912i	−0.164736	+	0.687650i
$251$	81.9263			0.326400			0.163200	−	0.986593i	$-0.447818\pi$
$251$	81.9263			0.326400			0.163200	+	0.986593i	$0.447818\pi$
$252$	−11.2250	+	11.2250i	−0.0445435	+	0.0445435i
$253$	−82.7154	−	82.7154i	−0.326938	−	0.326938i
$254$			169.992i			0.669260i
$255$	74.7058	−	211.072i	0.292964	−	0.827732i
$256$	16.0000			0.0625000
$257$	−266.743	+	266.743i	−1.03791	+	1.03791i	−0.0386594	+	0.999252i	$0.512309\pi$
$257$	−266.743	+	266.743i	−1.03791	+	1.03791i	−0.999252	+	0.0386594i	$0.987691\pi$
$258$	−88.4877	−	88.4877i	−0.342975	−	0.342975i
$259$		−	4.62479i		−	0.0178563i
$260$	−14.9169	−	31.2608i	−0.0573725	−	0.120234i
$261$	−12.5565			−0.0481092
$262$	220.554	−	220.554i	0.841808	−	0.841808i
$263$	−77.4514	−	77.4514i	−0.294492	−	0.294492i	0.544360	−	0.838852i	$-0.316773\pi$
$263$	−77.4514	−	77.4514i	−0.294492	−	0.294492i	−0.838852	+	0.544360i	$0.816773\pi$
$264$		−	24.6701i		−	0.0934472i
$265$	−241.855	+	115.407i	−0.912661	+	0.435499i
$266$	−35.7871			−0.134538
$267$	−20.3301	+	20.3301i	−0.0761427	+	0.0761427i
$268$	−60.9737	−	60.9737i	−0.227514	−	0.227514i
$269$		−	51.5262i		−	0.191547i	−0.995403	−	0.0957737i	$-0.969467\pi$
$269$		−	51.5262i		−	0.191547i	0.995403	−	0.0957737i	$-0.0305325\pi$
$270$	34.6369	+	12.2592i	0.128285	+	0.0454045i
$271$	143.162			0.528273			0.264137	−	0.964485i	$-0.414913\pi$
$271$	143.162			0.528273			0.264137	+	0.964485i	$0.414913\pi$
$272$	73.1262	−	73.1262i	0.268846	−	0.268846i
$273$	11.2238	+	11.2238i	0.0411128	+	0.0411128i
$274$		−	232.078i		−	0.846999i
$275$	97.8637	+	79.1958i	0.355868	+	0.287985i
$276$	80.4688			0.291553
$277$	−66.2523	+	66.2523i	−0.239178	+	0.239178i	−0.816510	−	0.577332i	$-0.804094\pi$
$277$	−66.2523	+	66.2523i	−0.239178	+	0.239178i	0.577332	+	0.816510i	$0.304094\pi$
$278$	−270.544	−	270.544i	−0.973180	−	0.973180i
$279$		−	165.423i		−	0.592913i
$280$	12.4842	−	35.2724i	0.0445864	−	0.125973i
$281$	484.413			1.72389			0.861945	−	0.507002i	$-0.169246\pi$
$281$	484.413			1.72389			0.861945	+	0.507002i	$0.169246\pi$
$282$	−45.7851	+	45.7851i	−0.162359	+	0.162359i
$283$	248.349	+	248.349i	0.877559	+	0.877559i	0.993282	−	0.115723i	$-0.0369184\pi$
$283$	248.349	+	248.349i	0.877559	+	0.877559i	−0.115723	+	0.993282i	$0.536918\pi$
$284$		−	230.389i		−	0.811229i
$285$	35.6718	+	74.7562i	0.125164	+	0.262302i
$286$	−24.6675			−0.0862500
$287$	22.8561	−	22.8561i	0.0796381	−	0.0796381i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	379.430i		−	1.31290i
$290$	26.7108	−	12.7457i	0.0921063	−	0.0439508i
$291$	174.336			0.599091
$292$	109.741	−	109.741i	0.375826	−	0.375826i
$293$	−201.337	−	201.337i	−0.687158	−	0.687158i	0.274445	−	0.961603i	$-0.411506\pi$
$293$	−201.337	−	201.337i	−0.687158	−	0.687158i	−0.961603	+	0.274445i	$0.911506\pi$
$294$			17.1464i			0.0583212i
$295$	−338.187	−	119.696i	−1.14640	−	0.405750i
$296$	−4.94411			−0.0167031
$297$	18.5026	−	18.5026i	0.0622982	−	0.0622982i
$298$	101.794	+	101.794i	0.341592	+	0.341592i
$299$		−	80.4603i		−	0.269098i
$300$	−86.1252	+	9.08041i	−0.287084	+	0.0302680i
$301$	−135.167			−0.449060
$302$	−166.350	+	166.350i	−0.550826	+	0.550826i
$303$	−178.295	−	178.295i	−0.588432	−	0.588432i
$304$			38.2580i			0.125849i
$305$	−101.447	+	286.626i	−0.332614	+	0.939759i
$306$	109.689			0.358462
$307$	−2.87888	+	2.87888i	−0.00937745	+	0.00937745i	−0.711780	−	0.702403i	$-0.752111\pi$
$307$	−2.87888	+	2.87888i	−0.00937745	+	0.00937745i	0.702403	+	0.711780i	$0.252111\pi$
$308$	−18.8421	−	18.8421i	−0.0611756	−	0.0611756i
$309$			257.447i			0.833161i
$310$	167.916	+	351.896i	0.541664	+	1.13515i
$311$	−127.446			−0.409793			−0.204897	−	0.978784i	$-0.565686\pi$
$311$	−127.446			−0.409793			−0.204897	+	0.978784i	$0.565686\pi$
$312$	11.9987	−	11.9987i	0.0384575	−	0.0384575i
$313$	−73.9562	−	73.9562i	−0.236282	−	0.236282i	0.579027	−	0.815309i	$-0.303433\pi$
$313$	−73.9562	−	73.9562i	−0.236282	−	0.236282i	−0.815309	+	0.579027i	$0.803433\pi$
$314$		−	212.165i		−	0.675686i
$315$	35.8175	−	17.0912i	0.113706	−	0.0542578i
$316$	125.198			0.396197
$317$	377.411	−	377.411i	1.19057	−	1.19057i	0.213664	−	0.976907i	$-0.431460\pi$
$317$	377.411	−	377.411i	1.19057	−	1.19057i	0.976907	−	0.213664i	$-0.0685397\pi$
$318$	−92.8306	−	92.8306i	−0.291920	−	0.291920i
$319$		−	21.0772i		−	0.0660727i
$320$	−37.7078	−	13.3461i	−0.117837	−	0.0417067i
$321$	−111.739			−0.348097
$322$	61.4590	−	61.4590i	0.190867	−	0.190867i
$323$	174.854	+	174.854i	0.541343	+	0.541343i
$324$			18.0000i			0.0555556i
$325$	9.07946	+	86.1162i	0.0279368	+	0.264973i
$326$	−109.535			−0.335996
$327$	191.431	−	191.431i	0.585417	−	0.585417i
$328$	−24.4342	−	24.4342i	−0.0744947	−	0.0744947i
$329$			69.9379i			0.212577i
$330$	−20.5782	+	58.1409i	−0.0623580	+	0.176185i
$331$	−505.056			−1.52585			−0.762924	−	0.646488i	$-0.776237\pi$
$331$	−505.056			−1.52585			−0.762924	+	0.646488i	$0.776237\pi$
$332$	105.753	−	105.753i	0.318535	−	0.318535i
$333$	−3.70808	−	3.70808i	−0.0111354	−	0.0111354i
$334$			24.4966i			0.0733432i
$335$	92.8388	+	194.559i	0.277131	+	0.580774i
$336$	18.3303			0.0545545
$337$	−389.840	+	389.840i	−1.15680	+	1.15680i	−0.171635	+	0.985161i	$0.554905\pi$
$337$	−389.840	+	389.840i	−1.15680	+	1.15680i	−0.985161	+	0.171635i	$0.945095\pi$
$338$	157.003	+	157.003i	0.464504	+	0.464504i
$339$		−	191.900i		−	0.566076i
$340$	−233.336	+	111.342i	−0.686283	+	0.327477i
$341$	277.676			0.814300
$342$	−28.6935	+	28.6935i	−0.0838991	+	0.0838991i
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$			144.500i			0.420057i
$345$	−189.644	−	67.1218i	−0.549692	−	0.194556i
$346$	421.254			1.21750
$347$	−306.559	+	306.559i	−0.883456	+	0.883456i	−0.993884	−	0.110428i	$-0.964778\pi$
$347$	−306.559	+	306.559i	−0.883456	+	0.883456i	0.110428	+	0.993884i	$0.464778\pi$
$348$	10.2523	+	10.2523i	0.0294608	+	0.0294608i
$349$			509.585i			1.46013i	0.683379	+	0.730064i	$0.260510\pi$
$349$			509.585i			1.46013i	−0.683379	+	0.730064i	$0.739490\pi$
$350$	−58.8439	+	72.7145i	−0.168125	+	0.207756i
$351$	17.9981			0.0512767
$352$	−20.1430	+	20.1430i	−0.0572245	+	0.0572245i
$353$	330.387	+	330.387i	0.935941	+	0.935941i	0.998068	−	0.0621272i	$-0.0197884\pi$
$353$	330.387	+	330.387i	0.935941	+	0.935941i	−0.0621272	+	0.998068i	$0.519788\pi$
$354$		−	175.748i		−	0.496463i
$355$	−192.176	+	542.967i	−0.541340	+	1.52949i
$356$	33.1989			0.0932553
$357$	83.7765	−	83.7765i	0.234668	−	0.234668i
$358$	141.089	+	141.089i	0.394104	+	0.394104i
$359$		−	152.593i		−	0.425051i	−0.977155	−	0.212526i	$-0.931831\pi$
$359$		−	152.593i		−	0.425051i	0.977155	−	0.212526i	$-0.0681689\pi$
$360$	−18.2713	−	38.2905i	−0.0507535	−	0.106362i
$361$	269.520			0.746594
$362$	14.5190	−	14.5190i	0.0401077	−	0.0401077i
$363$	−117.136	−	117.136i	−0.322689	−	0.322689i
$364$		−	18.3284i		−	0.0503527i
$365$	−350.170	+	167.092i	−0.959370	+	0.457787i
$366$	−148.953			−0.406976
$367$	−105.176	+	105.176i	−0.286583	+	0.286583i	−0.835727	−	0.549145i	$-0.814954\pi$
$367$	−105.176	+	105.176i	−0.286583	+	0.286583i	0.549145	+	0.835727i	$0.314954\pi$
$368$	−65.7025	−	65.7025i	−0.178539	−	0.178539i
$369$		−	36.6514i		−	0.0993262i
$370$	11.6520	+	4.12405i	0.0314918	+	0.0111461i
$371$	−141.801			−0.382213
$372$	−135.067	+	135.067i	−0.363084	+	0.363084i
$373$	−304.851	−	304.851i	−0.817294	−	0.817294i	0.168421	−	0.985715i	$-0.446133\pi$
$373$	−304.851	−	304.851i	−0.817294	−	0.817294i	−0.985715	+	0.168421i	$0.946133\pi$
$374$			184.123i			0.492307i
$375$	210.549	+	50.4398i	0.561464	+	0.134506i
$376$	74.7668			0.198848
$377$	10.2513	−	10.2513i	0.0271917	−	0.0271917i
$378$	13.7477	+	13.7477i	0.0363696	+	0.0363696i
$379$		−	157.708i		−	0.416117i	−0.978116	−	0.208059i	$-0.933286\pi$
$379$		−	157.708i		−	0.416117i	0.978116	−	0.208059i	$-0.0667145\pi$
$380$	31.9123	−	90.1641i	0.0839797	−	0.237274i
$381$	208.197			0.546448
$382$	−336.312	+	336.312i	−0.880398	+	0.880398i
$383$	−429.631	−	429.631i	−1.12175	−	1.12175i	−0.991478	−	0.130275i	$-0.958414\pi$
$383$	−429.631	−	429.631i	−1.12175	−	1.12175i	−0.130275	−	0.991478i	$-0.541586\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	28.6890	+	60.1227i	0.0745170	+	0.156163i
$386$	−31.5169			−0.0816500
$387$	−108.375	+	108.375i	−0.280038	+	0.280038i
$388$	−142.344	−	142.344i	−0.366867	−	0.366867i
$389$		−	168.931i		−	0.434269i	−0.976142	−	0.217135i	$-0.930329\pi$
$389$		−	168.931i		−	0.434269i	0.976142	−	0.217135i	$-0.0696711\pi$
$390$	−38.2865	+	18.2693i	−0.0981704	+	0.0468445i
$391$	−600.571			−1.53599
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$	−270.122	−	270.122i	−0.687334	−	0.687334i
$394$		−	320.416i		−	0.813239i
$395$	−295.060	−	104.432i	−0.746987	−	0.264385i
$396$	−30.2145			−0.0762994
$397$	514.413	−	514.413i	1.29575	−	1.29575i	0.364579	−	0.931172i	$-0.381213\pi$
$397$	514.413	−	514.413i	1.29575	−	1.29575i	0.931172	−	0.364579i	$-0.118787\pi$
$398$	161.286	+	161.286i	0.405242	+	0.405242i
$399$			43.8300i			0.109850i
$400$	77.7350	+	62.9068i	0.194338	+	0.157267i
$401$	542.884			1.35383			0.676913	−	0.736063i	$-0.263317\pi$
$401$	542.884			1.35383			0.676913	+	0.736063i	$0.263317\pi$
$402$	−74.6772	+	74.6772i	−0.185764	+	0.185764i
$403$	135.053	+	135.053i	0.335119	+	0.335119i
$404$			291.154i			0.720679i
$405$	15.0144	−	42.4213i	0.0370726	−	0.104744i
$406$	15.6607			0.0385732
$407$	6.22434	−	6.22434i	0.0152932	−	0.0152932i
$408$	−89.5609	−	89.5609i	−0.219512	−	0.219512i
$409$		−	454.920i		−	1.11227i	−0.831091	−	0.556137i	$-0.812283\pi$
$409$		−	454.920i		−	1.11227i	0.831091	−	0.556137i	$-0.187717\pi$
$410$	37.2037	+	77.9666i	0.0907408	+	0.190162i
$411$	−284.236			−0.691572
$412$	210.204	−	210.204i	0.510205	−	0.510205i
$413$	−134.230	−	134.230i	−0.325012	−	0.325012i
$414$		−	98.5537i		−	0.238052i
$415$	−337.446	+	161.021i	−0.813123	+	0.388002i
$416$	−19.5939			−0.0471006
$417$	−331.347	+	331.347i	−0.794598	+	0.794598i
$418$	−48.1645	−	48.1645i	−0.115226	−	0.115226i
$419$			597.925i			1.42703i	0.700641	+	0.713514i	$0.252898\pi$
$419$			597.925i			1.42703i	−0.700641	+	0.713514i	$0.747102\pi$
$420$	−43.1997	−	15.2899i	−0.102857	−	0.0364046i
$421$	−607.858			−1.44384			−0.721921	−	0.691975i	$-0.756741\pi$
$421$	−607.858			−1.44384			−0.721921	+	0.691975i	$0.756741\pi$
$422$	76.5522	−	76.5522i	0.181403	−	0.181403i
$423$	56.0751	+	56.0751i	0.132565	+	0.132565i
$424$			151.592i			0.357528i
$425$	642.787	−	67.7708i	1.51244	−	0.159461i
$426$	−282.168			−0.662366
$427$	−113.765	+	113.765i	−0.266429	+	0.266429i
$428$	91.2347	+	91.2347i	0.213165	+	0.213165i
$429$			30.2114i			0.0704228i
$430$	120.532	−	340.548i	0.280307	−	0.791973i
$431$	291.207			0.675655			0.337827	−	0.941208i	$-0.390308\pi$
$431$	291.207			0.675655			0.337827	+	0.941208i	$0.390308\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	−47.9051	−	47.9051i	−0.110635	−	0.110635i	0.649622	−	0.760257i	$-0.274927\pi$
$433$	−47.9051	−	47.9051i	−0.110635	−	0.110635i	−0.760257	+	0.649622i	$0.774927\pi$
$434$			206.319i			0.475388i
$435$	−15.6103	−	32.7140i	−0.0358857	−	0.0752045i
$436$	−312.606			−0.716987
$437$	157.103	−	157.103i	0.359503	−	0.359503i
$438$	−134.405	−	134.405i	−0.306860	−	0.306860i
$439$		−	652.062i		−	1.48533i	−0.669660	−	0.742667i	$-0.733560\pi$
$439$		−	652.062i		−	1.48533i	0.669660	−	0.742667i	$-0.266440\pi$
$440$	64.2739	−	30.6699i	0.146077	−	0.0697043i
$441$	21.0000			0.0476190
$442$	−89.5515	+	89.5515i	−0.202605	+	0.202605i
$443$	−146.273	−	146.273i	−0.330187	−	0.330187i	0.522470	−	0.852657i	$-0.325011\pi$
$443$	−146.273	−	146.273i	−0.330187	−	0.330187i	−0.852657	+	0.522470i	$0.825011\pi$
$444$			6.05527i			0.0136380i
$445$	−78.2411	−	27.6923i	−0.175823	−	0.0622300i
$446$	−494.273			−1.10823
$447$	124.672	−	124.672i	0.278909	−	0.278909i
$448$	−14.9666	−	14.9666i	−0.0334077	−	0.0334077i
$449$			213.815i			0.476203i	0.971240	+	0.238101i	$0.0765251\pi$
$449$			213.815i			0.476203i	−0.971240	+	0.238101i	$0.923475\pi$
$450$	11.1212	+	105.481i	0.0247137	+	0.234403i
$451$	61.5225			0.136413
$452$	−156.686	+	156.686i	−0.346650	+	0.346650i
$453$	203.736	+	203.736i	0.449748	+	0.449748i
$454$		−	391.984i		−	0.863402i
$455$	−15.2883	+	43.1952i	−0.0336007	+	0.0949345i
$456$	46.8562			0.102755
$457$	339.531	−	339.531i	0.742956	−	0.742956i	−0.230189	−	0.973146i	$-0.573935\pi$
$457$	339.531	−	339.531i	0.742956	−	0.742956i	0.973146	+	0.230189i	$0.0739346\pi$
$458$	70.9486	+	70.9486i	0.154910	+	0.154910i
$459$		−	134.341i		−	0.292683i
$460$	100.039	+	209.648i	0.217476	+	0.455757i
$461$	580.456			1.25912			0.629562	−	0.776951i	$-0.283235\pi$
$461$	580.456			1.25912			0.629562	+	0.776951i	$0.283235\pi$
$462$	−23.0767	+	23.0767i	−0.0499497	+	0.0499497i
$463$	551.037	+	551.037i	1.19014	+	1.19014i	0.977026	+	0.213119i	$0.0683621\pi$
$463$	551.037	+	551.037i	1.19014	+	1.19014i	0.213119	+	0.977026i	$0.431638\pi$
$464$		−	16.7420i		−	0.0360819i
$465$	430.982	−	205.654i	0.926844	−	0.442267i
$466$	27.0239			0.0579912
$467$	293.344	−	293.344i	0.628145	−	0.628145i	−0.319456	−	0.947601i	$-0.603500\pi$
$467$	293.344	−	293.344i	0.628145	−	0.628145i	0.947601	+	0.319456i	$0.103500\pi$
$468$	−14.6954	−	14.6954i	−0.0314004	−	0.0314004i
$469$			114.071i			0.243222i
$470$	−176.206	−	62.3655i	−0.374906	−	0.132693i
$471$	−259.848			−0.551695
$472$	−143.498	+	143.498i	−0.304021	+	0.304021i
$473$	−181.916	−	181.916i	−0.384601	−	0.384601i
$474$		−	153.336i		−	0.323494i
$475$	−150.418	+	185.874i	−0.316669	+	0.391314i
$476$	−136.807			−0.287409
$477$	−113.694	+	113.694i	−0.238352	+	0.238352i
$478$	157.888	+	157.888i	0.330309	+	0.330309i
$479$		−	694.462i		−	1.44982i	−0.688846	−	0.724908i	$-0.741882\pi$
$479$		−	694.462i		−	1.44982i	0.688846	−	0.724908i	$-0.258118\pi$
$480$	−16.3456	+	46.1825i	−0.0340534	+	0.0962135i
$481$	6.05464			0.0125876
$482$	−142.701	+	142.701i	−0.296060	+	0.296060i
$483$	−75.2716	−	75.2716i	−0.155842	−	0.155842i
$484$			191.282i			0.395211i
$485$	216.734	+	454.203i	0.446875	+	0.936501i
$486$	22.0454			0.0453609
$487$	189.085	−	189.085i	0.388266	−	0.388266i	−0.485803	−	0.874068i	$-0.661473\pi$
$487$	189.085	−	189.085i	0.388266	−	0.388266i	0.874068	+	0.485803i	$0.161473\pi$
$488$	121.620	+	121.620i	0.249221	+	0.249221i
$489$			134.152i			0.274340i
$490$	−44.6722	+	21.3165i	−0.0911678	+	0.0435030i
$491$	587.867			1.19729			0.598643	−	0.801016i	$-0.295707\pi$
$491$	587.867			1.19729			0.598643	+	0.801016i	$0.295707\pi$
$492$	−29.9257	+	29.9257i	−0.0608246	+	0.0608246i
$493$	−76.5175	−	76.5175i	−0.155208	−	0.155208i
$494$		−	46.8513i		−	0.0948408i
$495$	71.2078	+	25.2030i	0.143854	+	0.0509151i
$496$	220.564			0.444685
$497$	−215.509	+	215.509i	−0.433620	+	0.433620i
$498$	−129.521	−	129.521i	−0.260082	−	0.260082i
$499$			13.5102i			0.0270745i	0.999908	+	0.0135373i	$0.00430918\pi$
$499$			13.5102i			0.0270745i	−0.999908	+	0.0135373i	$0.995691\pi$
$500$	−130.728	−	213.096i	−0.261457	−	0.426193i
$501$	30.0021			0.0598845
$502$	−81.9263	+	81.9263i	−0.163200	+	0.163200i
$503$	231.640	+	231.640i	0.460516	+	0.460516i	0.898825	−	0.438309i	$-0.144422\pi$
$503$	231.640	+	231.640i	0.460516	+	0.460516i	−0.438309	+	0.898825i	$0.644422\pi$
$504$		−	22.4499i		−	0.0445435i
$505$	242.862	−	686.175i	0.480914	−	1.35876i
$506$	165.431			0.326938
$507$	192.288	−	192.288i	0.379266	−	0.379266i
$508$	−169.992	−	169.992i	−0.334630	−	0.334630i
$509$			737.211i			1.44835i	0.689616	+	0.724176i	$0.257780\pi$
$509$			737.211i			1.44835i	−0.689616	+	0.724176i	$0.742220\pi$
$510$	136.366	+	285.778i	0.267384	+	0.560348i
$511$	−205.307			−0.401775
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	35.1422	+	35.1422i	0.0685033	+	0.0685033i
$514$		−	533.487i		−	1.03791i
$515$	−670.736	+	320.058i	−1.30240	+	0.621472i
$516$	176.975			0.342975
$517$	−94.1268	+	94.1268i	−0.182063	+	0.182063i
$518$	4.62479	+	4.62479i	0.00892817	+	0.00892817i
$519$		−	515.929i		−	0.994083i
$520$	46.1776	+	16.3439i	0.0888031	+	0.0314306i
$521$	209.021			0.401191			0.200596	−	0.979674i	$-0.435712\pi$
$521$	209.021			0.401191			0.200596	+	0.979674i	$0.435712\pi$
$522$	12.5565	−	12.5565i	0.0240546	−	0.0240546i
$523$	99.0847	+	99.0847i	0.189455	+	0.189455i	0.795460	−	0.606006i	$-0.207229\pi$
$523$	99.0847	+	99.0847i	0.189455	+	0.189455i	−0.606006	+	0.795460i	$0.707229\pi$
$524$			441.108i			0.841808i
$525$	89.0567	+	72.0688i	0.169632	+	0.137274i
$526$	154.903			0.294492
$527$	1008.06	−	1008.06i	1.91283	−	1.91283i
$528$	24.6701	+	24.6701i	0.0467236	+	0.0467236i
$529$			10.6017i			0.0200410i
$530$	126.448	−	357.262i	0.238581	−	0.674080i
$531$	−215.247			−0.405361
$532$	35.7871	−	35.7871i	0.0672689	−	0.0672689i
$533$	29.9226	+	29.9226i	0.0561399	+	0.0561399i
$534$		−	40.6602i		−	0.0761427i
$535$	−138.914	−	291.118i	−0.259653	−	0.544147i
$536$	121.947			0.227514
$537$	172.798	−	172.798i	0.321784	−	0.321784i
$538$	51.5262	+	51.5262i	0.0957737	+	0.0957737i
$539$			35.2503i			0.0653994i
$540$	−46.8961	+	22.3776i	−0.0868446	+	0.0414401i
$541$	599.763			1.10862			0.554310	−	0.832311i	$-0.312982\pi$
$541$	599.763			1.10862			0.554310	+	0.832311i	$0.312982\pi$
$542$	−143.162	+	143.162i	−0.264137	+	0.264137i
$543$	−17.7820	−	17.7820i	−0.0327478	−	0.0327478i
$544$			146.252i			0.268846i
$545$	736.731	+	260.756i	1.35180	+	0.478451i
$546$	−22.4476			−0.0411128
$547$	−332.261	+	332.261i	−0.607424	+	0.607424i	−0.942272	−	0.334848i	$-0.891315\pi$
$547$	−332.261	+	332.261i	−0.607424	+	0.607424i	0.334848	+	0.942272i	$0.391315\pi$
$548$	232.078	+	232.078i	0.423499	+	0.423499i
$549$			182.430i			0.332295i
$550$	−177.060	+	18.6679i	−0.321926	+	0.0339416i
$551$	40.0322			0.0726538
$552$	−80.4688	+	80.4688i	−0.145777	+	0.145777i
$553$	−117.112	−	117.112i	−0.211776	−	0.211776i
$554$		−	132.505i		−	0.239178i
$555$	5.05091	−	14.2707i	0.00910074	−	0.0257130i
$556$	541.088			0.973180
$557$	−624.562	+	624.562i	−1.12130	+	1.12130i	−0.129750	+	0.991547i	$0.541417\pi$
$557$	−624.562	+	624.562i	−1.12130	+	1.12130i	−0.991547	+	0.129750i	$0.958583\pi$
$558$	165.423	+	165.423i	0.296457	+	0.296457i
$559$		−	176.957i		−	0.316560i
$560$	22.7883	+	47.7566i	0.0406933	+	0.0852797i
$561$	225.503			0.401967
$562$	−484.413	+	484.413i	−0.861945	+	0.861945i
$563$	−385.579	−	385.579i	−0.684865	−	0.684865i	0.276228	−	0.961092i	$-0.410916\pi$
$563$	−385.579	−	385.579i	−0.684865	−	0.684865i	−0.961092	+	0.276228i	$0.910916\pi$
$564$		−	91.5702i		−	0.162359i
$565$	499.964	−	238.570i	0.884892	−	0.422248i
$566$	−496.698			−0.877559
$567$	16.8375	−	16.8375i	0.0296957	−	0.0296957i
$568$	230.389	+	230.389i	0.405615	+	0.405615i
$569$			578.028i			1.01587i	0.861397	+	0.507933i	$0.169590\pi$
$569$			578.028i			1.01587i	−0.861397	+	0.507933i	$0.830410\pi$
$570$	−110.428	−	39.0844i	−0.193733	−	0.0685691i
$571$	−14.7710			−0.0258687			−0.0129344	−	0.999916i	$-0.504117\pi$
$571$	−14.7710			−0.0258687			−0.0129344	+	0.999916i	$0.504117\pi$
$572$	24.6675	−	24.6675i	0.0431250	−	0.0431250i
$573$	411.897	+	411.897i	0.718842	+	0.718842i
$574$			45.7123i			0.0796381i
$575$	−60.8908	−	577.532i	−0.105897	−	1.00440i
$576$	−24.0000			−0.0416667
$577$	359.827	−	359.827i	0.623617	−	0.623617i	−0.322838	−	0.946454i	$-0.604637\pi$
$577$	359.827	−	359.827i	0.623617	−	0.623617i	0.946454	+	0.322838i	$0.104637\pi$
$578$	379.430	+	379.430i	0.656452	+	0.656452i
$579$			38.6002i			0.0666670i
$580$	−13.9651	+	39.4566i	−0.0240777	+	0.0680286i
$581$	−197.847			−0.340528
$582$	−174.336	+	174.336i	−0.299546	+	0.299546i
$583$	−190.845	−	190.845i	−0.327350	−	0.327350i
$584$			219.482i			0.375826i
$585$	22.3753	+	46.8912i	0.0382484	+	0.0801558i
$586$	402.675			0.687158
$587$	628.762	−	628.762i	1.07115	−	1.07115i	0.0738780	−	0.997267i	$-0.476462\pi$
$587$	628.762	−	628.762i	1.07115	−	1.07115i	0.997267	−	0.0738780i	$-0.0235375\pi$
$588$	−17.1464	−	17.1464i	−0.0291606	−	0.0291606i
$589$			527.395i			0.895408i
$590$	457.883	−	218.490i	0.776073	−	0.370322i
$591$	−392.428			−0.664007
$592$	4.94411	−	4.94411i	0.00835154	−	0.00835154i
$593$	−221.183	−	221.183i	−0.372991	−	0.372991i	0.495575	−	0.868565i	$-0.334957\pi$
$593$	−221.183	−	221.183i	−0.372991	−	0.372991i	−0.868565	+	0.495575i	$0.834957\pi$
$594$			37.0051i			0.0622982i
$595$	322.417	+	114.115i	0.541878	+	0.191790i
$596$	−203.589			−0.341592
$597$	197.534	−	197.534i	0.330878	−	0.330878i
$598$	80.4603	+	80.4603i	0.134549	+	0.134549i
$599$			227.599i			0.379966i	0.981787	+	0.189983i	$0.0608432\pi$
$599$			227.599i			0.379966i	−0.981787	+	0.189983i	$0.939157\pi$
$600$	77.0448	−	95.2056i	0.128408	−	0.158676i
$601$	−772.444			−1.28527			−0.642633	−	0.766175i	$-0.722158\pi$
$601$	−772.444			−1.28527			−0.642633	+	0.766175i	$0.722158\pi$
$602$	135.167	−	135.167i	0.224530	−	0.224530i
$603$	91.4605	+	91.4605i	0.151676	+	0.151676i
$604$		−	332.699i		−	0.550826i
$605$	159.555	−	450.802i	0.263727	−	0.745128i
$606$	356.590			0.588432
$607$	−145.543	+	145.543i	−0.239774	+	0.239774i	−0.816757	−	0.576982i	$-0.804230\pi$
$607$	−145.543	+	145.543i	−0.239774	+	0.239774i	0.576982	+	0.816757i	$0.304230\pi$
$608$	−38.2580	−	38.2580i	−0.0629243	−	0.0629243i
$609$		−	19.1804i		−	0.0314949i
$610$	−185.179	−	388.074i	−0.303572	−	0.636187i
$611$	−91.5606			−0.149854
$612$	−109.689	+	109.689i	−0.179231	+	0.179231i
$613$	−443.832	−	443.832i	−0.724033	−	0.724033i	0.245391	−	0.969424i	$-0.421084\pi$
$613$	−443.832	−	443.832i	−0.724033	−	0.724033i	−0.969424	+	0.245391i	$0.921084\pi$
$614$		−	5.75775i		−	0.00937745i
$615$	95.4892	−	45.5651i	0.155267	−	0.0740895i
$616$	37.6842			0.0611756
$617$	−490.933	+	490.933i	−0.795678	+	0.795678i	−0.982411	−	0.186733i	$-0.940210\pi$
$617$	−490.933	+	490.933i	−0.795678	+	0.795678i	0.186733	+	0.982411i	$0.440210\pi$
$618$	−257.447	−	257.447i	−0.416580	−	0.416580i
$619$			570.340i			0.921390i	0.887559	+	0.460695i	$0.152400\pi$
$619$			570.340i			0.921390i	−0.887559	+	0.460695i	$0.847600\pi$
$620$	−519.811	−	183.980i	−0.838405	−	0.296742i
$621$	−120.703			−0.194369
$622$	127.446	−	127.446i	0.204897	−	0.204897i
$623$	−31.0547	−	31.0547i	−0.0498471	−	0.0498471i
$624$			23.9975i			0.0384575i
$625$	130.342	+	611.258i	0.208547	+	0.978012i
$626$	147.912			0.236282
$627$	−58.9892	+	58.9892i	−0.0940816	+	0.0940816i
$628$	212.165	+	212.165i	0.337843	+	0.337843i
$629$		−	45.1930i		−	0.0718489i
$630$	−18.7263	+	52.9087i	−0.0297242	+	0.0839820i
$631$	471.145			0.746665			0.373332	−	0.927698i	$-0.378215\pi$
$631$	471.145			0.746665			0.373332	+	0.927698i	$0.378215\pi$
$632$	−125.198	+	125.198i	−0.198099	+	0.198099i
$633$	−93.7569	−	93.7569i	−0.148115	−	0.148115i
$634$			754.822i			1.19057i
$635$	258.831	+	542.423i	0.407607	+	0.854209i
$636$	185.661			0.291920
$637$	−17.1446	+	17.1446i	−0.0269147	+	0.0269147i
$638$	21.0772	+	21.0772i	0.0330363	+	0.0330363i
$639$			345.584i			0.540820i
$640$	51.0540	−	24.3617i	0.0797718	−	0.0380651i
$641$	−684.550			−1.06794			−0.533971	−	0.845503i	$-0.679301\pi$
$641$	−684.550			−1.06794			−0.533971	+	0.845503i	$0.679301\pi$
$642$	111.739	−	111.739i	0.174049	−	0.174049i
$643$	−521.636	−	521.636i	−0.811253	−	0.811253i	0.173569	−	0.984822i	$-0.444470\pi$
$643$	−521.636	−	521.636i	−0.811253	−	0.811253i	−0.984822	+	0.173569i	$0.944470\pi$
$644$			122.918i			0.190867i
$645$	−417.085	−	147.621i	−0.646643	−	0.228870i
$646$	−349.707			−0.541343
$647$	−72.9658	+	72.9658i	−0.112776	+	0.112776i	−0.761243	−	0.648467i	$-0.775410\pi$
$647$	−72.9658	+	72.9658i	−0.112776	+	0.112776i	0.648467	+	0.761243i	$0.275410\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	361.310i		−	0.556718i
$650$	−95.1956	−	77.0367i	−0.146455	−	0.118518i
$651$	252.688			0.388153
$652$	109.535	−	109.535i	0.167998	−	0.167998i
$653$	334.041	+	334.041i	0.511549	+	0.511549i	0.915001	−	0.403452i	$-0.132190\pi$
$653$	334.041	+	334.041i	0.511549	+	0.511549i	−0.403452	+	0.915001i	$0.632190\pi$
$654$			382.863i			0.585417i
$655$	367.943	−	1039.58i	0.561745	−	1.58714i
$656$	48.8685			0.0744947
$657$	−164.612	+	164.612i	−0.250550	+	0.250550i
$658$	−69.9379	−	69.9379i	−0.106289	−	0.106289i
$659$		−	177.497i		−	0.269343i	−0.990890	−	0.134672i	$-0.957002\pi$
$659$		−	177.497i		−	0.269343i	0.990890	−	0.134672i	$-0.0429980\pi$
$660$	−37.5628	−	78.7191i	−0.0569133	−	0.119271i
$661$	917.415			1.38792			0.693960	−	0.720013i	$-0.255864\pi$
$661$	917.415			1.38792			0.693960	+	0.720013i	$0.255864\pi$
$662$	505.056	−	505.056i	0.762924	−	0.762924i
$663$	109.678	+	109.678i	0.165426	+	0.165426i
$664$			211.507i			0.318535i
$665$	−114.192	+	54.4895i	−0.171717	+	0.0819392i
$666$	7.41617			0.0111354
$667$	−68.7495	+	68.7495i	−0.103073	+	0.103073i
$668$	−24.4966	−	24.4966i	−0.0366716	−	0.0366716i
$669$			605.358i			0.904870i
$670$	−287.398	−	101.720i	−0.428952	−	0.151822i
$671$	−306.224			−0.456370
$672$	−18.3303	+	18.3303i	−0.0272772	+	0.0272772i
$673$	725.252	+	725.252i	1.07764	+	1.07764i	0.996721	+	0.0809191i	$0.0257855\pi$
$673$	725.252	+	725.252i	1.07764	+	1.07764i	0.0809191	+	0.996721i	$0.474214\pi$
$674$		−	779.680i		−	1.15680i
$675$	129.188	−	13.6206i	0.191389	−	0.0201787i
$676$	−314.005			−0.464504
$677$	−378.779	+	378.779i	−0.559496	+	0.559496i	−0.929164	−	0.369668i	$-0.879472\pi$
$677$	−378.779	+	378.779i	−0.559496	+	0.559496i	0.369668	+	0.929164i	$0.379472\pi$
$678$	191.900	+	191.900i	0.283038	+	0.283038i
$679$			266.302i			0.392197i
$680$	121.994	−	344.679i	0.179403	−	0.506880i
$681$	−480.081			−0.704965
$682$	−277.676	+	277.676i	−0.407150	+	0.407150i
$683$	19.0537	+	19.0537i	0.0278971	+	0.0278971i	0.720918	−	0.693021i	$-0.243721\pi$
$683$	19.0537	+	19.0537i	0.0278971	+	0.0278971i	−0.693021	+	0.720918i	$0.743721\pi$
$684$		−	57.3870i		−	0.0838991i
$685$	−353.363	−	740.530i	−0.515858	−	1.08107i
$686$	−26.1916			−0.0381802
$687$	86.8939	−	86.8939i	0.126483	−	0.126483i
$688$	−144.500	−	144.500i	−0.210029	−	0.210029i
$689$		−	185.642i		−	0.269437i
$690$	256.766	−	122.522i	0.372124	−	0.177568i
$691$	−1010.25			−1.46202			−0.731008	−	0.682369i	$-0.760950\pi$
$691$	−1010.25			−1.46202			−0.731008	+	0.682369i	$0.760950\pi$
$692$	−421.254	+	421.254i	−0.608749	+	0.608749i
$693$	28.2631	+	28.2631i	0.0407837	+	0.0407837i
$694$		−	613.118i		−	0.883456i
$695$	−1275.20	−	451.340i	−1.83482	−	0.649410i
$696$	−20.5047			−0.0294608
$697$	223.348	−	223.348i	0.320442	−	0.320442i
$698$	−509.585	−	509.585i	−0.730064	−	0.730064i
$699$		−	33.0974i		−	0.0473496i
$700$	−13.8706	−	131.558i	−0.0198151	−	0.187941i
$701$	80.0820			0.114240			0.0571198	−	0.998367i	$-0.481808\pi$
$701$	80.0820			0.114240			0.0571198	+	0.998367i	$0.481808\pi$
$702$	−17.9981	+	17.9981i	−0.0256383	+	0.0256383i
$703$	11.8220	+	11.8220i	0.0168165	+	0.0168165i
$704$		−	40.2861i		−	0.0572245i
$705$	−76.3819	+	215.807i	−0.108343	+	0.306109i
$706$	−660.774			−0.935941
$707$	272.350	−	272.350i	0.385219	−	0.385219i
$708$	175.748	+	175.748i	0.248232	+	0.248232i
$709$			1012.82i			1.42852i	0.699879	+	0.714261i	$0.253237\pi$
$709$			1012.82i			1.42852i	−0.699879	+	0.714261i	$0.746763\pi$
$710$	−350.792	−	735.143i	−0.494073	−	1.03541i
$711$	−187.797			−0.264131
$712$	−33.1989	+	33.1989i	−0.0466277	+	0.0466277i
$713$	−905.724	−	905.724i	−1.27030	−	1.27030i
$714$			167.553i			0.234668i
$715$	−78.7108	+	37.5588i	−0.110085	+	0.0525298i
$716$	−282.178			−0.394104
$717$	193.372	−	193.372i	0.269696	−	0.269696i
$718$	152.593	+	152.593i	0.212526	+	0.212526i
$719$			289.247i			0.402290i	0.979561	+	0.201145i	$0.0644663\pi$
$719$			289.247i			0.402290i	−0.979561	+	0.201145i	$0.935534\pi$
$720$	56.5617	+	20.0192i	0.0785580	+	0.0278045i
$721$	−393.256			−0.545432
$722$	−269.520	+	269.520i	−0.373297	+	0.373297i
$723$	174.772	+	174.772i	0.241732	+	0.241732i
$724$			29.0379i			0.0401077i
$725$	65.8242	−	81.3401i	0.0907919	−	0.112193i
$726$	234.272			0.322689
$727$	444.891	−	444.891i	0.611954	−	0.611954i	−0.331501	−	0.943455i	$-0.607555\pi$
$727$	444.891	−	444.891i	0.611954	−	0.611954i	0.943455	+	0.331501i	$0.107555\pi$
$728$	18.3284	+	18.3284i	0.0251764	+	0.0251764i
$729$		−	27.0000i		−	0.0370370i
$730$	183.078	−	517.262i	0.250791	−	0.708578i
$731$	−1320.84			−1.80689
$732$	148.953	−	148.953i	0.203488	−	0.203488i
$733$	−169.024	−	169.024i	−0.230592	−	0.230592i	0.582348	−	0.812940i	$-0.302134\pi$
$733$	−169.024	−	169.024i	−0.230592	−	0.230592i	−0.812940	+	0.582348i	$0.802134\pi$
$734$		−	210.352i		−	0.286583i
$735$	26.1072	+	54.7121i	0.0355200	+	0.0744382i
$736$	131.405			0.178539
$737$	−153.524	+	153.524i	−0.208310	+	0.208310i
$738$	36.6514	+	36.6514i	0.0496631	+	0.0496631i
$739$			153.342i			0.207499i	0.994603	+	0.103749i	$0.0330840\pi$
$739$			153.342i			0.207499i	−0.994603	+	0.103749i	$0.966916\pi$
$740$	−15.7760	+	7.52793i	−0.0213190	+	0.0101729i
$741$	−57.3809			−0.0774372
$742$	141.801	−	141.801i	0.191107	−	0.191107i
$743$	−402.717	−	402.717i	−0.542015	−	0.542015i	0.382104	−	0.924119i	$-0.375200\pi$
$743$	−402.717	−	402.717i	−0.542015	−	0.542015i	−0.924119	+	0.382104i	$0.875200\pi$
$744$		−	270.134i		−	0.363084i
$745$	479.806	+	169.821i	0.644035	+	0.227947i
$746$	609.701			0.817294
$747$	−158.630	+	158.630i	−0.212356	+	0.212356i
$748$	−184.123	−	184.123i	−0.246153	−	0.246153i
$749$		−	170.684i		−	0.227883i
$750$	−260.989	+	160.109i	−0.347985	+	0.213479i
$751$	−549.263			−0.731376			−0.365688	−	0.930738i	$-0.619166\pi$
$751$	−549.263			−0.731376			−0.365688	+	0.930738i	$0.619166\pi$
$752$	−74.7668	+	74.7668i	−0.0994239	+	0.0994239i
$753$	100.339	+	100.339i	0.133252	+	0.133252i
$754$			20.5026i			0.0271917i
$755$	−277.516	+	784.085i	−0.367571	+	1.03852i
$756$	−27.4955			−0.0363696
$757$	−838.559	+	838.559i	−1.10774	+	1.10774i	−0.114292	+	0.993447i	$0.536460\pi$
$757$	−838.559	+	838.559i	−1.10774	+	1.10774i	−0.993447	+	0.114292i	$0.963540\pi$
$758$	157.708	+	157.708i	0.208059	+	0.208059i
$759$		−	202.611i		−	0.266944i
$760$	58.2518	+	122.076i	0.0766471	+	0.160627i
$761$	−1207.74			−1.58705			−0.793524	−	0.608538i	$-0.791756\pi$
$761$	−1207.74			−1.58705			−0.793524	+	0.608538i	$0.791756\pi$
$762$	−208.197	+	208.197i	−0.273224	+	0.273224i
$763$	292.416	+	292.416i	0.383246	+	0.383246i
$764$		−	672.624i		−	0.880398i
$765$	350.005	−	167.013i	0.457522	−	0.218318i
$766$	859.263			1.12175
$767$	175.730	−	175.730i	0.229113	−	0.229113i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$			1284.27i			1.67006i	0.550206	+	0.835029i	$0.314549\pi$
$769$			1284.27i			1.67006i	−0.550206	+	0.835029i	$0.685451\pi$
$770$	−88.8117	−	31.4336i	−0.115340	−	0.0408229i
$771$	−653.385			−0.847451
$772$	31.5169	−	31.5169i	0.0408250	−	0.0408250i
$773$	321.946	+	321.946i	0.416489	+	0.416489i	0.883992	−	0.467503i	$-0.154846\pi$
$773$	321.946	+	321.946i	0.416489	+	0.416489i	−0.467503	+	0.883992i	$0.654846\pi$
$774$		−	216.750i		−	0.280038i
$775$	1071.60	+	867.185i	1.38270	+	1.11895i
$776$	284.689			0.366867
$777$	5.66419	−	5.66419i	0.00728982	−	0.00728982i
$778$	168.931	+	168.931i	0.217135	+	0.217135i
$779$			116.851i			0.150001i
$780$	20.0171	−	56.5558i	0.0256630	−	0.0725075i
$781$	−580.092			−0.742755
$782$	600.571	−	600.571i	0.767994	−	0.767994i
$783$	−15.3785	−	15.3785i	−0.0196405	−	0.0196405i
$784$			28.0000i			0.0357143i
$785$	−323.044	−	676.992i	−0.411521	−	0.862411i
$786$	540.244			0.687334
$787$	−792.563	+	792.563i	−1.00707	+	1.00707i	−0.00709380	+	0.999975i	$0.502258\pi$
$787$	−792.563	+	792.563i	−1.00707	+	1.00707i	−0.999975	+	0.00709380i	$0.997742\pi$
$788$	320.416	+	320.416i	0.406620	+	0.406620i
$789$		−	189.716i		−	0.240452i
$790$	399.492	−	190.628i	0.505686	−	0.241301i
$791$	293.132			0.370584
$792$	30.2145	−	30.2145i	0.0381497	−	0.0381497i
$793$	−148.938	−	148.938i	−0.187816	−	0.187816i
$794$			1028.83i			1.29575i
$795$	−437.555	−	154.866i	−0.550384	−	0.194801i
$796$	−322.572			−0.405242
$797$	754.256	−	754.256i	0.946369	−	0.946369i	−0.0522640	−	0.998633i	$-0.516644\pi$
$797$	754.256	−	754.256i	0.946369	−	0.946369i	0.998633	+	0.0522640i	$0.0166437\pi$
$798$	−43.8300	−	43.8300i	−0.0549248	−	0.0549248i
$799$			683.426i			0.855352i
$800$	−140.642	+	14.8282i	−0.175802	+	0.0185353i
$801$	−49.7983			−0.0621702
$802$	−542.884	+	542.884i	−0.676913	+	0.676913i
$803$	−276.315	−	276.315i	−0.344103	−	0.344103i
$804$		−	149.354i		−	0.185764i
$805$	102.530	−	289.686i	0.127367	−	0.359858i
$806$	−270.106			−0.335119
$807$	63.1065	−	63.1065i	0.0781989	−	0.0781989i
$808$	−291.154	−	291.154i	−0.360339	−	0.360339i
$809$		−	286.564i		−	0.354220i	−0.984191	−	0.177110i	$-0.943325\pi$
$809$		−	286.564i		−	0.354220i	0.984191	−	0.177110i	$-0.0566749\pi$
$810$	27.4069	+	57.4357i	0.0338357	+	0.0709083i
$811$	130.099			0.160418			0.0802091	−	0.996778i	$-0.474441\pi$
$811$	130.099			0.160418			0.0802091	+	0.996778i	$0.474441\pi$
$812$	−15.6607	+	15.6607i	−0.0192866	+	0.0192866i
$813$	175.337	+	175.337i	0.215667	+	0.215667i
$814$			12.4487i			0.0152932i
$815$	−349.512	+	166.778i	−0.428849	+	0.204636i
$816$	179.122			0.219512
$817$	345.517	−	345.517i	0.422909	−	0.422909i
$818$	454.920	+	454.920i	0.556137	+	0.556137i
$819$			27.4926i			0.0335685i
$820$	−115.170	−	40.7629i	−0.140452	−	0.0497108i
$821$	−647.519			−0.788695			−0.394348	−	0.918961i	$-0.629029\pi$
$821$	−647.519			−0.788695			−0.394348	+	0.918961i	$0.629029\pi$
$822$	284.236	−	284.236i	0.345786	−	0.345786i
$823$	1076.83	+	1076.83i	1.30842	+	1.30842i	0.922556	+	0.385863i	$0.126096\pi$
$823$	1076.83	+	1076.83i	1.30842	+	1.30842i	0.385863	+	0.922556i	$0.373904\pi$
$824$			420.409i			0.510205i
$825$	22.8634	+	216.853i	0.0277132	+	0.262852i
$826$	268.460			0.325012
$827$	−201.783	+	201.783i	−0.243994	+	0.243994i	−0.818500	−	0.574506i	$-0.805194\pi$
$827$	−201.783	+	201.783i	−0.243994	+	0.243994i	0.574506	+	0.818500i	$0.305194\pi$
$828$	98.5537	+	98.5537i	0.119026	+	0.119026i
$829$			33.3580i			0.0402388i	0.999798	+	0.0201194i	$0.00640464\pi$
$829$			33.3580i			0.0402388i	−0.999798	+	0.0201194i	$0.993595\pi$
$830$	176.425	−	498.467i	0.212561	−	0.600562i
$831$	−162.284			−0.195288
$832$	19.5939	−	19.5939i	0.0235503	−	0.0235503i
$833$	127.971	+	127.971i	0.153626	+	0.153626i
$834$		−	662.695i		−	0.794598i
$835$	37.2987	+	78.1657i	0.0446691	+	0.0936116i
$836$	96.3289			0.115226
$837$	202.601	−	202.601i	0.242056	−	0.242056i
$838$	−597.925	−	597.925i	−0.713514	−	0.713514i
$839$		−	1231.60i		−	1.46794i	−0.679181	−	0.733971i	$-0.737665\pi$
$839$		−	1231.60i		−	1.46794i	0.679181	−	0.733971i	$-0.262335\pi$
$840$	58.4897	−	27.9098i	0.0696306	−	0.0332260i
$841$	823.482			0.979170
$842$	607.858	−	607.858i	0.721921	−	0.721921i
$843$	593.282	+	593.282i	0.703775	+	0.703775i
$844$			153.104i			0.181403i
$845$	740.028	+	261.922i	0.875773	+	0.309967i
$846$	−112.150			−0.132565
$847$	178.928	−	178.928i	0.211249	−	0.211249i
$848$	−151.592	−	151.592i	−0.178764	−	0.178764i
$849$			608.329i			0.716524i
$850$	−575.017	+	710.558i	−0.676490	+	0.835951i
$851$	−40.6050			−0.0477145
$852$	282.168	−	282.168i	0.331183	−	0.331183i
$853$	134.357	+	134.357i	0.157511	+	0.157511i	0.781463	−	0.623952i	$-0.214474\pi$
$853$	134.357	+	134.357i	0.157511	+	0.157511i	−0.623952	+	0.781463i	$0.714474\pi$
$854$		−	227.530i		−	0.266429i
$855$	−47.8684	+	135.246i	−0.0559865	+	0.158183i
$856$	−182.469			−0.213165
$857$	−271.551	+	271.551i	−0.316862	+	0.316862i	−0.847561	−	0.530698i	$-0.821930\pi$
$857$	−271.551	+	271.551i	−0.316862	+	0.316862i	0.530698	+	0.847561i	$0.321930\pi$
$858$	−30.2114	−	30.2114i	−0.0352114	−	0.0352114i
$859$		−	93.6478i		−	0.109020i	−0.998513	−	0.0545098i	$-0.982640\pi$
$859$		−	93.6478i		−	0.109020i	0.998513	−	0.0545098i	$-0.0173596\pi$
$860$	220.016	+	461.080i	0.255833	+	0.536140i
$861$	55.9859			0.0650243
$862$	−291.207	+	291.207i	−0.337827	+	0.337827i
$863$	1072.78	+	1072.78i	1.24308	+	1.24308i	0.958717	+	0.284361i	$0.0917814\pi$
$863$	1072.78	+	1072.78i	1.24308	+	1.24308i	0.284361	+	0.958717i	$0.408219\pi$
$864$			29.3939i			0.0340207i
$865$	1344.17	−	641.404i	1.55395	−	0.741507i
$866$	95.8102			0.110635
$867$	464.704	−	464.704i	0.535991	−	0.535991i
$868$	−206.319	−	206.319i	−0.237694	−	0.237694i
$869$		−	315.234i		−	0.362755i
$870$	48.3242	+	17.1037i	0.0555451	+	0.0196594i
$871$	−149.339			−0.171457
$872$	312.606	−	312.606i	0.358493	−	0.358493i
$873$	213.517	+	213.517i	0.244578	+	0.244578i
$874$			314.205i			0.359503i
$875$	−77.0481	+	321.619i	−0.0880550	+	0.367564i
$876$	268.810			0.306860
$877$	797.374	−	797.374i	0.909206	−	0.909206i	−0.0870020	−	0.996208i	$-0.527729\pi$
$877$	797.374	−	797.374i	0.909206	−	0.909206i	0.996208	+	0.0870020i	$0.0277287\pi$
$878$	652.062	+	652.062i	0.742667	+	0.742667i
$879$		−	493.174i		−	0.561062i
$880$	−33.6040	+	94.9437i	−0.0381863	+	0.107891i
$881$	−808.680			−0.917911			−0.458956	−	0.888459i	$-0.651776\pi$
$881$	−808.680			−0.917911			−0.458956	+	0.888459i	$0.651776\pi$
$882$	−21.0000	+	21.0000i	−0.0238095	+	0.0238095i
$883$	619.669	+	619.669i	0.701777	+	0.701777i	0.964792	−	0.263015i	$-0.0847168\pi$
$883$	619.669	+	619.669i	0.701777	+	0.701777i	−0.263015	+	0.964792i	$0.584717\pi$
$884$		−	179.103i		−	0.202605i
$885$	−267.595	−	560.790i	−0.302367	−	0.633661i
$886$	292.546			0.330187
$887$	−339.213	+	339.213i	−0.382428	+	0.382428i	−0.871976	−	0.489549i	$-0.837162\pi$
$887$	−339.213	+	339.213i	−0.382428	+	0.382428i	0.489549	+	0.871976i	$0.337162\pi$
$888$	−6.05527	−	6.05527i	−0.00681900	−	0.00681900i
$889$			318.026i			0.357734i
$890$	105.933	−	50.5488i	0.119026	−	0.0567964i
$891$	45.3218			0.0508662
$892$	494.273	−	494.273i	0.554117	−	0.554117i
$893$	−178.777	−	178.777i	−0.200198	−	0.200198i
$894$			249.344i			0.278909i
$895$	665.021	+	235.375i	0.743040	+	0.262988i
$896$	29.9333			0.0334077
$897$	98.5434	−	98.5434i	0.109859	−	0.109859i
$898$	−213.815	−	213.815i	−0.238101	−	0.238101i
$899$		−	230.793i		−	0.256722i
$900$	−116.603	−	94.3602i	−0.129558	−	0.104845i
$901$	−1385.67			−1.53792
$902$	−61.5225	+	61.5225i	−0.0682067	+	0.0682067i
$903$	−165.545	−	165.545i	−0.183328	−	0.183328i
$904$		−	313.371i		−	0.346650i
$905$	24.2216	−	68.4349i	0.0267641	−	0.0756186i
$906$	−407.472			−0.449748
$907$	1097.10	−	1097.10i	1.20959	−	1.20959i	0.238436	−	0.971158i	$-0.423365\pi$
$907$	1097.10	−	1097.10i	1.20959	−	1.20959i	0.971158	−	0.238436i	$-0.0766346\pi$
$908$	391.984	+	391.984i	0.431701	+	0.431701i
$909$		−	436.731i		−	0.480453i
$910$	−27.9069	−	58.4836i	−0.0306669	−	0.0642676i
$911$	1028.80			1.12930			0.564652	−	0.825329i	$-0.309011\pi$
$911$	1028.80			1.12930			0.564652	+	0.825329i	$0.309011\pi$
$912$	−46.8562	+	46.8562i	−0.0513775	+	0.0513775i
$913$	−266.274	−	266.274i	−0.291648	−	0.291648i
$914$			679.062i			0.742956i
$915$	−475.291	+	226.797i	−0.519444	+	0.247866i
$916$	−141.897			−0.154910
$917$	412.618	−	412.618i	0.449966	−	0.449966i
$918$	134.341	+	134.341i	0.146341	+	0.146341i
$919$		−	175.940i		−	0.191447i	−0.995408	−	0.0957237i	$-0.969483\pi$
$919$		−	175.940i		−	0.191447i	0.995408	−	0.0957237i	$-0.0305165\pi$
$920$	−309.687	−	109.609i	−0.336616	−	0.119141i
$921$	−7.05178			−0.00765665
$922$	−580.456	+	580.456i	−0.629562	+	0.629562i
$923$	−282.138	−	282.138i	−0.305675	−	0.305675i
$924$		−	46.1535i		−	0.0499497i
$925$	43.4593	−	4.58203i	0.0469830	−	0.00495355i
$926$	−1102.07			−1.19014
$927$	−315.307	+	315.307i	−0.340136	+	0.340136i
$928$	16.7420	+	16.7420i	0.0180410	+	0.0180410i
$929$		−	745.229i		−	0.802184i	−0.916038	−	0.401092i	$-0.868631\pi$
$929$		−	745.229i		−	0.802184i	0.916038	−	0.401092i	$-0.131369\pi$
$930$	−225.328	+	636.636i	−0.242289	+	0.684555i
$931$	−66.9514			−0.0719135
$932$	−27.0239	+	27.0239i	−0.0289956	+	0.0289956i
$933$	−156.088	−	156.088i	−0.167297	−	0.167297i
$934$			586.687i			0.628145i
$935$	280.346	+	587.513i	0.299836	+	0.628356i
$936$	29.3908			0.0314004
$937$	646.673	−	646.673i	0.690152	−	0.690152i	−0.272113	−	0.962265i	$-0.587723\pi$
$937$	646.673	−	646.673i	0.690152	−	0.690152i	0.962265	+	0.272113i	$0.0877225\pi$
$938$	−114.071	−	114.071i	−0.121611	−	0.121611i
$939$		−	181.155i		−	0.192923i
$940$	238.571	−	113.840i	0.253799	−	0.121107i
$941$	780.569			0.829510			0.414755	−	0.909933i	$-0.363867\pi$
$941$	780.569			0.829510			0.414755	+	0.909933i	$0.363867\pi$
$942$	259.848	−	259.848i	0.275847	−	0.275847i
$943$	−200.674	−	200.674i	−0.212804	−	0.212804i
$944$		−	286.995i		−	0.304021i
$945$	64.7996	+	22.9349i	0.0685710	+	0.0242697i
$946$	363.833			0.384601
$947$	−436.209	+	436.209i	−0.460622	+	0.460622i	−0.898859	−	0.438237i	$-0.855603\pi$
$947$	−436.209	+	436.209i	−0.460622	+	0.460622i	0.438237	+	0.898859i	$0.355603\pi$
$948$	153.336	+	153.336i	0.161747	+	0.161747i
$949$		−	268.782i		−	0.283226i
$950$	−35.4562	−	336.292i	−0.0373223	−	0.353991i
$951$	924.464			0.972097
$952$	136.807	−	136.807i	0.143704	−	0.143704i
$953$	−144.567	−	144.567i	−0.151697	−	0.151697i	0.627178	−	0.778876i	$-0.284210\pi$
$953$	−144.567	−	144.567i	−0.151697	−	0.151697i	−0.778876	+	0.627178i	$0.784210\pi$
$954$		−	227.388i		−	0.238352i
$955$	−561.059	+	1585.20i	−0.587496	+	1.65990i
$956$	−315.775			−0.330309
$957$	25.8142	−	25.8142i	0.0269741	−	0.0269741i
$958$	694.462	+	694.462i	0.724908	+	0.724908i
$959$		−	434.178i		−	0.452740i
$960$	−29.8368	−	62.5281i	−0.0310800	−	0.0651334i
$961$	2079.52			2.16392
$962$	−6.05464	+	6.05464i	−0.00629381	+	0.00629381i
$963$	−136.852	−	136.852i	−0.142110	−	0.142110i
$964$		−	285.402i		−	0.296060i
$965$	−100.567	+	47.9878i	−0.104214	+	0.0497283i
$966$	150.543			0.155842
$967$	896.278	−	896.278i	0.926865	−	0.926865i	−0.0706371	−	0.997502i	$-0.522503\pi$
$967$	896.278	−	896.278i	0.926865	−	0.926865i	0.997502	+	0.0706371i	$0.0225032\pi$
$968$	−191.282	−	191.282i	−0.197606	−	0.197606i
$969$			428.302i			0.442004i
$970$	−670.937	−	237.469i	−0.691688	−	0.244813i
$971$	−386.872			−0.398426			−0.199213	−	0.979956i	$-0.563839\pi$
$971$	−386.872			−0.398426			−0.199213	+	0.979956i	$0.563839\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−506.141	−	506.141i	−0.520186	−	0.520186i
$974$			378.171i			0.388266i
$975$	−94.3503	+	116.590i	−0.0967695	+	0.119580i
$976$	−243.240			−0.249221
$977$	906.290	−	906.290i	0.927626	−	0.927626i	−0.0699265	−	0.997552i	$-0.522276\pi$
$977$	906.290	−	906.290i	0.927626	−	0.927626i	0.997552	+	0.0699265i	$0.0222765\pi$
$978$	−134.152	−	134.152i	−0.137170	−	0.137170i
$979$		−	83.5908i		−	0.0853839i
$980$	23.3558	−	65.9887i	0.0238324	−	0.0673354i
$981$	468.909			0.477991
$982$	−587.867	+	587.867i	−0.598643	+	0.598643i
$983$	647.728	+	647.728i	0.658930	+	0.658930i	0.955127	−	0.296197i	$-0.0957185\pi$
$983$	647.728	+	647.728i	0.658930	+	0.658930i	−0.296197	+	0.955127i	$0.595718\pi$
$984$		−	59.8514i		−	0.0608246i
$985$	−487.867	−	1022.41i	−0.495297	−	1.03798i
$986$	153.035			0.155208
$987$	−85.6561	+	85.6561i	−0.0867843	+	0.0867843i
$988$	46.8513	+	46.8513i	0.0474204	+	0.0474204i
$989$			1186.75i			1.19995i
$990$	−96.4108	+	46.0048i	−0.0973846	+	0.0464695i
$991$	1308.46			1.32034			0.660169	−	0.751117i	$-0.270485\pi$
$991$	1308.46			1.32034			0.660169	+	0.751117i	$0.270485\pi$
$992$	−220.564	+	220.564i	−0.222343	+	0.222343i
$993$	−618.564	−	618.564i	−0.622925	−	0.622925i
$994$		−	431.019i		−	0.433620i
$995$	760.219	+	269.069i	0.764039	+	0.270421i
$996$	259.042			0.260082
$997$	−1347.69	+	1347.69i	−1.35174	+	1.35174i	−0.468033	+	0.883711i	$0.655037\pi$
$997$	−1347.69	+	1347.69i	−1.35174	+	1.35174i	−0.883711	+	0.468033i	$0.844963\pi$
$998$	−13.5102	−	13.5102i	−0.0135373	−	0.0135373i
$999$		−	9.08291i		−	0.00909200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.l.b.43.7	✓	16
3.2	odd	2		630.3.o.f.253.4		16
5.2	odd	4	inner	210.3.l.b.127.7	yes	16
5.3	odd	4		1050.3.l.h.757.3		16
5.4	even	2		1050.3.l.h.43.3		16
15.2	even	4		630.3.o.f.127.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.7	✓	16	1.1	even	1	trivial
210.3.l.b.127.7	yes	16	5.2	odd	4	inner
630.3.o.f.127.4		16	15.2	even	4
630.3.o.f.253.4		16	3.2	odd	2
1050.3.l.h.43.3		16	5.4	even	2
1050.3.l.h.757.3		16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-1.66827 + 4.71348i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-1.66827 + 4.71348i) q^{5} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-3.04521 - 6.38175i) q^{10} -5.03576 q^{11} +(2.44949 - 2.44949i) q^{12} +(-2.44923 - 2.44923i) q^{13} -3.74166i q^{14} +(-7.81601 + 3.72961i) q^{15} -4.00000 q^{16} +(-18.2815 + 18.2815i) q^{17} +(-3.00000 - 3.00000i) q^{18} -9.56449i q^{19} +(9.42696 + 3.33654i) q^{20} -4.58258 q^{21} +(5.03576 - 5.03576i) q^{22} +(16.4256 + 16.4256i) q^{23} +4.89898i q^{24} +(-19.4338 - 15.7267i) q^{25} +4.89847 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} +4.18550i q^{29} +(4.08641 - 11.5456i) q^{30} -55.1410 q^{31} +(4.00000 - 4.00000i) q^{32} +(-6.16752 - 6.16752i) q^{33} -36.5631i q^{34} +(-5.69707 - 11.9392i) q^{35} +6.00000 q^{36} +(-1.23603 + 1.23603i) q^{37} +(9.56449 + 9.56449i) q^{38} -5.99937i q^{39} +(-12.7635 + 6.09042i) q^{40} -12.2171 q^{41} +(4.58258 - 4.58258i) q^{42} +(36.1249 + 36.1249i) q^{43} +10.0715i q^{44} +(-14.1404 - 5.00481i) q^{45} -32.8512 q^{46} +(18.6917 - 18.6917i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +(35.1605 - 3.70706i) q^{50} -44.7804 q^{51} +(-4.89847 + 4.89847i) q^{52} +(37.8979 + 37.8979i) q^{53} -7.34847i q^{54} +(8.40100 - 23.7359i) q^{55} -7.48331 q^{56} +(11.7141 - 11.7141i) q^{57} +(-4.18550 - 4.18550i) q^{58} +71.7488i q^{59} +(7.45921 + 15.6320i) q^{60} +60.8100 q^{61} +(55.1410 - 55.1410i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} +(15.6304 - 7.45843i) q^{65} +12.3350 q^{66} +(30.4868 - 30.4868i) q^{67} +(36.5631 + 36.5631i) q^{68} +40.2344i q^{69} +(17.6362 + 6.24209i) q^{70} +115.195 q^{71} +(-6.00000 + 6.00000i) q^{72} +(54.8705 + 54.8705i) q^{73} -2.47206i q^{74} +(-4.54020 - 43.0626i) q^{75} -19.1290 q^{76} +(9.42104 - 9.42104i) q^{77} +(5.99937 + 5.99937i) q^{78} +62.5991i q^{79} +(6.67307 - 18.8539i) q^{80} -9.00000 q^{81} +(12.2171 - 12.2171i) q^{82} +(52.8767 + 52.8767i) q^{83} +9.16515i q^{84} +(-55.6711 - 116.668i) q^{85} -72.2499 q^{86} +(-5.12617 + 5.12617i) q^{87} +(-10.0715 - 10.0715i) q^{88} +16.5994i q^{89} +(19.1452 - 9.13563i) q^{90} +9.16419 q^{91} +(32.8512 - 32.8512i) q^{92} +(-67.5336 - 67.5336i) q^{93} +37.3834i q^{94} +(45.0820 + 15.9561i) q^{95} +9.79796 q^{96} +(71.1722 - 71.1722i) q^{97} +(7.00000 + 7.00000i) q^{98} -15.1073i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8	\( 16 q - 16 q^{2} - 16 q^{5} + 32 q^{8} + 24 q^{10} + 8 q^{11} - 32 q^{13} - 12 q^{15} - 64 q^{16} + 56 q^{17} - 48 q^{18} - 16 q^{20} - 8 q^{22} + 24 q^{23} + 40 q^{25} + 64 q^{26} - 112 q^{31} + 64 q^{32} + 24 q^{33} + 28 q^{35} + 96 q^{36} - 152 q^{37} - 16 q^{40} + 24 q^{45} - 48 q^{46} + 80 q^{47} - 72 q^{50} - 72 q^{51} - 64 q^{52} + 48 q^{53} - 24 q^{55} + 24 q^{57} + 96 q^{58} + 24 q^{60} + 96 q^{61} + 112 q^{62} + 16 q^{65} - 48 q^{66} - 80 q^{67} - 112 q^{68} + 536 q^{71} - 96 q^{72} - 288 q^{75} - 168 q^{77} - 48 q^{78} + 64 q^{80} - 144 q^{81} - 256 q^{83} + 40 q^{85} - 144 q^{87} + 16 q^{88} + 24 q^{90} + 48 q^{92} + 192 q^{93} + 360 q^{95} + 688 q^{97} + 112 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 - 16 * q^5 + 32 * q^8 + 24 * q^10 + 8 * q^11 - 32 * q^13 - 12 * q^15 - 64 * q^16 + 56 * q^17 - 48 * q^18 - 16 * q^20 - 8 * q^22 + 24 * q^23 + 40 * q^25 + 64 * q^26 - 112 * q^31 + 64 * q^32 + 24 * q^33 + 28 * q^35 + 96 * q^36 - 152 * q^37 - 16 * q^40 + 24 * q^45 - 48 * q^46 + 80 * q^47 - 72 * q^50 - 72 * q^51 - 64 * q^52 + 48 * q^53 - 24 * q^55 + 24 * q^57 + 96 * q^58 + 24 * q^60 + 96 * q^61 + 112 * q^62 + 16 * q^65 - 48 * q^66 - 80 * q^67 - 112 * q^68 + 536 * q^71 - 96 * q^72 - 288 * q^75 - 168 * q^77 - 48 * q^78 + 64 * q^80 - 144 * q^81 - 256 * q^83 + 40 * q^85 - 144 * q^87 + 16 * q^88 + 24 * q^90 + 48 * q^92 + 192 * q^93 + 360 * q^95 + 688 * q^97 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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