LMFDB - Embedded newform 230.3.f.a.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 $ x^20 - 52x^17 + 1020x^16 - 1316x^15 + 1352x^14 - 18724x^13 + 250686x^12 - 439644x^11 + 460536x^10 - 1833716x^9 + 16970128x^8 - 36894604x^7 + 40544632x^6 - 4380588x^5 + 34721x^4 - 4419956x^3 + 9945800x^2 + 1329080*x + 88804
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.7
Root			$1.21198 - 1.21198i$ of defining polynomial
Character	$\chi$	$=$	230.47
Dual form			230.3.f.a.93.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.21198 - 1.21198i) q^{3} +2.00000i q^{4} +(-0.802406 + 4.93519i) q^{5} -2.42397 q^{6} +(-5.44701 - 5.44701i) q^{7} +(2.00000 - 2.00000i) q^{8} +6.06220i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.21198 - 1.21198i) q^{3} +2.00000i q^{4} +(-0.802406 + 4.93519i) q^{5} -2.42397 q^{6} +(-5.44701 - 5.44701i) q^{7} +(2.00000 - 2.00000i) q^{8} +6.06220i q^{9} +(5.73760 - 4.13279i) q^{10} -4.57608 q^{11} +(2.42397 + 2.42397i) q^{12} +(-14.3294 + 14.3294i) q^{13} +10.8940i q^{14} +(5.00887 + 6.95387i) q^{15} -4.00000 q^{16} +(-19.9013 - 19.9013i) q^{17} +(6.06220 - 6.06220i) q^{18} +11.0420i q^{19} +(-9.87039 - 1.60481i) q^{20} -13.2034 q^{21} +(4.57608 + 4.57608i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.84793i q^{24} +(-23.7123 - 7.92006i) q^{25} +28.6589 q^{26} +(18.2551 + 18.2551i) q^{27} +(10.8940 - 10.8940i) q^{28} +41.2003i q^{29} +(1.94500 - 11.9627i) q^{30} +36.2151 q^{31} +(4.00000 + 4.00000i) q^{32} +(-5.54614 + 5.54614i) q^{33} +39.8025i q^{34} +(31.2527 - 22.5113i) q^{35} -12.1244 q^{36} +(11.5853 + 11.5853i) q^{37} +(11.0420 - 11.0420i) q^{38} +34.7341i q^{39} +(8.26558 + 11.4752i) q^{40} -44.4257 q^{41} +(13.2034 + 13.2034i) q^{42} +(-20.7536 + 20.7536i) q^{43} -9.15217i q^{44} +(-29.9181 - 4.86434i) q^{45} +6.78233 q^{46} +(-10.9836 - 10.9836i) q^{47} +(-4.84793 + 4.84793i) q^{48} +10.3397i q^{49} +(15.7922 + 31.6323i) q^{50} -48.2399 q^{51} +(-28.6589 - 28.6589i) q^{52} +(29.6479 - 29.6479i) q^{53} -36.5102i q^{54} +(3.67188 - 22.5839i) q^{55} -21.7880 q^{56} +(13.3827 + 13.3827i) q^{57} +(41.2003 - 41.2003i) q^{58} -0.711008i q^{59} +(-13.9077 + 10.0177i) q^{60} +48.9711 q^{61} +(-36.2151 - 36.2151i) q^{62} +(33.0208 - 33.0208i) q^{63} -8.00000i q^{64} +(-59.2206 - 82.2166i) q^{65} +11.0923 q^{66} +(10.3968 + 10.3968i) q^{67} +(39.8025 - 39.8025i) q^{68} +8.22007i q^{69} +(-53.7641 - 8.74142i) q^{70} -98.2605 q^{71} +(12.1244 + 12.1244i) q^{72} +(73.7196 - 73.7196i) q^{73} -23.1705i q^{74} +(-38.3379 + 19.1399i) q^{75} -22.0839 q^{76} +(24.9260 + 24.9260i) q^{77} +(34.7341 - 34.7341i) q^{78} -94.5365i q^{79} +(3.20962 - 19.7408i) q^{80} -10.3100 q^{81} +(44.4257 + 44.4257i) q^{82} +(-49.2784 + 49.2784i) q^{83} -26.4067i q^{84} +(114.185 - 82.2477i) q^{85} +41.5073 q^{86} +(49.9341 + 49.9341i) q^{87} +(-9.15217 + 9.15217i) q^{88} +112.584i q^{89} +(25.0538 + 34.7825i) q^{90} +156.105 q^{91} +(-6.78233 - 6.78233i) q^{92} +(43.8921 - 43.8921i) q^{93} +21.9672i q^{94} +(-54.4942 - 8.86013i) q^{95} +9.69586 q^{96} +(-20.4455 - 20.4455i) q^{97} +(10.3397 - 10.3397i) q^{98} -27.7411i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.21198	−	1.21198i	0.403994	−	0.403994i	−0.475644	−	0.879638i	$-0.657785\pi$
$3$	1.21198	−	1.21198i	0.403994	−	0.403994i	0.879638	+	0.475644i	$0.157785\pi$
$4$			2.00000i			0.500000i
$5$	−0.802406	+	4.93519i	−0.160481	+	0.987039i
$5$	−0.802406	+	4.93519i	−0.160481	+	0.987039i
$6$	−2.42397			−0.403994
$7$	−5.44701	−	5.44701i	−0.778144	−	0.778144i	0.201371	−	0.979515i	$-0.435460\pi$
$7$	−5.44701	−	5.44701i	−0.778144	−	0.778144i	−0.979515	+	0.201371i	$0.935460\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			6.06220i			0.673577i
$10$	5.73760	−	4.13279i	0.573760	−	0.413279i
$11$	−4.57608			−0.416008			−0.208004	−	0.978128i	$-0.566697\pi$
$11$	−4.57608			−0.416008			−0.208004	+	0.978128i	$0.566697\pi$
$12$	2.42397	+	2.42397i	0.201997	+	0.201997i
$13$	−14.3294	+	14.3294i	−1.10227	+	1.10227i	−0.108128	+	0.994137i	$0.534486\pi$
$13$	−14.3294	+	14.3294i	−1.10227	+	1.10227i	−0.994137	+	0.108128i	$0.965514\pi$
$14$			10.8940i			0.778144i
$15$	5.00887	+	6.95387i	0.333925	+	0.463591i
$16$	−4.00000			−0.250000
$17$	−19.9013	−	19.9013i	−1.17066	−	1.17066i	−0.982052	−	0.188610i	$-0.939602\pi$
$17$	−19.9013	−	19.9013i	−1.17066	−	1.17066i	−0.188610	−	0.982052i	$-0.560398\pi$
$18$	6.06220	−	6.06220i	0.336789	−	0.336789i
$19$			11.0420i			0.581156i	0.956851	+	0.290578i	$0.0938475\pi$
$19$			11.0420i			0.581156i	−0.956851	+	0.290578i	$0.906152\pi$
$20$	−9.87039	−	1.60481i	−0.493519	−	0.0802406i
$21$	−13.2034			−0.628731
$22$	4.57608	+	4.57608i	0.208004	+	0.208004i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$		−	4.84793i		−	0.201997i
$25$	−23.7123	−	7.92006i	−0.948492	−	0.316802i
$26$	28.6589			1.10227
$27$	18.2551	+	18.2551i	0.676116	+	0.676116i
$28$	10.8940	−	10.8940i	0.389072	−	0.389072i
$29$			41.2003i			1.42070i	0.703848	+	0.710351i	$0.251464\pi$
$29$			41.2003i			1.42070i	−0.703848	+	0.710351i	$0.748536\pi$
$30$	1.94500	−	11.9627i	0.0648334	−	0.398758i
$31$	36.2151			1.16823			0.584114	−	0.811671i	$-0.301442\pi$
$31$	36.2151			1.16823			0.584114	+	0.811671i	$0.301442\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−5.54614	+	5.54614i	−0.168065	+	0.168065i
$34$			39.8025i			1.17066i
$35$	31.2527	−	22.5113i	0.892935	−	0.643181i
$36$	−12.1244			−0.336789
$37$	11.5853	+	11.5853i	0.313115	+	0.313115i	0.846115	−	0.533000i	$-0.178935\pi$
$37$	11.5853	+	11.5853i	0.313115	+	0.313115i	−0.533000	+	0.846115i	$0.678935\pi$
$38$	11.0420	−	11.0420i	0.290578	−	0.290578i
$39$			34.7341i			0.890618i
$40$	8.26558	+	11.4752i	0.206639	+	0.286880i
$41$	−44.4257			−1.08355			−0.541777	−	0.840522i	$-0.682248\pi$
$41$	−44.4257			−1.08355			−0.541777	+	0.840522i	$0.682248\pi$
$42$	13.2034	+	13.2034i	0.314366	+	0.314366i
$43$	−20.7536	+	20.7536i	−0.482642	+	0.482642i	−0.905975	−	0.423332i	$-0.860860\pi$
$43$	−20.7536	+	20.7536i	−0.482642	+	0.482642i	0.423332	+	0.905975i	$0.360860\pi$
$44$		−	9.15217i		−	0.208004i
$45$	−29.9181	−	4.86434i	−0.664847	−	0.108096i
$46$	6.78233			0.147442
$47$	−10.9836	−	10.9836i	−0.233694	−	0.233694i	0.580539	−	0.814232i	$-0.302842\pi$
$47$	−10.9836	−	10.9836i	−0.233694	−	0.233694i	−0.814232	+	0.580539i	$0.802842\pi$
$48$	−4.84793	+	4.84793i	−0.100999	+	0.100999i
$49$			10.3397i			0.211015i
$50$	15.7922	+	31.6323i	0.315845	+	0.632647i
$51$	−48.2399			−0.945881
$52$	−28.6589	−	28.6589i	−0.551133	−	0.551133i
$53$	29.6479	−	29.6479i	0.559395	−	0.559395i	−0.369740	−	0.929135i	$-0.620553\pi$
$53$	29.6479	−	29.6479i	0.559395	−	0.559395i	0.929135	+	0.369740i	$0.120553\pi$
$54$		−	36.5102i		−	0.676116i
$55$	3.67188	−	22.5839i	0.0667614	−	0.410616i
$56$	−21.7880			−0.389072
$57$	13.3827	+	13.3827i	0.234784	+	0.234784i
$58$	41.2003	−	41.2003i	0.710351	−	0.710351i
$59$		−	0.711008i		−	0.0120510i	−0.999982	−	0.00602549i	$-0.998082\pi$
$59$		−	0.711008i		−	0.0120510i	0.999982	−	0.00602549i	$-0.00191799\pi$
$60$	−13.9077	+	10.0177i	−0.231796	+	0.166962i
$61$	48.9711			0.802805			0.401402	−	0.915902i	$-0.368523\pi$
$61$	48.9711			0.802805			0.401402	+	0.915902i	$0.368523\pi$
$62$	−36.2151	−	36.2151i	−0.584114	−	0.584114i
$63$	33.0208	−	33.0208i	0.524140	−	0.524140i
$64$		−	8.00000i		−	0.125000i
$65$	−59.2206	−	82.2166i	−0.911086	−	1.26487i
$66$	11.0923			0.168065
$67$	10.3968	+	10.3968i	0.155175	+	0.155175i	0.780425	−	0.625249i	$-0.215003\pi$
$67$	10.3968	+	10.3968i	0.155175	+	0.155175i	−0.625249	+	0.780425i	$0.715003\pi$
$68$	39.8025	−	39.8025i	0.585331	−	0.585331i
$69$			8.22007i			0.119131i
$70$	−53.7641	−	8.74142i	−0.768058	−	0.124877i
$71$	−98.2605			−1.38395			−0.691975	−	0.721921i	$-0.743259\pi$
$71$	−98.2605			−1.38395			−0.691975	+	0.721921i	$0.743259\pi$
$72$	12.1244	+	12.1244i	0.168394	+	0.168394i
$73$	73.7196	−	73.7196i	1.00986	−	1.00986i	0.00990633	−	0.999951i	$-0.496847\pi$
$73$	73.7196	−	73.7196i	1.00986	−	1.00986i	0.999951	−	0.00990633i	$-0.00315333\pi$
$74$		−	23.1705i		−	0.313115i
$75$	−38.3379	+	19.1399i	−0.511171	+	0.255199i
$76$	−22.0839			−0.290578
$77$	24.9260	+	24.9260i	0.323714	+	0.323714i
$78$	34.7341	−	34.7341i	0.445309	−	0.445309i
$79$		−	94.5365i		−	1.19666i	−0.801248	−	0.598332i	$-0.795830\pi$
$79$		−	94.5365i		−	1.19666i	0.801248	−	0.598332i	$-0.204170\pi$
$80$	3.20962	−	19.7408i	0.0401203	−	0.246760i
$81$	−10.3100			−0.127284
$82$	44.4257	+	44.4257i	0.541777	+	0.541777i
$83$	−49.2784	+	49.2784i	−0.593715	+	0.593715i	−0.938633	−	0.344918i	$-0.887907\pi$
$83$	−49.2784	+	49.2784i	−0.593715	+	0.593715i	0.344918	+	0.938633i	$0.387907\pi$
$84$		−	26.4067i		−	0.314366i
$85$	114.185	−	82.2477i	1.34336	−	0.967620i
$86$	41.5073			0.482642
$87$	49.9341	+	49.9341i	0.573955	+	0.573955i
$88$	−9.15217	+	9.15217i	−0.104002	+	0.104002i
$89$			112.584i			1.26499i	0.774565	+	0.632494i	$0.217969\pi$
$89$			112.584i			1.26499i	−0.774565	+	0.632494i	$0.782031\pi$
$90$	25.0538	+	34.7825i	0.278375	+	0.386472i
$91$	156.105			1.71544
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	43.8921	−	43.8921i	0.471958	−	0.471958i
$94$			21.9672i			0.233694i
$95$	−54.4942	−	8.86013i	−0.573623	−	0.0932645i
$96$	9.69586			0.100999
$97$	−20.4455	−	20.4455i	−0.210778	−	0.210778i	0.593820	−	0.804598i	$-0.297619\pi$
$97$	−20.4455	−	20.4455i	−0.210778	−	0.210778i	−0.804598	+	0.593820i	$0.797619\pi$
$98$	10.3397	−	10.3397i	0.105508	−	0.105508i
$99$		−	27.7411i		−	0.280213i
$100$	15.8401	−	47.4246i	0.158401	−	0.474246i
$101$	−132.674			−1.31361			−0.656804	−	0.754062i	$-0.728092\pi$
$101$	−132.674			−1.31361			−0.656804	+	0.754062i	$0.728092\pi$
$102$	48.2399	+	48.2399i	0.472941	+	0.472941i
$103$	98.6862	−	98.6862i	0.958119	−	0.958119i	−0.0410388	−	0.999158i	$-0.513067\pi$
$103$	98.6862	−	98.6862i	0.958119	−	0.958119i	0.999158	+	0.0410388i	$0.0130667\pi$
$104$			57.3178i			0.551133i
$105$	10.5944	−	65.1611i	0.100899	−	0.620582i
$106$	−59.2959			−0.559395
$107$	−131.190	−	131.190i	−1.22608	−	1.22608i	−0.965435	−	0.260643i	$-0.916065\pi$
$107$	−131.190	−	131.190i	−1.22608	−	1.22608i	−0.260643	−	0.965435i	$-0.583935\pi$
$108$	−36.5102	+	36.5102i	−0.338058	+	0.338058i
$109$			1.77307i			0.0162667i	0.999967	+	0.00813334i	$0.00258895\pi$
$109$			1.77307i			0.0162667i	−0.999967	+	0.00813334i	$0.997411\pi$
$110$	−26.2557	+	18.9120i	−0.238689	+	0.171927i
$111$	28.0823			0.252993
$112$	21.7880	+	21.7880i	0.194536	+	0.194536i
$113$	−13.6157	+	13.6157i	−0.120493	+	0.120493i	−0.764782	−	0.644289i	$-0.777153\pi$
$113$	−13.6157	+	13.6157i	−0.120493	+	0.120493i	0.644289	+	0.764782i	$0.277153\pi$
$114$		−	26.7653i		−	0.234784i
$115$	−14.0150	−	19.4571i	−0.121869	−	0.169193i
$116$	−82.4007			−0.710351
$117$	−86.8679	−	86.8679i	−0.742461	−	0.742461i
$118$	−0.711008	+	0.711008i	−0.00602549	+	0.00602549i
$119$			216.804i			1.82189i
$120$	23.9255	+	3.89001i	0.199379	+	0.0324167i
$121$	−100.059			−0.826938
$122$	−48.9711	−	48.9711i	−0.401402	−	0.401402i
$123$	−53.8432	+	53.8432i	−0.437749	+	0.437749i
$124$			72.4302i			0.584114i
$125$	58.1139	−	110.670i	0.464911	−	0.885357i
$126$	−66.0416			−0.524140
$127$	166.174	+	166.174i	1.30846	+	1.30846i	0.922528	+	0.385930i	$0.126119\pi$
$127$	166.174	+	166.174i	1.30846	+	1.30846i	0.385930	+	0.922528i	$0.373881\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			50.3061i			0.389970i
$130$	−22.9961	+	141.437i	−0.176893	+	1.08798i
$131$	159.952			1.22101			0.610505	−	0.792012i	$-0.290966\pi$
$131$	159.952			1.22101			0.610505	+	0.792012i	$0.290966\pi$
$132$	−11.0923	−	11.0923i	−0.0840324	−	0.0840324i
$133$	60.1456	−	60.1456i	0.452223	−	0.452223i
$134$		−	20.7935i		−	0.155175i
$135$	−104.741	+	75.4446i	−0.775856	+	0.558849i
$136$	−79.6050			−0.585331
$137$	80.8498	+	80.8498i	0.590144	+	0.590144i	0.937670	−	0.347526i	$-0.112978\pi$
$137$	80.8498	+	80.8498i	0.590144	+	0.590144i	−0.347526	+	0.937670i	$0.612978\pi$
$138$	8.22007	−	8.22007i	0.0595657	−	0.0595657i
$139$			222.118i			1.59797i	0.601350	+	0.798986i	$0.294630\pi$
$139$			222.118i			1.59797i	−0.601350	+	0.798986i	$0.705370\pi$
$140$	45.0227	+	62.5055i	0.321590	+	0.446468i
$141$	−26.6239			−0.188822
$142$	98.2605	+	98.2605i	0.691975	+	0.691975i
$143$	65.5728	−	65.5728i	0.458551	−	0.458551i
$144$		−	24.2488i		−	0.168394i
$145$	−203.332	−	33.0594i	−1.40229	−	0.227996i
$146$	−147.439			−1.00986
$147$	12.5316	+	12.5316i	0.0852490	+	0.0852490i
$148$	−23.1705	+	23.1705i	−0.156558	+	0.156558i
$149$		−	70.4124i		−	0.472567i	−0.971684	−	0.236283i	$-0.924071\pi$
$149$		−	70.4124i		−	0.472567i	0.971684	−	0.236283i	$-0.0759294\pi$
$150$	57.4778	+	19.1979i	0.383185	+	0.127986i
$151$	−2.52184			−0.0167009			−0.00835045	−	0.999965i	$-0.502658\pi$
$151$	−2.52184			−0.0167009			−0.00835045	+	0.999965i	$0.502658\pi$
$152$	22.0839	+	22.0839i	0.145289	+	0.145289i
$153$	120.645	−	120.645i	0.788531	−	0.788531i
$154$		−	49.8519i		−	0.323714i
$155$	−29.0592	+	178.729i	−0.187479	+	1.15309i
$156$	−69.4682			−0.445309
$157$	216.807	+	216.807i	1.38094	+	1.38094i	0.842955	+	0.537984i	$0.180814\pi$
$157$	216.807	+	216.807i	1.38094	+	1.38094i	0.537984	+	0.842955i	$0.319186\pi$
$158$	−94.5365	+	94.5365i	−0.598332	+	0.598332i
$159$		−	71.8656i		−	0.451985i
$160$	−22.9504	+	16.5312i	−0.143440	+	0.103320i
$161$	36.9434			0.229462
$162$	10.3100	+	10.3100i	0.0636419	+	0.0636419i
$163$	−163.632	+	163.632i	−1.00388	+	1.00388i	−0.00388720	+	0.999992i	$0.501237\pi$
$163$	−163.632	+	163.632i	−1.00388	+	1.00388i	−0.999992	+	0.00388720i	$0.998763\pi$
$164$		−	88.8514i		−	0.541777i
$165$	−22.9210	−	31.8215i	−0.138915	−	0.192858i
$166$	98.5567			0.593715
$167$	86.4343	+	86.4343i	0.517571	+	0.517571i	0.916836	−	0.399265i	$-0.130735\pi$
$167$	86.4343	+	86.4343i	0.517571	+	0.517571i	−0.399265	+	0.916836i	$0.630735\pi$
$168$	−26.4067	+	26.4067i	−0.157183	+	0.157183i
$169$		−	241.666i		−	1.42998i
$170$	−196.433	−	31.9377i	−1.15549	−	0.187869i
$171$	−66.9385			−0.391453
$172$	−41.5073	−	41.5073i	−0.241321	−	0.241321i
$173$	−231.547	+	231.547i	−1.33842	+	1.33842i	−0.440830	+	0.897591i	$0.645316\pi$
$173$	−231.547	+	231.547i	−1.33842	+	1.33842i	−0.897591	+	0.440830i	$0.854684\pi$
$174$		−	99.8682i		−	0.573955i
$175$	86.0204	+	172.302i	0.491545	+	0.984580i
$176$	18.3043			0.104002
$177$	−0.861730	−	0.861730i	−0.00486853	−	0.00486853i
$178$	112.584	−	112.584i	0.632494	−	0.632494i
$179$			166.689i			0.931225i	0.884989	+	0.465613i	$0.154166\pi$
$179$			166.689i			0.931225i	−0.884989	+	0.465613i	$0.845834\pi$
$180$	9.72868	−	59.8362i	0.0540482	−	0.332424i
$181$	105.385			0.582237			0.291119	−	0.956687i	$-0.405973\pi$
$181$	105.385			0.582237			0.291119	+	0.956687i	$0.405973\pi$
$182$	−156.105	−	156.105i	−0.857721	−	0.857721i
$183$	59.3521	−	59.3521i	0.324328	−	0.324328i
$184$			13.5647i			0.0737210i
$185$	−66.4716	+	47.8794i	−0.359306	+	0.258808i
$186$	−87.7841			−0.471958
$187$	91.0698	+	91.0698i	0.487004	+	0.487004i
$188$	21.9672	−	21.9672i	0.116847	−	0.116847i
$189$		−	198.872i		−	1.05223i
$190$	45.6341	+	63.3544i	0.240179	+	0.333444i
$191$	263.782			1.38106			0.690528	−	0.723306i	$-0.257378\pi$
$191$	263.782			1.38106			0.690528	+	0.723306i	$0.257378\pi$
$192$	−9.69586	−	9.69586i	−0.0504993	−	0.0504993i
$193$	40.7072	−	40.7072i	0.210918	−	0.210918i	−0.593739	−	0.804657i	$-0.702349\pi$
$193$	40.7072	−	40.7072i	0.210918	−	0.210918i	0.804657	+	0.593739i	$0.202349\pi$
$194$			40.8910i			0.210778i
$195$	−171.419	−	27.8708i	−0.879074	−	0.142927i
$196$	−20.6795			−0.105508
$197$	−116.608	−	116.608i	−0.591916	−	0.591916i	0.346232	−	0.938149i	$-0.387461\pi$
$197$	−116.608	−	116.608i	−0.591916	−	0.591916i	−0.938149	+	0.346232i	$0.887461\pi$
$198$	−27.7411	+	27.7411i	−0.140107	+	0.140107i
$199$		−	6.54168i		−	0.0328728i	−0.999865	−	0.0164364i	$-0.994768\pi$
$199$		−	6.54168i		−	0.0328728i	0.999865	−	0.0164364i	$-0.00523210\pi$
$200$	−63.2647	+	31.5845i	−0.316323	+	0.157922i
$201$	25.2014			0.125380
$202$	132.674	+	132.674i	0.656804	+	0.656804i
$203$	224.419	−	224.419i	1.10551	−	1.10551i
$204$		−	96.4799i		−	0.472941i
$205$	35.6474	−	219.249i	0.173890	−	1.06951i
$206$	−197.372			−0.958119
$207$	−20.5579	−	20.5579i	−0.0993136	−	0.0993136i
$208$	57.3178	−	57.3178i	0.275566	−	0.275566i
$209$		−	50.5289i		−	0.241765i
$210$	−75.7556	+	54.5667i	−0.360741	+	0.259841i
$211$	63.3270			0.300128			0.150064	−	0.988676i	$-0.452052\pi$
$211$	63.3270			0.300128			0.150064	+	0.988676i	$0.452052\pi$
$212$	59.2959	+	59.2959i	0.279698	+	0.279698i
$213$	−119.090	+	119.090i	−0.559108	+	0.559108i
$214$			262.381i			1.22608i
$215$	−85.7704	−	119.076i	−0.398932	−	0.553842i
$216$	73.0205			0.338058
$217$	−197.264	−	197.264i	−0.909050	−	0.909050i
$218$	1.77307	−	1.77307i	0.00813334	−	0.00813334i
$219$		−	178.694i		−	0.815953i
$220$	45.1677	+	7.34375i	0.205308	+	0.0333807i
$221$	570.348			2.58076
$222$	−28.0823	−	28.0823i	−0.126497	−	0.126497i
$223$	−173.536	+	173.536i	−0.778190	+	0.778190i	−0.979523	−	0.201333i	$-0.935473\pi$
$223$	−173.536	+	173.536i	−0.778190	+	0.778190i	0.201333	+	0.979523i	$0.435473\pi$
$224$		−	43.5760i		−	0.194536i
$225$	48.0129	−	143.749i	0.213391	−	0.638882i
$226$	27.2315			0.120493
$227$	−142.825	−	142.825i	−0.629183	−	0.629183i	0.318680	−	0.947863i	$-0.396761\pi$
$227$	−142.825	−	142.825i	−0.629183	−	0.629183i	−0.947863	+	0.318680i	$0.896761\pi$
$228$	−26.7653	+	26.7653i	−0.117392	+	0.117392i
$229$			216.004i			0.943247i	0.881800	+	0.471624i	$0.156332\pi$
$229$			216.004i			0.943247i	−0.881800	+	0.471624i	$0.843668\pi$
$230$	−5.44218	+	33.4721i	−0.0236616	+	0.145531i
$231$	60.4197			0.261557
$232$	82.4007	+	82.4007i	0.355175	+	0.355175i
$233$	−95.5641	+	95.5641i	−0.410146	+	0.410146i	−0.881789	−	0.471643i	$-0.843661\pi$
$233$	−95.5641	+	95.5641i	−0.410146	+	0.410146i	0.471643	+	0.881789i	$0.343661\pi$
$234$			173.736i			0.742461i
$235$	63.0195	−	45.3929i	0.268168	−	0.193161i
$236$	1.42202			0.00602549
$237$	−114.577	−	114.577i	−0.483446	−	0.483446i
$238$	216.804	−	216.804i	0.910943	−	0.910943i
$239$		−	38.4925i		−	0.161057i	−0.996752	−	0.0805283i	$-0.974339\pi$
$239$		−	38.4925i		−	0.161057i	0.996752	−	0.0805283i	$-0.0256607\pi$
$240$	−20.0355	−	27.8155i	−0.0834811	−	0.115898i
$241$	−189.881			−0.787887			−0.393943	−	0.919135i	$-0.628889\pi$
$241$	−189.881			−0.787887			−0.393943	+	0.919135i	$0.628889\pi$
$242$	100.059	+	100.059i	0.413469	+	0.413469i
$243$	−176.792	+	176.792i	−0.727537	+	0.727537i
$244$			97.9422i			0.401402i
$245$	−51.0287	−	8.29667i	−0.208280	−	0.0338640i
$246$	107.686			0.437749
$247$	−158.225	−	158.225i	−0.640588	−	0.640588i
$248$	72.4302	−	72.4302i	0.292057	−	0.292057i
$249$			119.449i			0.479715i
$250$	−168.784	+	52.5558i	−0.675134	+	0.210223i
$251$	171.563			0.683519			0.341759	−	0.939787i	$-0.388977\pi$
$251$	171.563			0.683519			0.341759	+	0.939787i	$0.388977\pi$
$252$	66.0416	+	66.0416i	0.262070	+	0.262070i
$253$	15.5183	−	15.5183i	0.0613370	−	0.0613370i
$254$		−	332.348i		−	1.30846i
$255$	38.7080	−	238.074i	0.151796	−	0.933622i
$256$	16.0000			0.0625000
$257$	−273.227	−	273.227i	−1.06314	−	1.06314i	−0.997867	−	0.0652746i	$-0.979208\pi$
$257$	−273.227	−	273.227i	−1.06314	−	1.06314i	−0.0652746	−	0.997867i	$-0.520792\pi$
$258$	50.3061	−	50.3061i	0.194985	−	0.194985i
$259$		−	126.210i		−	0.487297i
$260$	164.433	−	118.441i	0.632436	−	0.455543i
$261$	−249.765			−0.956952
$262$	−159.952	−	159.952i	−0.610505	−	0.610505i
$263$	−83.6219	+	83.6219i	−0.317954	+	0.317954i	−0.847981	−	0.530027i	$-0.822182\pi$
$263$	−83.6219	+	83.6219i	−0.317954	+	0.317954i	0.530027	+	0.847981i	$0.322182\pi$
$264$			22.1845i			0.0840324i
$265$	122.529	+	170.108i	0.462372	+	0.641917i
$266$	−120.291			−0.452223
$267$	136.450	+	136.450i	0.511048	+	0.511048i
$268$	−20.7935	+	20.7935i	−0.0775877	+	0.0775877i
$269$		−	238.961i		−	0.888331i	−0.895945	−	0.444166i	$-0.853500\pi$
$269$		−	238.961i		−	0.888331i	0.895945	−	0.444166i	$-0.146500\pi$
$270$	180.185	+	29.2960i	0.667352	+	0.108504i
$271$	189.960			0.700960			0.350480	−	0.936570i	$-0.386018\pi$
$271$	189.960			0.700960			0.350480	+	0.936570i	$0.386018\pi$
$272$	79.6050	+	79.6050i	0.292665	+	0.292665i
$273$	189.197	−	189.197i	0.693028	−	0.693028i
$274$		−	161.700i		−	0.590144i
$275$	108.509	+	36.2428i	0.394580	+	0.131792i
$276$	−16.4401			−0.0595657
$277$	−12.8005	−	12.8005i	−0.0462112	−	0.0462112i	0.683624	−	0.729835i	$-0.260403\pi$
$277$	−12.8005	−	12.8005i	−0.0462112	−	0.0462112i	−0.729835	+	0.683624i	$0.760403\pi$
$278$	222.118	−	222.118i	0.798986	−	0.798986i
$279$			219.543i			0.786892i
$280$	17.4828	−	107.528i	0.0624387	−	0.384029i
$281$	−36.9842			−0.131617			−0.0658083	−	0.997832i	$-0.520963\pi$
$281$	−36.9842			−0.131617			−0.0658083	+	0.997832i	$0.520963\pi$
$282$	26.6239	+	26.6239i	0.0944108	+	0.0944108i
$283$	−130.175	+	130.175i	−0.459982	+	0.459982i	−0.898649	−	0.438667i	$-0.855451\pi$
$283$	−130.175	+	130.175i	−0.459982	+	0.459982i	0.438667	+	0.898649i	$0.355451\pi$
$284$		−	196.521i		−	0.691975i
$285$	−76.7844	+	55.3077i	−0.269419	+	0.194062i
$286$	−131.146			−0.458551
$287$	241.987	+	241.987i	0.843160	+	0.843160i
$288$	−24.2488	+	24.2488i	−0.0841972	+	0.0841972i
$289$			503.120i			1.74090i
$290$	170.272	+	236.391i	0.587146	+	0.815142i
$291$	−49.5592			−0.170306
$292$	147.439	+	147.439i	0.504929	+	0.504929i
$293$	−88.7345	+	88.7345i	−0.302848	+	0.302848i	−0.842127	−	0.539279i	$-0.818697\pi$
$293$	−88.7345	+	88.7345i	−0.302848	+	0.302848i	0.539279	+	0.842127i	$0.318697\pi$
$294$		−	25.0632i		−	0.0852490i
$295$	3.50896	+	0.570517i	0.0118948	+	0.00193396i
$296$	46.3410			0.156558
$297$	−83.5370	−	83.5370i	−0.281269	−	0.281269i
$298$	−70.4124	+	70.4124i	−0.236283	+	0.236283i
$299$		−	97.1870i		−	0.325040i
$300$	−38.2798	−	76.6757i	−0.127599	−	0.255586i
$301$	226.090			0.751130
$302$	2.52184	+	2.52184i	0.00835045	+	0.00835045i
$303$	−160.799	+	160.799i	−0.530690	+	0.530690i
$304$		−	44.1678i		−	0.145289i
$305$	−39.2947	+	241.682i	−0.128835	+	0.792400i
$306$	−241.291			−0.788531
$307$	−386.644	−	386.644i	−1.25943	−	1.25943i	−0.951366	−	0.308062i	$-0.900320\pi$
$307$	−386.644	−	386.644i	−1.25943	−	1.25943i	−0.308062	−	0.951366i	$-0.599680\pi$
$308$	−49.8519	+	49.8519i	−0.161857	+	0.161857i
$309$		−	239.212i		−	0.774149i
$310$	207.788	−	149.669i	0.670283	−	0.482804i
$311$	234.994			0.755607			0.377803	−	0.925886i	$-0.376680\pi$
$311$	234.994			0.755607			0.377803	+	0.925886i	$0.376680\pi$
$312$	69.4682	+	69.4682i	0.222654	+	0.222654i
$313$	20.5782	−	20.5782i	0.0657449	−	0.0657449i	−0.673470	−	0.739215i	$-0.735197\pi$
$313$	20.5782	−	20.5782i	0.0657449	−	0.0657449i	0.739215	+	0.673470i	$0.235197\pi$
$314$		−	433.615i		−	1.38094i
$315$	136.468	+	189.460i	0.433232	+	0.601461i
$316$	189.073			0.598332
$317$	−2.05991	−	2.05991i	−0.00649813	−	0.00649813i	0.703850	−	0.710348i	$-0.251463\pi$
$317$	−2.05991	−	2.05991i	−0.00649813	−	0.00649813i	−0.710348	+	0.703850i	$0.751463\pi$
$318$	−71.8656	+	71.8656i	−0.225992	+	0.225992i
$319$		−	188.536i		−	0.591023i
$320$	39.4816	+	6.41924i	0.123380	+	0.0200601i
$321$	−318.001			−0.990657
$322$	−36.9434	−	36.9434i	−0.114731	−	0.114731i
$323$	219.749	−	219.749i	0.680337	−	0.680337i
$324$		−	20.6200i		−	0.0636419i
$325$	453.274	−	226.294i	1.39469	−	0.696289i
$326$	327.265			1.00388
$327$	2.14893	+	2.14893i	0.00657164	+	0.00657164i
$328$	−88.8514	+	88.8514i	−0.270888	+	0.270888i
$329$			119.655i			0.363694i
$330$	−8.90050	+	54.7425i	−0.0269712	+	0.165886i
$331$	3.99957			0.0120833			0.00604165	−	0.999982i	$-0.498077\pi$
$331$	3.99957			0.0120833			0.00604165	+	0.999982i	$0.498077\pi$
$332$	−98.5567	−	98.5567i	−0.296858	−	0.296858i
$333$	−70.2321	+	70.2321i	−0.210907	+	0.210907i
$334$		−	172.869i		−	0.517571i
$335$	−59.6524	+	42.9676i	−0.178067	+	0.128261i
$336$	52.8134			0.157183
$337$	−140.199	−	140.199i	−0.416021	−	0.416021i	0.467809	−	0.883830i	$-0.345044\pi$
$337$	−140.199	−	140.199i	−0.416021	−	0.416021i	−0.883830	+	0.467809i	$0.845044\pi$
$338$	−241.666	+	241.666i	−0.714989	+	0.714989i
$339$			33.0041i			0.0973572i
$340$	164.495	+	228.371i	0.483810	+	0.671679i
$341$	−165.723			−0.485992
$342$	66.9385	+	66.9385i	0.195727	+	0.195727i
$343$	−210.583	+	210.583i	−0.613943	+	0.613943i
$344$			83.0145i			0.241321i
$345$	−40.5676	−	6.59583i	−0.117587	−	0.0191183i
$346$	463.093			1.33842
$347$	−100.859	−	100.859i	−0.290660	−	0.290660i	0.546681	−	0.837341i	$-0.315891\pi$
$347$	−100.859	−	100.859i	−0.290660	−	0.290660i	−0.837341	+	0.546681i	$0.815891\pi$
$348$	−99.8682	+	99.8682i	−0.286978	+	0.286978i
$349$			501.448i			1.43681i	0.695623	+	0.718407i	$0.255128\pi$
$349$			501.448i			1.43681i	−0.695623	+	0.718407i	$0.744872\pi$
$350$	86.2812	−	258.322i	0.246518	−	0.738063i
$351$	−523.172			−1.49052
$352$	−18.3043	−	18.3043i	−0.0520010	−	0.0520010i
$353$	9.48375	−	9.48375i	0.0268661	−	0.0268661i	−0.693546	−	0.720412i	$-0.743953\pi$
$353$	9.48375	−	9.48375i	0.0268661	−	0.0268661i	0.720412	+	0.693546i	$0.243953\pi$
$354$			1.72346i			0.00486853i
$355$	78.8447	−	484.934i	0.222098	−	1.36601i
$356$	−225.168			−0.632494
$357$	262.763	+	262.763i	0.736032	+	0.736032i
$358$	166.689	−	166.689i	0.465613	−	0.465613i
$359$			398.005i			1.10865i	0.832301	+	0.554324i	$0.187023\pi$
$359$			398.005i			1.10865i	−0.832301	+	0.554324i	$0.812977\pi$
$360$	−69.5649	+	50.1076i	−0.193236	+	0.139188i
$361$	239.075			0.662258
$362$	−105.385	−	105.385i	−0.291119	−	0.291119i
$363$	−121.270	+	121.270i	−0.334078	+	0.334078i
$364$			312.210i			0.857721i
$365$	304.667	+	422.973i	0.834705	+	1.15883i
$366$	−118.704			−0.324328
$367$	357.545	+	357.545i	0.974238	+	0.974238i	0.999676	−	0.0254389i	$-0.00809832\pi$
$367$	357.545	+	357.545i	0.974238	+	0.974238i	−0.0254389	+	0.999676i	$0.508098\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$		−	269.317i		−	0.729857i
$370$	114.351	+	18.5922i	0.309057	+	0.0502491i
$371$	−322.985			−0.870580
$372$	87.7841	+	87.7841i	0.235979	+	0.235979i
$373$	126.123	−	126.123i	0.338131	−	0.338131i	−0.517532	−	0.855664i	$-0.673149\pi$
$373$	126.123	−	126.123i	0.338131	−	0.338131i	0.855664	+	0.517532i	$0.173149\pi$
$374$		−	182.140i		−	0.487004i
$375$	−63.6967	−	204.563i	−0.169858	−	0.545501i
$376$	−43.9344			−0.116847
$377$	−590.378	−	590.378i	−1.56599	−	1.56599i
$378$	−198.872	+	198.872i	−0.526115	+	0.526115i
$379$		−	551.551i		−	1.45528i	−0.685959	−	0.727640i	$-0.740617\pi$
$379$		−	551.551i		−	1.45528i	0.685959	−	0.727640i	$-0.259383\pi$
$380$	17.7203	−	108.988i	0.0466323	−	0.286812i
$381$	402.801			1.05722
$382$	−263.782	−	263.782i	−0.690528	−	0.690528i
$383$	−350.165	+	350.165i	−0.914270	+	0.914270i	−0.996605	−	0.0823352i	$-0.973762\pi$
$383$	−350.165	+	350.165i	−0.914270	+	0.914270i	0.0823352	+	0.996605i	$0.473762\pi$
$384$			19.3917i			0.0504993i
$385$	−143.015	+	103.014i	−0.371468	+	0.267568i
$386$	−81.4144			−0.210918
$387$	−125.813	−	125.813i	−0.325097	−	0.325097i
$388$	40.8910	−	40.8910i	0.105389	−	0.105389i
$389$		−	386.345i		−	0.993175i	−0.867987	−	0.496587i	$-0.834586\pi$
$389$		−	386.345i		−	0.993175i	0.867987	−	0.496587i	$-0.165414\pi$
$390$	143.549	+	199.290i	0.368073	+	0.511001i
$391$	134.977			0.345209
$392$	20.6795	+	20.6795i	0.0527538	+	0.0527538i
$393$	193.860	−	193.860i	0.493281	−	0.493281i
$394$			233.215i			0.591916i
$395$	466.556	+	75.8566i	1.18115	+	0.192042i
$396$	55.4822			0.140107
$397$	208.587	+	208.587i	0.525409	+	0.525409i	0.919200	−	0.393791i	$-0.128837\pi$
$397$	208.587	+	208.587i	0.525409	+	0.525409i	−0.393791	+	0.919200i	$0.628837\pi$
$398$	−6.54168	+	6.54168i	−0.0164364	+	0.0164364i
$399$		−	145.791i		−	0.365391i
$400$	94.8492	+	31.6802i	0.237123	+	0.0792006i
$401$	−549.142			−1.36943			−0.684716	−	0.728810i	$-0.740074\pi$
$401$	−549.142			−1.36943			−0.684716	+	0.728810i	$0.740074\pi$
$402$	−25.2014	−	25.2014i	−0.0626900	−	0.0626900i
$403$	−518.942	+	518.942i	−1.28770	+	1.28770i
$404$		−	265.349i		−	0.656804i
$405$	8.27279	−	50.8818i	0.0204266	−	0.125634i
$406$	−448.837			−1.10551
$407$	−53.0151	−	53.0151i	−0.130258	−	0.130258i
$408$	−96.4799	+	96.4799i	−0.236470	+	0.236470i
$409$			622.797i			1.52273i	0.648322	+	0.761366i	$0.275471\pi$
$409$			622.797i			1.52273i	−0.648322	+	0.761366i	$0.724529\pi$
$410$	−254.897	+	183.602i	−0.621700	+	0.447810i
$411$	195.977			0.476830
$412$	197.372	+	197.372i	0.479059	+	0.479059i
$413$	−3.87287	+	3.87287i	−0.00937740	+	0.00937740i
$414$			41.1158i			0.0993136i
$415$	−203.657	−	282.740i	−0.490740	−	0.681300i
$416$	−114.636			−0.275566
$417$	269.203	+	269.203i	0.645571	+	0.645571i
$418$	−50.5289	+	50.5289i	−0.120883	+	0.120883i
$419$			217.540i			0.519187i	0.965718	+	0.259594i	$0.0835887\pi$
$419$			217.540i			0.519187i	−0.965718	+	0.259594i	$0.916411\pi$
$420$	130.322	+	21.1889i	0.310291	+	0.0504497i
$421$	−172.844			−0.410557			−0.205278	−	0.978704i	$-0.565810\pi$
$421$	−172.844			−0.410557			−0.205278	+	0.978704i	$0.565810\pi$
$422$	−63.3270	−	63.3270i	−0.150064	−	0.150064i
$423$	66.5847	−	66.5847i	0.157411	−	0.157411i
$424$		−	118.592i		−	0.279698i
$425$	314.285	+	629.523i	0.739495	+	1.48123i
$426$	238.180			0.559108
$427$	−266.746	−	266.746i	−0.624697	−	0.624697i
$428$	262.381	−	262.381i	0.613039	−	0.613039i
$429$		−	158.946i		−	0.370504i
$430$	−33.3057	+	204.846i	−0.0774550	+	0.476387i
$431$	−23.1272			−0.0536595			−0.0268297	−	0.999640i	$-0.508541\pi$
$431$	−23.1272			−0.0536595			−0.0268297	+	0.999640i	$0.508541\pi$
$432$	−73.0205	−	73.0205i	−0.169029	−	0.169029i
$433$	−401.473	+	401.473i	−0.927190	+	0.927190i	−0.997524	−	0.0703332i	$-0.977594\pi$
$433$	−401.473	+	401.473i	−0.927190	+	0.927190i	0.0703332	+	0.997524i	$0.477594\pi$
$434$			394.528i			0.909050i
$435$	−286.502	+	206.367i	−0.658625	+	0.474407i
$436$	−3.54613			−0.00813334
$437$	−37.4451	−	37.4451i	−0.0856867	−	0.0856867i
$438$	−178.694	+	178.694i	−0.407977	+	0.407977i
$439$		−	437.828i		−	0.997331i	−0.866794	−	0.498666i	$-0.833824\pi$
$439$		−	437.828i		−	0.997331i	0.866794	−	0.498666i	$-0.166176\pi$
$440$	−37.8240	−	52.5115i	−0.0859636	−	0.119344i
$441$	−62.6816			−0.142135
$442$	−570.348	−	570.348i	−1.29038	−	1.29038i
$443$	25.3106	−	25.3106i	0.0571345	−	0.0571345i	−0.677962	−	0.735097i	$-0.737137\pi$
$443$	25.3106	−	25.3106i	0.0571345	−	0.0571345i	0.735097	+	0.677962i	$0.237137\pi$
$444$			56.1645i			0.126497i
$445$	−555.623	−	90.3379i	−1.24859	−	0.203007i
$446$	347.073			0.778190
$447$	−85.3387	−	85.3387i	−0.190914	−	0.190914i
$448$	−43.5760	+	43.5760i	−0.0972680	+	0.0972680i
$449$			856.476i			1.90752i	0.300571	+	0.953759i	$0.402823\pi$
$449$			856.476i			1.90752i	−0.300571	+	0.953759i	$0.597177\pi$
$450$	−191.761	+	95.7356i	−0.426137	+	0.212746i
$451$	203.296			0.450767
$452$	−27.2315	−	27.2315i	−0.0602466	−	0.0602466i
$453$	−3.05642	+	3.05642i	−0.00674707	+	0.00674707i
$454$			285.649i			0.629183i
$455$	−125.260	+	770.409i	−0.275296	+	1.69321i
$456$	53.5307			0.117392
$457$	−253.911	−	253.911i	−0.555604	−	0.555604i	0.372449	−	0.928053i	$-0.378518\pi$
$457$	−253.911	−	253.911i	−0.555604	−	0.555604i	−0.928053	+	0.372449i	$0.878518\pi$
$458$	216.004	−	216.004i	0.471624	−	0.471624i
$459$		−	726.599i		−	1.58301i
$460$	38.9143	−	28.0299i	0.0845963	−	0.0609346i
$461$	−316.325			−0.686172			−0.343086	−	0.939304i	$-0.611472\pi$
$461$	−316.325			−0.686172			−0.343086	+	0.939304i	$0.611472\pi$
$462$	−60.4197	−	60.4197i	−0.130779	−	0.130779i
$463$	−373.150	+	373.150i	−0.805940	+	0.805940i	−0.984017	−	0.178077i	$-0.943013\pi$
$463$	−373.150	+	373.150i	−0.805940	+	0.805940i	0.178077	+	0.984017i	$0.443013\pi$
$464$		−	164.801i		−	0.355175i
$465$	181.397	+	251.835i	0.390100	+	0.541581i
$466$	191.128			0.410146
$467$	638.354	+	638.354i	1.36693	+	1.36693i	0.864787	+	0.502138i	$0.167453\pi$
$467$	638.354	+	638.354i	1.36693	+	1.36693i	0.502138	+	0.864787i	$0.332547\pi$
$468$	173.736	−	173.736i	0.371230	−	0.371230i
$469$		−	113.262i		−	0.241498i
$470$	−108.412	−	17.6266i	−0.230665	−	0.0375034i
$471$	525.534			1.11578
$472$	−1.42202	−	1.42202i	−0.00301275	−	0.00301275i
$473$	94.9704	−	94.9704i	0.200783	−	0.200783i
$474$			229.153i			0.483446i
$475$	87.4529	−	261.830i	0.184111	−	0.551221i
$476$	−433.609			−0.910943
$477$	179.732	+	179.732i	0.376796	+	0.376796i
$478$	−38.4925	+	38.4925i	−0.0805283	+	0.0805283i
$479$		−	664.201i		−	1.38664i	−0.720629	−	0.693320i	$-0.756147\pi$
$479$		−	664.201i		−	1.38664i	0.720629	−	0.693320i	$-0.243853\pi$
$480$	−7.78001	+	47.8510i	−0.0162084	+	0.0996895i
$481$	−332.021			−0.690272
$482$	189.881	+	189.881i	0.393943	+	0.393943i
$483$	44.7748	−	44.7748i	0.0927014	−	0.0927014i
$484$		−	200.119i		−	0.413469i
$485$	117.308	−	84.4969i	0.241872	−	0.174220i
$486$	353.583			0.727537
$487$	297.098	+	297.098i	0.610057	+	0.610057i	0.942961	−	0.332904i	$-0.108029\pi$
$487$	297.098	+	297.098i	0.610057	+	0.610057i	−0.332904	+	0.942961i	$0.608029\pi$
$488$	97.9422	−	97.9422i	0.200701	−	0.200701i
$489$			396.639i			0.811123i
$490$	42.7320	+	59.3253i	0.0872082	+	0.121072i
$491$	707.506			1.44095			0.720475	−	0.693481i	$-0.243924\pi$
$491$	707.506			1.44095			0.720475	+	0.693481i	$0.243924\pi$
$492$	−107.686	−	107.686i	−0.218875	−	0.218875i
$493$	819.938	−	819.938i	1.66316	−	1.66316i
$494$			316.450i			0.640588i
$495$	136.908	+	22.2596i	0.276581	+	0.0449690i
$496$	−144.860			−0.292057
$497$	535.225	+	535.225i	1.07691	+	1.07691i
$498$	119.449	−	119.449i	0.239858	−	0.239858i
$499$		−	626.773i		−	1.25606i	−0.778190	−	0.628029i	$-0.783862\pi$
$499$		−	626.773i		−	1.25606i	0.778190	−	0.628029i	$-0.216138\pi$
$500$	221.339	+	116.228i	0.442679	+	0.232456i
$501$	209.514			0.418191
$502$	−171.563	−	171.563i	−0.341759	−	0.341759i
$503$	676.425	−	676.425i	1.34478	−	1.34478i	0.453550	−	0.891231i	$-0.350157\pi$
$503$	676.425	−	676.425i	1.34478	−	1.34478i	0.891231	−	0.453550i	$-0.149843\pi$
$504$		−	132.083i		−	0.262070i
$505$	106.459	−	654.774i	0.210809	−	1.29658i
$506$	−31.0365			−0.0613370
$507$	−292.895	−	292.895i	−0.577703	−	0.577703i
$508$	−332.348	+	332.348i	−0.654229	+	0.654229i
$509$			156.217i			0.306909i	0.988156	+	0.153455i	$0.0490399\pi$
$509$			156.217i			0.306909i	−0.988156	+	0.153455i	$0.950960\pi$
$510$	−276.782	+	199.366i	−0.542709	+	0.390913i
$511$	−803.102			−1.57163
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−201.572	+	201.572i	−0.392928	+	0.392928i
$514$			546.455i			1.06314i
$515$	407.849	+	566.222i	0.791941	+	1.09946i
$516$	−100.612			−0.194985
$517$	50.2619	+	50.2619i	0.0972183	+	0.0972183i
$518$	−126.210	+	126.210i	−0.243649	+	0.243649i
$519$			561.261i			1.08143i
$520$	−282.874	−	45.9921i	−0.543989	−	0.0884464i
$521$	−114.920			−0.220575			−0.110288	−	0.993900i	$-0.535177\pi$
$521$	−114.920			−0.220575			−0.110288	+	0.993900i	$0.535177\pi$
$522$	249.765	+	249.765i	0.478476	+	0.478476i
$523$	−163.639	+	163.639i	−0.312885	+	0.312885i	−0.846026	−	0.533141i	$-0.821011\pi$
$523$	−163.639	+	163.639i	−0.312885	+	0.312885i	0.533141	+	0.846026i	$0.321011\pi$
$524$			319.905i			0.610505i
$525$	313.082	+	104.571i	0.596346	+	0.199183i
$526$	167.244			0.317954
$527$	−720.726	−	720.726i	−1.36760	−	1.36760i
$528$	22.1845	−	22.1845i	0.0420162	−	0.0420162i
$529$		−	23.0000i		−	0.0434783i
$530$	47.5793	−	292.637i	0.0897724	−	0.552145i
$531$	4.31027			0.00811727
$532$	120.291	+	120.291i	0.226111	+	0.226111i
$533$	636.596	−	636.596i	1.19436	−	1.19436i
$534$		−	272.899i		−	0.511048i
$535$	752.718	−	542.182i	1.40695	−	1.01342i
$536$	41.5870			0.0775877
$537$	202.025	+	202.025i	0.376210	+	0.376210i
$538$	−238.961	+	238.961i	−0.444166	+	0.444166i
$539$		−	47.3156i		−	0.0877840i
$540$	−150.889	−	209.481i	−0.279424	−	0.387928i
$541$	329.018			0.608166			0.304083	−	0.952646i	$-0.401650\pi$
$541$	329.018			0.608166			0.304083	+	0.952646i	$0.401650\pi$
$542$	−189.960	−	189.960i	−0.350480	−	0.350480i
$543$	127.725	−	127.725i	0.235220	−	0.235220i
$544$		−	159.210i		−	0.292665i
$545$	−8.75043	−	1.42272i	−0.0160558	−	0.00261049i
$546$	−378.394			−0.693028
$547$	441.884	+	441.884i	0.807832	+	0.807832i	0.984305	−	0.176474i	$-0.0564691\pi$
$547$	441.884	+	441.884i	0.807832	+	0.807832i	−0.176474	+	0.984305i	$0.556469\pi$
$548$	−161.700	+	161.700i	−0.295072	+	0.295072i
$549$			296.872i			0.540751i
$550$	−72.2666	−	144.752i	−0.131394	−	0.263186i
$551$	−454.933			−0.825649
$552$	16.4401	+	16.4401i	0.0297829	+	0.0297829i
$553$	−514.941	+	514.941i	−0.931177	+	0.931177i
$554$			25.6010i			0.0462112i
$555$	−22.5334	+	138.591i	−0.0406007	+	0.249714i
$556$	−444.236			−0.798986
$557$	−669.503	−	669.503i	−1.20198	−	1.20198i	−0.973564	−	0.228416i	$-0.926645\pi$
$557$	−669.503	−	669.503i	−1.20198	−	1.20198i	−0.228416	−	0.973564i	$-0.573355\pi$
$558$	219.543	−	219.543i	0.393446	−	0.393446i
$559$		−	594.776i		−	1.06400i
$560$	−125.011	+	90.0453i	−0.223234	+	0.160795i
$561$	220.750			0.393494
$562$	36.9842	+	36.9842i	0.0658083	+	0.0658083i
$563$	52.7348	−	52.7348i	0.0936675	−	0.0936675i	−0.658720	−	0.752388i	$-0.728902\pi$
$563$	52.7348	−	52.7348i	0.0936675	−	0.0936675i	0.752388	+	0.658720i	$0.228902\pi$
$564$		−	53.2477i		−	0.0944108i
$565$	−56.2710	−	78.1217i	−0.0995946	−	0.138268i
$566$	260.350			0.459982
$567$	56.1585	+	56.1585i	0.0990450	+	0.0990450i
$568$	−196.521	+	196.521i	−0.345988	+	0.345988i
$569$			610.597i			1.07311i	0.843867	+	0.536553i	$0.180274\pi$
$569$			610.597i			1.07311i	−0.843867	+	0.536553i	$0.819726\pi$
$570$	132.092	+	21.4766i	0.231741	+	0.0376783i
$571$	−77.9436			−0.136504			−0.0682519	−	0.997668i	$-0.521742\pi$
$571$	−77.9436			−0.136504			−0.0682519	+	0.997668i	$0.521742\pi$
$572$	131.146	+	131.146i	0.229275	+	0.229275i
$573$	319.699	−	319.699i	0.557939	−	0.557939i
$574$		−	483.974i		−	0.843160i
$575$	107.271	−	53.5541i	0.186557	−	0.0931375i
$576$	48.4976			0.0841972
$577$	−507.604	−	507.604i	−0.879730	−	0.879730i	0.113776	−	0.993506i	$-0.463705\pi$
$577$	−507.604	−	507.604i	−0.879730	−	0.879730i	−0.993506	+	0.113776i	$0.963705\pi$
$578$	503.120	−	503.120i	0.870449	−	0.870449i
$579$		−	98.6729i		−	0.170419i
$580$	66.1188	−	406.663i	0.113998	−	0.701144i
$581$	536.839			0.923992
$582$	49.5592	+	49.5592i	0.0851532	+	0.0851532i
$583$	−135.671	+	135.671i	−0.232713	+	0.232713i
$584$		−	294.878i		−	0.504929i
$585$	498.413	−	359.007i	0.851989	−	0.613687i
$586$	177.469			0.302848
$587$	−105.920	−	105.920i	−0.180443	−	0.180443i	0.611106	−	0.791549i	$-0.290725\pi$
$587$	−105.920	−	105.920i	−0.180443	−	0.180443i	−0.791549	+	0.611106i	$0.790725\pi$
$588$	−25.0632	+	25.0632i	−0.0426245	+	0.0426245i
$589$			399.886i			0.678923i
$590$	−2.93845	−	4.07948i	−0.00498042	−	0.00691437i
$591$	−282.653			−0.478262
$592$	−46.3410	−	46.3410i	−0.0782788	−	0.0782788i
$593$	−434.460	+	434.460i	−0.732648	+	0.732648i	−0.971144	−	0.238496i	$-0.923346\pi$
$593$	−434.460	+	434.460i	−0.732648	+	0.732648i	0.238496	+	0.971144i	$0.423346\pi$
$594$			167.074i			0.281269i
$595$	−1069.97	−	173.965i	−1.79827	−	0.292378i
$596$	140.825			0.236283
$597$	−7.92841	−	7.92841i	−0.0132804	−	0.0132804i
$598$	−97.1870	+	97.1870i	−0.162520	+	0.162520i
$599$		−	894.980i		−	1.49412i	−0.664754	−	0.747062i	$-0.731464\pi$
$599$		−	894.980i		−	1.49412i	0.664754	−	0.747062i	$-0.268536\pi$
$600$	−38.3959	+	114.956i	−0.0639931	+	0.191593i
$601$	213.837			0.355803			0.177901	−	0.984048i	$-0.443069\pi$
$601$	213.837			0.355803			0.177901	+	0.984048i	$0.443069\pi$
$602$	−226.090	−	226.090i	−0.375565	−	0.375565i
$603$	−63.0272	+	63.0272i	−0.104523	+	0.104523i
$604$		−	5.04367i		−	0.00835045i
$605$	80.2883	−	493.813i	0.132708	−	0.816220i
$606$	321.598			0.530690
$607$	18.6303	+	18.6303i	0.0306924	+	0.0306924i	0.722286	−	0.691594i	$-0.243091\pi$
$607$	18.6303	+	18.6303i	0.0306924	+	0.0306924i	−0.691594	+	0.722286i	$0.743091\pi$
$608$	−44.1678	+	44.1678i	−0.0726445	+	0.0726445i
$609$		−	543.983i		−	0.893239i
$610$	280.977	−	202.387i	0.460617	−	0.331782i
$611$	314.778			0.515184
$612$	241.291	+	241.291i	0.394266	+	0.394266i
$613$	546.325	−	546.325i	0.891232	−	0.891232i	−0.103407	−	0.994639i	$-0.532974\pi$
$613$	546.325	−	546.325i	0.891232	−	0.891232i	0.994639	+	0.103407i	$0.0329744\pi$
$614$			773.289i			1.25943i
$615$	−222.522	−	308.931i	−0.361825	−	0.502326i
$616$	99.7038			0.161857
$617$	−10.8633	−	10.8633i	−0.0176066	−	0.0176066i	0.698249	−	0.715855i	$-0.253963\pi$
$617$	−10.8633	−	10.8633i	−0.0176066	−	0.0176066i	−0.715855	+	0.698249i	$0.753963\pi$
$618$	−239.212	+	239.212i	−0.387074	+	0.387074i
$619$		−	1082.29i		−	1.74845i	−0.485517	−	0.874227i	$-0.661369\pi$
$619$		−	1082.29i		−	1.74845i	0.485517	−	0.874227i	$-0.338631\pi$
$620$	−357.457	−	58.1184i	−0.576544	−	0.0937393i
$621$	−123.812			−0.199376
$622$	−234.994	−	234.994i	−0.377803	−	0.377803i
$623$	613.245	−	613.245i	0.984342	−	0.984342i
$624$		−	138.936i		−	0.222654i
$625$	499.545	+	375.605i	0.799273	+	0.600968i
$626$	−41.1563			−0.0657449
$627$	−61.2402	−	61.2402i	−0.0976718	−	0.0976718i
$628$	−433.615	+	433.615i	−0.690470	+	0.690470i
$629$		−	461.122i		−	0.733104i
$630$	52.9922	−	325.928i	0.0841146	−	0.517347i
$631$	−55.4217			−0.0878316			−0.0439158	−	0.999035i	$-0.513983\pi$
$631$	−55.4217			−0.0878316			−0.0439158	+	0.999035i	$0.513983\pi$
$632$	−189.073	−	189.073i	−0.299166	−	0.299166i
$633$	76.7513	−	76.7513i	0.121250	−	0.121250i
$634$			4.11981i			0.00649813i
$635$	−953.441	+	686.763i	−1.50148	+	1.08152i
$636$	143.731			0.225992
$637$	−148.163	−	148.163i	−0.232595	−	0.232595i
$638$	−188.536	+	188.536i	−0.295511	+	0.295511i
$639$		−	595.674i		−	0.932197i
$640$	−33.0623	−	45.9008i	−0.0516599	−	0.0717200i
$641$	278.912			0.435120			0.217560	−	0.976047i	$-0.430190\pi$
$641$	278.912			0.435120			0.217560	+	0.976047i	$0.430190\pi$
$642$	318.001	+	318.001i	0.495329	+	0.495329i
$643$	−159.124	+	159.124i	−0.247472	+	0.247472i	−0.819932	−	0.572460i	$-0.805989\pi$
$643$	−159.124	+	159.124i	−0.247472	+	0.247472i	0.572460	+	0.819932i	$0.305989\pi$
$644$			73.8868i			0.114731i
$645$	−248.270	−	40.3659i	−0.384915	−	0.0625828i
$646$	−439.498			−0.680337
$647$	533.430	+	533.430i	0.824466	+	0.824466i	0.986745	−	0.162279i	$-0.0518843\pi$
$647$	533.430	+	533.430i	0.824466	+	0.824466i	−0.162279	+	0.986745i	$0.551884\pi$
$648$	−20.6200	+	20.6200i	−0.0318209	+	0.0318209i
$649$			3.25363i			0.00501330i
$650$	−679.568	−	226.980i	−1.04549	−	0.349200i
$651$	−478.161			−0.734502
$652$	−327.265	−	327.265i	−0.501940	−	0.501940i
$653$	−542.883	+	542.883i	−0.831367	+	0.831367i	−0.987704	−	0.156337i	$-0.950032\pi$
$653$	−542.883	+	542.883i	−0.831367	+	0.831367i	0.156337	+	0.987704i	$0.450032\pi$
$654$		−	4.29785i		−	0.00657164i
$655$	−128.347	+	789.396i	−0.195949	+	1.20519i
$656$	177.703			0.270888
$657$	446.903	+	446.903i	0.680217	+	0.680217i
$658$	119.655	−	119.655i	0.181847	−	0.181847i
$659$			237.009i			0.359650i	0.983699	+	0.179825i	$0.0575531\pi$
$659$			237.009i			0.359650i	−0.983699	+	0.179825i	$0.942447\pi$
$660$	63.6430	−	45.8420i	0.0964288	−	0.0694576i
$661$	143.004			0.216346			0.108173	−	0.994132i	$-0.465500\pi$
$661$	143.004			0.216346			0.108173	+	0.994132i	$0.465500\pi$
$662$	−3.99957	−	3.99957i	−0.00604165	−	0.00604165i
$663$	691.252	−	691.252i	1.04261	−	1.04261i
$664$			197.113i			0.296858i
$665$	248.569	+	345.092i	0.373788	+	0.518935i
$666$	140.464			0.210907
$667$	−139.717	−	139.717i	−0.209471	−	0.209471i
$668$	−172.869	+	172.869i	−0.258785	+	0.258785i
$669$			420.646i			0.628769i
$670$	102.620	+	16.6848i	0.153164	+	0.0249027i
$671$	−224.096			−0.333973
$672$	−52.8134	−	52.8134i	−0.0785914	−	0.0785914i
$673$	2.30268	−	2.30268i	0.00342152	−	0.00342152i	−0.705394	−	0.708815i	$-0.749230\pi$
$673$	2.30268	−	2.30268i	0.00342152	−	0.00342152i	0.708815	+	0.705394i	$0.249230\pi$
$674$			280.398i			0.416021i
$675$	−288.289	−	577.452i	−0.427095	−	0.855485i
$676$	483.332			0.714989
$677$	308.359	+	308.359i	0.455479	+	0.455479i	0.897168	−	0.441689i	$-0.145621\pi$
$677$	308.359	+	308.359i	0.455479	+	0.455479i	−0.441689	+	0.897168i	$0.645621\pi$
$678$	33.0041	−	33.0041i	0.0486786	−	0.0486786i
$679$			222.733i			0.328032i
$680$	63.8755	−	392.866i	0.0939346	−	0.577744i
$681$	−346.202			−0.508373
$682$	165.723	+	165.723i	0.242996	+	0.242996i
$683$	599.924	−	599.924i	0.878366	−	0.878366i	−0.114999	−	0.993366i	$-0.536687\pi$
$683$	599.924	−	599.924i	0.878366	−	0.878366i	0.993366	+	0.114999i	$0.0366866\pi$
$684$		−	133.877i		−	0.195727i
$685$	−463.884	+	334.135i	−0.677202	+	0.487788i
$686$	421.165			0.613943
$687$	261.793	+	261.793i	0.381066	+	0.381066i
$688$	83.0145	−	83.0145i	0.120661	−	0.120661i
$689$			849.677i			1.23320i
$690$	33.9718	+	47.1635i	0.0492345	+	0.0683528i
$691$	726.534			1.05142			0.525712	−	0.850663i	$-0.323799\pi$
$691$	726.534			1.05142			0.525712	+	0.850663i	$0.323799\pi$
$692$	−463.093	−	463.093i	−0.669210	−	0.669210i
$693$	−151.106	+	151.106i	−0.218046	+	0.218046i
$694$			201.718i			0.290660i
$695$	−1096.20	−	178.229i	−1.57726	−	0.256444i
$696$	199.736			0.286978
$697$	884.127	+	884.127i	1.26847	+	1.26847i
$698$	501.448	−	501.448i	0.718407	−	0.718407i
$699$			231.644i			0.331393i
$700$	−344.603	+	172.041i	−0.492290	+	0.245773i
$701$	−498.607			−0.711280			−0.355640	−	0.934623i	$-0.615737\pi$
$701$	−498.607			−0.711280			−0.355640	+	0.934623i	$0.615737\pi$
$702$	523.172	+	523.172i	0.745259	+	0.745259i
$703$	−127.924	+	127.924i	−0.181969	+	0.181969i
$704$			36.6087i			0.0520010i
$705$	21.3631	−	131.394i	0.0303023	−	0.186374i
$706$	−18.9675			−0.0268661
$707$	722.678	+	722.678i	1.02218	+	1.02218i
$708$	1.72346	−	1.72346i	0.00243426	−	0.00243426i
$709$		−	976.562i		−	1.37738i	−0.725056	−	0.688690i	$-0.758186\pi$
$709$		−	976.562i		−	1.37738i	0.725056	−	0.688690i	$-0.241814\pi$
$710$	−563.779	+	406.090i	−0.794055	+	0.571957i
$711$	573.099			0.806046
$712$	225.168	+	225.168i	0.316247	+	0.316247i
$713$	−122.811	+	122.811i	−0.172246	+	0.172246i
$714$		−	525.527i		−	0.736032i
$715$	270.998	+	376.230i	0.379019	+	0.526196i
$716$	−333.379			−0.465613
$717$	−46.6523	−	46.6523i	−0.0650660	−	0.0650660i
$718$	398.005	−	398.005i	0.554324	−	0.554324i
$719$			100.914i			0.140354i	0.997535	+	0.0701769i	$0.0223564\pi$
$719$			100.914i			0.140354i	−0.997535	+	0.0701769i	$0.977644\pi$
$720$	119.672	+	19.4574i	0.166212	+	0.0270241i
$721$	−1075.09			−1.49111
$722$	−239.075	−	239.075i	−0.331129	−	0.331129i
$723$	−230.132	+	230.132i	−0.318302	+	0.318302i
$724$			210.770i			0.291119i
$725$	326.309	−	976.955i	0.450081	−	1.34752i
$726$	242.541			0.334078
$727$	−141.746	−	141.746i	−0.194974	−	0.194974i	0.602867	−	0.797842i	$-0.294025\pi$
$727$	−141.746	−	141.746i	−0.194974	−	0.194974i	−0.797842	+	0.602867i	$0.794025\pi$
$728$	312.210	−	312.210i	0.428860	−	0.428860i
$729$			335.747i			0.460558i
$730$	118.306	−	727.641i	0.162063	−	0.996768i
$731$	826.046			1.13002
$732$	118.704	+	118.704i	0.162164	+	0.162164i
$733$	88.5143	−	88.5143i	0.120756	−	0.120756i	−0.644146	−	0.764902i	$-0.722787\pi$
$733$	88.5143	−	88.5143i	0.120756	−	0.120756i	0.764902	+	0.644146i	$0.222787\pi$
$734$		−	715.090i		−	0.974238i
$735$	−71.9013	+	51.7904i	−0.0978249	+	0.0704632i
$736$	−27.1293			−0.0368605
$737$	−47.5764	−	47.5764i	−0.0645542	−	0.0645542i
$738$	−269.317	+	269.317i	−0.364928	+	0.364928i
$739$			408.910i			0.553329i	0.960967	+	0.276665i	$0.0892291\pi$
$739$			408.910i			0.553329i	−0.960967	+	0.276665i	$0.910771\pi$
$740$	−95.7589	−	132.943i	−0.129404	−	0.179653i
$741$	−383.532			−0.517588
$742$	322.985	+	322.985i	0.435290	+	0.435290i
$743$	579.264	−	579.264i	0.779629	−	0.779629i	−0.200139	−	0.979768i	$-0.564139\pi$
$743$	579.264	−	579.264i	0.779629	−	0.779629i	0.979768	+	0.200139i	$0.0641394\pi$
$744$		−	175.568i		−	0.235979i
$745$	347.499	+	56.4993i	0.466442	+	0.0758380i
$746$	−252.246			−0.338131
$747$	−298.735	−	298.735i	−0.399913	−	0.399913i
$748$	−182.140	+	182.140i	−0.243502	+	0.243502i
$749$			1429.19i			1.90813i
$750$	−140.866	+	268.259i	−0.187821	+	0.357679i
$751$	−833.492			−1.10984			−0.554921	−	0.831903i	$-0.687252\pi$
$751$	−833.492			−1.10984			−0.554921	+	0.831903i	$0.687252\pi$
$752$	43.9344	+	43.9344i	0.0584234	+	0.0584234i
$753$	207.932	−	207.932i	0.276138	−	0.276138i
$754$			1180.76i			1.56599i
$755$	2.02354	−	12.4458i	0.00268018	−	0.0164844i
$756$	397.743			0.526115
$757$	383.684	+	383.684i	0.506847	+	0.506847i	0.913557	−	0.406710i	$-0.133324\pi$
$757$	383.684	+	383.684i	0.506847	+	0.506847i	−0.406710	+	0.913557i	$0.633324\pi$
$758$	−551.551	+	551.551i	−0.727640	+	0.727640i
$759$		−	37.6157i		−	0.0495596i
$760$	−126.709	+	91.2682i	−0.166722	+	0.120090i
$761$	−870.019			−1.14326			−0.571629	−	0.820512i	$-0.693688\pi$
$761$	−870.019			−1.14326			−0.571629	+	0.820512i	$0.693688\pi$
$762$	−402.801	−	402.801i	−0.528610	−	0.528610i
$763$	9.65791	−	9.65791i	0.0126578	−	0.0126578i
$764$			527.564i			0.690528i
$765$	498.601	+	692.214i	0.651767	+	0.904855i
$766$	700.330			0.914270
$767$	10.1884	+	10.1884i	0.0132834	+	0.0132834i
$768$	19.3917	−	19.3917i	0.0252496	−	0.0252496i
$769$		−	763.597i		−	0.992973i	−0.868044	−	0.496487i	$-0.834623\pi$
$769$		−	763.597i		−	0.992973i	0.868044	−	0.496487i	$-0.165377\pi$
$770$	246.029	+	40.0015i	0.319518	+	0.0519499i
$771$	−662.294			−0.859006
$772$	81.4144	+	81.4144i	0.105459	+	0.105459i
$773$	−682.434	+	682.434i	−0.882838	+	0.882838i	−0.993822	−	0.110984i	$-0.964600\pi$
$773$	−682.434	+	682.434i	−0.882838	+	0.882838i	0.110984	+	0.993822i	$0.464600\pi$
$774$			251.625i			0.325097i
$775$	−858.743	−	286.825i	−1.10806	−	0.370097i
$776$	−81.7820			−0.105389
$777$	−152.964	−	152.964i	−0.196865	−	0.196865i
$778$	−386.345	+	386.345i	−0.496587	+	0.496587i
$779$		−	490.547i		−	0.629713i
$780$	55.7416	−	342.839i	0.0714637	−	0.439537i
$781$	449.648			0.575734
$782$	−134.977	−	134.977i	−0.172605	−	0.172605i
$783$	−752.117	+	752.117i	−0.960558	+	0.960558i
$784$		−	41.3590i		−	0.0527538i
$785$	−1243.95	+	896.019i	−1.58466	+	1.14143i
$786$	−387.719			−0.493281
$787$	715.957	+	715.957i	0.909729	+	0.909729i	0.996250	−	0.0865212i	$-0.0275750\pi$
$787$	715.957	+	715.957i	0.909729	+	0.909729i	−0.0865212	+	0.996250i	$0.527575\pi$
$788$	233.215	−	233.215i	0.295958	−	0.295958i
$789$			202.697i			0.256903i
$790$	−390.699	−	542.413i	−0.494556	−	0.686598i
$791$	148.330			0.187522
$792$	−55.4822	−	55.4822i	−0.0700533	−	0.0700533i
$793$	−701.729	+	701.729i	−0.884904	+	0.884904i
$794$		−	417.174i		−	0.525409i
$795$	354.671	+	57.6653i	0.446127	+	0.0725350i
$796$	13.0834			0.0164364
$797$	114.511	+	114.511i	0.143677	+	0.143677i	0.775287	−	0.631609i	$-0.217605\pi$
$797$	114.511	+	114.511i	0.143677	+	0.143677i	−0.631609	+	0.775287i	$0.717605\pi$
$798$	−145.791	+	145.791i	−0.182695	+	0.182695i
$799$			437.175i			0.547152i
$800$	−63.1689	−	126.529i	−0.0789612	−	0.158162i
$801$	−682.506			−0.852067
$802$	549.142	+	549.142i	0.684716	+	0.684716i
$803$	−337.347	+	337.347i	−0.420108	+	0.420108i
$804$			50.4028i			0.0626900i
$805$	−29.6436	+	182.323i	−0.0368243	+	0.226488i
$806$	1037.88			1.28770
$807$	−289.617	−	289.617i	−0.358881	−	0.358881i
$808$	−265.349	+	265.349i	−0.328402	+	0.328402i
$809$		−	612.311i		−	0.756874i	−0.925627	−	0.378437i	$-0.876462\pi$
$809$		−	612.311i		−	0.756874i	0.925627	−	0.378437i	$-0.123538\pi$
$810$	−59.1546	+	42.6090i	−0.0730303	+	0.0526037i
$811$	−1080.99			−1.33291			−0.666455	−	0.745545i	$-0.732189\pi$
$811$	−1080.99			−1.33291			−0.666455	+	0.745545i	$0.732189\pi$
$812$	448.837	+	448.837i	0.552755	+	0.552755i
$813$	230.228	−	230.228i	0.283184	−	0.283184i
$814$			106.030i			0.130258i
$815$	−676.258	−	938.857i	−0.829765	−	1.15197i
$816$	192.960			0.236470
$817$	−229.161	−	229.161i	−0.280490	−	0.280490i
$818$	622.797	−	622.797i	0.761366	−	0.761366i
$819$			946.340i			1.15548i
$820$	438.499	+	71.2948i	0.534755	+	0.0869449i
$821$	542.078			0.660266			0.330133	−	0.943934i	$-0.392906\pi$
$821$	542.078			0.660266			0.330133	+	0.943934i	$0.392906\pi$
$822$	−195.977	−	195.977i	−0.238415	−	0.238415i
$823$	353.910	−	353.910i	0.430024	−	0.430024i	−0.458612	−	0.888637i	$-0.651653\pi$
$823$	353.910	−	353.910i	0.430024	−	0.430024i	0.888637	+	0.458612i	$0.151653\pi$
$824$		−	394.745i		−	0.479059i
$825$	175.437	−	87.5859i	0.212651	−	0.106165i
$826$	7.74573			0.00937740
$827$	−137.486	−	137.486i	−0.166247	−	0.166247i	0.619081	−	0.785327i	$-0.287505\pi$
$827$	−137.486	−	137.486i	−0.166247	−	0.166247i	−0.785327	+	0.619081i	$0.787505\pi$
$828$	41.1158	−	41.1158i	0.0496568	−	0.0496568i
$829$			1219.64i			1.47122i	0.677403	+	0.735612i	$0.263105\pi$
$829$			1219.64i			1.47122i	−0.677403	+	0.735612i	$0.736895\pi$
$830$	−79.0825	+	486.397i	−0.0952801	+	0.586020i
$831$	−31.0280			−0.0373381
$832$	114.636	+	114.636i	0.137783	+	0.137783i
$833$	205.774	−	205.774i	0.247028	−	0.247028i
$834$		−	538.406i		−	0.645571i
$835$	−495.926	+	357.215i	−0.593923	+	0.427802i
$836$	101.058			0.120883
$837$	661.111	+	661.111i	0.789858	+	0.789858i
$838$	217.540	−	217.540i	0.259594	−	0.259594i
$839$			1047.03i			1.24795i	0.781442	+	0.623977i	$0.214484\pi$
$839$			1047.03i			1.24795i	−0.781442	+	0.623977i	$0.785516\pi$
$840$	−109.133	−	151.511i	−0.129921	−	0.180370i
$841$	−856.469			−1.01839
$842$	172.844	+	172.844i	0.205278	+	0.205278i
$843$	−44.8243	+	44.8243i	−0.0531723	+	0.0531723i
$844$			126.654i			0.150064i
$845$	1192.67	+	193.914i	1.41144	+	0.229484i
$846$	−133.169			−0.157411
$847$	545.024	+	545.024i	0.643476	+	0.643476i
$848$	−118.592	+	118.592i	−0.139849	+	0.139849i
$849$			315.540i			0.371660i
$850$	315.238	−	943.808i	0.370868	−	1.11036i
$851$	−78.5750			−0.0923326
$852$	−238.180	−	238.180i	−0.279554	−	0.279554i
$853$	692.971	−	692.971i	0.812393	−	0.812393i	−0.172599	−	0.984992i	$-0.555216\pi$
$853$	692.971	−	692.971i	0.812393	−	0.812393i	0.984992	+	0.172599i	$0.0552165\pi$
$854$			533.492i			0.624697i
$855$	53.7118	−	330.355i	0.0628209	−	0.386380i
$856$	−524.762			−0.613039
$857$	494.859	+	494.859i	0.577432	+	0.577432i	0.934195	−	0.356763i	$-0.116120\pi$
$857$	494.859	+	494.859i	0.577432	+	0.577432i	−0.356763	+	0.934195i	$0.616120\pi$
$858$	−158.946	+	158.946i	−0.185252	+	0.185252i
$859$			67.9105i			0.0790576i	0.999218	+	0.0395288i	$0.0125857\pi$
$859$			67.9105i			0.0790576i	−0.999218	+	0.0395288i	$0.987414\pi$
$860$	238.152	−	171.541i	0.276921	−	0.199466i
$861$	586.568			0.681264
$862$	23.1272	+	23.1272i	0.0268297	+	0.0268297i
$863$	−172.718	+	172.718i	−0.200137	+	0.200137i	−0.800059	−	0.599922i	$-0.795198\pi$
$863$	−172.718	+	172.718i	−0.200137	+	0.200137i	0.599922	+	0.800059i	$0.295198\pi$
$864$			146.041i			0.169029i
$865$	−956.934	−	1328.52i	−1.10628	−	1.53586i
$866$	802.947			0.927190
$867$	609.772	+	609.772i	0.703313	+	0.703313i
$868$	394.528	−	394.528i	0.454525	−	0.454525i
$869$			432.607i			0.497822i
$870$	492.869	+	80.1348i	0.566516	+	0.0921090i
$871$	−297.960			−0.342089
$872$	3.54613	+	3.54613i	0.00406667	+	0.00406667i
$873$	123.945	−	123.945i	0.141975	−	0.141975i
$874$			74.8902i			0.0856867i
$875$	−919.365	+	286.272i	−1.05070	+	0.327168i
$876$	357.387			0.407977
$877$	−488.190	−	488.190i	−0.556659	−	0.556659i	0.371696	−	0.928355i	$-0.378776\pi$
$877$	−488.190	−	488.190i	−0.556659	−	0.556659i	−0.928355	+	0.371696i	$0.878776\pi$
$878$	−437.828	+	437.828i	−0.498666	+	0.498666i
$879$			215.089i			0.244698i
$880$	−14.6875	+	90.3355i	−0.0166903	+	0.102654i
$881$	166.359			0.188829			0.0944146	−	0.995533i	$-0.469902\pi$
$881$	166.359			0.188829			0.0944146	+	0.995533i	$0.469902\pi$
$882$	62.6816	+	62.6816i	0.0710676	+	0.0710676i
$883$	289.480	−	289.480i	0.327837	−	0.327837i	−0.523927	−	0.851763i	$-0.675533\pi$
$883$	289.480	−	289.480i	0.327837	−	0.327837i	0.851763	+	0.523927i	$0.175533\pi$
$884$			1140.70i			1.29038i
$885$	4.94426	−	3.56135i	0.00558673	−	0.00402412i
$886$	−50.6212			−0.0571345
$887$	463.997	+	463.997i	0.523108	+	0.523108i	0.918509	−	0.395400i	$-0.129394\pi$
$887$	463.997	+	463.997i	0.523108	+	0.523108i	−0.395400	+	0.918509i	$0.629394\pi$
$888$	56.1645	−	56.1645i	0.0632483	−	0.0632483i
$889$		−	1810.30i		−	2.03634i
$890$	465.285	+	645.961i	0.522793	+	0.725799i
$891$	47.1793			0.0529510
$892$	−347.073	−	347.073i	−0.389095	−	0.389095i
$893$	121.280	−	121.280i	0.135812	−	0.135812i
$894$			170.677i			0.190914i
$895$	−822.644	−	133.752i	−0.919156	−	0.149444i
$896$	87.1521			0.0972680
$897$	−117.789	−	117.789i	−0.131314	−	0.131314i
$898$	856.476	−	856.476i	0.953759	−	0.953759i
$899$			1492.07i			1.65970i
$900$	287.497	+	96.0259i	0.319441	+	0.106695i
$901$	−1180.06			−1.30972
$902$	−203.296	−	203.296i	−0.225383	−	0.225383i
$903$	274.017	−	274.017i	0.303452	−	0.303452i
$904$			54.4630i			0.0602466i
$905$	−84.5614	+	520.095i	−0.0934380	+	0.574691i
$906$	6.11284			0.00674707
$907$	−1048.61	−	1048.61i	−1.15613	−	1.15613i	−0.985301	−	0.170829i	$-0.945355\pi$
$907$	−1048.61	−	1048.61i	−1.15613	−	1.15613i	−0.170829	−	0.985301i	$-0.554645\pi$
$908$	285.649	−	285.649i	0.314591	−	0.314591i
$909$		−	804.298i		−	0.884816i
$910$	895.669	−	645.150i	0.984252	−	0.708956i
$911$	−621.762			−0.682505			−0.341252	−	0.939972i	$-0.610851\pi$
$911$	−621.762			−0.682505			−0.341252	+	0.939972i	$0.610851\pi$
$912$	−53.5307	−	53.5307i	−0.0586959	−	0.0586959i
$913$	225.502	−	225.502i	0.246990	−	0.246990i
$914$			507.822i			0.555604i
$915$	245.290	+	340.539i	0.268076	+	0.372173i
$916$	−432.007			−0.471624
$917$	−871.262	−	871.262i	−0.950122	−	0.950122i
$918$	−726.599	+	726.599i	−0.791503	+	0.791503i
$919$		−	766.157i		−	0.833686i	−0.908978	−	0.416843i	$-0.863136\pi$
$919$		−	766.157i		−	0.833686i	0.908978	−	0.416843i	$-0.136864\pi$
$920$	−66.9442	−	10.8844i	−0.0727655	−	0.0118308i
$921$	−937.213			−1.01760
$922$	316.325	+	316.325i	0.343086	+	0.343086i
$923$	1408.02	−	1408.02i	1.52548	−	1.52548i
$924$			120.839i			0.130779i
$925$	−182.957	−	366.469i	−0.197791	−	0.396183i
$926$	746.301			0.805940
$927$	598.255	+	598.255i	0.645367	+	0.645367i
$928$	−164.801	+	164.801i	−0.177588	+	0.177588i
$929$		−	854.661i		−	0.919980i	−0.887924	−	0.459990i	$-0.847853\pi$
$929$		−	854.661i		−	0.919980i	0.887924	−	0.459990i	$-0.152147\pi$
$930$	70.4385	−	433.232i	0.0757403	−	0.465841i
$931$	−114.171			−0.122633
$932$	−191.128	−	191.128i	−0.205073	−	0.205073i
$933$	284.808	−	284.808i	0.305261	−	0.305261i
$934$		−	1276.71i		−	1.36693i
$935$	−522.522	+	376.372i	−0.558847	+	0.402537i
$936$	−347.472			−0.371230
$937$	−1054.10	−	1054.10i	−1.12497	−	1.12497i	−0.990983	−	0.133988i	$-0.957222\pi$
$937$	−1054.10	−	1054.10i	−1.12497	−	1.12497i	−0.133988	−	0.990983i	$-0.542778\pi$
$938$	−113.262	+	113.262i	−0.120749	+	0.120749i
$939$		−	49.8807i		−	0.0531211i
$940$	90.7858	+	126.039i	0.0965806	+	0.134084i
$941$	−333.543			−0.354456			−0.177228	−	0.984170i	$-0.556713\pi$
$941$	−333.543			−0.354456			−0.177228	+	0.984170i	$0.556713\pi$
$942$	−525.534	−	525.534i	−0.557891	−	0.557891i
$943$	150.655	−	150.655i	0.159761	−	0.159761i
$944$			2.84403i			0.00301275i
$945$	981.470	+	159.576i	1.03859	+	0.168863i
$946$	−189.941			−0.200783
$947$	−1143.97	−	1143.97i	−1.20799	−	1.20799i	−0.971677	−	0.236312i	$-0.924061\pi$
$947$	−1143.97	−	1143.97i	−1.20799	−	1.20799i	−0.236312	−	0.971677i	$-0.575939\pi$
$948$	229.153	−	229.153i	0.241723	−	0.241723i
$949$			2112.72i			2.22626i
$950$	−349.283	+	174.377i	−0.367666	+	0.183555i
$951$	−4.99314			−0.00525041
$952$	433.609	+	433.609i	0.455472	+	0.455472i
$953$	714.632	−	714.632i	0.749877	−	0.749877i	−0.224579	−	0.974456i	$-0.572101\pi$
$953$	714.632	−	714.632i	0.749877	−	0.749877i	0.974456	+	0.224579i	$0.0721008\pi$
$954$		−	359.463i		−	0.376796i
$955$	−211.660	+	1301.81i	−0.221633	+	1.36316i
$956$	76.9851			0.0805283
$957$	−228.503	−	228.503i	−0.238770	−	0.238770i
$958$	−664.201	+	664.201i	−0.693320	+	0.693320i
$959$		−	880.778i		−	0.918434i
$960$	55.6310	−	40.0710i	0.0579489	−	0.0417406i
$961$	350.533			0.364758
$962$	332.021	+	332.021i	0.345136	+	0.345136i
$963$	795.302	−	795.302i	0.825859	−	0.825859i
$964$		−	379.761i		−	0.393943i
$965$	168.234	+	233.562i	0.174336	+	0.242033i
$966$	−89.5495			−0.0927014
$967$	−623.196	−	623.196i	−0.644464	−	0.644464i	0.307186	−	0.951650i	$-0.400613\pi$
$967$	−623.196	−	623.196i	−0.644464	−	0.644464i	−0.951650	+	0.307186i	$0.900613\pi$
$968$	−200.119	+	200.119i	−0.206734	+	0.206734i
$969$		−	532.664i		−	0.549704i
$970$	−201.805	−	32.8112i	−0.208046	−	0.0338259i
$971$	795.980			0.819753			0.409877	−	0.912141i	$-0.365572\pi$
$971$	795.980			0.819753			0.409877	+	0.912141i	$0.365572\pi$
$972$	−353.583	−	353.583i	−0.363769	−	0.363769i
$973$	1209.88	−	1209.88i	1.24345	−	1.24345i
$974$		−	594.195i		−	0.610057i
$975$	275.096	−	823.625i	0.282150	−	0.844743i
$976$	−195.884			−0.200701
$977$	−1167.31	−	1167.31i	−1.19479	−	1.19479i	−0.975705	−	0.219088i	$-0.929692\pi$
$977$	−1167.31	−	1167.31i	−1.19479	−	1.19479i	−0.219088	−	0.975705i	$-0.570308\pi$
$978$	396.639	−	396.639i	0.405562	−	0.405562i
$979$		−	515.193i		−	0.526245i
$980$	16.5933	−	102.057i	0.0169320	−	0.104140i
$981$	−10.7487			−0.0109569
$982$	−707.506	−	707.506i	−0.720475	−	0.720475i
$983$	−192.953	+	192.953i	−0.196290	+	0.196290i	−0.798407	−	0.602118i	$-0.794324\pi$
$983$	−192.953	+	192.953i	−0.196290	+	0.196290i	0.602118	+	0.798407i	$0.294324\pi$
$984$			215.373i			0.218875i
$985$	669.047	−	481.914i	0.679236	−	0.489253i
$986$	−1639.88			−1.66316
$987$	145.020	+	145.020i	0.146930	+	0.146930i
$988$	316.450	−	316.450i	0.320294	−	0.320294i
$989$		−	140.758i		−	0.142324i
$990$	−114.648	−	159.167i	−0.115806	−	0.160775i
$991$	1151.44			1.16190			0.580948	−	0.813940i	$-0.302682\pi$
$991$	1151.44			1.16190			0.580948	+	0.813940i	$0.302682\pi$
$992$	144.860	+	144.860i	0.146029	+	0.146029i
$993$	4.84742	−	4.84742i	0.00488159	−	0.00488159i
$994$		−	1070.45i		−	1.07691i
$995$	32.2845	+	5.24908i	0.0324467	+	0.00527546i
$996$	−238.898			−0.239858
$997$	1216.07	+	1216.07i	1.21973	+	1.21973i	0.967726	+	0.252003i	$0.0810892\pi$
$997$	1216.07	+	1216.07i	1.21973	+	1.21973i	0.252003	+	0.967726i	$0.418911\pi$
$998$	−626.773	+	626.773i	−0.628029	+	0.628029i
$999$			422.981i			0.423404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.47.7	✓	20
5.3	odd	4	inner	230.3.f.a.93.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.7	✓	20	1.1	even	1	trivial
230.3.f.a.93.7	yes	20	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.21198 - 1.21198i) q^{3} +2.00000i q^{4} +(-0.802406 + 4.93519i) q^{5} -2.42397 q^{6} +(-5.44701 - 5.44701i) q^{7} +(2.00000 - 2.00000i) q^{8} +6.06220i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.21198 - 1.21198i) q^{3} +2.00000i q^{4} +(-0.802406 + 4.93519i) q^{5} -2.42397 q^{6} +(-5.44701 - 5.44701i) q^{7} +(2.00000 - 2.00000i) q^{8} +6.06220i q^{9} +(5.73760 - 4.13279i) q^{10} -4.57608 q^{11} +(2.42397 + 2.42397i) q^{12} +(-14.3294 + 14.3294i) q^{13} +10.8940i q^{14} +(5.00887 + 6.95387i) q^{15} -4.00000 q^{16} +(-19.9013 - 19.9013i) q^{17} +(6.06220 - 6.06220i) q^{18} +11.0420i q^{19} +(-9.87039 - 1.60481i) q^{20} -13.2034 q^{21} +(4.57608 + 4.57608i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.84793i q^{24} +(-23.7123 - 7.92006i) q^{25} +28.6589 q^{26} +(18.2551 + 18.2551i) q^{27} +(10.8940 - 10.8940i) q^{28} +41.2003i q^{29} +(1.94500 - 11.9627i) q^{30} +36.2151 q^{31} +(4.00000 + 4.00000i) q^{32} +(-5.54614 + 5.54614i) q^{33} +39.8025i q^{34} +(31.2527 - 22.5113i) q^{35} -12.1244 q^{36} +(11.5853 + 11.5853i) q^{37} +(11.0420 - 11.0420i) q^{38} +34.7341i q^{39} +(8.26558 + 11.4752i) q^{40} -44.4257 q^{41} +(13.2034 + 13.2034i) q^{42} +(-20.7536 + 20.7536i) q^{43} -9.15217i q^{44} +(-29.9181 - 4.86434i) q^{45} +6.78233 q^{46} +(-10.9836 - 10.9836i) q^{47} +(-4.84793 + 4.84793i) q^{48} +10.3397i q^{49} +(15.7922 + 31.6323i) q^{50} -48.2399 q^{51} +(-28.6589 - 28.6589i) q^{52} +(29.6479 - 29.6479i) q^{53} -36.5102i q^{54} +(3.67188 - 22.5839i) q^{55} -21.7880 q^{56} +(13.3827 + 13.3827i) q^{57} +(41.2003 - 41.2003i) q^{58} -0.711008i q^{59} +(-13.9077 + 10.0177i) q^{60} +48.9711 q^{61} +(-36.2151 - 36.2151i) q^{62} +(33.0208 - 33.0208i) q^{63} -8.00000i q^{64} +(-59.2206 - 82.2166i) q^{65} +11.0923 q^{66} +(10.3968 + 10.3968i) q^{67} +(39.8025 - 39.8025i) q^{68} +8.22007i q^{69} +(-53.7641 - 8.74142i) q^{70} -98.2605 q^{71} +(12.1244 + 12.1244i) q^{72} +(73.7196 - 73.7196i) q^{73} -23.1705i q^{74} +(-38.3379 + 19.1399i) q^{75} -22.0839 q^{76} +(24.9260 + 24.9260i) q^{77} +(34.7341 - 34.7341i) q^{78} -94.5365i q^{79} +(3.20962 - 19.7408i) q^{80} -10.3100 q^{81} +(44.4257 + 44.4257i) q^{82} +(-49.2784 + 49.2784i) q^{83} -26.4067i q^{84} +(114.185 - 82.2477i) q^{85} +41.5073 q^{86} +(49.9341 + 49.9341i) q^{87} +(-9.15217 + 9.15217i) q^{88} +112.584i q^{89} +(25.0538 + 34.7825i) q^{90} +156.105 q^{91} +(-6.78233 - 6.78233i) q^{92} +(43.8921 - 43.8921i) q^{93} +21.9672i q^{94} +(-54.4942 - 8.86013i) q^{95} +9.69586 q^{96} +(-20.4455 - 20.4455i) q^{97} +(10.3397 - 10.3397i) q^{98} -27.7411i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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