LMFDB - Embedded newform 230.3.f.a.93.1

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			93.1
Root			$-4.03398 - 4.03398i$ of defining polynomial
Character	$\chi$	$=$	230.93
Dual form			230.3.f.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-4.03398 - 4.03398i) q^{3} -2.00000i q^{4} +(4.54274 + 2.08891i) q^{5} +8.06796 q^{6} +(-1.88621 + 1.88621i) q^{7} +(2.00000 + 2.00000i) q^{8} +23.5460i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-4.03398 - 4.03398i) q^{3} -2.00000i q^{4} +(4.54274 + 2.08891i) q^{5} +8.06796 q^{6} +(-1.88621 + 1.88621i) q^{7} +(2.00000 + 2.00000i) q^{8} +23.5460i q^{9} +(-6.63165 + 2.45382i) q^{10} +20.0905 q^{11} +(-8.06796 + 8.06796i) q^{12} +(-7.55126 - 7.55126i) q^{13} -3.77242i q^{14} +(-9.89867 - 26.7519i) q^{15} -4.00000 q^{16} +(-0.682982 + 0.682982i) q^{17} +(-23.5460 - 23.5460i) q^{18} -35.2221i q^{19} +(4.17783 - 9.08547i) q^{20} +15.2179 q^{21} +(-20.0905 + 20.0905i) q^{22} +(3.39116 + 3.39116i) q^{23} -16.1359i q^{24} +(16.2729 + 18.9788i) q^{25} +15.1025 q^{26} +(58.6782 - 58.6782i) q^{27} +(3.77242 + 3.77242i) q^{28} -17.4778i q^{29} +(36.6506 + 16.8533i) q^{30} +5.61239 q^{31} +(4.00000 - 4.00000i) q^{32} +(-81.0446 - 81.0446i) q^{33} -1.36596i q^{34} +(-12.5087 + 4.62842i) q^{35} +47.0920 q^{36} +(23.5363 - 23.5363i) q^{37} +(35.2221 + 35.2221i) q^{38} +60.9233i q^{39} +(4.90764 + 13.2633i) q^{40} -15.5983 q^{41} +(-15.2179 + 15.2179i) q^{42} +(-16.4004 - 16.4004i) q^{43} -40.1810i q^{44} +(-49.1855 + 106.963i) q^{45} -6.78233 q^{46} +(51.8217 - 51.8217i) q^{47} +(16.1359 + 16.1359i) q^{48} +41.8844i q^{49} +(-35.2516 - 2.70587i) q^{50} +5.51027 q^{51} +(-15.1025 + 15.1025i) q^{52} +(-34.4887 - 34.4887i) q^{53} +117.356i q^{54} +(91.2657 + 41.9673i) q^{55} -7.54484 q^{56} +(-142.085 + 142.085i) q^{57} +(17.4778 + 17.4778i) q^{58} -16.4129i q^{59} +(-53.5039 + 19.7973i) q^{60} +65.5138 q^{61} +(-5.61239 + 5.61239i) q^{62} +(-44.4126 - 44.4126i) q^{63} +8.00000i q^{64} +(-18.5295 - 50.0773i) q^{65} +162.089 q^{66} +(29.2101 - 29.2101i) q^{67} +(1.36596 + 1.36596i) q^{68} -27.3598i q^{69} +(7.88025 - 17.1371i) q^{70} -15.2240 q^{71} +(-47.0920 + 47.0920i) q^{72} +(39.7893 + 39.7893i) q^{73} +47.0726i q^{74} +(10.9154 - 142.204i) q^{75} -70.4442 q^{76} +(-37.8948 + 37.8948i) q^{77} +(-60.9233 - 60.9233i) q^{78} +17.5152i q^{79} +(-18.1709 - 8.35565i) q^{80} -261.500 q^{81} +(15.5983 - 15.5983i) q^{82} +(10.8971 + 10.8971i) q^{83} -30.4357i q^{84} +(-4.52929 + 1.67592i) q^{85} +32.8007 q^{86} +(-70.5051 + 70.5051i) q^{87} +(40.1810 + 40.1810i) q^{88} -177.339i q^{89} +(-57.7777 - 156.149i) q^{90} +28.4865 q^{91} +(6.78233 - 6.78233i) q^{92} +(-22.6403 - 22.6403i) q^{93} +103.643i q^{94} +(73.5759 - 160.005i) q^{95} -32.2718 q^{96} +(-53.5011 + 53.5011i) q^{97} +(-41.8844 - 41.8844i) q^{98} +473.050i 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
$3$	−4.03398	−	4.03398i	−1.34466	−	1.34466i	−0.891356	−	0.453304i	$-0.850245\pi$
$3$	−4.03398	−	4.03398i	−1.34466	−	1.34466i	−0.453304	−	0.891356i	$-0.649755\pi$
$4$		−	2.00000i		−	0.500000i
$5$	4.54274	+	2.08891i	0.908547	+	0.417783i
$5$	4.54274	+	2.08891i	0.908547	+	0.417783i
$6$	8.06796			1.34466
$7$	−1.88621	+	1.88621i	−0.269458	+	0.269458i	−0.828882	−	0.559424i	$-0.811023\pi$
$7$	−1.88621	+	1.88621i	−0.269458	+	0.269458i	0.559424	+	0.828882i	$0.311023\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			23.5460i			2.61622i
$10$	−6.63165	+	2.45382i	−0.663165	+	0.245382i
$11$	20.0905			1.82641			0.913204	−	0.407503i	$-0.133601\pi$
$11$	20.0905			1.82641			0.913204	+	0.407503i	$0.133601\pi$
$12$	−8.06796	+	8.06796i	−0.672330	+	0.672330i
$13$	−7.55126	−	7.55126i	−0.580866	−	0.580866i	0.354275	−	0.935141i	$-0.384728\pi$
$13$	−7.55126	−	7.55126i	−0.580866	−	0.580866i	−0.935141	+	0.354275i	$0.884728\pi$
$14$		−	3.77242i		−	0.269458i
$15$	−9.89867	−	26.7519i	−0.659911	−	1.78346i
$16$	−4.00000			−0.250000
$17$	−0.682982	+	0.682982i	−0.0401754	+	0.0401754i	−0.726909	−	0.686734i	$-0.759044\pi$
$17$	−0.682982	+	0.682982i	−0.0401754	+	0.0401754i	0.686734	+	0.726909i	$0.259044\pi$
$18$	−23.5460	−	23.5460i	−1.30811	−	1.30811i
$19$		−	35.2221i		−	1.85379i	−0.375315	−	0.926897i	$-0.622466\pi$
$19$		−	35.2221i		−	1.85379i	0.375315	−	0.926897i	$-0.377534\pi$
$20$	4.17783	−	9.08547i	0.208891	−	0.454274i
$21$	15.2179			0.724660
$22$	−20.0905	+	20.0905i	−0.913204	+	0.913204i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	16.1359i		−	0.672330i
$25$	16.2729	+	18.9788i	0.650915	+	0.759150i
$26$	15.1025			0.580866
$27$	58.6782	−	58.6782i	2.17327	−	2.17327i
$28$	3.77242	+	3.77242i	0.134729	+	0.134729i
$29$		−	17.4778i		−	0.602683i	−0.953516	−	0.301341i	$-0.902566\pi$
$29$		−	17.4778i		−	0.602683i	0.953516	−	0.301341i	$-0.0974344\pi$
$30$	36.6506	+	16.8533i	1.22169	+	0.561776i
$31$	5.61239			0.181045			0.0905224	−	0.995894i	$-0.471146\pi$
$31$	5.61239			0.181045			0.0905224	+	0.995894i	$0.471146\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−81.0446	−	81.0446i	−2.45590	−	2.45590i
$34$		−	1.36596i		−	0.0401754i
$35$	−12.5087	+	4.62842i	−0.357391	+	0.132241i
$36$	47.0920			1.30811
$37$	23.5363	−	23.5363i	0.636116	−	0.636116i	−0.313479	−	0.949595i	$-0.601494\pi$
$37$	23.5363	−	23.5363i	0.636116	−	0.636116i	0.949595	+	0.313479i	$0.101494\pi$
$38$	35.2221	+	35.2221i	0.926897	+	0.926897i
$39$			60.9233i			1.56214i
$40$	4.90764	+	13.2633i	0.122691	+	0.331582i
$41$	−15.5983			−0.380447			−0.190223	−	0.981741i	$-0.560921\pi$
$41$	−15.5983			−0.380447			−0.190223	+	0.981741i	$0.560921\pi$
$42$	−15.2179	+	15.2179i	−0.362330	+	0.362330i
$43$	−16.4004	−	16.4004i	−0.381404	−	0.381404i	0.490204	−	0.871608i	$-0.336922\pi$
$43$	−16.4004	−	16.4004i	−0.381404	−	0.381404i	−0.871608	+	0.490204i	$0.836922\pi$
$44$		−	40.1810i		−	0.913204i
$45$	−49.1855	+	106.963i	−1.09301	+	2.37696i
$46$	−6.78233			−0.147442
$47$	51.8217	−	51.8217i	1.10259	−	1.10259i	0.108493	−	0.994097i	$-0.465397\pi$
$47$	51.8217	−	51.8217i	1.10259	−	1.10259i	0.994097	−	0.108493i	$-0.0346025\pi$
$48$	16.1359	+	16.1359i	0.336165	+	0.336165i
$49$			41.8844i			0.854784i
$50$	−35.2516	−	2.70587i	−0.705033	−	0.0541174i
$51$	5.51027			0.108044
$52$	−15.1025	+	15.1025i	−0.290433	+	0.290433i
$53$	−34.4887	−	34.4887i	−0.650730	−	0.650730i	0.302439	−	0.953169i	$-0.402199\pi$
$53$	−34.4887	−	34.4887i	−0.650730	−	0.650730i	−0.953169	+	0.302439i	$0.902199\pi$
$54$			117.356i			2.17327i
$55$	91.2657	+	41.9673i	1.65938	+	0.763041i
$56$	−7.54484			−0.134729
$57$	−142.085	+	142.085i	−2.49272	+	2.49272i
$58$	17.4778	+	17.4778i	0.301341	+	0.301341i
$59$		−	16.4129i		−	0.278184i	−0.990279	−	0.139092i	$-0.955582\pi$
$59$		−	16.4129i		−	0.278184i	0.990279	−	0.139092i	$-0.0444184\pi$
$60$	−53.5039	+	19.7973i	−0.891731	+	0.329956i
$61$	65.5138			1.07400			0.536998	−	0.843583i	$-0.319558\pi$
$61$	65.5138			1.07400			0.536998	+	0.843583i	$0.319558\pi$
$62$	−5.61239	+	5.61239i	−0.0905224	+	0.0905224i
$63$	−44.4126	−	44.4126i	−0.704963	−	0.704963i
$64$			8.00000i			0.125000i
$65$	−18.5295	−	50.0773i	−0.285069	−	0.770420i
$66$	162.089			2.45590
$67$	29.2101	−	29.2101i	0.435972	−	0.435972i	−0.454682	−	0.890654i	$-0.650247\pi$
$67$	29.2101	−	29.2101i	0.435972	−	0.435972i	0.890654	+	0.454682i	$0.150247\pi$
$68$	1.36596	+	1.36596i	0.0200877	+	0.0200877i
$69$		−	27.3598i		−	0.396519i
$70$	7.88025	−	17.1371i	0.112575	−	0.244816i
$71$	−15.2240			−0.214423			−0.107212	−	0.994236i	$-0.534192\pi$
$71$	−15.2240			−0.214423			−0.107212	+	0.994236i	$0.534192\pi$
$72$	−47.0920	+	47.0920i	−0.654055	+	0.654055i
$73$	39.7893	+	39.7893i	0.545059	+	0.545059i	0.925007	−	0.379949i	$-0.124058\pi$
$73$	39.7893	+	39.7893i	0.545059	+	0.545059i	−0.379949	+	0.925007i	$0.624058\pi$
$74$			47.0726i			0.636116i
$75$	10.9154	−	142.204i	0.145539	−	1.89606i
$76$	−70.4442			−0.926897
$77$	−37.8948	+	37.8948i	−0.492141	+	0.492141i
$78$	−60.9233	−	60.9233i	−0.781068	−	0.781068i
$79$			17.5152i			0.221711i	0.993837	+	0.110856i	$0.0353591\pi$
$79$			17.5152i			0.221711i	−0.993837	+	0.110856i	$0.964641\pi$
$80$	−18.1709	−	8.35565i	−0.227137	−	0.104446i
$81$	−261.500			−3.22839
$82$	15.5983	−	15.5983i	0.190223	−	0.190223i
$83$	10.8971	+	10.8971i	0.131290	+	0.131290i	0.769698	−	0.638408i	$-0.220407\pi$
$83$	10.8971	+	10.8971i	0.131290	+	0.131290i	−0.638408	+	0.769698i	$0.720407\pi$
$84$		−	30.4357i		−	0.362330i
$85$	−4.52929	+	1.67592i	−0.0532858	+	0.0197167i
$86$	32.8007			0.381404
$87$	−70.5051	+	70.5051i	−0.810404	+	0.810404i
$88$	40.1810	+	40.1810i	0.456602	+	0.456602i
$89$		−	177.339i		−	1.99258i	−0.0860819	−	0.996288i	$-0.527435\pi$
$89$		−	177.339i		−	1.99258i	0.0860819	−	0.996288i	$-0.472565\pi$
$90$	−57.7777	−	156.149i	−0.641974	−	1.73499i
$91$	28.4865			0.313039
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−22.6403	−	22.6403i	−0.243444	−	0.243444i
$94$			103.643i			1.10259i
$95$	73.5759	−	160.005i	0.774483	−	1.68426i
$96$	−32.2718			−0.336165
$97$	−53.5011	+	53.5011i	−0.551557	+	0.551557i	−0.926890	−	0.375333i	$-0.877528\pi$
$97$	−53.5011	+	53.5011i	−0.551557	+	0.551557i	0.375333	+	0.926890i	$0.377528\pi$
$98$	−41.8844	−	41.8844i	−0.427392	−	0.427392i
$99$			473.050i			4.77828i
$100$	37.9575	−	32.5458i	0.379575	−	0.325458i
$101$	125.940			1.24694			0.623468	−	0.781849i	$-0.285723\pi$
$101$	125.940			1.24694			0.623468	+	0.781849i	$0.285723\pi$
$102$	−5.51027	+	5.51027i	−0.0540222	+	0.0540222i
$103$	22.0075	+	22.0075i	0.213665	+	0.213665i	0.805822	−	0.592157i	$-0.201724\pi$
$103$	22.0075	+	22.0075i	0.213665	+	0.213665i	−0.592157	+	0.805822i	$0.701724\pi$
$104$		−	30.2050i		−	0.290433i
$105$	69.1307	+	31.7888i	0.658388	+	0.302750i
$106$	68.9774			0.650730
$107$	−3.25963	+	3.25963i	−0.0304638	+	0.0304638i	−0.722175	−	0.691711i	$-0.756857\pi$
$107$	−3.25963	+	3.25963i	−0.0304638	+	0.0304638i	0.691711	+	0.722175i	$0.256857\pi$
$108$	−117.356	−	117.356i	−1.08663	−	1.08663i
$109$			111.109i			1.01935i	0.860366	+	0.509676i	$0.170235\pi$
$109$			111.109i			1.01935i	−0.860366	+	0.509676i	$0.829765\pi$
$110$	−133.233	+	49.2985i	−1.21121	+	0.448168i
$111$	−189.890			−1.71072
$112$	7.54484	−	7.54484i	0.0673646	−	0.0673646i
$113$	129.531	+	129.531i	1.14629	+	1.14629i	0.987277	+	0.159011i	$0.0508305\pi$
$113$	129.531	+	129.531i	1.14629	+	1.14629i	0.159011	+	0.987277i	$0.449169\pi$
$114$		−	284.170i		−	2.49272i
$115$	8.32132	+	22.4890i	0.0723593	+	0.195557i
$116$	−34.9556			−0.301341
$117$	177.802	−	177.802i	1.51967	−	1.51967i
$118$	16.4129	+	16.4129i	0.139092	+	0.139092i
$119$		−	2.57649i		−	0.0216512i
$120$	33.7065	−	73.3012i	0.280888	−	0.610843i
$121$	282.627			2.33576
$122$	−65.5138	+	65.5138i	−0.536998	+	0.536998i
$123$	62.9233	+	62.9233i	0.511572	+	0.511572i
$124$		−	11.2248i		−	0.0905224i
$125$	34.2784	+	120.208i	0.274227	+	0.961665i
$126$	88.8253			0.704963
$127$	35.6528	−	35.6528i	0.280731	−	0.280731i	−0.552670	−	0.833400i	$-0.686391\pi$
$127$	35.6528	−	35.6528i	0.280731	−	0.280731i	0.833400	+	0.552670i	$0.186391\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			132.318i			1.02572i
$130$	68.6068	+	31.5479i	0.527744	+	0.242676i
$131$	−75.6903			−0.577788			−0.288894	−	0.957361i	$-0.593288\pi$
$131$	−75.6903			−0.577788			−0.288894	+	0.957361i	$0.593288\pi$
$132$	−162.089	+	162.089i	−1.22795	+	1.22795i
$133$	66.4362	+	66.4362i	0.499521	+	0.499521i
$134$			58.4203i			0.435972i
$135$	389.133	−	143.986i	2.88247	−	1.06656i
$136$	−2.73193			−0.0200877
$137$	28.2659	−	28.2659i	0.206320	−	0.206320i	−0.596381	−	0.802701i	$-0.703395\pi$
$137$	28.2659	−	28.2659i	0.206320	−	0.206320i	0.802701	+	0.596381i	$0.203395\pi$
$138$	27.3598	+	27.3598i	0.198259	+	0.198259i
$139$		−	122.072i		−	0.878212i	−0.898435	−	0.439106i	$-0.855295\pi$
$139$		−	122.072i		−	0.878212i	0.898435	−	0.439106i	$-0.144705\pi$
$140$	9.25684	+	25.0173i	0.0661203	+	0.178695i
$141$	−418.096			−2.96522
$142$	15.2240	−	15.2240i	0.107212	−	0.107212i
$143$	−151.708	−	151.708i	−1.06090	−	1.06090i
$144$		−	94.1839i		−	0.654055i
$145$	36.5096	−	79.3970i	0.251790	−	0.547566i
$146$	−79.5786			−0.545059
$147$	168.961	−	168.961i	1.14939	−	1.14939i
$148$	−47.0726	−	47.0726i	−0.318058	−	0.318058i
$149$			125.669i			0.843416i	0.906732	+	0.421708i	$0.138569\pi$
$149$			125.669i			0.843416i	−0.906732	+	0.421708i	$0.861431\pi$
$150$	131.289	+	153.120i	0.875260	+	1.02080i
$151$	−286.279			−1.89589			−0.947943	−	0.318441i	$-0.896841\pi$
$151$	−286.279			−1.89589			−0.947943	+	0.318441i	$0.896841\pi$
$152$	70.4442	−	70.4442i	0.463449	−	0.463449i
$153$	−16.0815	−	16.0815i	−0.105108	−	0.105108i
$154$		−	75.7897i		−	0.492141i
$155$	25.4956	+	11.7238i	0.164488	+	0.0756373i
$156$	121.847			0.781068
$157$	−13.8888	+	13.8888i	−0.0884634	+	0.0884634i	−0.749954	−	0.661490i	$-0.769924\pi$
$157$	−13.8888	+	13.8888i	−0.0884634	+	0.0884634i	0.661490	+	0.749954i	$0.269924\pi$
$158$	−17.5152	−	17.5152i	−0.110856	−	0.110856i
$159$			278.254i			1.75002i
$160$	26.5266	−	9.81529i	0.165791	−	0.0613456i
$161$	−12.7929			−0.0794590
$162$	261.500	−	261.500i	1.61419	−	1.61419i
$163$	52.5171	+	52.5171i	0.322191	+	0.322191i	0.849607	−	0.527416i	$-0.176839\pi$
$163$	52.5171	+	52.5171i	0.322191	+	0.322191i	−0.527416	+	0.849607i	$0.676839\pi$
$164$			31.1966i			0.190223i
$165$	−198.869	−	537.459i	−1.20527	−	3.25733i
$166$	−21.7941			−0.131290
$167$	−113.997	+	113.997i	−0.682619	+	0.682619i	−0.960590	−	0.277970i	$-0.910338\pi$
$167$	−113.997	+	113.997i	−0.682619	+	0.682619i	0.277970	+	0.960590i	$0.410338\pi$
$168$	30.4357	+	30.4357i	0.181165	+	0.181165i
$169$		−	54.9569i		−	0.325189i
$170$	2.85338	−	6.20521i	0.0167846	−	0.0365012i
$171$	829.339			4.84994
$172$	−32.8007	+	32.8007i	−0.190702	+	0.190702i
$173$	−136.316	−	136.316i	−0.787955	−	0.787955i	0.193204	−	0.981159i	$-0.438112\pi$
$173$	−136.316	−	136.316i	−0.787955	−	0.787955i	−0.981159	+	0.193204i	$0.938112\pi$
$174$		−	141.010i		−	0.810404i
$175$	−66.4920	−	5.10384i	−0.379954	−	0.0291648i
$176$	−80.3619			−0.456602
$177$	−66.2092	+	66.2092i	−0.374063	+	0.374063i
$178$	177.339	+	177.339i	0.996288	+	0.996288i
$179$			108.813i			0.607894i	0.952689	+	0.303947i	$0.0983046\pi$
$179$			108.813i			0.607894i	−0.952689	+	0.303947i	$0.901695\pi$
$180$	213.926	+	98.3710i	1.18848	+	0.546506i
$181$	−125.598			−0.693914			−0.346957	−	0.937881i	$-0.612785\pi$
$181$	−125.598			−0.693914			−0.346957	+	0.937881i	$0.612785\pi$
$182$	−28.4865	+	28.4865i	−0.156519	+	0.156519i
$183$	−264.281	−	264.281i	−1.44416	−	1.44416i
$184$			13.5647i			0.0737210i
$185$	156.084	−	57.7539i	0.843700	−	0.312183i
$186$	45.2805			0.243444
$187$	−13.7214	+	13.7214i	−0.0733766	+	0.0733766i
$188$	−103.643	−	103.643i	−0.551295	−	0.551295i
$189$			221.359i			1.17121i
$190$	86.4288	+	233.581i	0.454888	+	1.22937i
$191$	−277.559			−1.45319			−0.726594	−	0.687067i	$-0.758898\pi$
$191$	−277.559			−1.45319			−0.726594	+	0.687067i	$0.758898\pi$
$192$	32.2718	−	32.2718i	0.168082	−	0.168082i
$193$	77.1056	+	77.1056i	0.399511	+	0.399511i	0.878060	−	0.478550i	$-0.158837\pi$
$193$	77.1056	+	77.1056i	0.399511	+	0.399511i	−0.478550	+	0.878060i	$0.658837\pi$
$194$		−	107.002i		−	0.551557i
$195$	−127.263	+	276.758i	−0.652633	+	1.41927i
$196$	83.7689			0.427392
$197$	33.3964	−	33.3964i	0.169525	−	0.169525i	−0.617246	−	0.786770i	$-0.711752\pi$
$197$	33.3964	−	33.3964i	0.169525	−	0.169525i	0.786770	+	0.617246i	$0.211752\pi$
$198$	−473.050	−	473.050i	−2.38914	−	2.38914i
$199$		−	193.467i		−	0.972198i	−0.873904	−	0.486099i	$-0.838419\pi$
$199$		−	193.467i		−	0.972198i	0.873904	−	0.486099i	$-0.161581\pi$
$200$	−5.41174	+	70.5033i	−0.0270587	+	0.352516i
$201$	−235.666			−1.17247
$202$	−125.940	+	125.940i	−0.623468	+	0.623468i
$203$	32.9668	+	32.9668i	0.162398	+	0.162398i
$204$		−	11.0205i		−	0.0540222i
$205$	−70.8590	−	32.5835i	−0.345654	−	0.158944i
$206$	−44.0150			−0.213665
$207$	−79.8483	+	79.8483i	−0.385741	+	0.385741i
$208$	30.2050	+	30.2050i	0.145217	+	0.145217i
$209$		−	707.629i		−	3.38578i
$210$	−100.919	+	37.3419i	−0.480569	+	0.177819i
$211$	86.4981			0.409944			0.204972	−	0.978768i	$-0.434290\pi$
$211$	86.4981			0.409944			0.204972	+	0.978768i	$0.434290\pi$
$212$	−68.9774	+	68.9774i	−0.325365	+	0.325365i
$213$	61.4135	+	61.4135i	0.288326	+	0.288326i
$214$		−	6.51925i		−	0.0304638i
$215$	−40.2436	−	108.761i	−0.187179	−	0.505867i
$216$	234.713			1.08663
$217$	−10.5861	+	10.5861i	−0.0487840	+	0.0487840i
$218$	−111.109	−	111.109i	−0.509676	−	0.509676i
$219$		−	321.018i		−	1.46584i
$220$	83.9345	−	182.531i	0.381521	−	0.829688i
$221$	10.3147			0.0466731
$222$	189.890	−	189.890i	0.855360	−	0.855360i
$223$	187.060	+	187.060i	0.838834	+	0.838834i	0.988705	−	0.149872i	$-0.0478860\pi$
$223$	187.060	+	187.060i	0.838834	+	0.838834i	−0.149872	+	0.988705i	$0.547886\pi$
$224$			15.0897i			0.0673646i
$225$	−446.874	+	383.161i	−1.98610	+	1.70294i
$226$	−259.061			−1.14629
$227$	−187.941	+	187.941i	−0.827934	+	0.827934i	−0.987231	−	0.159297i	$-0.949077\pi$
$227$	−187.941	+	187.941i	−0.827934	+	0.827934i	0.159297	+	0.987231i	$0.449077\pi$
$228$	284.170	+	284.170i	1.24636	+	1.24636i
$229$		−	39.4344i		−	0.172203i	−0.996286	−	0.0861014i	$-0.972559\pi$
$229$		−	39.4344i		−	0.172203i	0.996286	−	0.0861014i	$-0.0274409\pi$
$230$	−30.8103	−	14.1677i	−0.133958	−	0.0615987i
$231$	305.734			1.32352
$232$	34.9556	−	34.9556i	0.150671	−	0.150671i
$233$	294.485	+	294.485i	1.26389	+	1.26389i	0.949194	+	0.314693i	$0.101901\pi$
$233$	294.485	+	294.485i	1.26389	+	1.26389i	0.314693	+	0.949194i	$0.398099\pi$
$234$			355.604i			1.51967i
$235$	343.664	−	127.161i	1.46240	−	0.541112i
$236$	−32.8258			−0.139092
$237$	70.6560	−	70.6560i	0.298126	−	0.298126i
$238$	2.57649	+	2.57649i	0.0108256	+	0.0108256i
$239$		−	261.434i		−	1.09387i	−0.837177	−	0.546933i	$-0.815795\pi$
$239$		−	261.434i		−	1.09387i	0.837177	−	0.546933i	$-0.184205\pi$
$240$	39.5947	+	107.008i	0.164978	+	0.445866i
$241$	−73.8241			−0.306324			−0.153162	−	0.988201i	$-0.548946\pi$
$241$	−73.8241			−0.306324			−0.153162	+	0.988201i	$0.548946\pi$
$242$	−282.627	+	282.627i	−1.16788	+	1.16788i
$243$	526.780	+	526.780i	2.16782	+	2.16782i
$244$		−	131.028i		−	0.536998i
$245$	−87.4929	+	190.270i	−0.357114	+	0.776612i
$246$	−125.847			−0.511572
$247$	−265.971	+	265.971i	−1.07681	+	1.07681i
$248$	11.2248	+	11.2248i	0.0452612	+	0.0452612i
$249$		−	87.9170i		−	0.353080i
$250$	−154.487	−	85.9297i	−0.617946	−	0.343719i
$251$	−252.912			−1.00762			−0.503810	−	0.863815i	$-0.668069\pi$
$251$	−252.912			−1.00762			−0.503810	+	0.863815i	$0.668069\pi$
$252$	−88.8253	+	88.8253i	−0.352481	+	0.352481i
$253$	68.1301	+	68.1301i	0.269289	+	0.269289i
$254$			71.3056i			0.280731i
$255$	25.0317	+	11.5105i	0.0981635	+	0.0451391i
$256$	16.0000			0.0625000
$257$	198.861	−	198.861i	0.773778	−	0.773778i	−0.204987	−	0.978765i	$-0.565715\pi$
$257$	198.861	−	198.861i	0.773778	−	0.773778i	0.978765	+	0.204987i	$0.0657152\pi$
$258$	−132.318	−	132.318i	−0.512859	−	0.512859i
$259$			88.7888i			0.342814i
$260$	−100.155	+	37.0589i	−0.385210	+	0.142534i
$261$	411.532			1.57675
$262$	75.6903	−	75.6903i	0.288894	−	0.288894i
$263$	−43.3194	−	43.3194i	−0.164713	−	0.164713i	0.619938	−	0.784651i	$-0.287158\pi$
$263$	−43.3194	−	43.3194i	−0.164713	−	0.164713i	−0.784651	+	0.619938i	$0.787158\pi$
$264$		−	324.178i		−	1.22795i
$265$	−84.6292	−	228.717i	−0.319355	−	0.863083i
$266$	−132.872			−0.499521
$267$	−715.383	+	715.383i	−2.67934	+	2.67934i
$268$	−58.4203	−	58.4203i	−0.217986	−	0.217986i
$269$			125.372i			0.466067i	0.972469	+	0.233034i	$0.0748652\pi$
$269$			125.372i			0.466067i	−0.972469	+	0.233034i	$0.925135\pi$
$270$	−245.147	+	533.119i	−0.907953	+	1.97452i
$271$	14.9242			0.0550709			0.0275354	−	0.999621i	$-0.491234\pi$
$271$	14.9242			0.0550709			0.0275354	+	0.999621i	$0.491234\pi$
$272$	2.73193	−	2.73193i	0.0100438	−	0.0100438i
$273$	−114.914	−	114.914i	−0.420931	−	0.420931i
$274$			56.5318i			0.206320i
$275$	326.930	+	381.292i	1.18884	+	1.38652i
$276$	−54.7196			−0.198259
$277$	−319.426	+	319.426i	−1.15316	+	1.15316i	−0.167249	+	0.985915i	$0.553488\pi$
$277$	−319.426	+	319.426i	−1.15316	+	1.15316i	−0.985915	+	0.167249i	$0.946512\pi$
$278$	122.072	+	122.072i	0.439106	+	0.439106i
$279$			132.149i			0.473653i
$280$	−34.2742	−	15.7605i	−0.122408	−	0.0562875i
$281$	−212.129			−0.754907			−0.377453	−	0.926029i	$-0.623200\pi$
$281$	−212.129			−0.754907			−0.377453	+	0.926029i	$0.623200\pi$
$282$	418.096	−	418.096i	1.48261	−	1.48261i
$283$	185.167	+	185.167i	0.654300	+	0.654300i	0.954025	−	0.299726i	$-0.0968951\pi$
$283$	185.167	+	185.167i	0.654300	+	0.654300i	−0.299726	+	0.954025i	$0.596895\pi$
$284$			30.4481i			0.107212i
$285$	−942.259	+	348.652i	−3.30617	+	1.22334i
$286$	303.417			1.06090
$287$	29.4217	−	29.4217i	0.102515	−	0.102515i
$288$	94.1839	+	94.1839i	0.327028	+	0.327028i
$289$			288.067i			0.996772i
$290$	42.8874	+	115.907i	0.147888	+	0.399678i
$291$	431.644			1.48331
$292$	79.5786	−	79.5786i	0.272529	−	0.272529i
$293$	−153.465	−	153.465i	−0.523772	−	0.523772i	0.394937	−	0.918708i	$-0.370767\pi$
$293$	−153.465	−	153.465i	−0.523772	−	0.523772i	−0.918708	+	0.394937i	$0.870767\pi$
$294$			337.922i			1.14939i
$295$	34.2851	−	74.5594i	0.116221	−	0.252744i
$296$	94.1452			0.318058
$297$	1178.87	−	1178.87i	3.96927	−	3.96927i
$298$	−125.669	−	125.669i	−0.421708	−	0.421708i
$299$		−	51.2152i		−	0.171288i
$300$	−284.409	−	21.8309i	−0.948029	−	0.0727696i
$301$	61.8690			0.205545
$302$	286.279	−	286.279i	0.947943	−	0.947943i
$303$	−508.041	−	508.041i	−1.67670	−	1.67670i
$304$			140.888i			0.463449i
$305$	297.612	+	136.853i	0.975776	+	0.448697i
$306$	32.1630			0.105108
$307$	−283.232	+	283.232i	−0.922580	+	0.922580i	−0.997211	−	0.0746308i	$-0.976222\pi$
$307$	−283.232	+	283.232i	−0.922580	+	0.922580i	0.0746308	+	0.997211i	$0.476222\pi$
$308$	75.7897	+	75.7897i	0.246070	+	0.246070i
$309$		−	177.556i		−	0.574614i
$310$	−37.2194	+	13.7718i	−0.120062	+	0.0444252i
$311$	140.570			0.451994			0.225997	−	0.974128i	$-0.427436\pi$
$311$	140.570			0.451994			0.225997	+	0.974128i	$0.427436\pi$
$312$	−121.847	+	121.847i	−0.390534	+	0.390534i
$313$	−188.126	−	188.126i	−0.601042	−	0.601042i	0.339547	−	0.940589i	$-0.389726\pi$
$313$	−188.126	−	188.126i	−0.601042	−	0.601042i	−0.940589	+	0.339547i	$0.889726\pi$
$314$		−	27.7775i		−	0.0884634i
$315$	−108.981	−	294.529i	−0.345971	−	0.935013i
$316$	35.0304			0.110856
$317$	−92.2012	+	92.2012i	−0.290856	+	0.290856i	−0.837418	−	0.546563i	$-0.815936\pi$
$317$	−92.2012	+	92.2012i	−0.290856	+	0.290856i	0.546563	+	0.837418i	$0.315936\pi$
$318$	−278.254	−	278.254i	−0.875011	−	0.875011i
$319$		−	351.138i		−	1.10074i
$320$	−16.7113	+	36.3419i	−0.0522228	+	0.113568i
$321$	26.2985			0.0819269
$322$	12.7929	−	12.7929i	0.0397295	−	0.0397295i
$323$	24.0560	+	24.0560i	0.0744769	+	0.0744769i
$324$			522.999i			1.61419i
$325$	20.4327	−	266.194i	0.0628700	−	0.819060i
$326$	−105.034			−0.322191
$327$	448.213	−	448.213i	1.37068	−	1.37068i
$328$	−31.1966	−	31.1966i	−0.0951117	−	0.0951117i
$329$			195.493i			0.594204i
$330$	736.328	+	338.590i	2.23130	+	1.02603i
$331$	209.749			0.633683			0.316842	−	0.948478i	$-0.397378\pi$
$331$	209.749			0.633683			0.316842	+	0.948478i	$0.397378\pi$
$332$	21.7941	−	21.7941i	0.0656449	−	0.0656449i
$333$	554.185	+	554.185i	1.66422	+	1.66422i
$334$		−	227.995i		−	0.682619i
$335$	193.711	−	71.6765i	0.578243	−	0.213960i
$336$	−60.8714			−0.181165
$337$	−42.6009	+	42.6009i	−0.126412	+	0.126412i	−0.767482	−	0.641070i	$-0.778491\pi$
$337$	−42.6009	+	42.6009i	−0.126412	+	0.126412i	0.641070	+	0.767482i	$0.278491\pi$
$338$	54.9569	+	54.9569i	0.162594	+	0.162594i
$339$		−	1045.05i		−	3.08273i
$340$	3.35183	+	9.05859i	0.00985833	+	0.0266429i
$341$	112.756			0.330661
$342$	−829.339	+	829.339i	−2.42497	+	2.42497i
$343$	−171.427	−	171.427i	−0.499787	−	0.499787i
$344$		−	65.6015i		−	0.190702i
$345$	57.1522	−	124.288i	0.165659	−	0.360256i
$346$	272.632			0.787955
$347$	175.961	−	175.961i	0.507092	−	0.507092i	−0.406541	−	0.913633i	$-0.633265\pi$
$347$	175.961	−	175.961i	0.507092	−	0.507092i	0.913633	+	0.406541i	$0.133265\pi$
$348$	141.010	+	141.010i	0.405202	+	0.405202i
$349$			520.820i			1.49232i	0.665767	+	0.746160i	$0.268105\pi$
$349$			520.820i			1.49232i	−0.665767	+	0.746160i	$0.731895\pi$
$350$	71.5958	−	61.3881i	0.204559	−	0.175395i
$351$	−886.189			−2.52476
$352$	80.3619	−	80.3619i	0.228301	−	0.228301i
$353$	206.698	+	206.698i	0.585547	+	0.585547i	0.936422	−	0.350875i	$-0.114116\pi$
$353$	206.698	+	206.698i	0.585547	+	0.585547i	−0.350875	+	0.936422i	$0.614116\pi$
$354$		−	132.418i		−	0.374063i
$355$	−69.1588	−	31.8017i	−0.194813	−	0.0895822i
$356$	−354.679			−0.996288
$357$	−10.3935	+	10.3935i	−0.0291135	+	0.0291135i
$358$	−108.813	−	108.813i	−0.303947	−	0.303947i
$359$			495.671i			1.38070i	0.723476	+	0.690349i	$0.242543\pi$
$359$			495.671i			1.38070i	−0.723476	+	0.690349i	$0.757457\pi$
$360$	−312.297	+	115.555i	−0.867493	+	0.320987i
$361$	−879.596			−2.43655
$362$	125.598	−	125.598i	0.346957	−	0.346957i
$363$	−1140.11	−	1140.11i	−3.14081	−	3.14081i
$364$		−	56.9730i		−	0.156519i
$365$	97.6358	+	263.868i	0.267495	+	0.722927i
$366$	528.563			1.44416
$367$	−98.8167	+	98.8167i	−0.269255	+	0.269255i	−0.828800	−	0.559545i	$-0.810976\pi$
$367$	−98.8167	+	98.8167i	−0.269255	+	0.269255i	0.559545	+	0.828800i	$0.310976\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$		−	367.278i		−	0.995333i
$370$	−98.3306	+	213.838i	−0.265758	+	0.577942i
$371$	130.106			0.350690
$372$	−45.2805	+	45.2805i	−0.121722	+	0.121722i
$373$	80.9822	+	80.9822i	0.217111	+	0.217111i	0.807280	−	0.590169i	$-0.200939\pi$
$373$	80.9822	+	80.9822i	0.217111	+	0.217111i	−0.590169	+	0.807280i	$0.700939\pi$
$374$		−	27.4429i		−	0.0733766i
$375$	346.639	−	623.196i	0.924369	−	1.66185i
$376$	207.287			0.551295
$377$	−131.979	+	131.979i	−0.350078	+	0.350078i
$378$	−221.359	−	221.359i	−0.585605	−	0.585605i
$379$			239.887i			0.632946i	0.948601	+	0.316473i	$0.102499\pi$
$379$			239.887i			0.632946i	−0.948601	+	0.316473i	$0.897501\pi$
$380$	−320.009	−	147.152i	−0.842130	−	0.387242i
$381$	−287.645			−0.754975
$382$	277.559	−	277.559i	0.726594	−	0.726594i
$383$	125.770	+	125.770i	0.328382	+	0.328382i	0.851971	−	0.523589i	$-0.175407\pi$
$383$	125.770	+	125.770i	0.328382	+	0.328382i	−0.523589	+	0.851971i	$0.675407\pi$
$384$			64.5437i			0.168082i
$385$	−251.305	+	92.9872i	−0.652741	+	0.241525i
$386$	−154.211			−0.399511
$387$	386.163	−	386.163i	0.997837	−	0.997837i
$388$	107.002	+	107.002i	0.275779	+	0.275779i
$389$		−	66.1562i		−	0.170067i	−0.996378	−	0.0850337i	$-0.972900\pi$
$389$		−	66.1562i		−	0.170067i	0.996378	−	0.0850337i	$-0.0270998\pi$
$390$	−149.495	−	404.022i	−0.383320	−	1.03595i
$391$	−4.63221			−0.0118471
$392$	−83.7689	+	83.7689i	−0.213696	+	0.213696i
$393$	305.333	+	305.333i	0.776929	+	0.776929i
$394$			66.7928i			0.169525i
$395$	−36.5877	+	79.5669i	−0.0926272	+	0.201435i
$396$	946.100			2.38914
$397$	−5.18783	+	5.18783i	−0.0130676	+	0.0130676i	−0.713610	−	0.700543i	$-0.752941\pi$
$397$	−5.18783	+	5.18783i	−0.0130676	+	0.0130676i	0.700543	+	0.713610i	$0.252941\pi$
$398$	193.467	+	193.467i	0.486099	+	0.486099i
$399$		−	536.005i		−	1.34337i
$400$	−65.0915	−	75.9150i	−0.162729	−	0.189788i
$401$	345.727			0.862162			0.431081	−	0.902313i	$-0.358132\pi$
$401$	345.727			0.862162			0.431081	+	0.902313i	$0.358132\pi$
$402$	235.666	−	235.666i	0.586234	−	0.586234i
$403$	−42.3806	−	42.3806i	−0.105163	−	0.105163i
$404$		−	251.881i		−	0.623468i
$405$	−1187.92	−	546.250i	−2.93314	−	1.34876i
$406$	−65.9336			−0.162398
$407$	472.856	−	472.856i	1.16181	−	1.16181i
$408$	11.0205	+	11.0205i	0.0270111	+	0.0270111i
$409$		−	272.912i		−	0.667267i	−0.942703	−	0.333634i	$-0.891725\pi$
$409$		−	272.912i		−	0.667267i	0.942703	−	0.333634i	$-0.108275\pi$
$410$	103.443	−	38.2755i	0.252299	−	0.0933549i
$411$	−228.048			−0.554861
$412$	44.0150	−	44.0150i	0.106833	−	0.106833i
$413$	30.9581	+	30.9581i	0.0749591	+	0.0749591i
$414$		−	159.697i		−	0.385741i
$415$	26.7394	+	72.2654i	0.0644324	+	0.174134i
$416$	−60.4101			−0.145217
$417$	−492.434	+	492.434i	−1.18090	+	1.18090i
$418$	707.629	+	707.629i	1.69289	+	1.69289i
$419$			470.105i			1.12197i	0.827826	+	0.560985i	$0.189577\pi$
$419$			470.105i			1.12197i	−0.827826	+	0.560985i	$0.810423\pi$
$420$	63.5776	−	138.261i	0.151375	−	0.329194i
$421$	674.119			1.60123			0.800616	−	0.599177i	$-0.204506\pi$
$421$	674.119			1.60123			0.800616	+	0.599177i	$0.204506\pi$
$422$	−86.4981	+	86.4981i	−0.204972	+	0.204972i
$423$	1220.19	+	1220.19i	2.88462	+	2.88462i
$424$		−	137.955i		−	0.325365i
$425$	−24.0762	−	1.84806i	−0.0566499	−	0.00434838i
$426$	−122.827			−0.288326
$427$	−123.573	+	123.573i	−0.289397	+	0.289397i
$428$	6.51925	+	6.51925i	0.0152319	+	0.0152319i
$429$			1223.98i			2.85310i
$430$	149.005	+	68.5179i	0.346523	+	0.159344i
$431$	−223.842			−0.519356			−0.259678	−	0.965695i	$-0.583616\pi$
$431$	−223.842			−0.519356			−0.259678	+	0.965695i	$0.583616\pi$
$432$	−234.713	+	234.713i	−0.543317	+	0.543317i
$433$	312.683	+	312.683i	0.722131	+	0.722131i	0.969039	−	0.246908i	$-0.0794146\pi$
$433$	312.683	+	312.683i	0.722131	+	0.722131i	−0.246908	+	0.969039i	$0.579415\pi$
$434$		−	21.1723i		−	0.0487840i
$435$	−467.565	+	173.007i	−1.07486	+	0.397717i
$436$	222.219			0.509676
$437$	119.444	−	119.444i	0.273327	−	0.273327i
$438$	321.018	+	321.018i	0.732918	+	0.732918i
$439$			363.650i			0.828360i	0.910195	+	0.414180i	$0.135932\pi$
$439$			363.650i			0.828360i	−0.910195	+	0.414180i	$0.864068\pi$
$440$	98.5969	+	266.466i	0.224084	+	0.605605i
$441$	−986.210			−2.23630
$442$	−10.3147	+	10.3147i	−0.0233365	+	0.0233365i
$443$	−92.5985	−	92.5985i	−0.209026	−	0.209026i	0.594827	−	0.803853i	$-0.297220\pi$
$443$	−92.5985	−	92.5985i	−0.209026	−	0.209026i	−0.803853	+	0.594827i	$0.797220\pi$
$444$			379.780i			0.855360i
$445$	370.446	−	805.605i	0.832464	−	1.81035i
$446$	−374.120			−0.838834
$447$	506.946	−	506.946i	1.13411	−	1.13411i
$448$	−15.0897	−	15.0897i	−0.0336823	−	0.0336823i
$449$		−	507.629i		−	1.13058i	−0.824893	−	0.565289i	$-0.808765\pi$
$449$		−	507.629i		−	1.13058i	0.824893	−	0.565289i	$-0.191235\pi$
$450$	63.7124	−	830.035i	0.141583	−	1.84452i
$451$	−313.378			−0.694851
$452$	259.061	−	259.061i	0.573144	−	0.573144i
$453$	1154.84	+	1154.84i	2.54932	+	2.54932i
$454$		−	375.882i		−	0.827934i
$455$	129.407	+	59.5059i	0.284410	+	0.130782i
$456$	−568.341			−1.24636
$457$	225.631	−	225.631i	0.493723	−	0.493723i	−0.415754	−	0.909477i	$-0.636482\pi$
$457$	225.631	−	225.631i	0.493723	−	0.493723i	0.909477	+	0.415754i	$0.136482\pi$
$458$	39.4344	+	39.4344i	0.0861014	+	0.0861014i
$459$			80.1523i			0.174624i
$460$	44.9780	−	16.6426i	0.0977783	−	0.0361796i
$461$	52.9823			0.114929			0.0574645	−	0.998348i	$-0.481698\pi$
$461$	52.9823			0.114929			0.0574645	+	0.998348i	$0.481698\pi$
$462$	−305.734	+	305.734i	−0.661762	+	0.661762i
$463$	−67.3078	−	67.3078i	−0.145373	−	0.145373i	0.630674	−	0.776048i	$-0.282778\pi$
$463$	−67.3078	−	67.3078i	−0.145373	−	0.145373i	−0.776048	+	0.630674i	$0.782778\pi$
$464$			69.9112i			0.150671i
$465$	−55.5551	−	150.142i	−0.119473	−	0.322886i
$466$	−588.971			−1.26389
$467$	144.478	−	144.478i	0.309375	−	0.309375i	−0.535292	−	0.844667i	$-0.679798\pi$
$467$	144.478	−	144.478i	0.309375	−	0.309375i	0.844667	+	0.535292i	$0.179798\pi$
$468$	−355.604	−	355.604i	−0.759837	−	0.759837i
$469$			110.193i			0.234953i
$470$	−216.502	+	470.825i	−0.460643	+	1.00176i
$471$	112.054			0.237906
$472$	32.8258	−	32.8258i	0.0695461	−	0.0695461i
$473$	−329.491	−	329.491i	−0.696599	−	0.696599i
$474$			141.312i			0.298126i
$475$	668.472	−	573.165i	1.40731	−	1.20666i
$476$	−5.15299			−0.0108256
$477$	812.071	−	812.071i	1.70245	−	1.70245i
$478$	261.434	+	261.434i	0.546933	+	0.546933i
$479$		−	816.501i		−	1.70460i	−0.523057	−	0.852298i	$-0.675208\pi$
$479$		−	816.501i		−	1.70460i	0.523057	−	0.852298i	$-0.324792\pi$
$480$	−146.602	−	67.4131i	−0.305422	−	0.140444i
$481$	−355.458			−0.738997
$482$	73.8241	−	73.8241i	0.153162	−	0.153162i
$483$	51.6063	+	51.6063i	0.106845	+	0.106845i
$484$		−	565.255i		−	1.16788i
$485$	−354.800	+	131.282i	−0.731547	+	0.270685i
$486$	−1053.56			−2.16782
$487$	−426.380	+	426.380i	−0.875524	+	0.875524i	−0.993068	−	0.117543i	$-0.962498\pi$
$487$	−426.380	+	426.380i	−0.875524	+	0.875524i	0.117543	+	0.993068i	$0.462498\pi$
$488$	131.028	+	131.028i	0.268499	+	0.268499i
$489$		−	423.706i		−	0.866474i
$490$	−102.777	−	277.763i	−0.209749	−	0.566863i
$491$	629.728			1.28254			0.641271	−	0.767314i	$-0.278407\pi$
$491$	629.728			1.28254			0.641271	+	0.767314i	$0.278407\pi$
$492$	125.847	−	125.847i	0.255786	−	0.255786i
$493$	11.9370	+	11.9370i	0.0242130	+	0.0242130i
$494$		−	531.943i		−	1.07681i
$495$	−988.161	+	2148.94i	−1.99628	+	4.34130i
$496$	−22.4495			−0.0452612
$497$	28.7157	−	28.7157i	0.0577781	−	0.0577781i
$498$	87.9170	+	87.9170i	0.176540	+	0.176540i
$499$		−	889.589i		−	1.78274i	−0.453272	−	0.891372i	$-0.649744\pi$
$499$		−	889.589i		−	1.78274i	0.453272	−	0.891372i	$-0.350256\pi$
$500$	240.416	−	68.5569i	0.480832	−	0.137114i
$501$	919.726			1.83578
$502$	252.912	−	252.912i	0.503810	−	0.503810i
$503$	−294.309	−	294.309i	−0.585107	−	0.585107i	0.351195	−	0.936302i	$-0.385775\pi$
$503$	−294.309	−	294.309i	−0.585107	−	0.585107i	−0.936302	+	0.351195i	$0.885775\pi$
$504$		−	177.651i		−	0.352481i
$505$	572.114	+	263.079i	1.13290	+	0.520948i
$506$	−136.260			−0.269289
$507$	−221.695	+	221.695i	−0.437268	+	0.437268i
$508$	−71.3056	−	71.3056i	−0.140365	−	0.140365i
$509$			654.951i			1.28674i	0.765555	+	0.643370i	$0.222464\pi$
$509$			654.951i			1.28674i	−0.765555	+	0.643370i	$0.777536\pi$
$510$	−36.5422	+	13.5212i	−0.0716513	+	0.0265122i
$511$	−150.102			−0.293741
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−2066.77	−	2066.77i	−4.02879	−	4.02879i
$514$			397.722i			0.773778i
$515$	54.0025	+	145.946i	0.104859	+	0.283390i
$516$	264.635			0.512859
$517$	1041.12	−	1041.12i	2.01378	−	2.01378i
$518$	−88.7888	−	88.7888i	−0.171407	−	0.171407i
$519$			1099.79i			2.11906i
$520$	63.0957	−	137.214i	0.121338	−	0.263872i
$521$	725.838			1.39316			0.696582	−	0.717477i	$-0.254703\pi$
$521$	725.838			1.39316			0.696582	+	0.717477i	$0.254703\pi$
$522$	−411.532	+	411.532i	−0.788376	+	0.788376i
$523$	395.077	+	395.077i	0.755406	+	0.755406i	0.975483	−	0.220077i	$-0.0706308\pi$
$523$	395.077	+	395.077i	0.755406	+	0.755406i	−0.220077	+	0.975483i	$0.570631\pi$
$524$			151.381i			0.288894i
$525$	247.638	+	288.816i	0.471692	+	0.550126i
$526$	86.6388			0.164713
$527$	−3.83316	+	3.83316i	−0.00727354	+	0.00727354i
$528$	324.178	+	324.178i	0.613974	+	0.613974i
$529$			23.0000i			0.0434783i
$530$	313.346	+	144.088i	0.591219	+	0.271864i
$531$	386.457			0.727792
$532$	132.872	−	132.872i	0.249760	−	0.249760i
$533$	117.787	+	117.787i	0.220989	+	0.220989i
$534$		−	1430.77i		−	2.67934i
$535$	−21.6167	+	7.99854i	−0.0404050	+	0.0149505i
$536$	116.841			0.217986
$537$	438.950	−	438.950i	0.817411	−	0.817411i
$538$	−125.372	−	125.372i	−0.233034	−	0.233034i
$539$			841.478i			1.56118i
$540$	−287.972	−	778.266i	−0.533281	−	1.44123i
$541$	−940.313			−1.73810			−0.869051	−	0.494723i	$-0.835270\pi$
$541$	−940.313			−1.73810			−0.869051	+	0.494723i	$0.835270\pi$
$542$	−14.9242	+	14.9242i	−0.0275354	+	0.0275354i
$543$	506.661	+	506.661i	0.933078	+	0.933078i
$544$			5.46385i			0.0100438i
$545$	−232.098	+	504.741i	−0.425868	+	0.926130i
$546$	229.828			0.420931
$547$	−410.004	+	410.004i	−0.749550	+	0.749550i	−0.974395	−	0.224844i	$-0.927813\pi$
$547$	−410.004	+	410.004i	−0.749550	+	0.749550i	0.224844	+	0.974395i	$0.427813\pi$
$548$	−56.5318	−	56.5318i	−0.103160	−	0.103160i
$549$			1542.59i			2.80981i
$550$	−708.222	−	54.3623i	−1.28768	−	0.0988405i
$551$	−615.605			−1.11725
$552$	54.7196	−	54.7196i	0.0991296	−	0.0991296i
$553$	−33.0373	−	33.0373i	−0.0597420	−	0.0597420i
$554$		−	638.853i		−	1.15316i
$555$	−862.620	−	396.664i	−1.55427	−	0.714709i
$556$	−244.143			−0.439106
$557$	54.4225	−	54.4225i	0.0977065	−	0.0977065i	−0.656564	−	0.754270i	$-0.727991\pi$
$557$	54.4225	−	54.4225i	0.0977065	−	0.0977065i	0.754270	+	0.656564i	$0.227991\pi$
$558$	−132.149	−	132.149i	−0.236826	−	0.236826i
$559$			247.687i			0.443089i
$560$	50.0347	−	18.5137i	0.0893477	−	0.0330602i
$561$	110.704			0.197333
$562$	212.129	−	212.129i	0.377453	−	0.377453i
$563$	−590.460	−	590.460i	−1.04877	−	1.04877i	−0.998748	−	0.0500266i	$-0.984069\pi$
$563$	−590.460	−	590.460i	−1.04877	−	1.04877i	−0.0500266	−	0.998748i	$-0.515931\pi$
$564$			836.191i			1.48261i
$565$	317.845	+	859.001i	0.562557	+	1.52036i
$566$	−370.334			−0.654300
$567$	493.243	−	493.243i	0.869917	−	0.869917i
$568$	−30.4481	−	30.4481i	−0.0536058	−	0.0536058i
$569$		−	256.363i		−	0.450549i	−0.974295	−	0.225275i	$-0.927672\pi$
$569$		−	256.363i		−	0.450549i	0.974295	−	0.225275i	$-0.0723280\pi$
$570$	593.607	−	1290.91i	1.04142	−	2.26476i
$571$	−503.583			−0.881932			−0.440966	−	0.897524i	$-0.645364\pi$
$571$	−503.583			−0.881932			−0.440966	+	0.897524i	$0.645364\pi$
$572$	−303.417	+	303.417i	−0.530449	+	0.530449i
$573$	1119.67	+	1119.67i	1.95404	+	1.95404i
$574$			58.8434i			0.102515i
$575$	−9.17606	+	119.544i	−0.0159584	+	0.207903i
$576$	−188.368			−0.327028
$577$	−426.083	+	426.083i	−0.738445	+	0.738445i	−0.972277	−	0.233832i	$-0.924874\pi$
$577$	−426.083	+	426.083i	−0.738445	+	0.738445i	0.233832	+	0.972277i	$0.424874\pi$
$578$	−288.067	−	288.067i	−0.498386	−	0.498386i
$579$		−	622.085i		−	1.07441i
$580$	−158.794	−	73.0192i	−0.273783	−	0.125895i
$581$	−41.1082			−0.0707543
$582$	−431.644	+	431.644i	−0.741657	+	0.741657i
$583$	−692.895	−	692.895i	−1.18850	−	1.18850i
$584$			159.157i			0.272529i
$585$	1179.12	−	436.294i	2.01559	−	0.745802i
$586$	306.930			0.523772
$587$	531.894	−	531.894i	0.906122	−	0.906122i	−0.0898343	−	0.995957i	$-0.528634\pi$
$587$	531.894	−	531.894i	0.906122	−	0.906122i	0.995957	+	0.0898343i	$0.0286337\pi$
$588$	−337.922	−	337.922i	−0.574697	−	0.574697i
$589$		−	197.680i		−	0.335620i
$590$	40.2743	+	108.844i	0.0682615	+	0.184482i
$591$	−269.441			−0.455906
$592$	−94.1452	+	94.1452i	−0.159029	+	0.159029i
$593$	−390.563	−	390.563i	−0.658622	−	0.658622i	0.296432	−	0.955054i	$-0.404203\pi$
$593$	−390.563	−	390.563i	−0.658622	−	0.658622i	−0.955054	+	0.296432i	$0.904203\pi$
$594$			2357.75i			3.96927i
$595$	5.38207	−	11.7043i	0.00904549	−	0.0196711i
$596$	251.338			0.421708
$597$	−780.444	+	780.444i	−1.30728	+	1.30728i
$598$	51.2152	+	51.2152i	0.0856441	+	0.0856441i
$599$			867.565i			1.44836i	0.689613	+	0.724178i	$0.257781\pi$
$599$			867.565i			1.44836i	−0.689613	+	0.724178i	$0.742219\pi$
$600$	306.240	−	262.578i	0.510399	−	0.437630i
$601$	−345.554			−0.574965			−0.287483	−	0.957786i	$-0.592818\pi$
$601$	−345.554			−0.574965			−0.287483	+	0.957786i	$0.592818\pi$
$602$	−61.8690	+	61.8690i	−0.102772	+	0.102772i
$603$	687.781	+	687.781i	1.14060	+	1.14060i
$604$			572.557i			0.947943i
$605$	1283.90	+	590.384i	2.12215	+	0.975841i
$606$	1016.08			1.67670
$607$	−103.808	+	103.808i	−0.171018	+	0.171018i	−0.787426	−	0.616409i	$-0.788587\pi$
$607$	−103.808	+	103.808i	−0.171018	+	0.171018i	0.616409	+	0.787426i	$0.288587\pi$
$608$	−140.888	−	140.888i	−0.231724	−	0.231724i
$609$		−	265.975i		−	0.436740i
$610$	−434.464	+	160.759i	−0.712237	+	0.263540i
$611$	−782.639			−1.28092
$612$	−32.1630	+	32.1630i	−0.0525538	+	0.0525538i
$613$	−506.763	−	506.763i	−0.826694	−	0.826694i	0.160364	−	0.987058i	$-0.448733\pi$
$613$	−506.763	−	506.763i	−0.826694	−	0.826694i	−0.987058	+	0.160364i	$0.948733\pi$
$614$		−	566.464i		−	0.922580i
$615$	154.403	+	417.285i	0.251061	+	0.678512i
$616$	−151.579			−0.246070
$617$	−507.705	+	507.705i	−0.822861	+	0.822861i	−0.986517	−	0.163656i	$-0.947671\pi$
$617$	−507.705	+	507.705i	−0.822861	+	0.822861i	0.163656	+	0.986517i	$0.447671\pi$
$618$	177.556	+	177.556i	0.287307	+	0.287307i
$619$		−	99.4733i		−	0.160700i	−0.996767	−	0.0803500i	$-0.974396\pi$
$619$		−	99.4733i		−	0.160700i	0.996767	−	0.0803500i	$-0.0256038\pi$
$620$	23.4476	−	50.9912i	0.0378187	−	0.0822438i
$621$	397.975			0.640861
$622$	−140.570	+	140.570i	−0.225997	+	0.225997i
$623$	334.499	+	334.499i	0.536916	+	0.536916i
$624$		−	243.693i		−	0.390534i
$625$	−95.3864	+	617.678i	−0.152618	+	0.988285i
$626$	376.252			0.601042
$627$	−2854.56	+	2854.56i	−4.55273	+	4.55273i
$628$	27.7775	+	27.7775i	0.0442317	+	0.0442317i
$629$			32.1497i			0.0511125i
$630$	403.510	+	185.548i	0.640492	+	0.294521i
$631$	−1038.63			−1.64601			−0.823004	−	0.568036i	$-0.807704\pi$
$631$	−1038.63			−1.64601			−0.823004	+	0.568036i	$0.807704\pi$
$632$	−35.0304	+	35.0304i	−0.0554279	+	0.0554279i
$633$	−348.932	−	348.932i	−0.551235	−	0.551235i
$634$		−	184.402i		−	0.290856i
$635$	236.437	−	87.4856i	0.372341	−	0.137773i
$636$	556.507			0.875011
$637$	316.280	−	316.280i	0.496515	−	0.496515i
$638$	351.138	+	351.138i	0.550372	+	0.550372i
$639$		−	358.465i		−	0.560978i
$640$	−19.6306	−	53.0532i	−0.0306728	−	0.0828956i
$641$	696.446			1.08650			0.543250	−	0.839571i	$-0.317194\pi$
$641$	696.446			1.08650			0.543250	+	0.839571i	$0.317194\pi$
$642$	−26.2985	+	26.2985i	−0.0409634	+	0.0409634i
$643$	−108.518	−	108.518i	−0.168768	−	0.168768i	0.617670	−	0.786438i	$-0.288077\pi$
$643$	−108.518	−	108.518i	−0.168768	−	0.168768i	−0.786438	+	0.617670i	$0.788077\pi$
$644$			25.5858i			0.0397295i
$645$	−276.400	+	601.083i	−0.428527	+	0.931912i
$646$	−48.1121			−0.0744769
$647$	−151.928	+	151.928i	−0.234820	+	0.234820i	−0.814701	−	0.579881i	$-0.803099\pi$
$647$	−151.928	+	151.928i	−0.234820	+	0.234820i	0.579881	+	0.814701i	$0.303099\pi$
$648$	−522.999	−	522.999i	−0.807097	−	0.807097i
$649$		−	329.743i		−	0.508078i
$650$	245.762	+	286.627i	0.378095	+	0.440965i
$651$	85.4085			0.131196
$652$	105.034	−	105.034i	0.161095	−	0.161095i
$653$	−855.346	−	855.346i	−1.30987	−	1.30987i	−0.921505	−	0.388366i	$-0.873040\pi$
$653$	−855.346	−	855.346i	−1.30987	−	1.30987i	−0.388366	−	0.921505i	$-0.626960\pi$
$654$			896.426i			1.37068i
$655$	−343.841	−	158.110i	−0.524948	−	0.241390i
$656$	62.3933			0.0951117
$657$	−936.878	+	936.878i	−1.42599	+	1.42599i
$658$	−195.493	−	195.493i	−0.297102	−	0.297102i
$659$		−	61.8242i		−	0.0938151i	−0.998899	−	0.0469076i	$-0.985063\pi$
$659$		−	61.8242i		−	0.0938151i	0.998899	−	0.0469076i	$-0.0149366\pi$
$660$	−1074.92	+	397.738i	−1.62866	+	0.602633i
$661$	839.834			1.27055			0.635275	−	0.772286i	$-0.280887\pi$
$661$	839.834			1.27055			0.635275	+	0.772286i	$0.280887\pi$
$662$	−209.749	+	209.749i	−0.316842	+	0.316842i
$663$	−41.6095	−	41.6095i	−0.0627594	−	0.0627594i
$664$			43.5882i			0.0656449i
$665$	163.023	+	440.582i	0.245147	+	0.662529i
$666$	−1108.37			−1.66422
$667$	59.2701	−	59.2701i	0.0888608	−	0.0888608i
$668$	227.995	+	227.995i	0.341310	+	0.341310i
$669$		−	1509.19i		−	2.25589i
$670$	−122.035	+	265.388i	−0.182142	+	0.396101i
$671$	1316.20			1.96156
$672$	60.8714	−	60.8714i	0.0905825	−	0.0905825i
$673$	723.930	+	723.930i	1.07568	+	1.07568i	0.996892	+	0.0787838i	$0.0251037\pi$
$673$	723.930	+	723.930i	1.07568	+	1.07568i	0.0787838	+	0.996892i	$0.474896\pi$
$674$		−	85.2019i		−	0.126412i
$675$	2068.50	+	158.776i	3.06445	+	0.235223i
$676$	−109.914			−0.162594
$677$	328.540	−	328.540i	0.485289	−	0.485289i	−0.421527	−	0.906816i	$-0.638506\pi$
$677$	328.540	−	328.540i	0.485289	−	0.485289i	0.906816	+	0.421527i	$0.138506\pi$
$678$	1045.05	+	1045.05i	1.54137	+	1.54137i
$679$		−	201.828i		−	0.297244i
$680$	−12.4104	−	5.70676i	−0.0182506	−	0.00839229i
$681$	1516.30			2.22658
$682$	−112.756	+	112.756i	−0.165331	+	0.165331i
$683$	−230.183	−	230.183i	−0.337018	−	0.337018i	0.518226	−	0.855244i	$-0.326593\pi$
$683$	−230.183	−	230.183i	−0.337018	−	0.337018i	−0.855244	+	0.518226i	$0.826593\pi$
$684$		−	1658.68i		−	2.42497i
$685$	187.449	−	69.3594i	0.273649	−	0.101255i
$686$	342.854			0.499787
$687$	−159.078	+	159.078i	−0.231554	+	0.231554i
$688$	65.6015	+	65.6015i	0.0953510	+	0.0953510i
$689$			520.867i			0.755975i
$690$	67.1360	+	181.440i	0.0972986	+	0.262957i
$691$	1055.02			1.52680			0.763402	−	0.645923i	$-0.223527\pi$
$691$	1055.02			1.52680			0.763402	+	0.645923i	$0.223527\pi$
$692$	−272.632	+	272.632i	−0.393978	+	0.393978i
$693$	−892.271	−	892.271i	−1.28755	−	1.28755i
$694$			351.922i			0.507092i
$695$	254.997	−	554.539i	0.366902	−	0.797897i
$696$	−282.020			−0.405202
$697$	10.6534	−	10.6534i	0.0152846	−	0.0152846i
$698$	−520.820	−	520.820i	−0.746160	−	0.746160i
$699$		−	2375.90i		−	3.39899i
$700$	−10.2077	+	132.984i	−0.0145824	+	0.189977i
$701$	−543.030			−0.774651			−0.387325	−	0.921943i	$-0.626601\pi$
$701$	−543.030			−0.774651			−0.387325	+	0.921943i	$0.626601\pi$
$702$	886.189	−	886.189i	1.26238	−	1.26238i
$703$	−828.998	−	828.998i	−1.17923	−	1.17923i
$704$			160.724i			0.228301i
$705$	−1899.30	−	873.366i	−2.69404	−	1.23882i
$706$	−413.396			−0.585547
$707$	−237.550	+	237.550i	−0.335997	+	0.335997i
$708$	132.418	+	132.418i	0.187032	+	0.187032i
$709$		−	320.268i		−	0.451717i	−0.974160	−	0.225859i	$-0.927481\pi$
$709$		−	320.268i		−	0.451717i	0.974160	−	0.225859i	$-0.0725188\pi$
$710$	100.960	−	37.3571i	0.142198	−	0.0526156i
$711$	−412.413			−0.580046
$712$	354.679	−	354.679i	0.498144	−	0.498144i
$713$	19.0325	+	19.0325i	0.0266936	+	0.0266936i
$714$		−	20.7870i		−	0.0291135i
$715$	−372.266	−	1006.08i	−0.520651	−	1.40710i
$716$	217.626			0.303947
$717$	−1054.62	+	1054.62i	−1.47088	+	1.47088i
$718$	−495.671	−	495.671i	−0.690349	−	0.690349i
$719$			760.314i			1.05746i	0.848790	+	0.528731i	$0.177332\pi$
$719$			760.314i			1.05746i	−0.848790	+	0.528731i	$0.822668\pi$
$720$	196.742	−	427.853i	0.273253	−	0.594240i
$721$	−83.0215			−0.115148
$722$	879.596	−	879.596i	1.21828	−	1.21828i
$723$	297.805	+	297.805i	0.411902	+	0.411902i
$724$			251.197i			0.346957i
$725$	331.707	−	284.414i	0.457527	−	0.392296i
$726$	2280.23			3.14081
$727$	415.843	−	415.843i	0.571998	−	0.571998i	−0.360688	−	0.932686i	$-0.617458\pi$
$727$	415.843	−	415.843i	0.571998	−	0.571998i	0.932686	+	0.360688i	$0.117458\pi$
$728$	56.9730	+	56.9730i	0.0782597	+	0.0782597i
$729$		−	1896.54i		−	2.60157i
$730$	−361.504	−	166.233i	−0.495211	−	0.227716i
$731$	22.4023			0.0306461
$732$	−528.563	+	528.563i	−0.722080	+	0.722080i
$733$	−755.714	−	755.714i	−1.03099	−	1.03099i	−0.999504	−	0.0314835i	$-0.989977\pi$
$733$	−755.714	−	755.714i	−1.03099	−	1.03099i	−0.0314835	−	0.999504i	$-0.510023\pi$
$734$		−	197.633i		−	0.269255i
$735$	1120.49	−	414.600i	1.52448	−	0.564082i
$736$	27.1293			0.0368605
$737$	586.846	−	586.846i	0.796263	−	0.796263i
$738$	367.278	+	367.278i	0.497666	+	0.497666i
$739$		−	1293.47i		−	1.75029i	−0.483860	−	0.875146i	$-0.660765\pi$
$739$		−	1293.47i		−	1.75029i	0.483860	−	0.875146i	$-0.339235\pi$
$740$	−115.508	−	312.169i	−0.156092	−	0.421850i
$741$	2145.85			2.89588
$742$	−130.106	+	130.106i	−0.175345	+	0.175345i
$743$	−666.497	−	666.497i	−0.897035	−	0.897035i	0.0981383	−	0.995173i	$-0.468711\pi$
$743$	−666.497	−	666.497i	−0.897035	−	0.897035i	−0.995173	+	0.0981383i	$0.968711\pi$
$744$		−	90.5610i		−	0.121722i
$745$	−262.512	+	570.881i	−0.352365	+	0.766283i
$746$	−161.964			−0.217111
$747$	−256.582	+	256.582i	−0.343483	+	0.343483i
$748$	27.4429	+	27.4429i	0.0366883	+	0.0366883i
$749$		−	12.2967i		−	0.0164174i
$750$	276.557	+	969.834i	0.368743	+	1.29311i
$751$	−207.594			−0.276424			−0.138212	−	0.990403i	$-0.544135\pi$
$751$	−207.594			−0.276424			−0.138212	+	0.990403i	$0.544135\pi$
$752$	−207.287	+	207.287i	−0.275648	+	0.275648i
$753$	1020.24	+	1020.24i	1.35490	+	1.35490i
$754$		−	263.959i		−	0.350078i
$755$	−1300.49	−	598.011i	−1.72250	−	0.792068i
$756$	442.717			0.585605
$757$	227.972	−	227.972i	0.301152	−	0.301152i	−0.540313	−	0.841464i	$-0.681694\pi$
$757$	227.972	−	227.972i	0.301152	−	0.301152i	0.841464	+	0.540313i	$0.181694\pi$
$758$	−239.887	−	239.887i	−0.316473	−	0.316473i
$759$		−	549.671i		−	0.724204i
$760$	467.161	−	172.858i	0.614686	−	0.227444i
$761$	−434.855			−0.571425			−0.285713	−	0.958315i	$-0.592230\pi$
$761$	−434.855			−0.571425			−0.285713	+	0.958315i	$0.592230\pi$
$762$	287.645	−	287.645i	0.377487	−	0.377487i
$763$	−209.576	−	209.576i	−0.274673	−	0.274673i
$764$			555.118i			0.726594i
$765$	−39.4611	−	106.647i	−0.0515831	−	0.139407i
$766$	−251.541			−0.328382
$767$	−123.938	+	123.938i	−0.161588	+	0.161588i
$768$	−64.5437	−	64.5437i	−0.0840412	−	0.0840412i
$769$			455.407i			0.592207i	0.955156	+	0.296103i	$0.0956873\pi$
$769$			455.407i			0.592207i	−0.955156	+	0.296103i	$0.904313\pi$
$770$	158.318	−	344.292i	0.205608	−	0.447133i
$771$	−1604.40			−2.08094
$772$	154.211	−	154.211i	0.199755	−	0.199755i
$773$	−126.005	−	126.005i	−0.163008	−	0.163008i	0.620890	−	0.783898i	$-0.286771\pi$
$773$	−126.005	−	126.005i	−0.163008	−	0.163008i	−0.783898	+	0.620890i	$0.786771\pi$
$774$			772.326i			0.997837i
$775$	91.3297	+	106.516i	0.117845	+	0.137440i
$776$	−214.004			−0.275779
$777$	358.172	−	358.172i	0.460968	−	0.460968i
$778$	66.1562	+	66.1562i	0.0850337	+	0.0850337i
$779$			549.405i			0.705270i
$780$	553.517	+	254.527i	0.709637	+	0.326316i
$781$	−305.858			−0.391624
$782$	4.63221	−	4.63221i	0.00592354	−	0.00592354i
$783$	−1025.57	−	1025.57i	−1.30979	−	1.30979i
$784$		−	167.538i		−	0.213696i
$785$	−92.1053	+	34.0805i	−0.117332	+	0.0434147i
$786$	−610.666			−0.776929
$787$	−488.802	+	488.802i	−0.621095	+	0.621095i	−0.945812	−	0.324716i	$-0.894731\pi$
$787$	−488.802	+	488.802i	−0.621095	+	0.621095i	0.324716	+	0.945812i	$0.394731\pi$
$788$	−66.7928	−	66.7928i	−0.0847624	−	0.0847624i
$789$			349.499i			0.442965i
$790$	−42.9792	−	116.155i	−0.0544040	−	0.147031i
$791$	−488.643			−0.617754
$792$	−946.100	+	946.100i	−1.19457	+	1.19457i
$793$	−494.712	−	494.712i	−0.623848	−	0.623848i
$794$		−	10.3757i		−	0.0130676i
$795$	−581.247	+	1264.03i	−0.731129	+	1.58998i
$796$	−386.935			−0.486099
$797$	642.104	−	642.104i	0.805651	−	0.805651i	−0.178321	−	0.983972i	$-0.557067\pi$
$797$	642.104	−	642.104i	0.805651	−	0.805651i	0.983972	+	0.178321i	$0.0570665\pi$
$798$	536.005	+	536.005i	0.671685	+	0.671685i
$799$			70.7866i			0.0885940i
$800$	141.007	+	10.8235i	0.176258	+	0.0135294i
$801$	4175.63			5.21302
$802$	−345.727	+	345.727i	−0.431081	+	0.431081i
$803$	799.386	+	799.386i	0.995499	+	0.995499i
$804$			471.332i			0.586234i
$805$	−58.1147	−	26.7232i	−0.0721922	−	0.0331966i
$806$	84.7612			0.105163
$807$	505.749	−	505.749i	0.626702	−	0.626702i
$808$	251.881	+	251.881i	0.311734	+	0.311734i
$809$			221.052i			0.273241i	0.990623	+	0.136620i	$0.0436240\pi$
$809$			221.052i			0.273241i	−0.990623	+	0.136620i	$0.956376\pi$
$810$	1734.17	−	641.673i	2.14095	−	0.792189i
$811$	−385.078			−0.474819			−0.237409	−	0.971410i	$-0.576298\pi$
$811$	−385.078			−0.474819			−0.237409	+	0.971410i	$0.576298\pi$
$812$	65.9336	−	65.9336i	0.0811990	−	0.0811990i
$813$	−60.2040	−	60.2040i	−0.0740516	−	0.0740516i
$814$			945.711i			1.16181i
$815$	128.868	+	348.275i	0.158120	+	0.427331i
$816$	−22.0411			−0.0270111
$817$	−577.655	+	577.655i	−0.707044	+	0.707044i
$818$	272.912	+	272.912i	0.333634	+	0.333634i
$819$			670.743i			0.818978i
$820$	−65.1671	+	141.718i	−0.0794720	+	0.172827i
$821$	236.485			0.288045			0.144023	−	0.989574i	$-0.453996\pi$
$821$	236.485			0.288045			0.144023	+	0.989574i	$0.453996\pi$
$822$	228.048	−	228.048i	0.277431	−	0.277431i
$823$	852.042	+	852.042i	1.03529	+	1.03529i	0.999354	+	0.0359336i	$0.0114405\pi$
$823$	852.042	+	852.042i	1.03529	+	1.03529i	0.0359336	+	0.999354i	$0.488560\pi$
$824$			88.0300i			0.106833i
$825$	219.296	−	2856.95i	0.265814	−	3.46298i
$826$	−61.9162			−0.0749591
$827$	212.256	−	212.256i	0.256658	−	0.256658i	−0.567035	−	0.823693i	$-0.691910\pi$
$827$	212.256	−	212.256i	0.256658	−	0.256658i	0.823693	+	0.567035i	$0.191910\pi$
$828$	159.697	+	159.697i	0.192870	+	0.192870i
$829$			1501.51i			1.81123i	0.424099	+	0.905616i	$0.360591\pi$
$829$			1501.51i			1.81123i	−0.424099	+	0.905616i	$0.639409\pi$
$830$	−99.0048	−	45.5260i	−0.119283	−	0.0548506i
$831$	2577.12			3.10123
$832$	60.4101	−	60.4101i	0.0726083	−	0.0726083i
$833$	−28.6063	−	28.6063i	−0.0343413	−	0.0343413i
$834$		−	984.868i		−	1.18090i
$835$	−755.991	+	279.729i	−0.905378	+	0.335005i
$836$	−1415.26			−1.69289
$837$	329.325	−	329.325i	0.393458	−	0.393458i
$838$	−470.105	−	470.105i	−0.560985	−	0.560985i
$839$			292.872i			0.349073i	0.984651	+	0.174536i	$0.0558427\pi$
$839$			292.872i			0.349073i	−0.984651	+	0.174536i	$0.944157\pi$
$840$	74.6838	+	201.839i	0.0889093	+	0.240284i
$841$	535.526			0.636773
$842$	−674.119	+	674.119i	−0.800616	+	0.800616i
$843$	855.723	+	855.723i	1.01509	+	1.01509i
$844$		−	172.996i		−	0.204972i
$845$	114.800	−	249.655i	0.135858	−	0.295449i
$846$	−2440.39			−2.88462
$847$	−533.094	+	533.094i	−0.629391	+	0.629391i
$848$	137.955	+	137.955i	0.162683	+	0.162683i
$849$		−	1493.92i		−	1.75962i
$850$	25.9243	−	22.2282i	0.0304992	−	0.0261508i
$851$	159.631			0.187580
$852$	122.827	−	122.827i	0.144163	−	0.144163i
$853$	98.2665	+	98.2665i	0.115201	+	0.115201i	0.762357	−	0.647156i	$-0.224042\pi$
$853$	98.2665	+	98.2665i	0.115201	+	0.115201i	−0.647156	+	0.762357i	$0.724042\pi$
$854$		−	247.145i		−	0.289397i
$855$	3767.47	+	1732.42i	4.40639	+	2.02622i
$856$	−13.0385			−0.0152319
$857$	1141.88	−	1141.88i	1.33241	−	1.33241i	0.429205	−	0.903207i	$-0.358794\pi$
$857$	1141.88	−	1141.88i	1.33241	−	1.33241i	0.903207	−	0.429205i	$-0.141206\pi$
$858$	−1223.98	−	1223.98i	−1.42655	−	1.42655i
$859$			416.145i			0.484453i	0.970220	+	0.242227i	$0.0778778\pi$
$859$			416.145i			0.484453i	−0.970220	+	0.242227i	$0.922122\pi$
$860$	−217.523	+	80.4872i	−0.252934	+	0.0935897i
$861$	−237.373			−0.275695
$862$	223.842	−	223.842i	0.259678	−	0.259678i
$863$	899.043	+	899.043i	1.04176	+	1.04176i	0.999089	+	0.0426753i	$0.0135881\pi$
$863$	899.043	+	899.043i	1.04176	+	1.04176i	0.0426753	+	0.999089i	$0.486412\pi$
$864$		−	469.426i		−	0.543317i
$865$	−334.496	−	904.001i	−0.386700	−	1.04509i
$866$	−625.365			−0.722131
$867$	1162.06	−	1162.06i	1.34032	−	1.34032i
$868$	21.1723	+	21.1723i	0.0243920	+	0.0243920i
$869$			351.889i			0.404935i
$870$	294.558	−	640.572i	0.338573	−	0.736290i
$871$	−441.147			−0.506483
$872$	−222.219	+	222.219i	−0.254838	+	0.254838i
$873$	−1259.74	−	1259.74i	−1.44300	−	1.44300i
$874$			238.888i			0.273327i
$875$	−291.394	−	162.081i	−0.333022	−	0.185236i
$876$	−642.037			−0.732918
$877$	−738.672	+	738.672i	−0.842271	+	0.842271i	−0.989154	−	0.146883i	$-0.953076\pi$
$877$	−738.672	+	738.672i	−0.842271	+	0.842271i	0.146883	+	0.989154i	$0.453076\pi$
$878$	−363.650	−	363.650i	−0.414180	−	0.414180i
$879$			1238.15i			1.40859i
$880$	−365.063	−	167.869i	−0.414844	−	0.190760i
$881$	878.371			0.997016			0.498508	−	0.866885i	$-0.333881\pi$
$881$	878.371			0.997016			0.498508	+	0.866885i	$0.333881\pi$
$882$	986.210	−	986.210i	1.11815	−	1.11815i
$883$	661.908	+	661.908i	0.749613	+	0.749613i	0.974406	−	0.224794i	$-0.0721709\pi$
$883$	661.908	+	661.908i	0.749613	+	0.749613i	−0.224794	+	0.974406i	$0.572171\pi$
$884$		−	20.6295i		−	0.0233365i
$885$	−439.076	+	162.466i	−0.496131	+	0.183577i
$886$	185.197			0.209026
$887$	628.822	−	628.822i	0.708931	−	0.708931i	−0.257380	−	0.966310i	$-0.582859\pi$
$887$	628.822	−	628.822i	0.708931	−	0.708931i	0.966310	+	0.257380i	$0.0828591\pi$
$888$	−379.780	−	379.780i	−0.427680	−	0.427680i
$889$			134.497i			0.151290i
$890$	435.159	+	1176.05i	0.488943	+	1.32141i
$891$	−5253.65			−5.89635
$892$	374.120	−	374.120i	0.419417	−	0.419417i
$893$	−1825.27	−	1825.27i	−2.04398	−	2.04398i
$894$			1013.89i			1.13411i
$895$	−227.301	+	494.309i	−0.253968	+	0.552301i
$896$	30.1793			0.0336823
$897$	−206.601	+	206.601i	−0.230324	+	0.230324i
$898$	507.629	+	507.629i	0.565289	+	0.565289i
$899$		−	98.0922i		−	0.109113i
$900$	766.322	+	893.747i	0.851469	+	0.993052i
$901$	47.1103			0.0522867
$902$	313.378	−	313.378i	0.347425	−	0.347425i
$903$	−249.578	−	249.578i	−0.276388	−	0.276388i
$904$			518.122i			0.573144i
$905$	−570.560	−	262.364i	−0.630453	−	0.289905i
$906$	−2309.68			−2.54932
$907$	−335.187	+	335.187i	−0.369555	+	0.369555i	−0.867315	−	0.497760i	$-0.834156\pi$
$907$	−335.187	+	335.187i	−0.369555	+	0.369555i	0.497760	+	0.867315i	$0.334156\pi$
$908$	375.882	+	375.882i	0.413967	+	0.413967i
$909$			2965.39i			3.26226i
$910$	−188.913	+	69.9008i	−0.207596	+	0.0768141i
$911$	−1140.93			−1.25239			−0.626196	−	0.779665i	$-0.715389\pi$
$911$	−1140.93			−1.25239			−0.626196	+	0.779665i	$0.715389\pi$
$912$	568.341	−	568.341i	0.623181	−	0.623181i
$913$	218.927	+	218.927i	0.239789	+	0.239789i
$914$			451.262i			0.493723i
$915$	−648.499	−	1752.62i	−0.708742	−	1.91543i
$916$	−78.8689			−0.0861014
$917$	142.768	−	142.768i	0.155690	−	0.155690i
$918$	−80.1523	−	80.1523i	−0.0873119	−	0.0873119i
$919$			379.230i			0.412655i	0.978483	+	0.206328i	$0.0661513\pi$
$919$			379.230i			0.412655i	−0.978483	+	0.206328i	$0.933849\pi$
$920$	−28.3354	+	61.6207i	−0.0307993	+	0.0669790i
$921$	2285.11			2.48111
$922$	−52.9823	+	52.9823i	−0.0574645	+	0.0574645i
$923$	114.961	+	114.961i	0.124551	+	0.124551i
$924$		−	611.468i		−	0.661762i
$925$	829.693	+	63.6862i	0.896966	+	0.0688500i
$926$	134.616			0.145373
$927$	−518.188	+	518.188i	−0.558995	+	0.558995i
$928$	−69.9112	−	69.9112i	−0.0753354	−	0.0753354i
$929$			316.810i			0.341022i	0.985356	+	0.170511i	$0.0545419\pi$
$929$			316.810i			0.341022i	−0.985356	+	0.170511i	$0.945458\pi$
$930$	205.697	+	94.5870i	0.221180	+	0.101706i
$931$	1475.26			1.58459
$932$	588.971	−	588.971i	0.631943	−	0.631943i
$933$	−567.057	−	567.057i	−0.607778	−	0.607778i
$934$			288.956i			0.309375i
$935$	−90.9957	+	33.6700i	−0.0973216	+	0.0360106i
$936$	711.208			0.759837
$937$	−12.1287	+	12.1287i	−0.0129442	+	0.0129442i	−0.713549	−	0.700605i	$-0.752914\pi$
$937$	−12.1287	+	12.1287i	−0.0129442	+	0.0129442i	0.700605	+	0.713549i	$0.252914\pi$
$938$	−110.193	−	110.193i	−0.117476	−	0.117476i
$939$			1517.79i			1.61640i
$940$	−254.323	−	687.327i	−0.270556	−	0.731199i
$941$	485.852			0.516314			0.258157	−	0.966103i	$-0.416885\pi$
$941$	485.852			0.516314			0.258157	+	0.966103i	$0.416885\pi$
$942$	−112.054	+	112.054i	−0.118953	+	0.118953i
$943$	−52.8965	−	52.8965i	−0.0560938	−	0.0560938i
$944$			65.6515i			0.0695461i
$945$	−462.399	+	1005.57i	−0.489311	+	1.06410i
$946$	658.983			0.696599
$947$	102.008	−	102.008i	0.107717	−	0.107717i	−0.651194	−	0.758911i	$-0.725732\pi$
$947$	102.008	−	102.008i	0.107717	−	0.107717i	0.758911	+	0.651194i	$0.225732\pi$
$948$	−141.312	−	141.312i	−0.149063	−	0.149063i
$949$		−	600.919i		−	0.633212i
$950$	−95.3065	+	1241.64i	−0.100323	+	1.30699i
$951$	743.876			0.782204
$952$	5.15299	−	5.15299i	0.00541280	−	0.00541280i
$953$	−809.506	−	809.506i	−0.849429	−	0.849429i	0.140633	−	0.990062i	$-0.455086\pi$
$953$	−809.506	−	809.506i	−0.849429	−	0.849429i	−0.990062	+	0.140633i	$0.955086\pi$
$954$			1624.14i			1.70245i
$955$	−1260.88	−	579.797i	−1.32029	−	0.607117i
$956$	−522.867			−0.546933
$957$	−1416.48	+	1416.48i	−1.48013	+	1.48013i
$958$	816.501	+	816.501i	0.852298	+	0.852298i
$959$			106.631i			0.111189i
$960$	214.015	−	79.1894i	0.222933	−	0.0824889i
$961$	−929.501			−0.967223
$962$	355.458	−	355.458i	0.369499	−	0.369499i
$963$	−76.7511	−	76.7511i	−0.0797000	−	0.0797000i
$964$			147.648i			0.153162i
$965$	189.203	+	511.337i	0.196066	+	0.529883i
$966$	−103.213			−0.106845
$967$	−777.967	+	777.967i	−0.804516	+	0.804516i	−0.983798	−	0.179282i	$-0.942623\pi$
$967$	−777.967	+	777.967i	−0.804516	+	0.804516i	0.179282	+	0.983798i	$0.442623\pi$
$968$	565.255	+	565.255i	0.583941	+	0.583941i
$969$		−	194.083i		−	0.200292i
$970$	223.518	−	486.082i	0.230431	−	0.501116i
$971$	−501.613			−0.516594			−0.258297	−	0.966066i	$-0.583161\pi$
$971$	−501.613			−0.516594			−0.258297	+	0.966066i	$0.583161\pi$
$972$	1053.56	−	1053.56i	1.08391	−	1.08391i
$973$	230.252	+	230.252i	0.236642	+	0.236642i
$974$		−	852.761i		−	0.875524i
$975$	−1156.25	+	991.397i	−1.18590	+	1.01682i
$976$	−262.055			−0.268499
$977$	603.188	−	603.188i	0.617388	−	0.617388i	−0.327472	−	0.944861i	$-0.606197\pi$
$977$	603.188	−	603.188i	0.617388	−	0.617388i	0.944861	+	0.327472i	$0.106197\pi$
$978$	423.706	+	423.706i	0.433237	+	0.433237i
$979$		−	3562.83i		−	3.63926i
$980$	380.540	+	174.986i	0.388306	+	0.178557i
$981$	−2616.18			−2.66685
$982$	−629.728	+	629.728i	−0.641271	+	0.641271i
$983$	863.184	+	863.184i	0.878112	+	0.878112i	0.993339	−	0.115227i	$-0.0367597\pi$
$983$	863.184	+	863.184i	0.878112	+	0.878112i	−0.115227	+	0.993339i	$0.536760\pi$
$984$			251.693i			0.255786i
$985$	221.473	−	81.9488i	0.224846	−	0.0831968i
$986$	−23.8740			−0.0242130
$987$	788.616	−	788.616i	0.799003	−	0.799003i
$988$	531.943	+	531.943i	0.538403	+	0.538403i
$989$		−	111.233i		−	0.112470i
$990$	−1160.78	−	3137.10i	−1.17251	−	3.16879i
$991$	919.042			0.927388			0.463694	−	0.885995i	$-0.346524\pi$
$991$	919.042			0.927388			0.463694	+	0.885995i	$0.346524\pi$
$992$	22.4495	−	22.4495i	0.0226306	−	0.0226306i
$993$	−846.124	−	846.124i	−0.852088	−	0.852088i
$994$			57.4314i			0.0577781i
$995$	404.137	−	878.871i	0.406167	−	0.883288i
$996$	−175.834			−0.176540
$997$	−963.435	+	963.435i	−0.966334	+	0.966334i	−0.999451	−	0.0331173i	$-0.989457\pi$
$997$	−963.435	+	963.435i	−0.966334	+	0.966334i	0.0331173	+	0.999451i	$0.489457\pi$
$998$	889.589	+	889.589i	0.891372	+	0.891372i
$999$		−	2762.14i		−	2.76490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.93.1	yes	20
5.2	odd	4	inner	230.3.f.a.47.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.1	✓	20	5.2	odd	4	inner
230.3.f.a.93.1	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-4.03398 - 4.03398i) q^{3} -2.00000i q^{4} +(4.54274 + 2.08891i) q^{5} +8.06796 q^{6} +(-1.88621 + 1.88621i) q^{7} +(2.00000 + 2.00000i) q^{8} +23.5460i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-4.03398 - 4.03398i) q^{3} -2.00000i q^{4} +(4.54274 + 2.08891i) q^{5} +8.06796 q^{6} +(-1.88621 + 1.88621i) q^{7} +(2.00000 + 2.00000i) q^{8} +23.5460i q^{9} +(-6.63165 + 2.45382i) q^{10} +20.0905 q^{11} +(-8.06796 + 8.06796i) q^{12} +(-7.55126 - 7.55126i) q^{13} -3.77242i q^{14} +(-9.89867 - 26.7519i) q^{15} -4.00000 q^{16} +(-0.682982 + 0.682982i) q^{17} +(-23.5460 - 23.5460i) q^{18} -35.2221i q^{19} +(4.17783 - 9.08547i) q^{20} +15.2179 q^{21} +(-20.0905 + 20.0905i) q^{22} +(3.39116 + 3.39116i) q^{23} -16.1359i q^{24} +(16.2729 + 18.9788i) q^{25} +15.1025 q^{26} +(58.6782 - 58.6782i) q^{27} +(3.77242 + 3.77242i) q^{28} -17.4778i q^{29} +(36.6506 + 16.8533i) q^{30} +5.61239 q^{31} +(4.00000 - 4.00000i) q^{32} +(-81.0446 - 81.0446i) q^{33} -1.36596i q^{34} +(-12.5087 + 4.62842i) q^{35} +47.0920 q^{36} +(23.5363 - 23.5363i) q^{37} +(35.2221 + 35.2221i) q^{38} +60.9233i q^{39} +(4.90764 + 13.2633i) q^{40} -15.5983 q^{41} +(-15.2179 + 15.2179i) q^{42} +(-16.4004 - 16.4004i) q^{43} -40.1810i q^{44} +(-49.1855 + 106.963i) q^{45} -6.78233 q^{46} +(51.8217 - 51.8217i) q^{47} +(16.1359 + 16.1359i) q^{48} +41.8844i q^{49} +(-35.2516 - 2.70587i) q^{50} +5.51027 q^{51} +(-15.1025 + 15.1025i) q^{52} +(-34.4887 - 34.4887i) q^{53} +117.356i q^{54} +(91.2657 + 41.9673i) q^{55} -7.54484 q^{56} +(-142.085 + 142.085i) q^{57} +(17.4778 + 17.4778i) q^{58} -16.4129i q^{59} +(-53.5039 + 19.7973i) q^{60} +65.5138 q^{61} +(-5.61239 + 5.61239i) q^{62} +(-44.4126 - 44.4126i) q^{63} +8.00000i q^{64} +(-18.5295 - 50.0773i) q^{65} +162.089 q^{66} +(29.2101 - 29.2101i) q^{67} +(1.36596 + 1.36596i) q^{68} -27.3598i q^{69} +(7.88025 - 17.1371i) q^{70} -15.2240 q^{71} +(-47.0920 + 47.0920i) q^{72} +(39.7893 + 39.7893i) q^{73} +47.0726i q^{74} +(10.9154 - 142.204i) q^{75} -70.4442 q^{76} +(-37.8948 + 37.8948i) q^{77} +(-60.9233 - 60.9233i) q^{78} +17.5152i q^{79} +(-18.1709 - 8.35565i) q^{80} -261.500 q^{81} +(15.5983 - 15.5983i) q^{82} +(10.8971 + 10.8971i) q^{83} -30.4357i q^{84} +(-4.52929 + 1.67592i) q^{85} +32.8007 q^{86} +(-70.5051 + 70.5051i) q^{87} +(40.1810 + 40.1810i) q^{88} -177.339i q^{89} +(-57.7777 - 156.149i) q^{90} +28.4865 q^{91} +(6.78233 - 6.78233i) q^{92} +(-22.6403 - 22.6403i) q^{93} +103.643i q^{94} +(73.5759 - 160.005i) q^{95} -32.2718 q^{96} +(-53.5011 + 53.5011i) q^{97} +(-41.8844 - 41.8844i) q^{98} +473.050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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