LMFDB - Embedded newform 171.3.z.a.101.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,3,Mod(5,171)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("171.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([15, 16])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.z (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$38$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.16
Character	$\chi$	$=$	171.101
Dual form			171.3.z.a.149.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.920951 + 0.162389i) q^{2} +(-2.16595 + 2.07574i) q^{3} +(-2.93699 + 1.06898i) q^{4} +(-1.12152 - 1.33658i) q^{5} +(1.65766 - 2.26338i) q^{6} +(-3.88198 - 6.72379i) q^{7} +(5.77072 - 3.33173i) q^{8} +(0.382648 - 8.99186i) q^{9} +(1.24992 + 1.04880i) q^{10} +7.84544i q^{11} +(4.14245 - 8.41176i) q^{12} +(18.8192 + 15.7912i) q^{13} +(4.66699 + 5.56190i) q^{14} +(5.20355 + 0.566975i) q^{15} +(4.80351 - 4.03062i) q^{16} +(-2.20168 - 2.62386i) q^{17} +(1.10778 + 8.34320i) q^{18} +(18.3773 + 4.82451i) q^{19} +(4.72268 + 2.72664i) q^{20} +(22.3650 + 6.50541i) q^{21} +(-1.27401 - 7.22527i) q^{22} +(-10.0908 - 27.7241i) q^{23} +(-5.58329 + 19.1948i) q^{24} +(3.81257 - 21.6222i) q^{25} +(-19.8959 - 11.4869i) q^{26} +(17.8359 + 20.2702i) q^{27} +(18.5889 + 15.5980i) q^{28} +(-19.3894 - 53.2719i) q^{29} +(-4.88429 + 0.322841i) q^{30} +4.66857 q^{31} +(-20.9020 + 24.9100i) q^{32} +(-16.2851 - 16.9928i) q^{33} +(2.45373 + 2.05892i) q^{34} +(-4.63316 + 12.7295i) q^{35} +(8.48826 + 26.8180i) q^{36} +9.54356 q^{37} +(-17.7080 - 1.45888i) q^{38} +(-73.5397 + 4.86081i) q^{39} +(-10.9251 - 3.97642i) q^{40} +(64.9786 - 11.4575i) q^{41} +(-21.6535 - 2.35935i) q^{42} +(23.5636 + 8.57647i) q^{43} +(-8.38659 - 23.0420i) q^{44} +(-12.4475 + 9.57316i) q^{45} +(13.7952 + 23.8939i) q^{46} +(-17.1066 - 46.9999i) q^{47} +(-2.03764 + 18.7009i) q^{48} +(-5.63960 + 9.76808i) q^{49} +20.5321i q^{50} +(10.2152 + 1.11304i) q^{51} +(-72.1522 - 26.2612i) q^{52} +(18.6486 + 3.28826i) q^{53} +(-19.7177 - 15.7715i) q^{54} +(10.4861 - 8.79886i) q^{55} +(-44.8037 - 25.8674i) q^{56} +(-49.8186 + 27.6967i) q^{57} +(26.5074 + 45.9122i) q^{58} +(-24.7705 + 68.0563i) q^{59} +(-15.8889 + 3.89728i) q^{60} +(61.9930 + 52.0183i) q^{61} +(-4.29953 + 0.758122i) q^{62} +(-61.9449 + 32.3334i) q^{63} +(2.66355 - 4.61341i) q^{64} -42.8636i q^{65} +(17.7572 + 13.0050i) q^{66} +(20.3344 - 115.322i) q^{67} +(9.27116 + 5.35271i) q^{68} +(79.4039 + 39.1032i) q^{69} +(2.19979 - 12.4756i) q^{70} +(-60.3038 + 10.6332i) q^{71} +(-27.7503 - 53.1644i) q^{72} +(31.9632 + 11.6336i) q^{73} +(-8.78916 + 1.54977i) q^{74} +(36.6241 + 54.7464i) q^{75} +(-59.1311 + 5.47535i) q^{76} +(52.7511 - 30.4559i) q^{77} +(66.9371 - 16.4186i) q^{78} +(-40.2080 + 33.7385i) q^{79} +(-10.7745 - 1.89984i) q^{80} +(-80.7072 - 6.88144i) q^{81} +(-57.9816 + 21.1036i) q^{82} +(-57.9562 + 33.4610i) q^{83} +(-72.6399 + 4.80134i) q^{84} +(-1.03776 + 5.88545i) q^{85} +(-23.0937 - 4.07204i) q^{86} +(152.575 + 75.1368i) q^{87} +(26.1388 + 45.2738i) q^{88} +(-11.4254 - 31.3909i) q^{89} +(9.90897 - 10.8377i) q^{90} +(33.1208 - 187.837i) q^{91} +(59.2729 + 70.6386i) q^{92} +(-10.1119 + 9.69072i) q^{93} +(23.3866 + 40.5067i) q^{94} +(-14.1622 - 29.9735i) q^{95} +(-6.43402 - 97.3408i) q^{96} +(-27.9966 - 158.776i) q^{97} +(3.60758 - 9.91173i) q^{98} +(70.5451 + 3.00204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21}+ \cdots - 300 q^{99}+O(q^{100}) $ 228 * q - 9 * q^2 + 6 * q^3 - 3 * q^4 - 9 * q^5 - 30 * q^6 + 3 * q^7 + 30 * q^9 - 12 * q^10 - 3 * q^12 + 12 * q^13 - 9 * q^14 - 48 * q^15 + 9 * q^16 - 81 * q^17 - 60 * q^18 - 33 * q^19 - 18 * q^20 + 21 * q^21 + 81 * q^22 + 207 * q^23 - 222 * q^24 - 3 * q^25 - 216 * q^26 - 33 * q^27 - 36 * q^28 - 9 * q^29 + 171 * q^30 - 6 * q^31 - 9 * q^32 + 30 * q^33 + 33 * q^34 + 225 * q^35 - 246 * q^36 - 24 * q^37 - 9 * q^38 - 60 * q^39 - 177 * q^40 - 9 * q^41 - 15 * q^42 + 93 * q^43 + 441 * q^44 - 57 * q^45 - 6 * q^46 - 9 * q^47 - 774 * q^48 - 543 * q^49 - 81 * q^51 + 213 * q^52 + 393 * q^54 + 63 * q^55 - 459 * q^56 + 84 * q^57 - 6 * q^58 + 126 * q^59 - 333 * q^60 - 24 * q^61 - 36 * q^62 + 369 * q^63 + 372 * q^64 + 894 * q^66 + 39 * q^67 + 747 * q^68 + 231 * q^69 + 291 * q^70 + 204 * q^72 - 51 * q^73 + 333 * q^74 + 324 * q^75 - 3 * q^76 - 18 * q^77 - 1569 * q^78 - 105 * q^79 - 756 * q^80 + 1050 * q^81 + 132 * q^82 + 99 * q^83 - 69 * q^84 - 3 * q^85 - 495 * q^86 - 483 * q^87 + 387 * q^88 - 648 * q^89 - 339 * q^90 + 225 * q^91 + 27 * q^92 + 396 * q^93 - 6 * q^94 - 1305 * q^95 - 663 * q^96 - 543 * q^97 + 1125 * q^98 - 300 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−0.920951	+	0.162389i	−0.460476	+	0.0811943i	−0.399074	−	0.916919i	$-0.630668\pi$
$2$	−0.920951	+	0.162389i	−0.460476	+	0.0811943i	−0.0614019	+	0.998113i	$0.519557\pi$
$3$	−2.16595	+	2.07574i	−0.721982	+	0.691912i
$3$	−2.16595	+	2.07574i	−0.721982	+	0.691912i
$4$	−2.93699	+	1.06898i	−0.734247	+	0.267244i
$5$	−1.12152	−	1.33658i	−0.224305	−	0.267316i	0.642142	−	0.766586i	$-0.278046\pi$
$5$	−1.12152	−	1.33658i	−0.224305	−	0.267316i	−0.866447	+	0.499270i	$0.833602\pi$
$6$	1.65766	−	2.26338i	0.276276	−	0.377229i
$7$	−3.88198	−	6.72379i	−0.554569	−	0.960542i	−0.997937	−	0.0642022i	$-0.979550\pi$
$7$	−3.88198	−	6.72379i	−0.554569	−	0.960542i	0.443368	−	0.896340i	$-0.353784\pi$
$8$	5.77072	−	3.33173i	0.721340	−	0.416466i
$9$	0.382648	−	8.99186i	0.0425165	−	0.999096i
$10$	1.24992	+	1.04880i	0.124992	+	0.104880i
$11$			7.84544i			0.713222i	0.934253	+	0.356611i	$0.116068\pi$
$11$			7.84544i			0.713222i	−0.934253	+	0.356611i	$0.883932\pi$
$12$	4.14245	−	8.41176i	0.345204	−	0.700980i
$13$	18.8192	+	15.7912i	1.44763	+	1.21471i	0.934287	+	0.356523i	$0.116038\pi$
$13$	18.8192	+	15.7912i	1.44763	+	1.21471i	0.513344	+	0.858183i	$0.328407\pi$
$14$	4.66699	+	5.56190i	0.333356	+	0.397278i
$15$	5.20355	+	0.566975i	0.346903	+	0.0377983i
$16$	4.80351	−	4.03062i	0.300219	−	0.251914i
$17$	−2.20168	−	2.62386i	−0.129511	−	0.154345i	0.697392	−	0.716690i	$-0.254344\pi$
$17$	−2.20168	−	2.62386i	−0.129511	−	0.154345i	−0.826903	+	0.562345i	$0.809899\pi$
$18$	1.10778	+	8.34320i	0.0615431	+	0.463511i
$19$	18.3773	+	4.82451i	0.967225	+	0.253921i
$19$	18.3773	+	4.82451i	0.967225	+	0.253921i
$20$	4.72268	+	2.72664i	0.236134	+	0.136332i
$21$	22.3650	+	6.50541i	1.06500	+	0.309781i
$22$	−1.27401	−	7.22527i	−0.0579095	−	0.328421i
$23$	−10.0908	−	27.7241i	−0.438728	−	1.20540i	−0.940320	−	0.340292i	$-0.889474\pi$
$23$	−10.0908	−	27.7241i	−0.438728	−	1.20540i	0.501592	−	0.865105i	$-0.332748\pi$
$24$	−5.58329	+	19.1948i	−0.232637	+	0.799784i
$25$	3.81257	−	21.6222i	0.152503	−	0.864887i
$26$	−19.8959	−	11.4869i	−0.765226	−	0.441803i
$27$	17.8359	+	20.2702i	0.660590	+	0.750747i
$28$	18.5889	+	15.5980i	0.663890	+	0.557070i
$29$	−19.3894	−	53.2719i	−0.668599	−	1.83696i	−0.532834	−	0.846219i	$-0.678873\pi$
$29$	−19.3894	−	53.2719i	−0.668599	−	1.83696i	−0.135765	−	0.990741i	$-0.543349\pi$
$30$	−4.88429	+	0.322841i	−0.162810	+	0.0107614i
$31$	4.66857			0.150599			0.0752995	−	0.997161i	$-0.476009\pi$
$31$	4.66857			0.150599			0.0752995	+	0.997161i	$0.476009\pi$
$32$	−20.9020	+	24.9100i	−0.653188	+	0.778439i
$33$	−16.2851	−	16.9928i	−0.493486	−	0.514933i
$34$	2.45373	+	2.05892i	0.0721684	+	0.0605565i
$35$	−4.63316	+	12.7295i	−0.132376	+	0.363700i
$36$	8.48826	+	26.8180i	0.235785	+	0.744946i
$37$	9.54356			0.257934			0.128967	−	0.991649i	$-0.458834\pi$
$37$	9.54356			0.257934			0.128967	+	0.991649i	$0.458834\pi$
$38$	−17.7080	−	1.45888i	−0.466000	−	0.0383915i
$39$	−73.5397	+	4.86081i	−1.88563	+	0.124636i
$40$	−10.9251	−	3.97642i	−0.273128	−	0.0994105i
$41$	64.9786	−	11.4575i	1.58484	−	0.279451i	0.689318	−	0.724459i	$-0.257910\pi$
$41$	64.9786	−	11.4575i	1.58484	−	0.279451i	0.895526	+	0.445009i	$0.146799\pi$
$42$	−21.6535	−	2.35935i	−0.515559	−	0.0561749i
$43$	23.5636	+	8.57647i	0.547992	+	0.199453i	0.601154	−	0.799133i	$-0.294708\pi$
$43$	23.5636	+	8.57647i	0.547992	+	0.199453i	−0.0531622	+	0.998586i	$0.516930\pi$
$44$	−8.38659	−	23.0420i	−0.190604	−	0.523681i
$45$	−12.4475	+	9.57316i	−0.276611	+	0.212737i
$46$	13.7952	+	23.8939i	0.299895	+	0.519433i
$47$	−17.1066	−	46.9999i	−0.363969	−	0.999998i	−0.977612	−	0.210414i	$-0.932519\pi$
$47$	−17.1066	−	46.9999i	−0.363969	−	0.999998i	0.613643	−	0.789584i	$-0.289703\pi$
$48$	−2.03764	+	18.7009i	−0.0424508	+	0.389602i
$49$	−5.63960	+	9.76808i	−0.115094	+	0.199349i
$50$			20.5321i			0.410642i
$51$	10.2152	+	1.11304i	0.200297	+	0.0218243i
$52$	−72.1522	−	26.2612i	−1.38754	−	0.505024i
$53$	18.6486	+	3.28826i	0.351861	+	0.0620426i	0.346785	−	0.937945i	$-0.387273\pi$
$53$	18.6486	+	3.28826i	0.351861	+	0.0620426i	0.00507571	+	0.999987i	$0.498384\pi$
$54$	−19.7177	−	15.7715i	−0.365142	−	0.292065i
$55$	10.4861	−	8.79886i	0.190656	−	0.159979i
$56$	−44.8037	−	25.8674i	−0.800066	−	0.461918i
$57$	−49.8186	+	27.6967i	−0.874010	+	0.485907i
$58$	26.5074	+	45.9122i	0.457024	+	0.791589i
$59$	−24.7705	+	68.0563i	−0.419839	+	1.15350i	0.531959	+	0.846770i	$0.321456\pi$
$59$	−24.7705	+	68.0563i	−0.419839	+	1.15350i	−0.951798	+	0.306727i	$0.900766\pi$
$60$	−15.8889	+	3.89728i	−0.264814	+	0.0649546i
$61$	61.9930	+	52.0183i	1.01628	+	0.852759i	0.989155	−	0.146874i	$-0.0469210\pi$
$61$	61.9930	+	52.0183i	1.01628	+	0.852759i	0.0271228	+	0.999632i	$0.491365\pi$
$62$	−4.29953	+	0.758122i	−0.0693472	+	0.0122278i
$63$	−61.9449	+	32.3334i	−0.983252	+	0.513229i
$64$	2.66355	−	4.61341i	0.0416180	−	0.0720846i
$65$		−	42.8636i		−	0.659440i
$66$	17.7572	+	13.0050i	0.269048	+	0.197046i
$67$	20.3344	−	115.322i	0.303499	−	1.72123i	−0.326987	−	0.945029i	$-0.606033\pi$
$67$	20.3344	−	115.322i	0.303499	−	1.72123i	0.630486	−	0.776200i	$-0.282856\pi$
$68$	9.27116	+	5.35271i	0.136341	+	0.0787163i
$69$	79.4039	+	39.1032i	1.15078	+	0.566713i
$70$	2.19979	−	12.4756i	0.0314255	−	0.178223i
$71$	−60.3038	+	10.6332i	−0.849349	+	0.149763i	−0.581348	−	0.813655i	$-0.697474\pi$
$71$	−60.3038	+	10.6332i	−0.849349	+	0.149763i	−0.268002	+	0.963418i	$0.586363\pi$
$72$	−27.7503	−	53.1644i	−0.385420	−	0.738394i
$73$	31.9632	+	11.6336i	0.437852	+	0.159365i	0.551534	−	0.834152i	$-0.314043\pi$
$73$	31.9632	+	11.6336i	0.437852	+	0.159365i	−0.113683	+	0.993517i	$0.536265\pi$
$74$	−8.78916	+	1.54977i	−0.118772	+	0.0209428i
$75$	36.6241	+	54.7464i	0.488321	+	0.729952i
$76$	−59.1311	+	5.47535i	−0.778041	+	0.0720441i
$77$	52.7511	−	30.4559i	0.685079	−	0.395531i
$78$	66.9371	−	16.4186i	0.858168	−	0.210494i
$79$	−40.2080	+	33.7385i	−0.508962	+	0.427070i	−0.860764	−	0.509005i	$-0.830014\pi$
$79$	−40.2080	+	33.7385i	−0.508962	+	0.427070i	0.351802	+	0.936075i	$0.385569\pi$
$80$	−10.7745	−	1.89984i	−0.134681	−	0.0237480i
$81$	−80.7072	−	6.88144i	−0.996385	−	0.0849560i
$82$	−57.9816	+	21.1036i	−0.707092	+	0.257361i
$83$	−57.9562	+	33.4610i	−0.698268	+	0.403145i	−0.806702	−	0.590958i	$-0.798750\pi$
$83$	−57.9562	+	33.4610i	−0.698268	+	0.403145i	0.108434	+	0.994104i	$0.465416\pi$
$84$	−72.6399	+	4.80134i	−0.864760	+	0.0571588i
$85$	−1.03776	+	5.88545i	−0.0122090	+	0.0692406i
$86$	−23.0937	−	4.07204i	−0.268531	−	0.0473493i
$87$	152.575	+	75.1368i	1.75373	+	0.863641i
$88$	26.1388	+	45.2738i	0.297032	+	0.514475i
$89$	−11.4254	−	31.3909i	−0.128375	−	0.352707i	0.858809	−	0.512297i	$-0.171205\pi$
$89$	−11.4254	−	31.3909i	−0.128375	−	0.352707i	−0.987183	+	0.159590i	$0.948983\pi$
$90$	9.90897	−	10.8377i	0.110100	−	0.120419i
$91$	33.1208	−	187.837i	0.363965	−	2.06415i
$92$	59.2729	+	70.6386i	0.644270	+	0.767811i
$93$	−10.1119	+	9.69072i	−0.108730	+	0.104201i
$94$	23.3866	+	40.5067i	0.248793	+	0.430922i
$95$	−14.1622	−	29.9735i	−0.149076	−	0.315511i
$96$	−6.43402	−	97.3408i	−0.0670210	−	1.01397i
$97$	−27.9966	−	158.776i	−0.288624	−	1.63687i	−0.692045	−	0.721855i	$-0.743290\pi$
$97$	−27.9966	−	158.776i	−0.288624	−	1.63687i	0.403420	−	0.915015i	$-0.367821\pi$
$98$	3.60758	−	9.91173i	0.0368120	−	0.101140i
$99$	70.5451	+	3.00204i	0.712577	+	0.0303237i
$100$	11.9161	+	67.5797i	0.119161	+	0.675797i
$101$	−20.4912	−	3.61315i	−0.202883	−	0.0357737i	0.0712831	−	0.997456i	$-0.477291\pi$
$101$	−20.4912	−	3.61315i	−0.202883	−	0.0357737i	−0.274166	+	0.961682i	$0.588402\pi$
$102$	−9.58842	+	0.633774i	−0.0940041	+	0.00621347i
$103$	25.8595	−	44.7900i	0.251063	−	0.434854i	−0.712756	−	0.701413i	$-0.752553\pi$
$103$	25.8595	−	44.7900i	0.251063	−	0.434854i	0.963819	+	0.266558i	$0.0858864\pi$
$104$	161.212	+	28.4260i	1.55012	+	0.273327i
$105$	−16.3879	−	37.1886i	−0.156075	−	0.354177i
$106$	−17.7085			−0.167061
$107$	76.7814	+	44.3297i	0.717583	+	0.414297i	0.813862	−	0.581058i	$-0.197361\pi$
$107$	76.7814	+	44.3297i	0.717583	+	0.414297i	−0.0962795	+	0.995354i	$0.530694\pi$
$108$	−74.0523	−	40.4671i	−0.685669	−	0.374695i
$109$	21.2503	+	120.516i	0.194957	+	1.10565i	0.912480	+	0.409120i	$0.134164\pi$
$109$	21.2503	+	120.516i	0.194957	+	1.10565i	−0.717524	+	0.696534i	$0.754724\pi$
$110$	−8.22832	+	9.80613i	−0.0748029	+	0.0891467i
$111$	−20.6708	+	19.8099i	−0.186224	+	0.178468i
$112$	−45.7482	−	16.6510i	−0.408466	−	0.148670i
$113$	164.016	−	94.6946i	1.45147	−	0.838006i	0.452903	−	0.891560i	$-0.350388\pi$
$113$	164.016	−	94.6946i	1.45147	−	0.838006i	0.998565	+	0.0535539i	$0.0170549\pi$
$114$	41.3829	−	33.5973i	0.363008	−	0.294713i
$115$	−25.7385	+	44.5804i	−0.223813	+	0.387656i
$116$	113.893	+	135.732i	0.981834	+	1.17010i
$117$	149.193	−	163.177i	1.27516	−	1.39468i
$118$	11.7608	−	66.6990i	0.0996681	−	0.565246i
$119$	−9.09542	+	24.9895i	−0.0764321	+	0.209995i
$120$	31.9172	−	14.0650i	0.265977	−	0.117208i
$121$	59.4491			0.491315
$122$	−65.5397	−	37.8393i	−0.537210	−	0.310159i
$123$	−116.957	+	159.695i	−0.950874	+	1.29833i
$124$	−13.7115	+	4.99059i	−0.110577	+	0.0402467i
$125$	−70.9514	+	40.9638i	−0.567611	+	0.327710i
$126$	51.7976	−	39.8366i	0.411092	−	0.316164i
$127$	−74.1216	+	26.9780i	−0.583634	+	0.212426i	−0.616927	−	0.787020i	$-0.711623\pi$
$127$	−74.1216	+	26.9780i	−0.583634	+	0.212426i	0.0332929	+	0.999446i	$0.489401\pi$
$128$	42.7831	−	117.545i	0.334243	−	0.918324i
$129$	−68.8401	+	30.3357i	−0.533644	+	0.235161i
$130$	6.96056	+	39.4753i	0.0535427	+	0.303656i
$131$	−2.12778	+	5.84602i	−0.0162426	+	0.0446261i	−0.947549	−	0.319611i	$-0.896448\pi$
$131$	−2.12778	+	5.84602i	−0.0162426	+	0.0446261i	0.931306	+	0.364237i	$0.118670\pi$
$132$	65.9939	+	32.4993i	0.499954	+	0.246207i
$133$	−38.9013	−	142.294i	−0.292491	−	1.06988i
$134$			109.508i			0.817226i
$135$	7.08929	−	46.5727i	0.0525133	−	0.344983i
$136$	−21.4473	−	7.80617i	−0.157701	−	0.0573983i
$137$	91.4608	−	108.999i	0.667597	−	0.795612i	−0.320857	−	0.947128i	$-0.603971\pi$
$137$	91.4608	−	108.999i	0.667597	−	0.795612i	0.988455	+	0.151516i	$0.0484155\pi$
$138$	−79.4771	−	23.1179i	−0.575921	−	0.167521i
$139$	49.9244	+	41.8916i	0.359169	+	0.301378i	0.804459	−	0.594008i	$-0.202455\pi$
$139$	49.9244	+	41.8916i	0.359169	+	0.301378i	−0.445291	+	0.895386i	$0.646900\pi$
$140$		−	42.3391i		−	0.302422i
$141$	134.611	+	66.2906i	0.954690	+	0.470146i
$142$	53.8102	−	19.5853i	0.378945	−	0.137925i
$143$	−123.889	+	147.645i	−0.866355	+	1.03248i
$144$	−34.4047	−	44.7348i	−0.238922	−	0.310658i
$145$	−49.4565	+	85.6612i	−0.341079	+	0.590767i
$146$	−31.3257	−	5.52356i	−0.214559	−	0.0378326i
$147$	−8.06087	−	32.8635i	−0.0548358	−	0.223561i
$148$	−28.0293	+	10.2018i	−0.189387	+	0.0689314i
$149$	33.7625	−	5.95324i	0.226594	−	0.0399546i	−0.0591982	−	0.998246i	$-0.518854\pi$
$149$	33.7625	−	5.95324i	0.226594	−	0.0399546i	0.285792	+	0.958292i	$0.407743\pi$
$150$	−42.6192	−	44.4714i	−0.284128	−	0.296476i
$151$	−66.9780	+	116.009i	−0.443563	+	0.768273i	−0.997951	−	0.0639852i	$-0.979619\pi$
$151$	−66.9780	+	116.009i	−0.443563	+	0.768273i	0.554388	+	0.832258i	$0.312952\pi$
$152$	122.124	−	33.3872i	0.803447	−	0.219652i
$153$	−24.4359	+	18.7932i	−0.159712	+	0.122831i
$154$	−43.6355	+	36.6145i	−0.283348	+	0.237757i
$155$	−5.23592	−	6.23993i	−0.0337801	−	0.0402576i
$156$	210.789	−	92.8883i	1.35121	−	0.595438i
$157$	35.8011	−	30.0407i	0.228032	−	0.191342i	−0.521612	−	0.853183i	$-0.674669\pi$
$157$	35.8011	−	30.0407i	0.228032	−	0.191342i	0.749644	+	0.661841i	$0.230225\pi$
$158$	31.5509	−	37.6009i	0.199689	−	0.237980i
$159$	−47.2175	+	31.5874i	−0.296965	+	0.198663i
$160$	56.7364			0.354603
$161$	−147.239	+	175.473i	−0.914529	+	1.08989i
$162$	75.4448	−	6.76845i	0.465709	−	0.0417805i
$163$	−17.0326	−	29.5013i	−0.104494	−	0.180990i	0.809037	−	0.587758i	$-0.199989\pi$
$163$	−17.0326	−	29.5013i	−0.104494	−	0.180990i	−0.913532	+	0.406768i	$0.866656\pi$
$164$	−178.594	+	103.111i	−1.08899	+	0.628726i
$165$	−4.44817	+	40.8241i	−0.0269586	+	0.247419i
$166$	47.9412	−	40.2274i	0.288802	−	0.242334i
$167$	−85.3060	−	234.376i	−0.510814	−	1.40345i	−0.880390	−	0.474250i	$-0.842719\pi$
$167$	−85.3060	−	234.376i	−0.510814	−	1.40345i	0.369576	−	0.929200i	$-0.379503\pi$
$168$	150.736	−	36.9731i	0.897240	−	0.220078i
$169$	75.4542	+	427.922i	0.446474	+	2.53208i
$170$		−	5.58874i		−	0.0328749i
$171$	50.4133	−	163.400i	0.294815	−	0.955554i
$172$	−78.3742			−0.455664
$173$	103.984	−	18.3352i	0.601064	−	0.105984i	0.135167	−	0.990823i	$-0.456843\pi$
$173$	103.984	−	18.3352i	0.601064	−	0.105984i	0.465897	+	0.884839i	$0.345732\pi$
$174$	−152.715	−	44.4210i	−0.877673	−	0.255293i
$175$	−160.183	+	58.3020i	−0.915334	+	0.333154i
$176$	31.6220	+	37.6856i	0.179670	+	0.214123i
$177$	−87.6154	−	198.823i	−0.495002	−	1.12330i
$178$	15.6197	+	27.0542i	0.0877513	+	0.151990i
$179$	−5.78014	+	3.33717i	−0.0322913	+	0.0186434i	−0.516059	−	0.856553i	$-0.672601\pi$
$179$	−5.78014	+	3.33717i	−0.0322913	+	0.0186434i	0.483767	+	0.875197i	$0.339268\pi$
$180$	26.3247	−	41.4224i	0.146248	−	0.230124i
$181$	−252.386	−	211.777i	−1.39440	−	1.17004i	−0.963522	−	0.267631i	$-0.913759\pi$
$181$	−252.386	−	211.777i	−1.39440	−	1.17004i	−0.430878	−	0.902410i	$-0.641796\pi$
$182$			178.368i			0.980042i
$183$	−242.250	+	16.0122i	−1.32377	+	0.0874982i
$184$	−150.600	−	126.368i	−0.818478	−	0.686785i
$185$	−10.7033	−	12.7557i	−0.0578559	−	0.0689500i
$186$	7.73888	−	10.5667i	0.0416069	−	0.0568104i
$187$	20.5854	−	17.2732i	0.110082	−	0.0923699i
$188$	100.484	+	119.752i	0.534487	+	0.636977i
$189$	67.0536	−	198.614i	0.354781	−	1.05087i
$190$	17.9101	+	25.3044i	0.0942635	+	0.133181i
$191$	19.0097	+	10.9753i	0.0995274	+	0.0574622i	0.548938	−	0.835863i	$-0.315032\pi$
$191$	19.0097	+	10.9753i	0.0995274	+	0.0574622i	−0.449410	+	0.893326i	$0.648366\pi$
$192$	3.80710	+	15.5212i	0.0198287	+	0.0808398i
$193$	−13.5664	−	76.9387i	−0.0702921	−	0.398646i	−0.999572	−	0.0292688i	$-0.990682\pi$
$193$	−13.5664	−	76.9387i	−0.0702921	−	0.398646i	0.929280	−	0.369377i	$-0.120429\pi$
$194$	51.5669	+	141.679i	0.265809	+	0.730304i
$195$	88.9734	+	92.8402i	0.456274	+	0.476104i
$196$	6.12161	−	34.7174i	0.0312327	−	0.177129i
$197$	−201.502	−	116.337i	−1.02285	−	0.590544i	−0.107924	−	0.994159i	$-0.534420\pi$
$197$	−201.502	−	116.337i	−1.02285	−	0.590544i	−0.914929	+	0.403615i	$0.867754\pi$
$198$	−65.4561	+	8.69098i	−0.330586	+	0.0438938i
$199$	43.0850	+	36.1526i	0.216508	+	0.181672i	0.744591	−	0.667521i	$-0.232645\pi$
$199$	43.0850	+	36.1526i	0.216508	+	0.181672i	−0.528083	+	0.849193i	$0.677089\pi$
$200$	−50.0379	−	137.478i	−0.250189	−	0.687390i
$201$	195.335	+	291.991i	0.971818	+	1.45269i
$202$	19.4581			0.0963272
$203$	−282.920	+	337.171i	−1.39369	+	1.66094i
$204$	−31.1917	+	7.65080i	−0.152900	+	0.0375039i
$205$	−88.1890	−	73.9993i	−0.430190	−	0.360972i
$206$	−16.5420	+	45.4487i	−0.0803009	+	0.220625i
$207$	−253.153	+	80.1261i	−1.22296	+	0.387082i
$208$	154.046			0.740608
$209$	−37.8504	+	144.178i	−0.181102	+	0.689846i
$210$	21.1314	+	31.5877i	0.100626	+	0.150418i
$211$	−53.1980	−	19.3625i	−0.252123	−	0.0917653i	0.212867	−	0.977081i	$-0.431720\pi$
$211$	−53.1980	−	19.3625i	−0.252123	−	0.0917653i	−0.464990	+	0.885316i	$0.653942\pi$
$212$	−58.2859	+	10.2774i	−0.274934	+	0.0484782i
$213$	108.543	−	148.206i	0.509592	−	0.695801i
$214$	−77.9105	−	28.3571i	−0.364068	−	0.132510i
$215$	−14.9641	−	41.1135i	−0.0696003	−	0.191225i
$216$	170.461	+	57.5490i	0.789170	+	0.266431i
$217$	−18.1233	−	31.3905i	−0.0835176	−	0.144657i
$218$	−39.1409	−	107.539i	−0.179546	−	0.493298i
$219$	−93.3789	+	41.1492i	−0.426387	+	0.187896i
$220$	−21.3917	+	37.0515i	−0.0972350	+	0.168416i
$221$		−	84.1461i		−	0.380752i
$222$	15.8199	−	21.6007i	0.0712610	−	0.0973003i
$223$	168.904	+	61.4759i	0.757415	+	0.275677i	0.691723	−	0.722163i	$-0.256852\pi$
$223$	168.904	+	61.4759i	0.757415	+	0.275677i	0.0656927	+	0.997840i	$0.479074\pi$
$224$	248.631	+	43.8404i	1.10996	+	0.195716i
$225$	−192.965	−	42.5558i	−0.857621	−	0.189137i
$226$	−135.673	+	113.843i	−0.600325	+	0.503732i
$227$	191.278	+	110.435i	0.842636	+	0.486496i	0.858160	−	0.513383i	$-0.171608\pi$
$227$	191.278	+	110.435i	0.842636	+	0.486496i	−0.0155231	+	0.999880i	$0.504941\pi$
$228$	116.710	−	134.600i	0.511884	−	0.590350i
$229$	−43.7641	−	75.8017i	−0.191110	−	0.331012i	0.754508	−	0.656290i	$-0.227875\pi$
$229$	−43.7641	−	75.8017i	−0.191110	−	0.331012i	−0.945618	+	0.325278i	$0.894542\pi$
$230$	16.4646	−	45.2360i	0.0715850	−	0.196678i
$231$	−51.0378	+	175.463i	−0.220943	+	0.759581i
$232$	−289.378	−	242.817i	−1.24732	−	1.04662i
$233$	40.8175	−	7.19722i	0.175182	−	0.0308894i	−0.0853688	−	0.996349i	$-0.527207\pi$
$233$	40.8175	−	7.19722i	0.175182	−	0.0308894i	0.260551	+	0.965460i	$0.416096\pi$
$234$	−110.902	+	174.505i	−0.473938	+	0.745750i
$235$	−43.6338	+	75.5759i	−0.185676	+	0.321599i
$236$		−	226.360i		−	0.959151i
$237$	17.0562	−	156.537i	0.0719669	−	0.660494i
$238$	4.31843	−	24.4911i	0.0181447	−	0.102904i
$239$	223.880	+	129.257i	0.936735	+	0.540824i	0.888935	−	0.458033i	$-0.151446\pi$
$239$	223.880	+	129.257i	0.936735	+	0.540824i	0.0477994	+	0.998857i	$0.484779\pi$
$240$	27.2806	−	18.2501i	0.113669	−	0.0760420i
$241$	0.668933	−	3.79371i	0.00277566	−	0.0157415i	−0.983388	−	0.181513i	$-0.941900\pi$
$241$	0.668933	−	3.79371i	0.00277566	−	0.0157415i	0.986164	+	0.165772i	$0.0530115\pi$
$242$	−54.7497	+	9.65385i	−0.226238	+	0.0398919i
$243$	189.091	−	152.622i	0.778154	−	0.628073i
$244$	−237.679	−	86.5081i	−0.974094	−	0.354541i
$245$	19.3808	−	3.41736i	0.0791053	−	0.0139484i
$246$	81.7795	−	166.064i	0.332437	−	0.675055i
$247$	269.661	+	380.992i	1.09174	+	1.54248i
$248$	26.9410	−	15.5544i	0.108633	−	0.0627193i
$249$	56.0738	−	192.777i	0.225196	−	0.774203i
$250$	58.6907	−	49.2473i	0.234763	−	0.196989i
$251$	−232.675	−	41.0269i	−0.926993	−	0.163454i	−0.310283	−	0.950644i	$-0.600424\pi$
$251$	−232.675	−	41.0269i	−0.926993	−	0.163454i	−0.616710	+	0.787190i	$0.711535\pi$
$252$	147.368	−	161.181i	0.584793	−	0.639605i
$253$	217.508	−	79.1664i	0.859715	−	0.312911i
$254$	63.8814	−	36.8820i	0.251502	−	0.145205i
$255$	−9.96890	−	14.9017i	−0.0390937	−	0.0584381i
$256$	−24.0132	+	136.186i	−0.0938017	+	0.531976i
$257$	412.320	+	72.7031i	1.60436	+	0.282892i	0.902910	−	0.429829i	$-0.141426\pi$
$257$	412.320	+	72.7031i	1.60436	+	0.282892i	0.701448	+	0.712721i	$0.252537\pi$
$258$	58.4722	−	39.1166i	0.226636	−	0.151615i
$259$	−37.0480	−	64.1690i	−0.143042	−	0.247757i
$260$	45.8202	+	125.890i	0.176231	+	0.484192i
$261$	−486.432	+	153.962i	−1.86373	+	0.589893i
$262$	1.01025	−	5.72943i	0.00385593	−	0.0218680i
$263$	−52.9000	−	63.0438i	−0.201141	−	0.239710i	0.656040	−	0.754726i	$-0.272230\pi$
$263$	−52.9000	−	63.0438i	−0.201141	−	0.239710i	−0.857180	+	0.515016i	$0.827786\pi$
$264$	−150.592	−	43.8033i	−0.570423	−	0.165922i
$265$	−16.5199	−	28.6133i	−0.0623392	−	0.107975i
$266$	58.9331	+	124.728i	0.221553	+	0.468904i
$267$	89.9059	+	44.2750i	0.336726	+	0.165824i
$268$	63.5549	+	360.438i	0.237145	+	1.34492i
$269$	−50.1635	+	137.823i	−0.186482	+	0.512354i	−0.997340	−	0.0728884i	$-0.976778\pi$
$269$	−50.1635	+	137.823i	−0.186482	+	0.512354i	0.810859	+	0.585242i	$0.199001\pi$
$270$	1.03398	+	44.0424i	0.00382954	+	0.163120i
$271$	0.638885	+	3.62329i	0.00235751	+	0.0133701i	0.985964	−	0.166959i	$-0.0533948\pi$
$271$	0.638885	+	3.62329i	0.00235751	+	0.0133701i	−0.983606	+	0.180329i	$0.942284\pi$
$272$	−21.1516	−	3.72960i	−0.0777632	−	0.0137118i
$273$	318.163	+	475.596i	1.16543	+	1.74211i
$274$	−66.5308	+	115.235i	−0.242813	+	0.420565i
$275$	169.635	+	29.9113i	0.616856	+	0.108768i
$276$	−275.009	−	29.9648i	−0.996409	−	0.108568i
$277$	−29.0231			−0.104777			−0.0523883	−	0.998627i	$-0.516683\pi$
$277$	−29.0231			−0.104777			−0.0523883	+	0.998627i	$0.516683\pi$
$278$	−52.7807	−	30.4729i	−0.189859	−	0.109615i
$279$	1.78642	−	41.9791i	0.00640294	−	0.150463i
$280$	15.6745	+	88.8947i	0.0559805	+	0.317481i
$281$	−42.5974	+	50.7655i	−0.151592	+	0.180660i	−0.836496	−	0.547973i	$-0.815400\pi$
$281$	−42.5974	+	50.7655i	−0.151592	+	0.180660i	0.684904	+	0.728633i	$0.259844\pi$
$282$	−134.735	−	39.1911i	−0.477784	−	0.138975i
$283$	−107.205	−	39.0195i	−0.378817	−	0.137878i	0.145592	−	0.989345i	$-0.453491\pi$
$283$	−107.205	−	39.0195i	−0.378817	−	0.137878i	−0.524409	+	0.851467i	$0.675714\pi$
$284$	165.745	−	95.6929i	0.583609	−	0.336947i
$285$	92.8917	+	35.5240i	0.325936	+	0.124646i
$286$	90.1196	−	156.092i	0.315104	−	0.545776i
$287$	−329.284	−	392.425i	−1.14733	−	1.36733i
$288$	215.990	+	197.480i	0.749964	+	0.685693i
$289$	48.1471	−	273.056i	0.166599	−	0.944829i
$290$	31.6366	−	86.9209i	0.109092	−	0.299727i
$291$	390.217	+	285.788i	1.34095	+	0.982088i
$292$	−106.312			−0.364081
$293$	−278.176	−	160.605i	−0.949407	−	0.548140i	−0.0565101	−	0.998402i	$-0.517997\pi$
$293$	−278.176	−	160.605i	−0.949407	−	0.548140i	−0.892897	+	0.450262i	$0.851331\pi$
$294$	12.7603	+	28.9567i	0.0434024	+	0.0984920i
$295$	118.744	−	43.2191i	0.402520	−	0.146505i
$296$	55.0732	−	31.7965i	0.186058	−	0.107421i
$297$	−159.028	+	139.931i	−0.535449	+	0.471147i
$298$	−30.1269	+	10.9653i	−0.101097	+	0.0367963i
$299$	247.897	−	681.090i	0.829086	−	2.27789i
$300$	−166.087	−	121.639i	−0.553624	−	0.405464i
$301$	−33.8073	−	191.731i	−0.112317	−	0.636979i
$302$	42.8449	−	117.715i	0.141870	−	0.389786i
$303$	51.8827	−	34.7084i	0.171230	−	0.114549i
$304$	107.721	−	50.8973i	0.354346	−	0.167425i
$305$		−	141.198i		−	0.462946i
$306$	19.4525	−	21.2757i	0.0635701	−	0.0695285i
$307$	397.661	+	144.737i	1.29531	+	0.471455i	0.895467	−	0.445128i	$-0.146842\pi$
$307$	397.661	+	144.737i	1.29531	+	0.471455i	0.399845	+	0.916583i	$0.369064\pi$
$308$	−122.373	+	145.838i	−0.397314	+	0.473501i
$309$	36.9618	+	150.690i	0.119618	+	0.487671i
$310$	5.83532	+	4.89641i	0.0188236	+	0.0157949i
$311$			195.063i			0.627213i	0.949553	+	0.313607i	$0.101537\pi$
$311$			195.063i			0.627213i	−0.949553	+	0.313607i	$0.898463\pi$
$312$	−408.182	+	273.064i	−1.30827	+	0.875206i
$313$	242.698	−	88.3347i	0.775392	−	0.282220i	0.0761420	−	0.997097i	$-0.475740\pi$
$313$	242.698	−	88.3347i	0.775392	−	0.282220i	0.699250	+	0.714877i	$0.253518\pi$
$314$	−28.0928	+	33.4797i	−0.0894674	+	0.106623i
$315$	112.689	+	46.5316i	0.357743	+	0.147719i
$316$	82.0248	−	142.071i	0.259572	−	0.449592i
$317$	−323.524	−	57.0461i	−1.02058	−	0.179956i	−0.361773	−	0.932266i	$-0.617828\pi$
$317$	−323.524	−	57.0461i	−1.02058	−	0.179956i	−0.658809	+	0.752310i	$0.728940\pi$
$318$	38.3556	−	36.7581i	0.120615	−	0.115591i
$319$	417.941	−	152.118i	1.31016	−	0.476859i
$320$	−9.15344	+	1.61400i	−0.0286045	+	0.00504375i
$321$	−258.321	+	63.3619i	−0.804739	+	0.197389i
$322$	107.105	−	185.512i	0.332625	−	0.576123i
$323$	−27.8021	−	58.8415i	−0.0860745	−	0.182172i
$324$	244.392	−	66.0634i	0.754297	−	0.203899i
$325$	413.189	−	346.707i	1.27135	−	1.06679i
$326$	20.4769	+	24.4034i	0.0628125	+	0.0748570i
$327$	−296.187	−	216.922i	−0.905771	−	0.663370i
$328$	336.800	−	282.609i	1.02683	−	0.861612i
$329$	−249.610	+	297.474i	−0.758694	+	0.904176i
$330$	−2.53283	−	38.3194i	−0.00767524	−	0.116119i
$331$	122.719			0.370754			0.185377	−	0.982668i	$-0.440649\pi$
$331$	122.719			0.370754			0.185377	+	0.982668i	$0.440649\pi$
$332$	134.448	−	160.229i	0.404963	−	0.482616i
$333$	3.65183	−	85.8144i	0.0109664	−	0.257701i
$334$	116.623	+	201.996i	0.349170	+	0.604779i
$335$	−176.943	+	102.158i	−0.528189	+	0.304950i
$336$	133.651	−	58.8960i	0.397771	−	0.175286i
$337$	−127.509	+	106.992i	−0.378364	+	0.317485i	−0.812060	−	0.583574i	$-0.801654\pi$
$337$	−127.509	+	106.992i	−0.378364	+	0.317485i	0.433696	+	0.901059i	$0.357209\pi$
$338$	−138.979	−	381.842i	−0.411181	−	1.12971i
$339$	−158.689	+	545.557i	−0.468108	+	1.60931i
$340$	−3.24351	−	18.3949i	−0.00953974	−	0.0541025i
$341$			36.6270i			0.107411i
$342$	−19.8940	+	158.670i	−0.0581695	+	0.463947i
$343$	−292.863			−0.853828
$344$	164.554	−	29.0152i	0.478353	−	0.0843466i
$345$	−36.7889	−	149.985i	−0.106634	−	0.434739i
$346$	−92.7869	+	33.7717i	−0.268170	+	0.0976060i
$347$	−236.587	−	281.953i	−0.681806	−	0.812545i	0.308533	−	0.951214i	$-0.400162\pi$
$347$	−236.587	−	281.953i	−0.681806	−	0.812545i	−0.990339	+	0.138669i	$0.955718\pi$
$348$	−528.429	−	57.5773i	−1.51848	−	0.165452i
$349$	−17.7141	−	30.6817i	−0.0507567	−	0.0879131i	0.839531	−	0.543312i	$-0.182830\pi$
$349$	−17.7141	−	30.6817i	−0.0507567	−	0.0879131i	−0.890287	+	0.455399i	$0.849497\pi$
$350$	138.054	−	79.7052i	0.394439	−	0.227729i
$351$	15.5679	+	663.119i	0.0443531	+	1.88923i
$352$	−195.430	−	163.985i	−0.555199	−	0.465868i
$353$			561.727i			1.59129i	0.605760	+	0.795647i	$0.292869\pi$
$353$			561.727i			1.59129i	−0.605760	+	0.795647i	$0.707131\pi$
$354$	112.976	+	168.879i	0.319142	+	0.477059i
$355$	81.8444	+	68.6756i	0.230547	+	0.193452i
$356$	67.1123	+	79.9813i	0.188518	+	0.224667i
$357$	−32.1713	−	73.0055i	−0.0901157	−	0.204497i
$358$	4.78131	−	4.01200i	0.0133556	−	0.0112067i
$359$	178.437	+	212.653i	0.497038	+	0.592347i	0.954993	−	0.296628i	$-0.0958623\pi$
$359$	178.437	+	212.653i	0.497038	+	0.592347i	−0.457955	+	0.888976i	$0.651418\pi$
$360$	−39.9359	+	96.7157i	−0.110933	+	0.268655i
$361$	314.448	+	177.323i	0.871048	+	0.491198i
$362$	266.826	+	154.052i	0.737088	+	0.425558i
$363$	−128.764	+	123.401i	−0.354721	+	0.339946i
$364$	103.518	+	587.082i	0.284391	+	1.61286i
$365$	−20.2982	−	55.7688i	−0.0556115	−	0.152791i
$366$	220.500	−	54.0850i	0.602459	−	0.147773i
$367$	−10.9699	+	62.2134i	−0.0298907	+	0.169519i	−0.996099	−	0.0882445i	$-0.971874\pi$
$367$	−10.9699	+	62.2134i	−0.0298907	+	0.169519i	0.966208	+	0.257763i	$0.0829854\pi$
$368$	−160.216	−	92.5010i	−0.435371	−	0.251361i
$369$	−78.1601	−	588.663i	−0.211816	−	1.59529i
$370$	11.9286	+	10.0093i	0.0322396	+	0.0270522i
$371$	−50.2841	−	138.155i	−0.135537	−	0.372384i
$372$	19.3393	−	39.2709i	0.0519874	−	0.105567i
$373$	−154.974			−0.415479			−0.207739	−	0.978184i	$-0.566611\pi$
$373$	−154.974			−0.415479			−0.207739	+	0.978184i	$0.566611\pi$
$374$	−16.1531	+	19.2506i	−0.0431902	+	0.0514721i
$375$	68.6469	−	236.002i	0.183058	−	0.629338i
$376$	−255.308	−	214.229i	−0.679010	−	0.569757i
$377$	476.333	−	1308.71i	1.26348	−	3.47139i
$378$	−29.5006	+	193.802i	−0.0780438	+	0.512704i
$379$	−51.0803			−0.134776			−0.0673882	−	0.997727i	$-0.521467\pi$
$379$	−51.0803			−0.134776			−0.0673882	+	0.997727i	$0.521467\pi$
$380$	73.6353	+	72.8928i	0.193777	+	0.191823i
$381$	104.544	−	212.290i	0.274394	−	0.557191i
$382$	−19.2893	−	7.02073i	−0.0504956	−	0.0183789i
$383$	−233.789	+	41.2233i	−0.610415	+	0.107633i	−0.470306	−	0.882504i	$-0.655856\pi$
$383$	−233.789	+	41.2233i	−0.610415	+	0.107633i	−0.140109	+	0.990136i	$0.544745\pi$
$384$	151.327	+	343.404i	0.394082	+	0.894280i
$385$	−99.8684	−	36.3491i	−0.259399	−	0.0944134i
$386$	24.9879	+	68.6538i	0.0647356	+	0.177860i
$387$	86.1350	−	208.599i	0.222571	−	0.539016i
$388$	251.954	+	436.397i	0.649365	+	1.12473i
$389$	50.9408	+	139.959i	0.130953	+	0.359791i	0.987789	−	0.155799i	$-0.0497951\pi$
$389$	50.9408	+	139.959i	0.130953	+	0.359791i	−0.856836	+	0.515590i	$0.827573\pi$
$390$	−97.0164	−	71.0531i	−0.248760	−	0.182187i
$391$	−50.5276	+	87.5164i	−0.129227	+	0.223827i
$392$			75.1585i			0.191731i
$393$	−7.52614	−	17.0789i	−0.0191505	−	0.0434577i
$394$	204.465	+	74.4193i	0.518948	+	0.188881i
$395$	90.1886	+	15.9027i	0.228325	+	0.0402599i
$396$	−210.399	+	66.5941i	−0.531311	+	0.168167i
$397$	−197.141	+	165.421i	−0.496577	+	0.416677i	−0.856376	−	0.516352i	$-0.827290\pi$
$397$	−197.141	+	165.421i	−0.496577	+	0.416677i	0.359799	+	0.933030i	$0.382845\pi$
$398$	−45.5500	−	26.2983i	−0.114447	−	0.0660761i
$399$	379.622	+	227.452i	0.951434	+	0.570054i
$400$	−68.8371	−	119.229i	−0.172093	−	0.298073i
$401$	−56.8950	+	156.318i	−0.141883	+	0.389820i	−0.990198	−	0.139672i	$-0.955395\pi$
$401$	−56.8950	+	156.318i	−0.141883	+	0.389820i	0.848315	+	0.529492i	$0.177617\pi$
$402$	−227.310	−	237.189i	−0.565449	−	0.590023i
$403$	87.8587	+	73.7222i	0.218012	+	0.182934i
$404$	64.0447	−	11.2928i	0.158527	−	0.0279525i
$405$	81.3175	+	115.589i	0.200784	+	0.285406i
$406$	205.803	−	356.461i	0.506903	−	0.877982i
$407$			74.8734i			0.183964i
$408$	62.6572	−	27.6111i	0.153572	−	0.0676743i
$409$	−106.815	+	605.777i	−0.261161	+	1.48112i	0.518587	+	0.855025i	$0.326458\pi$
$409$	−106.815	+	605.777i	−0.261161	+	1.48112i	−0.779748	+	0.626093i	$0.784653\pi$
$410$	93.2344	+	53.8289i	0.227401	+	0.131290i
$411$	28.1533	+	425.934i	0.0684995	+	1.03634i
$412$	−28.0697	+	159.191i	−0.0681303	+	0.386386i
$413$	553.755	−	97.6420i	1.34081	−	0.236421i
$414$	220.130	−	114.901i	0.531714	−	0.277539i
$415$	109.723	+	39.9358i	0.264392	+	0.0962309i
$416$	−786.718	+	138.720i	−1.89115	+	0.333460i
$417$	−195.089	+	12.8950i	−0.467840	+	0.0309232i
$418$	11.4455	−	138.927i	0.0273816	−	0.332362i
$419$	−345.989	+	199.757i	−0.825749	+	0.476746i	−0.852395	−	0.522899i	$-0.824851\pi$
$419$	−345.989	+	199.757i	−0.825749	+	0.476746i	0.0266460	+	0.999645i	$0.491517\pi$
$420$	87.8848	+	91.7043i	0.209249	+	0.218343i
$421$	−116.445	+	97.7093i	−0.276592	+	0.232089i	−0.770522	−	0.637413i	$-0.780004\pi$
$421$	−116.445	+	97.7093i	−0.276592	+	0.232089i	0.493930	+	0.869502i	$0.335560\pi$
$422$	52.1370	+	9.19315i	0.123547	+	0.0217847i
$423$	−429.162	+	135.835i	−1.01457	+	0.321124i
$424$	118.572	−	43.1565i	0.279650	−	0.101784i
$425$	−65.1277	+	37.6015i	−0.153242	+	0.0884741i
$426$	−75.8960	+	154.116i	−0.178160	+	0.361775i
$427$	109.104	−	618.762i	0.255514	−	1.44909i
$428$	−272.894	−	48.1185i	−0.637602	−	0.112426i
$429$	−38.1352	−	576.951i	−0.0888933	−	1.34487i
$430$	20.4575	+	35.4335i	0.0475757	+	0.0824035i
$431$	166.298	+	456.900i	0.385843	+	1.06009i	0.968855	+	0.247630i	$0.0796518\pi$
$431$	166.298	+	456.900i	0.385843	+	1.06009i	−0.583012	+	0.812464i	$0.698126\pi$
$432$	167.376	+	25.4780i	0.387445	+	0.0589769i
$433$	6.27939	−	35.6122i	0.0145021	−	0.0822453i	−0.976698	−	0.214619i	$-0.931149\pi$
$433$	6.27939	−	35.6122i	0.0145021	−	0.0822453i	0.991200	+	0.132374i	$0.0422600\pi$
$434$	21.7882	+	25.9661i	0.0502031	+	0.0598297i
$435$	−70.6898	−	288.196i	−0.162505	−	0.662520i
$436$	−191.241	−	331.239i	−0.438626	−	0.759723i
$437$	−51.6853	−	558.176i	−0.118273	−	1.27729i
$438$	79.3152	−	53.0601i	0.181085	−	0.121142i
$439$	−79.8753	−	452.995i	−0.181948	−	1.03188i	−0.929814	−	0.368030i	$-0.880032\pi$
$439$	−79.8753	−	452.995i	−0.181948	−	1.03188i	0.747866	−	0.663850i	$-0.231079\pi$
$440$	31.1968	−	85.7124i	0.0709017	−	0.194801i
$441$	85.6753	+	54.4483i	0.194275	+	0.123465i
$442$	13.6644	+	77.4945i	0.0309149	+	0.175327i
$443$	−415.282	−	73.2253i	−0.937430	−	0.165294i	−0.315996	−	0.948761i	$-0.602339\pi$
$443$	−415.282	−	73.2253i	−0.937430	−	0.165294i	−0.621434	+	0.783466i	$0.713450\pi$
$444$	39.5337	−	80.2781i	0.0890399	−	0.180807i
$445$	−29.1427	+	50.4766i	−0.0654892	+	0.113431i
$446$	−165.535	−	29.1883i	−0.371155	−	0.0654446i
$447$	−60.7704	+	82.9764i	−0.135952	+	0.185630i
$448$	−41.3595			−0.0923203
$449$	−360.208	−	207.966i	−0.802245	−	0.463176i	0.0420106	−	0.999117i	$-0.486624\pi$
$449$	−360.208	−	207.966i	−0.802245	−	0.463176i	−0.844256	+	0.535941i	$0.819957\pi$
$450$	184.622	+	7.85657i	0.410270	+	0.0174590i
$451$	89.8890	+	509.786i	0.199310	+	1.13035i
$452$	−380.487	+	453.446i	−0.841785	+	1.00320i
$453$	−95.7337	−	390.298i	−0.211333	−	0.861585i
$454$	−194.091	−	70.6435i	−0.427514	−	0.155602i
$455$	−288.206	+	166.396i	−0.633420	+	0.365705i
$456$	−195.211	+	325.812i	−0.428095	+	0.714500i
$457$	−385.867	+	668.341i	−0.844348	+	1.46245i	0.0418391	+	0.999124i	$0.486678\pi$
$457$	−385.867	+	668.341i	−0.844348	+	1.46245i	−0.886187	+	0.463328i	$0.846655\pi$
$458$	52.6140	+	62.7029i	0.114878	+	0.136906i
$459$	13.9171	−	91.4275i	0.0303205	−	0.199188i
$460$	27.9383	−	158.446i	0.0607355	−	0.344448i
$461$	−22.5128	+	61.8535i	−0.0488348	+	0.134173i	−0.961712	−	0.274061i	$-0.911633\pi$
$461$	−22.5128	+	61.8535i	−0.0488348	+	0.134173i	0.912877	+	0.408234i	$0.133855\pi$
$462$	18.5101	−	169.881i	0.0400651	−	0.367708i
$463$	−517.215			−1.11709			−0.558547	−	0.829473i	$-0.688641\pi$
$463$	−517.215			−1.11709			−0.558547	+	0.829473i	$0.688641\pi$
$464$	−307.856	−	177.741i	−0.663482	−	0.383062i
$465$	24.2932	+	2.64696i	0.0522433	+	0.00569239i
$466$	−36.4222	+	13.2566i	−0.0781592	+	0.0284476i
$467$	−248.185	+	143.289i	−0.531444	+	0.306830i	−0.741604	−	0.670837i	$-0.765935\pi$
$467$	−248.185	+	143.289i	−0.531444	+	0.306830i	0.210160	+	0.977667i	$0.432602\pi$
$468$	−263.746	+	638.734i	−0.563561	+	1.36482i
$469$	−854.342	+	310.955i	−1.82162	+	0.663017i
$470$	27.9119	−	76.6873i	0.0593870	−	0.163164i
$471$	−15.1867	+	139.380i	−0.0322436	+	0.295924i
$472$	83.8016	+	475.262i	0.177546	+	1.00691i
$473$	−67.2861	+	184.867i	−0.142254	+	0.390840i
$474$	9.71193	+	146.933i	0.0204893	+	0.309984i
$475$	174.381	−	378.963i	0.367118	−	0.797816i
$476$		−	83.1165i		−	0.174615i
$477$	36.7034	−	166.428i	0.0769464	−	0.348905i
$478$	−227.172	−	82.6838i	−0.475255	−	0.172979i
$479$	457.694	−	545.459i	0.955520	−	1.13874i	−0.0347233	−	0.999397i	$-0.511055\pi$
$479$	457.694	−	545.459i	0.955520	−	1.13874i	0.990244	−	0.139348i	$-0.0445006\pi$
$480$	−122.888	+	117.770i	−0.256017	+	0.245354i
$481$	179.602	+	150.704i	0.373393	+	0.313314i
$482$			3.60245i			0.00747396i
$483$	−45.3229	−	685.694i	−0.0938362	−	1.41966i
$484$	−174.601	+	63.5497i	−0.360747	+	0.131301i
$485$	−180.819	+	215.491i	−0.372822	+	0.444312i
$486$	−149.360	+	171.264i	−0.307325	+	0.352394i
$487$	337.840	−	585.155i	0.693716	−	1.20155i	−0.276896	−	0.960900i	$-0.589306\pi$
$487$	337.840	−	585.155i	0.693716	−	1.20155i	0.970612	−	0.240651i	$-0.0773610\pi$
$488$	531.054	+	93.6392i	1.08823	+	0.191884i
$489$	98.1286	+	28.5431i	0.200672	+	0.0583704i
$490$	−17.2938	+	6.29444i	−0.0352935	+	0.0128458i
$491$	−217.647	+	38.3770i	−0.443273	+	0.0781609i	−0.390830	−	0.920463i	$-0.627812\pi$
$491$	−217.647	+	38.3770i	−0.443273	+	0.0781609i	−0.0524429	+	0.998624i	$0.516701\pi$
$492$	172.793	−	594.046i	0.351205	−	1.20741i
$493$	−97.0888	+	168.163i	−0.196935	+	0.341101i
$494$	−310.213	−	307.085i	−0.627962	−	0.621630i
$495$	−75.1056	−	97.6561i	−0.151729	−	0.197285i
$496$	22.4255	−	18.8172i	0.0452127	−	0.0379380i
$497$	305.594	+	364.193i	0.614877	+	0.732782i
$498$	−20.3365	+	186.644i	−0.0408364	+	0.374786i
$499$	260.726	−	218.775i	0.522497	−	0.438427i	−0.343004	−	0.939334i	$-0.611445\pi$
$499$	260.726	−	218.775i	0.522497	−	0.438427i	0.865501	+	0.500907i	$0.167000\pi$
$500$	164.594	−	196.156i	0.329188	−	0.392311i
$501$	671.271	+	330.574i	1.33986	+	0.659828i
$502$	220.945			0.440129
$503$	−29.7130	+	35.4106i	−0.0590716	+	0.0703987i	−0.794771	−	0.606909i	$-0.792409\pi$
$503$	−29.7130	+	35.4106i	−0.0590716	+	0.0703987i	0.735700	+	0.677308i	$0.236854\pi$
$504$	−249.740	+	392.970i	−0.495516	+	0.779703i
$505$	18.1521	+	31.4404i	0.0359447	+	0.0622581i
$506$	−187.458	+	108.229i	−0.370471	+	0.213892i
$507$	−1051.68	−	770.233i	−2.07432	−	1.51920i
$508$	188.855	−	158.468i	0.371763	−	0.311946i
$509$	191.635	+	526.514i	0.376494	+	1.03441i	0.972799	+	0.231651i	$0.0744127\pi$
$509$	191.635	+	526.514i	0.376494	+	1.03441i	−0.596305	+	0.802758i	$0.703365\pi$
$510$	11.6007	+	12.1049i	0.0227465	+	0.0237351i
$511$	−45.8583	−	260.075i	−0.0897423	−	0.508954i
$512$			371.037i			0.724682i
$513$	229.982	+	458.560i	0.448308	+	0.893879i
$514$	−391.533			−0.761737
$515$	−88.8676	+	15.6698i	−0.172558	+	0.0304267i
$516$	169.754	−	162.684i	0.328981	−	0.315279i
$517$	368.735	−	134.208i	0.713220	−	0.259591i
$518$	44.5397	+	53.0803i	0.0859839	+	0.102472i
$519$	−187.165	+	255.557i	−0.360626	+	0.492402i
$520$	−142.810	−	247.354i	−0.274634	−	0.475680i
$521$	656.679	−	379.134i	1.26042	−	0.727704i	0.287265	−	0.957851i	$-0.407254\pi$
$521$	656.679	−	379.134i	1.26042	−	0.727704i	0.973156	+	0.230147i	$0.0739206\pi$
$522$	422.979	−	220.783i	0.810304	−	0.422955i
$523$	−363.690	−	305.172i	−0.695393	−	0.583504i	0.225066	−	0.974344i	$-0.427740\pi$
$523$	−363.690	−	305.172i	−0.695393	−	0.583504i	−0.920459	+	0.390840i	$0.872185\pi$
$524$		−	19.4442i		−	0.0371073i
$525$	225.929	−	458.777i	0.430341	−	0.873861i
$526$	58.9559	+	49.4699i	0.112083	+	0.0940492i
$527$	−10.2787	−	12.2497i	−0.0195042	−	0.0232442i
$528$	−146.717	−	15.9862i	−0.277873	−	0.0302768i
$529$	−261.566	+	219.480i	−0.494453	+	0.414895i
$530$	19.8605	+	23.6688i	0.0374726	+	0.0446581i
$531$	602.475	+	248.774i	1.13460	+	0.468502i
$532$	266.361	+	376.330i	0.500679	+	0.707388i
$533$	1403.77	+	810.468i	2.63372	+	1.52058i
$534$	−89.9887	−	26.1754i	−0.168518	−	0.0490177i
$535$	−26.8619	−	152.341i	−0.0502092	−	0.284750i
$536$	−266.878	−	733.242i	−0.497907	−	1.36799i
$537$	5.59241	−	19.2262i	0.0104142	−	0.0358029i
$538$	23.8173	−	135.074i	0.0442700	−	0.251068i
$539$	−76.6349	−	44.2452i	−0.142180	−	0.0820875i
$540$	28.9639	+	144.362i	0.0536369	+	0.267337i
$541$	361.458	+	303.299i	0.668129	+	0.560627i	0.912511	−	0.409052i	$-0.134141\pi$
$541$	361.458	+	303.299i	0.668129	+	0.560627i	−0.244382	+	0.969679i	$0.578585\pi$
$542$	−1.17676	−	3.23313i	−0.00217115	−	0.00596518i
$543$	986.249	−	65.1889i	1.81630	−	0.120053i
$544$	111.380			0.204743
$545$	137.247	−	163.565i	0.251830	−	0.300119i
$546$	−370.244	−	386.335i	−0.678102	−	0.707573i
$547$	443.162	+	371.857i	0.810168	+	0.679812i	0.950648	−	0.310272i	$-0.100420\pi$
$547$	443.162	+	371.857i	0.810168	+	0.679812i	−0.140480	+	0.990084i	$0.544864\pi$
$548$	−152.102	+	417.898i	−0.277559	+	0.762587i
$549$	491.463	−	537.527i	0.895196	−	0.979103i
$550$	−161.083			−0.292879
$551$	−99.3133	−	1072.54i	−0.180242	−	1.94653i
$552$	588.499	−	38.8985i	1.06612	−	0.0704683i
$553$	382.938	+	139.378i	0.692473	+	0.252040i
$554$	26.7289	−	4.71302i	0.0482470	−	0.00850725i
$555$	49.6604	+	5.41096i	0.0894782	+	0.00974948i
$556$	−191.409	−	69.6671i	−0.344260	−	0.125300i
$557$	89.8782	+	246.938i	0.161361	+	0.443336i	0.993854	−	0.110700i	$-0.0353092\pi$
$557$	89.8782	+	246.938i	0.161361	+	0.443336i	−0.832493	+	0.554036i	$0.813087\pi$
$558$	5.17173	+	38.9508i	0.00926833	+	0.0698044i
$559$	308.016	+	533.500i	0.551013	+	0.954383i
$560$	29.0524	+	79.8207i	0.0518792	+	0.142537i
$561$	−8.73226	+	80.1425i	−0.0155655	+	0.142856i
$562$	30.9863	−	53.6699i	0.0551358	−	0.0954981i
$563$			723.536i			1.28514i	0.766225	+	0.642572i	$0.222133\pi$
$563$			723.536i			1.28514i	−0.766225	+	0.642572i	$0.777867\pi$
$564$	−466.215	−	50.7984i	−0.826622	−	0.0900681i
$565$	−310.515	−	113.018i	−0.549584	−	0.200032i
$566$	105.067	+	18.5262i	0.185631	+	0.0327318i
$567$	267.035	+	569.372i	0.470960	+	1.00418i
$568$	−312.569	+	262.277i	−0.550298	+	0.461755i
$569$	622.568	+	359.440i	1.09414	+	0.631704i	0.934677	−	0.355499i	$-0.115689\pi$
$569$	622.568	+	359.440i	1.09414	+	0.631704i	0.159467	+	0.987203i	$0.449023\pi$
$570$	−91.3174	−	17.6313i	−0.160206	−	0.0309322i
$571$	−291.776	−	505.371i	−0.510992	−	0.885064i	−0.999919	−	0.0127389i	$-0.995945\pi$
$571$	−291.776	−	505.371i	−0.510992	−	0.885064i	0.488927	−	0.872325i	$-0.337388\pi$
$572$	206.031	−	566.065i	0.360194	−	0.989625i
$573$	−63.9558	+	15.6873i	−0.111616	+	0.0273775i
$574$	366.979	+	307.932i	0.639337	+	0.536468i
$575$	−637.927	+	112.484i	−1.10944	+	0.195624i
$576$	−40.4640	−	25.7156i	−0.0702499	−	0.0446452i
$577$	114.672	−	198.618i	0.198738	−	0.344225i	−0.749381	−	0.662139i	$-0.769649\pi$
$577$	114.672	−	198.618i	0.198738	−	0.344225i	0.948120	+	0.317914i	$0.102982\pi$
$578$			259.289i			0.448598i
$579$	189.088	+	138.485i	0.326578	+	0.239180i
$580$	53.6834	−	304.454i	0.0925576	−	0.524920i
$581$	449.970	+	259.791i	0.774476	+	0.447144i
$582$	−405.779	−	199.830i	−0.697215	−	0.343350i
$583$	−25.7978	+	146.307i	−0.0442501	+	0.250955i
$584$	223.211	−	39.3580i	0.382210	−	0.0673939i
$585$	−385.423	−	16.4017i	−0.658843	−	0.0280370i
$586$	282.267	+	102.737i	0.481684	+	0.175319i
$587$	989.452	−	174.467i	1.68561	−	0.297218i	0.752976	−	0.658048i	$-0.228618\pi$
$587$	989.452	−	174.467i	1.68561	−	0.297218i	0.932632	+	0.360830i	$0.117507\pi$
$588$	58.8050	+	87.9028i	0.100008	+	0.149495i
$589$	85.7956	+	22.5236i	0.145663	+	0.0382403i
$590$	−102.339	+	59.0853i	−0.173455	+	0.100145i
$591$	677.928	−	166.285i	1.14709	−	0.281361i
$592$	45.8426	−	38.4665i	0.0774368	−	0.0649772i
$593$	−181.528	−	32.0083i	−0.306119	−	0.0539770i	0.0184788	−	0.999829i	$-0.494118\pi$
$593$	−181.528	−	32.0083i	−0.306119	−	0.0539770i	−0.324597	+	0.945852i	$0.605229\pi$
$594$	123.734	−	154.694i	0.208307	−	0.260427i
$595$	43.6012	−	15.8695i	0.0732793	−	0.0266715i
$596$	−92.7962	+	53.5759i	−0.155698	+	0.0898925i
$597$	−168.363	+	11.1284i	−0.282015	+	0.0186406i
$598$	−117.699	+	667.507i	−0.196822	+	1.11623i
$599$	620.828	+	109.469i	1.03644	+	0.182752i	0.665882	−	0.746057i	$-0.268055\pi$
$599$	620.828	+	109.469i	1.03644	+	0.182752i	0.370558	+	0.928809i	$0.379166\pi$
$600$	393.747	+	193.904i	0.656245	+	0.323174i
$601$	−16.6423	−	28.8253i	−0.0276910	−	0.0479622i	0.851848	−	0.523789i	$-0.175482\pi$
$601$	−16.6423	−	28.8253i	−0.0276910	−	0.0479622i	−0.879539	+	0.475827i	$0.842149\pi$
$602$	62.2698	+	171.085i	0.103438	+	0.284194i
$603$	−1029.18	−	226.972i	−1.70677	−	0.376405i
$604$	72.7024	−	412.316i	0.120368	−	0.682642i
$605$	−66.6736	−	79.4585i	−0.110204	−	0.131336i
$606$	−42.1452	+	40.3899i	−0.0695465	+	0.0666499i
$607$	−267.634	−	463.556i	−0.440913	−	0.763683i	0.556845	−	0.830617i	$-0.312012\pi$
$607$	−267.634	−	463.556i	−0.440913	−	0.763683i	−0.997757	+	0.0669333i	$0.978679\pi$
$608$	−504.300	+	356.937i	−0.829442	+	0.587067i
$609$	−87.0879	−	1317.56i	−0.143001	−	2.16348i
$610$	22.9290	+	130.037i	0.0375885	+	0.213175i
$611$	420.252	−	1154.63i	0.687810	−	1.88974i
$612$	51.6784	−	81.3168i	0.0844419	−	0.132871i
$613$	−131.688	−	746.842i	−0.214826	−	1.21834i	−0.881208	−	0.472728i	$-0.843269\pi$
$613$	−131.688	−	746.842i	−0.214826	−	1.21834i	0.666382	−	0.745610i	$-0.267842\pi$
$614$	−389.730	−	68.7199i	−0.634739	−	0.111922i
$615$	344.616	−	22.7783i	0.560351	−	0.0370380i
$616$	202.941	−	351.504i	0.329450	−	0.570624i
$617$	−11.1751	−	1.97047i	−0.0181119	−	0.00319362i	0.164585	−	0.986363i	$-0.447372\pi$
$617$	−11.1751	−	1.97047i	−0.0181119	−	0.00319362i	−0.182697	+	0.983169i	$0.558483\pi$
$618$	−58.5104	−	132.776i	−0.0946771	−	0.214848i
$619$	−88.7096			−0.143311			−0.0716556	−	0.997429i	$-0.522828\pi$
$619$	−88.7096			−0.143311			−0.0716556	+	0.997429i	$0.522828\pi$
$620$	22.0482	+	12.7295i	0.0355616	+	0.0205315i
$621$	381.995	−	699.027i	0.615128	−	1.12565i
$622$	−31.6760	−	179.644i	−0.0509261	−	0.288816i
$623$	−166.713	+	198.681i	−0.267597	+	0.318910i
$624$	−333.656	+	319.759i	−0.534705	+	0.512435i
$625$	−381.466	−	138.842i	−0.610345	−	0.222148i
$626$	−209.168	+	120.763i	−0.334134	+	0.192913i
$627$	−217.293	−	390.849i	−0.346560	−	0.623363i
$628$	−73.0346	+	126.500i	−0.116297	+	0.201432i
$629$	−21.0119	−	25.0410i	−0.0334052	−	0.0398108i
$630$	−111.337	−	24.5540i	−0.176726	−	0.0389745i
$631$	−107.346	+	608.790i	−0.170121	+	0.964801i	0.773506	+	0.633789i	$0.218501\pi$
$631$	−107.346	+	608.790i	−0.170121	+	0.964801i	−0.943626	+	0.331012i	$0.892610\pi$
$632$	−119.622	+	328.658i	−0.189275	+	0.520028i
$633$	155.415	−	68.4868i	0.245522	−	0.108194i
$634$	307.214			0.484565
$635$	119.188	+	68.8130i	0.187697	+	0.108367i
$636$	104.911	−	143.246i	0.164954	−	0.225230i
$637$	−260.382	+	94.7714i	−0.408763	+	0.148778i
$638$	−360.201	+	207.962i	−0.564579	+	0.325960i
$639$	72.5370	+	546.312i	0.113516	+	0.854949i
$640$	−205.091	+	74.6472i	−0.320455	+	0.116636i
$641$	−202.594	+	556.623i	−0.316060	+	0.868367i	0.675341	+	0.737506i	$0.263996\pi$
$641$	−202.594	+	556.623i	−0.316060	+	0.868367i	−0.991401	+	0.130861i	$0.958226\pi$
$642$	227.612	−	100.302i	0.354536	−	0.156233i
$643$	−6.71261	−	38.0691i	−0.0104395	−	0.0592055i	0.979143	−	0.203172i	$-0.0651252\pi$
$643$	−6.71261	−	38.0691i	−0.0104395	−	0.0592055i	−0.989582	+	0.143967i	$0.954014\pi$
$644$	244.863	−	672.757i	0.380223	−	1.04465i
$645$	117.752	+	57.9881i	0.182561	+	0.0899040i
$646$	35.1595	+	49.6754i	0.0544265	+	0.0768969i
$647$			350.168i			0.541218i	0.962689	+	0.270609i	$0.0872251\pi$
$647$			350.168i			0.541218i	−0.962689	+	0.270609i	$0.912775\pi$
$648$	−488.665	+	229.183i	−0.754113	+	0.353678i
$649$	−533.932	−	194.335i	−0.822699	−	0.299438i
$650$	−324.226	+	386.397i	−0.498809	+	0.594457i
$651$	104.413	+	30.3710i	0.160388	+	0.0466528i
$652$	81.5608	+	68.4376i	0.125093	+	0.104966i
$653$		−	570.199i		−	0.873199i	−0.899656	−	0.436600i	$-0.856183\pi$
$653$		−	570.199i		−	0.873199i	0.899656	−	0.436600i	$-0.143817\pi$
$654$	307.999	+	151.677i	0.470947	+	0.231922i
$655$	10.2000	−	3.71251i	0.0155726	−	0.00566795i
$656$	265.944	−	316.940i	0.405403	−	0.483141i
$657$	116.839	−	282.957i	0.177837	−	0.430680i
$658$	181.572	−	314.493i	0.275946	−	0.477953i
$659$	805.047	+	141.952i	1.22162	+	0.215405i	0.747023	−	0.664799i	$-0.231483\pi$
$659$	805.047	+	141.952i	1.22162	+	0.215405i	0.474597	+	0.880203i	$0.342594\pi$
$660$	−30.5758	−	124.655i	−0.0463270	−	0.188871i
$661$	−340.571	+	123.958i	−0.515237	+	0.187531i	−0.586534	−	0.809924i	$-0.699508\pi$
$661$	−340.571	+	123.958i	−0.515237	+	0.187531i	0.0712979	+	0.997455i	$0.477286\pi$
$662$	−113.019	+	19.9282i	−0.170723	+	0.0301031i
$663$	174.665	+	182.256i	0.263447	+	0.274896i
$664$	−222.966	+	386.189i	−0.335792	+	0.581609i
$665$	−146.558	+	211.581i	−0.220388	+	0.318166i
$666$	10.5721	+	79.6239i	0.0158741	+	0.119555i
$667$	−1281.26	+	1075.11i	−1.92093	+	1.61185i
$668$	501.085	+	597.170i	0.750128	+	0.893968i
$669$	−493.444	+	217.446i	−0.737584	+	0.325031i
$670$	146.367	−	122.816i	0.218458	−	0.183308i
$671$	−408.106	+	486.362i	−0.608206	+	0.724832i
$672$	−629.523	+	421.137i	−0.936790	+	0.626691i
$673$	−598.415			−0.889175			−0.444588	−	0.895735i	$-0.646650\pi$
$673$	−598.415			−0.889175			−0.444588	+	0.895735i	$0.646650\pi$
$674$	100.055	−	119.241i	0.148449	−	0.176915i
$675$	506.286	−	308.370i	0.750053	−	0.456845i
$676$	−679.047	−	1176.14i	−1.00451	−	1.73986i
$677$	397.535	−	229.517i	0.587202	−	0.339021i	−0.176789	−	0.984249i	$-0.556571\pi$
$677$	397.535	−	229.517i	0.587202	−	0.339021i	0.763990	+	0.645228i	$0.223238\pi$
$678$	57.5524	−	528.201i	0.0848855	−	0.779057i
$679$	−958.897	+	804.610i	−1.41222	+	1.18499i
$680$	13.6201	+	37.4208i	0.0200295	+	0.0550307i
$681$	−643.532	+	157.848i	−0.944981	+	0.231788i
$682$	−5.94780	−	33.7317i	−0.00872112	−	0.0494599i
$683$			78.3008i			0.114642i	0.998356	+	0.0573212i	$0.0182559\pi$
$683$			78.3008i			0.114642i	−0.998356	+	0.0573212i	$0.981744\pi$
$684$	26.6072	+	533.794i	0.0388994	+	0.780401i
$685$	−248.261			−0.362425
$686$	269.713	−	47.5576i	0.393167	−	0.0693260i
$687$	252.135	+	73.3397i	0.367009	+	0.106754i
$688$	147.757	−	53.7790i	0.214763	−	0.0781672i
$689$	299.027	+	356.366i	0.434001	+	0.517222i
$690$	58.2366	+	132.155i	0.0844009	+	0.191529i
$691$	−152.507	−	264.149i	−0.220704	−	0.382271i	0.734318	−	0.678806i	$-0.237502\pi$
$691$	−152.507	−	264.149i	−0.220704	−	0.382271i	−0.955022	+	0.296535i	$0.904169\pi$
$692$	−285.800	+	165.007i	−0.413006	+	0.238449i
$693$	−253.670	−	485.985i	−0.366046	−	0.701277i
$694$	263.671	+	221.246i	0.379929	+	0.318798i
$695$		−	113.711i		−	0.163612i
$696$	1130.80	−	74.7434i	1.62471	−	0.107390i
$697$	−173.125	−	145.269i	−0.248386	−	0.208421i
$698$	21.2962	+	25.3798i	0.0305102	+	0.0363607i
$699$	−73.4690	+	100.315i	−0.105106	+	0.143512i
$700$	408.133	−	342.465i	0.583048	−	0.489235i
$701$	509.103	+	606.725i	0.726253	+	0.865514i	0.995222	−	0.0976345i	$-0.0311276\pi$
$701$	509.103	+	606.725i	0.726253	+	0.865514i	−0.268970	+	0.963149i	$0.586683\pi$
$702$	−122.020	−	608.172i	−0.173818	−	0.866342i
$703$	175.385	+	46.0430i	0.249480	+	0.0654950i
$704$	36.1942	+	20.8968i	0.0514123	+	0.0296829i
$705$	−62.3671	−	254.265i	−0.0884640	−	0.360660i
$706$	−91.2180	−	517.323i	−0.129204	−	0.732752i
$707$	55.2524	+	151.805i	0.0781504	+	0.214717i
$708$	469.863	+	490.283i	0.663648	+	0.692490i
$709$	87.6073	−	496.846i	0.123565	−	0.700770i	−0.858585	−	0.512671i	$-0.828656\pi$
$709$	87.6073	−	496.846i	0.123565	−	0.700770i	0.982150	−	0.188099i	$-0.0602327\pi$
$710$	−86.5268	−	49.9563i	−0.121869	−	0.0703609i
$711$	287.987	+	374.455i	0.405044	+	0.526659i
$712$	−170.518	−	143.082i	−0.239492	−	0.200958i
$713$	−47.1094	−	129.432i	−0.0660721	−	0.181532i
$714$	41.4834	+	62.0102i	0.0581001	+	0.0868491i
$715$	336.284			0.470327
$716$	13.4089	−	15.9801i	0.0187275	−	0.0223185i
$717$	−753.214	+	184.751i	−1.05051	+	0.257672i
$718$	−198.864	−	166.867i	−0.276969	−	0.232405i
$719$	−117.623	+	323.168i	−0.163593	+	0.449468i	−0.994220	−	0.107361i	$-0.965760\pi$
$719$	−117.623	+	323.168i	−0.163593	+	0.449468i	0.830627	+	0.556829i	$0.187982\pi$
$720$	−21.2059	+	96.1559i	−0.0294527	+	0.133550i
$721$	−401.545			−0.556928
$722$	−318.387	−	112.243i	−0.440979	−	0.155461i
$723$	6.42586	+	9.60550i	0.00888778	+	0.0132856i
$724$	967.641	+	352.193i	1.33652	+	0.486454i
$725$	−1225.78	+	216.138i	−1.69073	+	0.298121i
$726$	98.5461	−	134.556i	0.135738	−	0.185338i
$727$	−797.988	−	290.444i	−1.09764	−	0.399510i	−0.271197	−	0.962524i	$-0.587420\pi$
$727$	−797.988	−	290.444i	−1.09764	−	0.399510i	−0.826448	+	0.563014i	$0.809642\pi$
$728$	−434.692	−	1194.31i	−0.597104	−	1.64053i
$729$	−92.7594	+	723.074i	−0.127242	+	0.991872i
$730$	27.7498	+	48.0641i	0.0380135	+	0.0658413i
$731$	−29.3762	−	80.7104i	−0.0401863	−	0.110411i
$732$	694.368	−	305.987i	0.948590	−	0.418015i
$733$	45.8232	−	79.3681i	0.0625146	−	0.108278i	−0.833074	−	0.553161i	$-0.813421\pi$
$733$	45.8232	−	79.3681i	0.0625146	−	0.108278i	0.895589	+	0.444883i	$0.146755\pi$
$734$		−	59.0769i		−	0.0804862i
$735$	−34.8842	+	47.6312i	−0.0474615	+	0.0648044i
$736$	901.526	+	328.129i	1.22490	+	0.445827i
$737$	904.754	+	159.533i	1.22762	+	0.216462i
$738$	167.574	+	529.437i	0.227065	+	0.717395i
$739$	605.596	−	508.155i	0.819480	−	0.687625i	−0.133370	−	0.991066i	$-0.542580\pi$
$739$	605.596	−	508.155i	0.819480	−	0.687625i	0.952850	+	0.303441i	$0.0981355\pi$
$740$	45.0712	+	26.0219i	0.0609070	+	0.0351647i
$741$	−1374.91	−	265.464i	−1.85548	−	0.358251i
$742$	68.7440	+	119.068i	0.0926469	+	0.160469i
$743$	−155.083	+	426.087i	−0.208726	+	0.573469i	−0.999240	−	0.0389743i	$-0.987591\pi$
$743$	−155.083	+	426.087i	−0.208726	+	0.573469i	0.790515	+	0.612443i	$0.209813\pi$
$744$	−26.0660	+	89.6124i	−0.0350349	+	0.120447i
$745$	−45.8225	−	38.4496i	−0.0615067	−	0.0516102i
$746$	142.723	−	25.1659i	0.191318	−	0.0337345i
$747$	278.700	+	533.938i	0.373093	+	0.714777i
$748$	−41.9944	+	72.7364i	−0.0561422	+	0.0972411i
$749$		−	688.349i		−	0.919025i
$750$	−24.8965	+	228.493i	−0.0331953	+	0.304658i
$751$	184.140	−	1044.31i	0.245193	−	1.39056i	−0.574852	−	0.818257i	$-0.694940\pi$
$751$	184.140	−	1044.31i	0.245193	−	1.39056i	0.820045	−	0.572299i	$-0.193948\pi$
$752$	−271.610	−	156.814i	−0.361184	−	0.208530i
$753$	589.123	−	394.110i	0.782368	−	0.523387i
$754$	−226.159	+	1282.61i	−0.299946	+	1.70108i
$755$	230.173	−	40.5857i	0.304865	−	0.0537560i
$756$	15.3774	+	655.005i	0.0203405	+	0.866408i
$757$	−143.086	−	52.0791i	−0.189017	−	0.0687967i	0.245777	−	0.969326i	$-0.420957\pi$
$757$	−143.086	−	52.0791i	−0.189017	−	0.0687967i	−0.434795	+	0.900530i	$0.643179\pi$
$758$	47.0424	−	8.29485i	0.0620612	−	0.0109431i
$759$	−306.782	+	622.959i	−0.404192	+	0.820763i
$760$	−181.590	−	125.784i	−0.238934	−	0.165505i
$761$	−1125.16	+	649.614i	−1.47853	+	0.853632i	−0.999705	−	0.0242773i	$-0.992272\pi$
$761$	−1125.16	+	649.614i	−1.47853	+	0.853632i	−0.478828	+	0.877909i	$0.658938\pi$
$762$	−61.8066	+	212.485i	−0.0811110	+	0.278852i
$763$	727.834	−	610.725i	0.953911	−	0.800426i
$764$	−67.5637	−	11.9133i	−0.0884342	−	0.0155933i
$765$	52.5241	+	11.5835i	0.0686590	+	0.0151418i
$766$	208.614	−	75.9293i	0.272342	−	0.0991244i
$767$	−1540.85	+	889.610i	−2.00893	+	1.15986i
$768$	−230.674	−	344.816i	−0.300357	−	0.448980i
$769$	26.9765	−	152.991i	0.0350800	−	0.198949i	−0.962231	−	0.272234i	$-0.912237\pi$
$769$	26.9765	−	152.991i	0.0350800	−	0.198949i	0.997311	+	0.0732858i	$0.0233485\pi$
$770$	97.8766	+	17.2583i	0.127113	+	0.0224134i
$771$	−1043.98	+	698.396i	−1.35405	+	0.905831i
$772$	122.090	+	211.466i	0.158148	+	0.273920i
$773$	254.349	+	698.819i	0.329042	+	0.904035i	0.988355	+	0.152166i	$0.0486249\pi$
$773$	254.349	+	698.819i	0.329042	+	0.904035i	−0.659313	+	0.751868i	$0.729153\pi$
$774$	−45.4520	+	206.097i	−0.0587235	+	0.266275i
$775$	17.7993	−	100.945i	0.0229668	−	0.130251i
$776$	−690.559	−	822.977i	−0.889896	−	1.06054i
$777$	213.442	+	62.0848i	0.274700	+	0.0799032i
$778$	−69.6417	−	120.623i	−0.0895138	−	0.155042i
$779$	1249.41	+	102.932i	1.60386	+	0.132134i
$780$	−360.558	−	177.560i	−0.462254	−	0.227641i
$781$	−83.4220	−	473.110i	−0.106814	−	0.605774i
$782$	32.3218	−	88.8035i	0.0413323	−	0.113559i
$783$	734.002	−	1343.18i	0.937423	−	1.71543i
$784$	12.2816	+	69.6522i	0.0156652	+	0.0888420i
$785$	−80.3036	−	14.1597i	−0.102298	−	0.0180378i
$786$	9.70462	+	14.5066i	0.0123468	+	0.0184563i
$787$	−689.746	+	1194.68i	−0.876424	+	1.51801i	−0.0211870	+	0.999776i	$0.506745\pi$
$787$	−689.746	+	1194.68i	−0.876424	+	1.51801i	−0.855238	+	0.518236i	$0.826589\pi$
$788$	716.171	+	126.280i	0.908847	+	0.160254i
$789$	245.441	+	26.7430i	0.311078	+	0.0338949i
$790$	−85.6417			−0.108407
$791$	−1273.41	−	735.206i	−1.60988	−	0.929464i
$792$	417.098	−	217.713i	0.526639	−	0.274890i
$793$	345.228	+	1957.88i	0.435344	+	2.46896i
$794$	154.695	−	184.358i	0.194830	−	0.232189i
$795$	95.1748	+	27.6839i	0.119717	+	0.0348226i
$796$	−165.187	−	60.1230i	−0.207521	−	0.0755314i
$797$	1072.45	−	619.181i	1.34561	−	0.776890i	0.357988	−	0.933726i	$-0.383463\pi$
$797$	1072.45	−	619.181i	1.34561	−	0.776890i	0.987625	+	0.156836i	$0.0501294\pi$
$798$	−386.549	−	147.826i	−0.484397	−	0.185245i
$799$	−85.6581	+	148.364i	−0.107207	+	0.185687i
$800$	458.919	+	546.918i	0.573649	+	0.683648i
$801$	−286.635	+	90.7236i	−0.357846	+	0.113263i
$802$	27.0133	−	153.200i	0.0336824	−	0.191023i
$803$	−91.2710	+	250.765i	−0.113663	+	0.312285i
$804$	−885.829	−	648.765i	−1.10178	−	0.806922i
$805$	399.666			0.496479
$806$	−92.8853	−	53.6273i	−0.115242	−	0.0665351i
$807$	−177.433	−	402.644i	−0.219867	−	0.498939i
$808$	−130.287	+	47.4205i	−0.161246	+	0.0586887i
$809$	−993.772	+	573.755i	−1.22840	+	0.709215i	−0.966694	−	0.255934i	$-0.917617\pi$
$809$	−993.772	+	573.755i	−1.22840	+	0.709215i	−0.261702	+	0.965149i	$0.584284\pi$
$810$	−93.6598	−	93.2472i	−0.115629	−	0.115120i
$811$	730.396	−	265.843i	0.900612	−	0.327796i	0.150114	−	0.988669i	$-0.452036\pi$
$811$	730.396	−	265.843i	0.900612	−	0.327796i	0.750498	+	0.660873i	$0.229814\pi$
$812$	470.505	−	1292.70i	0.579439	−	1.59200i
$813$	−8.90479	−	6.52171i	−0.0109530	−	0.00802178i
$814$	−12.1586	−	68.9548i	−0.0149368	−	0.0847110i
$815$	−20.3284	+	55.8519i	−0.0249429	+	0.0685300i
$816$	53.5549	−	35.8270i	0.0656310	−	0.0439056i
$817$	391.658	+	271.295i	0.479386	+	0.332062i
$818$		−	575.237i		−	0.703224i
$819$	−1676.34	−	369.693i	−2.04681	−	0.451396i
$820$	338.114	+	123.063i	0.412334	+	0.150077i
$821$	−644.997	+	768.677i	−0.785623	+	0.936269i	−0.999173	−	0.0406629i	$-0.987053\pi$
$821$	−644.997	+	768.677i	−0.785623	+	0.936269i	0.213550	+	0.976932i	$0.431497\pi$
$822$	−95.0946	−	387.693i	−0.115687	−	0.471646i
$823$	361.352	+	303.210i	0.439067	+	0.368421i	0.835360	−	0.549703i	$-0.185259\pi$
$823$	361.352	+	303.210i	0.439067	+	0.368421i	−0.396293	+	0.918124i	$0.629704\pi$
$824$		−	344.627i		−	0.418237i
$825$	−429.509	+	287.332i	−0.520617	+	0.348281i
$826$	−494.126	+	179.847i	−0.598215	+	0.217732i
$827$	−479.099	+	570.967i	−0.579321	+	0.690408i	−0.973516	−	0.228619i	$-0.926579\pi$
$827$	−479.099	+	570.967i	−0.579321	+	0.690408i	0.394195	+	0.919027i	$0.371024\pi$
$828$	657.854	−	505.944i	0.794509	−	0.611043i
$829$	207.825	−	359.963i	0.250694	−	0.434214i	−0.713023	−	0.701140i	$-0.752675\pi$
$829$	207.825	−	359.963i	0.250694	−	0.434214i	0.963717	+	0.266926i	$0.0860080\pi$
$830$	−107.534	−	18.9612i	−0.129560	−	0.0228448i
$831$	62.8625	−	60.2443i	0.0756468	−	0.0724961i
$832$	122.977	−	44.7600i	0.147809	−	0.0537981i
$833$	38.0467	−	6.70866i	0.0456743	−	0.00805362i
$834$	177.574	−	43.5560i	0.212918	−	0.0522254i
$835$	−217.590	+	376.877i	−0.260587	+	0.451350i
$836$	−42.9565	−	463.910i	−0.0513834	−	0.554916i
$837$	83.2683	+	94.6327i	0.0994842	+	0.113062i
$838$	286.201	−	240.151i	0.341528	−	0.286576i
$839$	−958.980	−	1142.87i	−1.14300	−	1.36218i	−0.922132	−	0.386876i	$-0.873554\pi$
$839$	−958.980	−	1142.87i	−1.14300	−	1.36218i	−0.220872	−	0.975303i	$-0.570890\pi$
$840$	−218.472	−	160.005i	−0.260086	−	0.190482i
$841$	−1817.70	+	1525.23i	−2.16136	+	1.81359i
$842$	91.3737	−	108.895i	0.108520	−	0.129329i
$843$	−13.1122	−	198.376i	−0.0155543	−	0.235322i
$844$	176.940			0.209644
$845$	487.329	−	580.776i	0.576720	−	0.687309i
$846$	373.179	−	194.789i	0.441111	−	0.230247i
$847$	−230.780	−	399.723i	−0.272468	−	0.471929i
$848$	102.833	−	59.3704i	0.121265	−	0.0700123i
$849$	313.195	−	138.016i	0.368899	−	0.162562i
$850$	53.8734	−	45.2051i	0.0633804	−	0.0531825i
$851$	−96.3017	−	264.587i	−0.113163	−	0.310913i
$852$	−160.362	+	551.309i	−0.188218	+	0.647076i
$853$	190.686	+	1081.43i	0.223548	+	1.26780i	0.865442	+	0.501008i	$0.167037\pi$
$853$	190.686	+	1081.43i	0.223548	+	1.26780i	−0.641895	+	0.766793i	$0.721851\pi$
$854$			587.567i			0.688017i
$855$	−274.937	+	115.875i	−0.321564	+	0.135527i
$856$	590.778			0.690161
$857$	95.1617	−	16.7796i	0.111040	−	0.0195794i	−0.117852	−	0.993031i	$-0.537601\pi$
$857$	95.1617	−	16.7796i	0.111040	−	0.0195794i	0.228892	+	0.973452i	$0.426490\pi$
$858$	128.811	+	525.151i	0.150129	+	0.612064i
$859$	−578.471	+	210.546i	−0.673423	+	0.245106i	−0.656021	−	0.754742i	$-0.727762\pi$
$859$	−578.471	+	210.546i	−0.673423	+	0.245106i	−0.0174022	+	0.999849i	$0.505540\pi$
$860$	87.8986	+	104.754i	0.102208	+	0.121806i
$861$	1527.78	+	166.466i	1.77443	+	0.193340i
$862$	−227.348	−	393.778i	−0.263745	−	0.456819i
$863$	1022.31	−	590.229i	1.18460	−	0.683927i	0.227523	−	0.973773i	$-0.426937\pi$
$863$	1022.31	−	590.229i	1.18460	−	0.683927i	0.957074	+	0.289845i	$0.0936039\pi$
$864$	−877.737	+	20.6065i	−1.01590	+	0.0238501i
$865$	−141.127	−	118.420i	−0.163153	−	0.136902i
$866$			33.8168i			0.0390494i
$867$	462.507	+	691.364i	0.533457	+	0.797421i
$868$	86.7837	+	72.8202i	0.0999812	+	0.0838942i
$869$	−264.693	−	315.449i	−0.304596	−	0.363003i
$870$	111.902	+	253.935i	0.128623	+	0.291880i
$871$	2203.75	−	1849.17i	2.53014	−	2.12304i
$872$	524.157	+	624.666i	0.601097	+	0.716360i
$873$	−1438.41	+	190.986i	−1.64766	+	0.218769i
$874$	138.241	+	505.660i	0.158171	+	0.578559i
$875$	550.864	+	318.042i	0.629559	+	0.363476i
$876$	230.265	−	220.675i	0.262860	−	0.251912i
$877$	95.3650	+	540.842i	0.108740	+	0.616695i	0.989660	+	0.143431i	$0.0458134\pi$
$877$	95.3650	+	540.842i	0.108740	+	0.616695i	−0.880920	+	0.473264i	$0.843075\pi$
$878$	147.123	+	404.216i	0.167566	+	0.460383i
$879$	935.888	−	229.558i	1.06472	−	0.261158i
$880$	14.9050	−	84.5307i	0.0169376	−	0.0960576i
$881$	−1276.06	−	736.735i	−1.44842	−	0.836248i	−0.450037	−	0.893010i	$-0.648589\pi$
$881$	−1276.06	−	736.735i	−1.44842	−	0.836248i	−0.998388	+	0.0567616i	$0.981923\pi$
$882$	−87.7445	−	36.2315i	−0.0994836	−	0.0410788i
$883$	25.8342	+	21.6775i	0.0292573	+	0.0245498i	0.657299	−	0.753630i	$-0.271699\pi$
$883$	25.8342	+	21.6775i	0.0292573	+	0.0245498i	−0.628042	+	0.778180i	$0.716143\pi$
$884$	89.9503	+	247.136i	0.101754	+	0.279566i
$885$	−167.481	+	340.090i	−0.189244	+	0.384283i
$886$	394.345			0.445085
$887$	1028.37	−	1225.56i	1.15938	−	1.38169i	0.248698	−	0.968581i	$-0.419997\pi$
$887$	1028.37	−	1225.56i	1.15938	−	1.38169i	0.910680	−	0.413112i	$-0.135558\pi$
$888$	−53.2845	+	183.187i	−0.0600050	+	0.206292i
$889$	469.134	+	393.650i	0.527709	+	0.442801i
$890$	18.6422	−	51.2189i	0.0209463	−	0.0575494i
$891$	53.9879	−	633.183i	0.0605925	−	0.710643i
$892$	−561.784			−0.629803
$893$	−87.6206	−	946.261i	−0.0981194	−	1.05964i
$894$	42.4922	−	86.2857i	0.0475304	−	0.0965164i
$895$	10.9430	+	3.98292i	0.0122268	+	0.00445018i
$896$	−956.435	+	168.645i	−1.06745	+	0.188220i
$897$	876.832	+	1989.77i	0.977516	+	2.21825i
$898$	365.505	+	133.033i	0.407022	+	0.148144i
$899$	−90.5207	−	248.703i	−0.100690	−	0.276645i
$900$	612.227	−	81.2888i	0.680252	−	0.0903209i
$901$	−32.4304	−	56.1712i	−0.0359938	−	0.0623431i
$902$	−165.567	−	454.891i	−0.183555	−	0.504313i
$903$	471.207	+	345.104i	0.521824	+	0.382175i
$904$	630.993	−	1092.91i	0.698001	−	1.20897i
$905$			574.849i			0.635192i
$906$	151.546	+	343.900i	0.167269	+	0.379580i
$907$	1359.77	+	494.917i	1.49920	+	0.545663i	0.955853	−	0.293846i	$-0.0949354\pi$
$907$	1359.77	+	494.917i	1.49920	+	0.545663i	0.543345	+	0.839510i	$0.317158\pi$
$908$	−679.835	−	119.873i	−0.748717	−	0.132019i
$909$	−40.3298	+	182.871i	−0.0443672	+	0.201178i
$910$	238.403	−	200.044i	0.261981	−	0.219828i
$911$	−1417.27	−	818.259i	−1.55573	−	0.898198i	−0.997658	−	0.0684027i	$-0.978210\pi$
$911$	−1417.27	−	818.259i	−1.55573	−	0.898198i	−0.558067	−	0.829796i	$-0.688457\pi$
$912$	−127.669	+	333.841i	−0.139988	+	0.366054i
$913$	−262.517	−	454.692i	−0.287532	−	0.498020i
$914$	246.834	−	678.170i	0.270059	−	0.741980i
$915$	293.091	+	305.828i	0.320318	+	0.334239i
$916$	209.565	+	175.846i	0.228783	+	0.191972i
$917$	47.5674	−	8.38742i	0.0518729	−	0.00914659i
$918$	2.02981	+	86.4602i	0.00221113	+	0.0941833i
$919$	647.655	−	1121.77i	0.704738	−	1.22064i	−0.262047	−	0.965055i	$-0.584398\pi$
$919$	647.655	−	1121.77i	0.704738	−	1.22064i	0.966786	−	0.255588i	$-0.0822690\pi$
$920$			343.015i			0.372842i
$921$	−1161.75	+	511.946i	−1.26140	+	0.555859i
$922$	10.6889	−	60.6199i	0.0115932	−	0.0657483i
$923$	−1302.78	−	752.160i	−1.41146	−	0.814908i
$924$	−37.6686	−	569.892i	−0.0407669	−	0.616766i
$925$	36.3855	−	206.353i	0.0393357	−	0.223084i
$926$	476.329	−	83.9897i	0.514395	−	0.0907016i
$927$	−392.850	−	249.664i	−0.423787	−	0.269325i
$928$	1732.28	+	630.499i	1.86668	+	0.679417i
$929$	489.015	−	86.2265i	0.526388	−	0.0928164i	0.0958622	−	0.995395i	$-0.469439\pi$
$929$	489.015	−	86.2265i	0.526388	−	0.0928164i	0.430526	+	0.902578i	$0.358328\pi$
$930$	−22.8026	+	1.50721i	−0.0245190	+	0.00162065i
$931$	−150.767	+	152.302i	−0.161941	+	0.163590i
$932$	−112.187	+	64.7711i	−0.120372	+	0.0694969i
$933$	−404.900	−	422.497i	−0.433976	−	0.452837i
$934$	205.297	−	172.265i	0.219804	−	0.184438i
$935$	−46.1740	−	8.14172i	−0.0493839	−	0.00870772i
$936$	317.291	−	1438.72i	0.338986	−	1.53709i
$937$	1590.88	−	579.034i	1.69785	−	0.617965i	0.702269	−	0.711912i	$-0.252170\pi$
$937$	1590.88	−	579.034i	1.69785	−	0.617965i	0.995577	+	0.0939464i	$0.0299482\pi$
$938$	736.312	−	425.110i	0.784980	−	0.453209i
$939$	−342.311	+	695.104i	−0.364548	+	0.740260i
$940$	47.3630	−	268.609i	0.0503862	−	0.285754i
$941$	1205.77	+	212.610i	1.28137	+	0.225940i	0.772562	−	0.634939i	$-0.218975\pi$
$941$	1205.77	+	212.610i	1.28137	+	0.225940i	0.508809	+	0.860879i	$0.330086\pi$
$942$	−8.64747	−	130.828i	−0.00917990	−	0.138884i
$943$	−973.331	−	1685.86i	−1.03216	−	1.78776i
$944$	155.324	+	426.749i	0.164538	+	0.452065i
$945$	−340.666	+	133.127i	−0.360493	+	0.140876i
$946$	31.9469	−	181.180i	0.0337706	−	0.191522i
$947$	−349.573	−	416.605i	−0.369137	−	0.439921i	0.549217	−	0.835680i	$-0.314926\pi$
$947$	−349.573	−	416.605i	−0.369137	−	0.439921i	−0.918354	+	0.395759i	$0.870482\pi$
$948$	117.241	+	477.980i	0.123672	+	0.504198i
$949$	417.812	+	723.672i	0.440266	+	0.762562i
$950$	−99.0572	+	377.324i	−0.104271	+	0.397183i
$951$	819.149	−	547.992i	0.861356	−	0.576227i
$952$	30.7709	+	174.511i	0.0323224	+	0.183309i
$953$	−278.801	+	766.000i	−0.292551	+	0.803778i	0.703140	+	0.711051i	$0.251780\pi$
$953$	−278.801	+	766.000i	−0.292551	+	0.803778i	−0.995692	+	0.0927266i	$0.970442\pi$
$954$	−6.77611	+	159.232i	−0.00710284	+	0.166910i
$955$	−6.65054	−	37.7171i	−0.00696392	−	0.0394944i
$956$	−795.705	−	140.304i	−0.832327	−	0.146762i
$957$	−589.481	+	1197.01i	−0.615968	+	1.25080i
$958$	−332.938	+	576.665i	−0.347534	+	0.601947i
$959$	−1087.94	−	191.832i	−1.13445	−	0.200034i
$960$	16.4756	−	22.4960i	0.0171621	−	0.0234333i
$961$	−939.204			−0.977320
$962$	−189.877	−	109.626i	−0.197378	−	0.113956i
$963$	427.987	−	673.445i	0.444431	−	0.699320i
$964$	2.09074	+	11.8572i	0.00216881	+	0.0123000i
$965$	−87.6198	+	104.421i	−0.0907977	+	0.108209i
$966$	153.089	+	624.131i	0.158477	+	0.646098i
$967$	1592.45	+	579.604i	1.64679	+	0.599383i	0.988207	−	0.153124i	$-0.0489332\pi$
$967$	1592.45	+	579.604i	1.64679	+	0.599383i	0.658585	+	0.752507i	$0.271155\pi$
$968$	343.064	−	198.068i	0.354405	−	0.204616i
$969$	182.357	+	69.7377i	0.188191	+	0.0719688i
$970$	131.532	−	227.820i	0.135600	−	0.234866i
$971$	1069.59	+	1274.69i	1.10154	+	1.31276i	0.945723	+	0.324974i	$0.105356\pi$
$971$	1069.59	+	1274.69i	1.10154	+	1.31276i	0.155814	+	0.987786i	$0.450200\pi$
$972$	−392.210	+	650.383i	−0.403509	+	0.669118i
$973$	87.8645	−	498.304i	0.0903026	−	0.512132i
$974$	−216.111	+	593.761i	−0.221880	+	0.609611i
$975$	−175.274	+	1608.62i	−0.179768	+	1.64987i
$976$	507.450			0.519928
$977$	252.156	+	145.582i	0.258092	+	0.149009i	0.623464	−	0.781852i	$-0.285725\pi$
$977$	252.156	+	145.582i	0.258092	+	0.149009i	−0.365372	+	0.930862i	$0.619058\pi$
$978$	−95.0067	−	10.3519i	−0.0971439	−	0.0105847i
$979$	246.276	−	89.6370i	0.251558	−	0.0915597i
$980$	−53.2681	+	30.7544i	−0.0543552	+	0.0313820i
$981$	1091.80	−	144.964i	1.11294	−	0.147772i
$982$	194.210	−	70.6867i	0.197770	−	0.0719824i
$983$	44.9405	−	123.473i	0.0457177	−	0.125608i	−0.914733	−	0.404060i	$-0.867599\pi$
$983$	44.9405	−	123.473i	0.0457177	−	0.125608i	0.960450	+	0.278451i	$0.0898211\pi$
$984$	−142.870	+	1311.22i	−0.145193	+	1.33254i
$985$	70.4953	+	399.799i	0.0715689	+	0.405887i
$986$	62.1063	−	170.636i	0.0629882	−	0.173059i
$987$	−76.8346	−	1162.44i	−0.0778466	−	1.17775i
$988$	−1199.26	−	830.709i	−1.21383	−	0.840798i
$989$		−	739.824i		−	0.748053i
$990$	85.0268	+	77.7402i	0.0858857	+	0.0785255i
$991$	466.034	+	169.623i	0.470267	+	0.171163i	0.566273	−	0.824218i	$-0.308385\pi$
$991$	466.034	+	169.623i	0.470267	+	0.171163i	−0.0960064	+	0.995381i	$0.530607\pi$
$992$	−97.5825	+	116.294i	−0.0983694	+	0.117232i
$993$	−265.804	+	254.733i	−0.267678	+	0.256529i
$994$	−340.578	−	285.779i	−0.342634	−	0.287504i
$995$		−	98.1327i		−	0.0986259i
$996$	41.3855	+	626.125i	0.0415517	+	0.628639i
$997$	−1535.37	+	558.829i	−1.53999	+	0.560510i	−0.966043	−	0.258383i	$-0.916810\pi$
$997$	−1535.37	+	558.829i	−1.53999	+	0.560510i	−0.573946	+	0.818893i	$0.694588\pi$
$998$	−204.589	+	243.820i	−0.204999	+	0.244309i
$999$	170.218	+	193.450i	0.170389	+	0.193643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.z.a.101.16	✓	228
9.5	odd	6		171.3.bf.a.158.16	yes	228
19.16	even	9		171.3.bf.a.92.16	yes	228
171.149	odd	18	inner	171.3.z.a.149.16	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.3.z.a.101.16	✓	228	1.1	even	1	trivial
171.3.z.a.149.16	yes	228	171.149	odd	18	inner
171.3.bf.a.92.16	yes	228	19.16	even	9
171.3.bf.a.158.16	yes	228	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.920951 + 0.162389i) q^{2} +(-2.16595 + 2.07574i) q^{3} +(-2.93699 + 1.06898i) q^{4} +(-1.12152 - 1.33658i) q^{5} +(1.65766 - 2.26338i) q^{6} +(-3.88198 - 6.72379i) q^{7} +(5.77072 - 3.33173i) q^{8} +(0.382648 - 8.99186i) q^{9} +(1.24992 + 1.04880i) q^{10} +7.84544i q^{11} +(4.14245 - 8.41176i) q^{12} +(18.8192 + 15.7912i) q^{13} +(4.66699 + 5.56190i) q^{14} +(5.20355 + 0.566975i) q^{15} +(4.80351 - 4.03062i) q^{16} +(-2.20168 - 2.62386i) q^{17} +(1.10778 + 8.34320i) q^{18} +(18.3773 + 4.82451i) q^{19} +(4.72268 + 2.72664i) q^{20} +(22.3650 + 6.50541i) q^{21} +(-1.27401 - 7.22527i) q^{22} +(-10.0908 - 27.7241i) q^{23} +(-5.58329 + 19.1948i) q^{24} +(3.81257 - 21.6222i) q^{25} +(-19.8959 - 11.4869i) q^{26} +(17.8359 + 20.2702i) q^{27} +(18.5889 + 15.5980i) q^{28} +(-19.3894 - 53.2719i) q^{29} +(-4.88429 + 0.322841i) q^{30} +4.66857 q^{31} +(-20.9020 + 24.9100i) q^{32} +(-16.2851 - 16.9928i) q^{33} +(2.45373 + 2.05892i) q^{34} +(-4.63316 + 12.7295i) q^{35} +(8.48826 + 26.8180i) q^{36} +9.54356 q^{37} +(-17.7080 - 1.45888i) q^{38} +(-73.5397 + 4.86081i) q^{39} +(-10.9251 - 3.97642i) q^{40} +(64.9786 - 11.4575i) q^{41} +(-21.6535 - 2.35935i) q^{42} +(23.5636 + 8.57647i) q^{43} +(-8.38659 - 23.0420i) q^{44} +(-12.4475 + 9.57316i) q^{45} +(13.7952 + 23.8939i) q^{46} +(-17.1066 - 46.9999i) q^{47} +(-2.03764 + 18.7009i) q^{48} +(-5.63960 + 9.76808i) q^{49} +20.5321i q^{50} +(10.2152 + 1.11304i) q^{51} +(-72.1522 - 26.2612i) q^{52} +(18.6486 + 3.28826i) q^{53} +(-19.7177 - 15.7715i) q^{54} +(10.4861 - 8.79886i) q^{55} +(-44.8037 - 25.8674i) q^{56} +(-49.8186 + 27.6967i) q^{57} +(26.5074 + 45.9122i) q^{58} +(-24.7705 + 68.0563i) q^{59} +(-15.8889 + 3.89728i) q^{60} +(61.9930 + 52.0183i) q^{61} +(-4.29953 + 0.758122i) q^{62} +(-61.9449 + 32.3334i) q^{63} +(2.66355 - 4.61341i) q^{64} -42.8636i q^{65} +(17.7572 + 13.0050i) q^{66} +(20.3344 - 115.322i) q^{67} +(9.27116 + 5.35271i) q^{68} +(79.4039 + 39.1032i) q^{69} +(2.19979 - 12.4756i) q^{70} +(-60.3038 + 10.6332i) q^{71} +(-27.7503 - 53.1644i) q^{72} +(31.9632 + 11.6336i) q^{73} +(-8.78916 + 1.54977i) q^{74} +(36.6241 + 54.7464i) q^{75} +(-59.1311 + 5.47535i) q^{76} +(52.7511 - 30.4559i) q^{77} +(66.9371 - 16.4186i) q^{78} +(-40.2080 + 33.7385i) q^{79} +(-10.7745 - 1.89984i) q^{80} +(-80.7072 - 6.88144i) q^{81} +(-57.9816 + 21.1036i) q^{82} +(-57.9562 + 33.4610i) q^{83} +(-72.6399 + 4.80134i) q^{84} +(-1.03776 + 5.88545i) q^{85} +(-23.0937 - 4.07204i) q^{86} +(152.575 + 75.1368i) q^{87} +(26.1388 + 45.2738i) q^{88} +(-11.4254 - 31.3909i) q^{89} +(9.90897 - 10.8377i) q^{90} +(33.1208 - 187.837i) q^{91} +(59.2729 + 70.6386i) q^{92} +(-10.1119 + 9.69072i) q^{93} +(23.3866 + 40.5067i) q^{94} +(-14.1622 - 29.9735i) q^{95} +(-6.43402 - 97.3408i) q^{96} +(-27.9966 - 158.776i) q^{97} +(3.60758 - 9.91173i) q^{98} +(70.5451 + 3.00204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21}+ \cdots - 300 q^{99}+O(q^{100}) \) 228 * q - 9 * q^2 + 6 * q^3 - 3 * q^4 - 9 * q^5 - 30 * q^6 + 3 * q^7 + 30 * q^9 - 12 * q^10 - 3 * q^12 + 12 * q^13 - 9 * q^14 - 48 * q^15 + 9 * q^16 - 81 * q^17 - 60 * q^18 - 33 * q^19 - 18 * q^20 + 21 * q^21 + 81 * q^22 + 207 * q^23 - 222 * q^24 - 3 * q^25 - 216 * q^26 - 33 * q^27 - 36 * q^28 - 9 * q^29 + 171 * q^30 - 6 * q^31 - 9 * q^32 + 30 * q^33 + 33 * q^34 + 225 * q^35 - 246 * q^36 - 24 * q^37 - 9 * q^38 - 60 * q^39 - 177 * q^40 - 9 * q^41 - 15 * q^42 + 93 * q^43 + 441 * q^44 - 57 * q^45 - 6 * q^46 - 9 * q^47 - 774 * q^48 - 543 * q^49 - 81 * q^51 + 213 * q^52 + 393 * q^54 + 63 * q^55 - 459 * q^56 + 84 * q^57 - 6 * q^58 + 126 * q^59 - 333 * q^60 - 24 * q^61 - 36 * q^62 + 369 * q^63 + 372 * q^64 + 894 * q^66 + 39 * q^67 + 747 * q^68 + 231 * q^69 + 291 * q^70 + 204 * q^72 - 51 * q^73 + 333 * q^74 + 324 * q^75 - 3 * q^76 - 18 * q^77 - 1569 * q^78 - 105 * q^79 - 756 * q^80 + 1050 * q^81 + 132 * q^82 + 99 * q^83 - 69 * q^84 - 3 * q^85 - 495 * q^86 - 483 * q^87 + 387 * q^88 - 648 * q^89 - 339 * q^90 + 225 * q^91 + 27 * q^92 + 396 * q^93 - 6 * q^94 - 1305 * q^95 - 663 * q^96 - 543 * q^97 + 1125 * q^98 - 300 * q^99

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