LMFDB - Embedded newform 171.2.h.c.49.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(7,171)] 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("171.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [32,-2,1,34,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	171.49
Dual form			171.2.h.c.7.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.39943 q^{2} +(-1.30020 + 1.14433i) q^{3} +3.75726 q^{4} +(-0.359839 - 0.623259i) q^{5} +(3.11973 - 2.74573i) q^{6} +(1.65862 + 2.87282i) q^{7} -4.21641 q^{8} +(0.381029 - 2.97570i) q^{9} +(0.863408 + 1.49547i) q^{10} +(0.550465 + 0.953433i) q^{11} +(-4.88518 + 4.29953i) q^{12} -4.74945 q^{13} +(-3.97975 - 6.89312i) q^{14} +(1.18107 + 0.398587i) q^{15} +2.60247 q^{16} +(-3.13488 + 5.42977i) q^{17} +(-0.914252 + 7.13999i) q^{18} +(-4.19132 + 1.19702i) q^{19} +(-1.35201 - 2.34175i) q^{20} +(-5.44398 - 1.83723i) q^{21} +(-1.32080 - 2.28769i) q^{22} -2.22814 q^{23} +(5.48217 - 4.82496i) q^{24} +(2.24103 - 3.88158i) q^{25} +11.3960 q^{26} +(2.90977 + 4.30503i) q^{27} +(6.23187 + 10.7939i) q^{28} +(-2.97098 + 5.14588i) q^{29} +(-2.83390 - 0.956381i) q^{30} +(-0.763210 + 1.32192i) q^{31} +2.18839 q^{32} +(-1.80675 - 0.609739i) q^{33} +(7.52192 - 13.0283i) q^{34} +(1.19367 - 2.06750i) q^{35} +(1.43162 - 11.1805i) q^{36} -3.69507 q^{37} +(10.0568 - 2.87216i) q^{38} +(6.17522 - 5.43492i) q^{39} +(1.51723 + 2.62792i) q^{40} +(-2.84053 - 4.91994i) q^{41} +(13.0624 + 4.40829i) q^{42} +4.61491 q^{43} +(2.06824 + 3.58229i) q^{44} +(-1.99175 + 0.833295i) q^{45} +5.34627 q^{46} +(-0.141619 + 0.245291i) q^{47} +(-3.38372 + 2.97807i) q^{48} +(-2.00206 + 3.46767i) q^{49} +(-5.37720 + 9.31358i) q^{50} +(-2.13747 - 10.6471i) q^{51} -17.8449 q^{52} +(1.90426 + 3.29828i) q^{53} +(-6.98178 - 10.3296i) q^{54} +(0.396157 - 0.686164i) q^{55} +(-6.99344 - 12.1130i) q^{56} +(4.07976 - 6.35260i) q^{57} +(7.12864 - 12.3472i) q^{58} +(6.68593 + 11.5804i) q^{59} +(4.43760 + 1.49759i) q^{60} +(-5.94603 + 10.2988i) q^{61} +(1.83127 - 3.17185i) q^{62} +(9.18064 - 3.84094i) q^{63} -10.4558 q^{64} +(1.70904 + 2.96014i) q^{65} +(4.33517 + 1.46303i) q^{66} -7.44592 q^{67} +(-11.7785 + 20.4010i) q^{68} +(2.89702 - 2.54972i) q^{69} +(-2.86414 + 4.96083i) q^{70} +(5.51472 - 9.55177i) q^{71} +(-1.60658 + 12.5468i) q^{72} +(-5.22640 + 9.05239i) q^{73} +8.86605 q^{74} +(1.52802 + 7.61130i) q^{75} +(-15.7479 + 4.49751i) q^{76} +(-1.82603 + 3.16277i) q^{77} +(-14.8170 + 13.0407i) q^{78} +12.2331 q^{79} +(-0.936469 - 1.62201i) q^{80} +(-8.70963 - 2.26766i) q^{81} +(6.81565 + 11.8050i) q^{82} +(-5.05059 - 8.74788i) q^{83} +(-20.4544 - 6.90293i) q^{84} +4.51221 q^{85} -11.0731 q^{86} +(-2.02572 - 10.0904i) q^{87} +(-2.32099 - 4.02007i) q^{88} +(4.23637 + 7.33760i) q^{89} +(4.77905 - 1.99943i) q^{90} +(-7.87754 - 13.6443i) q^{91} -8.37170 q^{92} +(-0.520384 - 2.59212i) q^{93} +(0.339804 - 0.588558i) q^{94} +(2.25425 + 2.18154i) q^{95} +(-2.84534 + 2.50424i) q^{96} +12.3306 q^{97} +(4.80380 - 8.32042i) q^{98} +(3.04688 - 1.27473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + q^{3} + 34 q^{4} + 3 q^{5} - 7 q^{6} + q^{7} - 36 q^{8} + 17 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} + 8 q^{13} + q^{14} - 14 q^{15} + 22 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20}+ \cdots - 49 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + q^3 + 34 * q^4 + 3 * q^5 - 7 * q^6 + q^7 - 36 * q^8 + 17 * q^9 - 8 * q^10 + 7 * q^11 - 3 * q^12 + 8 * q^13 + q^14 - 14 * q^15 + 22 * q^16 - 7 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 8 * q^21 - 8 * q^22 - 10 * q^23 - 39 * q^24 - 9 * q^25 - 4 * q^26 - 5 * q^27 - 10 * q^28 + 10 * q^29 - 5 * q^30 - 10 * q^31 - 34 * q^32 + q^33 - 13 * q^34 - 3 * q^35 - 19 * q^36 + 2 * q^37 - 46 * q^38 + 12 * q^40 + 6 * q^41 + 16 * q^42 - 14 * q^43 + 20 * q^44 - 35 * q^45 - 9 * q^47 - 15 * q^48 - 13 * q^49 + q^50 - 10 * q^51 - 38 * q^52 + 16 * q^53 - 40 * q^54 + 15 * q^55 - 6 * q^56 + 69 * q^57 + 37 * q^59 - 19 * q^60 - 12 * q^61 + 54 * q^62 + 21 * q^63 - 64 * q^64 + 54 * q^65 + 37 * q^66 + 22 * q^67 - 2 * q^68 + 3 * q^69 + 24 * q^70 + 9 * q^71 + 15 * q^72 - 10 * q^73 - 12 * q^74 - 76 * q^75 - 40 * q^76 + 46 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 + 17 * q^81 + 7 * q^82 + 3 * q^83 + 12 * q^84 + 54 * q^85 - 34 * q^86 - 9 * q^87 + 9 * q^88 + 30 * q^89 + 133 * q^90 - q^91 + 34 * q^92 + 27 * q^93 - 18 * q^94 + 3 * q^95 - 5 * q^96 + 18 * q^98 - 49 * q^99

Character values

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

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.39943			−1.69665			−0.848326	−	0.529474i	$-0.822389\pi$
$2$	−2.39943			−1.69665			−0.848326	+	0.529474i	$0.822389\pi$
$3$	−1.30020	+	1.14433i	−0.750670	+	0.660678i
$3$	−1.30020	+	1.14433i	−0.750670	+	0.660678i
$4$	3.75726			1.87863
$5$	−0.359839	−	0.623259i	−0.160925	−	0.278730i	0.774276	−	0.632848i	$-0.218114\pi$
$5$	−0.359839	−	0.623259i	−0.160925	−	0.278730i	−0.935201	+	0.354118i	$0.884781\pi$
$6$	3.11973	−	2.74573i	1.27363	−	1.12094i
$7$	1.65862	+	2.87282i	0.626900	+	1.08582i	0.988170	+	0.153362i	$0.0490101\pi$
$7$	1.65862	+	2.87282i	0.626900	+	1.08582i	−0.361270	+	0.932461i	$0.617657\pi$
$8$	−4.21641			−1.49073
$9$	0.381029	−	2.97570i	0.127010	−	0.991901i
$10$	0.863408	+	1.49547i	0.273034	+	0.472908i
$11$	0.550465	+	0.953433i	0.165971	+	0.287471i	0.937000	−	0.349330i	$-0.113591\pi$
$11$	0.550465	+	0.953433i	0.165971	+	0.287471i	−0.771028	+	0.636801i	$0.780257\pi$
$12$	−4.88518	+	4.29953i	−1.41023	+	1.24117i
$13$	−4.74945			−1.31726			−0.658630	−	0.752467i	$-0.728864\pi$
$13$	−4.74945			−1.31726			−0.658630	+	0.752467i	$0.728864\pi$
$14$	−3.97975	−	6.89312i	−1.06363	−	1.84226i
$15$	1.18107	+	0.398587i	0.304952	+	0.102915i
$16$	2.60247			0.650617
$17$	−3.13488	+	5.42977i	−0.760320	+	1.31691i	0.182366	+	0.983231i	$0.441624\pi$
$17$	−3.13488	+	5.42977i	−0.760320	+	1.31691i	−0.942686	+	0.333682i	$0.891709\pi$
$18$	−0.914252	+	7.13999i	−0.215491	+	1.68291i
$19$	−4.19132	+	1.19702i	−0.961554	+	0.274615i
$19$	−4.19132	+	1.19702i	−0.961554	+	0.274615i
$20$	−1.35201	−	2.34175i	−0.302318	−	0.523630i
$21$	−5.44398	−	1.83723i	−1.18797	−	0.400915i
$22$	−1.32080	−	2.28769i	−0.281596	−	0.487738i
$23$	−2.22814			−0.464600			−0.232300	−	0.972644i	$-0.574625\pi$
$23$	−2.22814			−0.464600			−0.232300	+	0.972644i	$0.574625\pi$
$24$	5.48217	−	4.82496i	1.11904	−	0.984890i
$25$	2.24103	−	3.88158i	0.448206	−	0.776316i
$26$	11.3960			2.23493
$27$	2.90977	+	4.30503i	0.559985	+	0.828503i
$28$	6.23187	+	10.7939i	1.17771	+	2.03986i
$29$	−2.97098	+	5.14588i	−0.551696	+	0.955566i	0.446456	+	0.894806i	$0.352686\pi$
$29$	−2.97098	+	5.14588i	−0.551696	+	0.955566i	−0.998152	+	0.0607606i	$0.980647\pi$
$30$	−2.83390	−	0.956381i	−0.517398	−	0.174610i
$31$	−0.763210	+	1.32192i	−0.137077	+	0.237424i	−0.926389	−	0.376568i	$-0.877104\pi$
$31$	−0.763210	+	1.32192i	−0.137077	+	0.237424i	0.789312	+	0.613992i	$0.210437\pi$
$32$	2.18839			0.386857
$33$	−1.80675	−	0.609739i	−0.314515	−	0.106142i
$34$	7.52192	−	13.0283i	1.29000	−	2.23434i
$35$	1.19367	−	2.06750i	0.201768	−	0.349472i
$36$	1.43162	−	11.1805i	0.238604	−	1.86341i
$37$	−3.69507			−0.607465			−0.303733	−	0.952757i	$-0.598233\pi$
$37$	−3.69507			−0.607465			−0.303733	+	0.952757i	$0.598233\pi$
$38$	10.0568	−	2.87216i	1.63142	−	0.465926i
$39$	6.17522	−	5.43492i	0.988827	−	0.870284i
$40$	1.51723	+	2.62792i	0.239895	+	0.415510i
$41$	−2.84053	−	4.91994i	−0.443616	−	0.768366i	0.554338	−	0.832291i	$-0.312971\pi$
$41$	−2.84053	−	4.91994i	−0.443616	−	0.768366i	−0.997955	+	0.0639255i	$0.979638\pi$
$42$	13.0624	+	4.40829i	2.01558	+	0.680214i
$43$	4.61491			0.703767			0.351884	−	0.936044i	$-0.385541\pi$
$43$	4.61491			0.703767			0.351884	+	0.936044i	$0.385541\pi$
$44$	2.06824	+	3.58229i	0.311798	+	0.540051i
$45$	−1.99175	+	0.833295i	−0.296912	+	0.124220i
$46$	5.34627			0.788264
$47$	−0.141619	+	0.245291i	−0.0206572	+	0.0357794i	−0.876169	−	0.482004i	$-0.839909\pi$
$47$	−0.141619	+	0.245291i	−0.0206572	+	0.0357794i	0.855512	+	0.517783i	$0.173243\pi$
$48$	−3.38372	+	2.97807i	−0.488398	+	0.429848i
$49$	−2.00206	+	3.46767i	−0.286008	+	0.495381i
$50$	−5.37720	+	9.31358i	−0.760450	+	1.31714i
$51$	−2.13747	−	10.6471i	−0.299306	−	1.49089i
$52$	−17.8449			−2.47464
$53$	1.90426	+	3.29828i	0.261570	+	0.453053i	0.966659	−	0.256066i	$-0.0824263\pi$
$53$	1.90426	+	3.29828i	0.261570	+	0.453053i	−0.705089	+	0.709119i	$0.749093\pi$
$54$	−6.98178	−	10.3296i	−0.950100	−	1.40568i
$55$	0.396157	−	0.686164i	0.0534178	−	0.0925224i
$56$	−6.99344	−	12.1130i	−0.934537	−	1.61867i
$57$	4.07976	−	6.35260i	0.540377	−	0.841423i
$58$	7.12864	−	12.3472i	0.936037	−	1.62126i
$59$	6.68593	+	11.5804i	0.870434	+	1.50764i	0.861549	+	0.507675i	$0.169495\pi$
$59$	6.68593	+	11.5804i	0.870434	+	1.50764i	0.00888460	+	0.999961i	$0.497172\pi$
$60$	4.43760	+	1.49759i	0.572892	+	0.193338i
$61$	−5.94603	+	10.2988i	−0.761311	+	1.31863i	0.180864	+	0.983508i	$0.442111\pi$
$61$	−5.94603	+	10.2988i	−0.761311	+	1.31863i	−0.942175	+	0.335122i	$0.891223\pi$
$62$	1.83127	−	3.17185i	0.232571	−	0.402825i
$63$	9.18064	−	3.84094i	1.15665	−	0.483913i
$64$	−10.4558			−1.30698
$65$	1.70904	+	2.96014i	0.211980	+	0.367160i
$66$	4.33517	+	1.46303i	0.533623	+	0.180086i
$67$	−7.44592			−0.909664			−0.454832	−	0.890577i	$-0.650301\pi$
$67$	−7.44592			−0.909664			−0.454832	+	0.890577i	$0.650301\pi$
$68$	−11.7785	+	20.4010i	−1.42836	+	2.47399i
$69$	2.89702	−	2.54972i	0.348761	−	0.306951i
$70$	−2.86414	+	4.96083i	−0.342330	+	0.592933i
$71$	5.51472	−	9.55177i	0.654477	−	1.13359i	−0.327548	−	0.944834i	$-0.606222\pi$
$71$	5.51472	−	9.55177i	0.654477	−	1.13359i	0.982025	−	0.188752i	$-0.0604443\pi$
$72$	−1.60658	+	12.5468i	−0.189337	+	1.47865i
$73$	−5.22640	+	9.05239i	−0.611703	+	1.05950i	0.379250	+	0.925294i	$0.376182\pi$
$73$	−5.22640	+	9.05239i	−0.611703	+	1.05950i	−0.990953	+	0.134207i	$0.957151\pi$
$74$	8.86605			1.03066
$75$	1.52802	+	7.61130i	0.176440	+	0.878877i
$76$	−15.7479	+	4.49751i	−1.80640	+	0.515900i
$77$	−1.82603	+	3.16277i	−0.208095	+	0.360431i
$78$	−14.8170	+	13.0407i	−1.67770	+	1.47657i
$79$	12.2331			1.37633			0.688164	−	0.725555i	$-0.258417\pi$
$79$	12.2331			1.37633			0.688164	+	0.725555i	$0.258417\pi$
$80$	−0.936469	−	1.62201i	−0.104700	−	0.181346i
$81$	−8.70963	−	2.26766i	−0.967737	−	0.251962i
$82$	6.81565	+	11.8050i	0.752662	+	1.30365i
$83$	−5.05059	−	8.74788i	−0.554374	−	0.960205i	−0.997952	−	0.0639687i	$-0.979624\pi$
$83$	−5.05059	−	8.74788i	−0.554374	−	0.960205i	0.443577	−	0.896236i	$-0.353709\pi$
$84$	−20.4544	−	6.90293i	−2.23176	−	0.753171i
$85$	4.51221			0.489418
$86$	−11.0731			−1.19405
$87$	−2.02572	−	10.0904i	−0.217180	−	1.08181i
$88$	−2.32099	−	4.02007i	−0.247418	−	0.428540i
$89$	4.23637	+	7.33760i	0.449054	+	0.777784i	0.998325	−	0.0578602i	$-0.0184278\pi$
$89$	4.23637	+	7.33760i	0.449054	+	0.777784i	−0.549271	+	0.835644i	$0.685094\pi$
$90$	4.77905	−	1.99943i	0.503756	−	0.210759i
$91$	−7.87754	−	13.6443i	−0.825791	−	1.43031i
$92$	−8.37170			−0.872810
$93$	−0.520384	−	2.59212i	−0.0539613	−	0.268790i
$94$	0.339804	−	0.588558i	0.0350481	−	0.0607051i
$95$	2.25425	+	2.18154i	0.231281	+	0.223822i
$96$	−2.84534	+	2.50424i	−0.290402	+	0.255588i
$97$	12.3306			1.25199			0.625993	−	0.779828i	$-0.284694\pi$
$97$	12.3306			1.25199			0.625993	+	0.779828i	$0.284694\pi$
$98$	4.80380	−	8.32042i	0.485257	−	0.840489i
$99$	3.04688	−	1.27473i	0.306223	−	0.128116i
$100$	8.42013	−	14.5841i	0.842013	−	1.45841i
$101$	7.51169	−	13.0106i	0.747441	−	1.29461i	−0.201604	−	0.979467i	$-0.564616\pi$
$101$	7.51169	−	13.0106i	0.747441	−	1.29461i	0.949046	−	0.315139i	$-0.102051\pi$
$102$	5.12871	+	25.5470i	0.507818	+	2.52953i
$103$	0.947555	−	1.64121i	0.0933654	−	0.161714i	−0.815560	−	0.578673i	$-0.803571\pi$
$103$	0.947555	−	1.64121i	0.0933654	−	0.161714i	0.908925	+	0.416959i	$0.136904\pi$
$104$	20.0256			1.96367
$105$	0.813890	+	4.05412i	0.0794275	+	0.395642i
$106$	−4.56914	−	7.91398i	−0.443794	−	0.768674i
$107$	−2.81175			−0.271822			−0.135911	−	0.990721i	$-0.543396\pi$
$107$	−2.81175			−0.271822			−0.135911	+	0.990721i	$0.543396\pi$
$108$	10.9327	+	16.1751i	1.05200	+	1.55645i
$109$	−1.58360	+	2.74287i	−0.151681	+	0.262719i	−0.931846	−	0.362855i	$-0.881802\pi$
$109$	−1.58360	+	2.74287i	−0.151681	+	0.262719i	0.780165	+	0.625574i	$0.215135\pi$
$110$	−0.950551	+	1.64640i	−0.0906315	+	0.156978i
$111$	4.80432	−	4.22837i	0.456006	−	0.401339i
$112$	4.31651	+	7.47642i	0.407872	+	0.706455i
$113$	6.93071	−	12.0043i	0.651986	−	1.12927i	−0.330654	−	0.943752i	$-0.607269\pi$
$113$	6.93071	−	12.0043i	0.651986	−	1.12927i	0.982640	−	0.185522i	$-0.0593975\pi$
$114$	−9.78909	+	15.2426i	−0.916833	+	1.42760i
$115$	0.801772	+	1.38871i	0.0747656	+	0.129498i
$116$	−11.1627	+	19.3344i	−1.03643	+	1.79515i
$117$	−1.80968	+	14.1330i	−0.167305	+	1.30659i
$118$	−16.0424	−	27.7863i	−1.47682	−	2.55793i
$119$	−20.7983			−1.90658
$120$	−4.97990	−	1.68061i	−0.454601	−	0.153418i
$121$	4.89398	−	8.47662i	0.444907	−	0.770602i
$122$	14.2671	−	24.7113i	1.29168	−	2.23726i
$123$	9.32328	+	3.14640i	0.840652	+	0.283701i
$124$	−2.86758	+	4.96679i	−0.257516	+	0.446031i
$125$	−6.82403			−0.610360
$126$	−22.0283	+	9.21607i	−1.96244	+	0.821033i
$127$	4.62043	+	8.00282i	0.409997	+	0.710136i	0.994889	−	0.100976i	$-0.0321964\pi$
$127$	4.62043	+	8.00282i	0.409997	+	0.710136i	−0.584892	+	0.811111i	$0.698863\pi$
$128$	20.7112			1.83063
$129$	−6.00030	+	5.28097i	−0.528297	+	0.464963i
$130$	−4.10071	−	7.10264i	−0.359656	−	0.622943i
$131$	3.63311	+	6.29273i	0.317426	+	0.549799i	0.979950	−	0.199242i	$-0.0638481\pi$
$131$	3.63311	+	6.29273i	0.317426	+	0.549799i	−0.662524	+	0.749041i	$0.730515\pi$
$132$	−6.78843	−	2.29095i	−0.590857	−	0.199401i
$133$	−10.3906	−	10.0555i	−0.900982	−	0.871922i
$134$	17.8660			1.54338
$135$	1.63610	−	3.36266i	0.140813	−	0.289411i
$136$	13.2179	−	22.8941i	1.13343	−	1.96316i
$137$	−9.22298	+	15.9747i	−0.787973	+	1.36481i	0.139234	+	0.990259i	$0.455536\pi$
$137$	−9.22298	+	15.9747i	−0.787973	+	1.36481i	−0.927207	+	0.374549i	$0.877798\pi$
$138$	−6.95120	+	6.11788i	−0.591726	+	0.520788i
$139$	13.2036			1.11991			0.559956	−	0.828522i	$-0.310818\pi$
$139$	13.2036			1.11991			0.559956	+	0.828522i	$0.310818\pi$
$140$	4.48494	−	7.76815i	0.379047	−	0.656528i
$141$	−0.0965607	−	0.480985i	−0.00813188	−	0.0405062i
$142$	−13.2322	+	22.9188i	−1.11042	+	1.92330i
$143$	−2.61440	−	4.52828i	−0.218627	−	0.378674i
$144$	0.991615	−	7.74417i	0.0826346	−	0.645348i
$145$	4.27629			0.355127
$146$	12.5404	−	21.7206i	1.03785	−	1.79761i
$147$	−1.36507	−	6.79966i	−0.112589	−	0.560827i
$148$	−13.8833			−1.14120
$149$	1.23511	+	2.13928i	0.101184	+	0.175256i	0.912173	−	0.409806i	$-0.134404\pi$
$149$	1.23511	+	2.13928i	0.101184	+	0.175256i	−0.810989	+	0.585062i	$0.801070\pi$
$150$	−3.66636	−	18.2628i	−0.299357	−	1.49115i
$151$	11.7861	+	20.4141i	0.959140	+	1.66128i	0.724597	+	0.689173i	$0.242026\pi$
$151$	11.7861	+	20.4141i	0.959140	+	1.66128i	0.234542	+	0.972106i	$0.424641\pi$
$152$	17.6723	−	5.04713i	1.43341	−	0.409376i
$153$	14.9629	+	11.3974i	1.20968	+	0.921423i
$154$	4.38142	−	7.58884i	0.353065	−	0.611526i
$155$	1.09853			0.0882361
$156$	23.2019	−	20.4204i	1.85764	−	1.63494i
$157$	−3.56184	−	6.16929i	−0.284266	−	0.492363i	0.688165	−	0.725554i	$-0.258416\pi$
$157$	−3.56184	−	6.16929i	−0.284266	−	0.492363i	−0.972431	+	0.233191i	$0.925083\pi$
$158$	−29.3524			−2.33515
$159$	−6.25023	−	2.10931i	−0.495675	−	0.167279i
$160$	−0.787469	−	1.36394i	−0.0622549	−	0.107829i
$161$	−3.69565	−	6.40105i	−0.291258	−	0.504473i
$162$	20.8981	+	5.44109i	1.64191	+	0.427492i
$163$	12.6404			0.990075			0.495038	−	0.868872i	$-0.335154\pi$
$163$	12.6404			0.990075			0.495038	+	0.868872i	$0.335154\pi$
$164$	−10.6726	−	18.4855i	−0.833390	−	1.44347i
$165$	0.270114	+	1.34548i	0.0210284	+	0.104746i
$166$	12.1185	+	20.9899i	0.940581	+	1.62913i
$167$	7.69530			0.595480			0.297740	−	0.954647i	$-0.403767\pi$
$167$	7.69530			0.595480			0.297740	+	0.954647i	$0.403767\pi$
$168$	22.9541	+	7.74650i	1.77095	+	0.597655i
$169$	9.55725			0.735173
$170$	−10.8267			−0.830371
$171$	1.96496	+	12.9282i	0.150264	+	0.988646i
$172$	17.3394			1.32212
$173$	3.35987			0.255447			0.127723	−	0.991810i	$-0.459233\pi$
$173$	3.35987			0.255447			0.127723	+	0.991810i	$0.459233\pi$
$174$	4.86056	+	24.2113i	0.368478	+	1.83545i
$175$	14.8681			1.12392
$176$	1.43257	+	2.48128i	0.107984	+	0.187033i
$177$	−21.9448	−	7.40588i	−1.64947	−	0.556660i
$178$	−10.1649	−	17.6060i	−0.761888	−	1.31963i
$179$	−17.3530			−1.29703			−0.648514	−	0.761203i	$-0.724609\pi$
$179$	−17.3530			−1.29703			−0.648514	+	0.761203i	$0.724609\pi$
$180$	−7.48350	+	3.13090i	−0.557787	+	0.233364i
$181$	−5.84752	−	10.1282i	−0.434643	−	0.752824i	0.562623	−	0.826713i	$-0.309792\pi$
$181$	−5.84752	−	10.1282i	−0.434643	−	0.752824i	−0.997266	+	0.0738895i	$0.976459\pi$
$182$	18.9016	+	32.7385i	1.40108	+	2.42674i
$183$	−4.05422	−	20.1947i	−0.299696	−	1.49284i
$184$	9.39476			0.692591
$185$	1.32963	+	2.30298i	0.0977563	+	0.169319i
$186$	1.24862	+	6.21960i	0.0915535	+	0.456043i
$187$	−6.90256			−0.504765
$188$	−0.532098	+	0.921621i	−0.0388072	+	0.0672161i
$189$	−7.54135	+	15.4996i	−0.548553	+	1.12743i
$190$	−5.40892	−	5.23446i	−0.392404	−	0.379748i
$191$	1.22344	+	2.11906i	0.0885251	+	0.153330i	0.906888	−	0.421372i	$-0.138451\pi$
$191$	1.22344	+	2.11906i	0.0885251	+	0.153330i	−0.818363	+	0.574702i	$0.805118\pi$
$192$	13.5946	−	11.9649i	0.981109	−	0.863491i
$193$	−6.18066	−	10.7052i	−0.444894	−	0.770578i	0.553151	−	0.833081i	$-0.313425\pi$
$193$	−6.18066	−	10.7052i	−0.444894	−	0.770578i	−0.998045	+	0.0625025i	$0.980092\pi$
$194$	−29.5865			−2.12419
$195$	−5.60945	−	1.89307i	−0.401701	−	0.135565i
$196$	−7.52225	+	13.0289i	−0.537303	+	0.930637i
$197$	−5.54586			−0.395126			−0.197563	−	0.980290i	$-0.563303\pi$
$197$	−5.54586			−0.395126			−0.197563	+	0.980290i	$0.563303\pi$
$198$	−7.31076	+	3.05863i	−0.519553	+	0.217368i
$199$	9.82630	+	17.0196i	0.696568	+	1.20649i	0.969649	+	0.244500i	$0.0786237\pi$
$199$	9.82630	+	17.0196i	0.696568	+	1.20649i	−0.273082	+	0.961991i	$0.588043\pi$
$200$	−9.44911	+	16.3663i	−0.668153	+	1.15728i
$201$	9.68117	−	8.52057i	0.682857	−	0.600995i
$202$	−18.0238	+	31.2181i	−1.26815	+	2.19650i
$203$	−19.7109			−1.38343
$204$	−8.03103	−	40.0039i	−0.562285	−	2.80083i
$205$	−2.04427	+	3.54077i	−0.142778	+	0.247298i
$206$	−2.27359	+	3.93797i	−0.158409	+	0.274372i
$207$	−0.848986	+	6.63029i	−0.0590086	+	0.460837i
$208$	−12.3603			−0.857031
$209$	−3.44845	−	3.33722i	−0.238534	−	0.230840i
$210$	−1.95287	−	9.72757i	−0.134761	−	0.671266i
$211$	−0.672234	−	1.16434i	−0.0462785	−	0.0801567i	0.841958	−	0.539543i	$-0.181403\pi$
$211$	−0.672234	−	1.16434i	−0.0462785	−	0.0801567i	−0.888237	+	0.459386i	$0.848070\pi$
$212$	7.15480	+	12.3925i	0.491394	+	0.851119i
$213$	3.76013	+	18.7298i	0.257640	+	1.28335i
$214$	6.74660			0.461188
$215$	−1.66062	−	2.87629i	−0.113254	−	0.196161i
$216$	−12.2688	−	18.1518i	−0.834785	−	1.23507i
$217$	−5.06351			−0.343733
$218$	3.79973	−	6.58132i	0.257350	−	0.445743i
$219$	−3.56354	−	17.7506i	−0.240802	−	1.19947i
$220$	1.48846	−	2.57810i	0.100352	−	0.173815i
$221$	14.8889	−	25.7884i	1.00154	−	1.73472i
$222$	−11.5276	+	10.1457i	−0.773683	+	0.680932i
$223$	−22.1351			−1.48228			−0.741139	−	0.671351i	$-0.765714\pi$
$223$	−22.1351			−1.48228			−0.741139	+	0.671351i	$0.765714\pi$
$224$	3.62972	+	6.28686i	0.242521	+	0.420058i
$225$	−10.6965	−	8.14764i	−0.713103	−	0.543176i
$226$	−16.6297	+	28.8036i	−1.10619	+	1.91598i
$227$	−2.63704	−	4.56749i	−0.175027	−	0.303155i	0.765144	−	0.643859i	$-0.222668\pi$
$227$	−2.63704	−	4.56749i	−0.175027	−	0.303155i	−0.940170	+	0.340704i	$0.889334\pi$
$228$	15.3287	−	23.8684i	1.01517	−	1.58072i
$229$	−8.36533	+	14.4892i	−0.552797	+	0.957472i	0.445275	+	0.895394i	$0.353106\pi$
$229$	−8.36533	+	14.4892i	−0.552797	+	0.957472i	−0.998071	+	0.0620777i	$0.980227\pi$
$230$	−1.92379	−	3.33211i	−0.126851	−	0.219713i
$231$	−1.24505	−	6.20180i	−0.0819182	−	0.408048i
$232$	12.5269	−	21.6972i	0.822429	−	1.42449i
$233$	0.652119	−	1.12950i	0.0427217	−	0.0739962i	−0.843874	−	0.536542i	$-0.819730\pi$
$233$	0.652119	−	1.12950i	0.0427217	−	0.0739962i	0.886596	+	0.462545i	$0.153064\pi$
$234$	4.34219	−	33.9110i	0.283858	−	2.21683i
$235$	0.203840			0.0132970
$236$	25.1207	+	43.5104i	1.63522	+	2.83229i
$237$	−15.9054	+	13.9986i	−1.03317	+	0.909310i
$238$	49.9041			3.23480
$239$	−9.60234	+	16.6317i	−0.621124	+	1.07582i	0.368153	+	0.929765i	$0.379990\pi$
$239$	−9.60234	+	16.6317i	−0.621124	+	1.07582i	−0.989277	+	0.146053i	$0.953343\pi$
$240$	3.07371	+	1.03731i	0.198407	+	0.0669580i
$241$	−0.895071	+	1.55031i	−0.0576566	+	0.0998642i	−0.893413	−	0.449236i	$-0.851696\pi$
$241$	−0.895071	+	1.55031i	−0.0576566	+	0.0998642i	0.835756	+	0.549100i	$0.185030\pi$
$242$	−11.7427	+	20.3390i	−0.754853	+	1.30744i
$243$	13.9192	−	7.01827i	0.892917	−	0.450222i
$244$	−22.3408	+	38.6953i	−1.43022	+	2.47722i
$245$	2.88167			0.184103
$246$	−22.3705	−	7.54957i	−1.42629	−	0.481343i
$247$	19.9064	−	5.68518i	1.26662	−	0.361739i
$248$	3.21801	−	5.57375i	0.204344	−	0.353934i
$249$	16.5772	+	5.59445i	1.05054	+	0.354534i
$250$	16.3738			1.03557
$251$	−3.17364	−	5.49691i	−0.200319	−	0.346962i	0.748312	−	0.663346i	$-0.230864\pi$
$251$	−3.17364	−	5.49691i	−0.200319	−	0.346962i	−0.948631	+	0.316384i	$0.897531\pi$
$252$	34.4940	−	14.4314i	2.17292	−	0.909094i
$253$	−1.22651	−	2.12438i	−0.0771102	−	0.133559i
$254$	−11.0864	−	19.2022i	−0.695622	−	1.20485i
$255$	−5.86676	+	5.16344i	−0.367391	+	0.323347i
$256$	−28.7834			−1.79897
$257$	23.8457			1.48745			0.743727	−	0.668484i	$-0.233056\pi$
$257$	23.8457			1.48745			0.743727	+	0.668484i	$0.233056\pi$
$258$	14.3973	−	12.6713i	0.896336	−	0.788881i
$259$	−6.12872	−	10.6153i	−0.380820	−	0.659600i
$260$	6.42129	+	11.1220i	0.398231	+	0.689757i
$261$	14.1806	+	10.8015i	0.877757	+	0.668595i
$262$	−8.71739	−	15.0990i	−0.538562	−	0.932817i
$263$	4.53048			0.279361			0.139681	−	0.990197i	$-0.455392\pi$
$263$	4.53048			0.279361			0.139681	+	0.990197i	$0.455392\pi$
$264$	7.61801	+	2.57091i	0.468856	+	0.158229i
$265$	1.37045	−	2.37370i	0.0841864	−	0.145815i
$266$	24.9316	+	24.1274i	1.52865	+	1.47935i
$267$	−13.9047	−	4.69254i	−0.850956	−	0.287179i
$268$	−27.9762			−1.70892
$269$	2.41294	−	4.17933i	0.147119	−	0.254818i	−0.783042	−	0.621968i	$-0.786333\pi$
$269$	2.41294	−	4.17933i	0.147119	−	0.254818i	0.930162	+	0.367150i	$0.119667\pi$
$270$	−3.92571	+	8.06845i	−0.238911	+	0.491030i
$271$	−1.69899	+	2.94273i	−0.103206	+	0.178758i	−0.913004	−	0.407951i	$-0.866243\pi$
$271$	−1.69899	+	2.94273i	−0.103206	+	0.178758i	0.809798	+	0.586709i	$0.199577\pi$
$272$	−8.15842	+	14.1308i	−0.494677	+	0.856805i
$273$	25.8559	+	8.72580i	1.56487	+	0.528110i
$274$	22.1299	−	38.3301i	1.33692	−	2.31561i
$275$	4.93443			0.297558
$276$	10.8849	−	9.57997i	0.655192	−	0.576646i
$277$	−7.98414	−	13.8289i	−0.479720	−	0.830900i	0.520009	−	0.854161i	$-0.325929\pi$
$277$	−7.98414	−	13.8289i	−0.479720	−	0.830900i	−0.999729	+	0.0232607i	$0.992595\pi$
$278$	−31.6810			−1.90010
$279$	3.64283	+	2.77478i	0.218091	+	0.166121i
$280$	−5.03302	+	8.71745i	−0.300781	+	0.520967i
$281$	−3.76974	+	6.52938i	−0.224884	+	0.389510i	−0.956285	−	0.292438i	$-0.905534\pi$
$281$	−3.76974	+	6.52938i	−0.224884	+	0.389510i	0.731401	+	0.681948i	$0.238867\pi$
$282$	0.231690	+	1.15409i	0.0137970	+	0.0687250i
$283$	−5.16192	−	8.94071i	−0.306844	−	0.531470i	0.670826	−	0.741615i	$-0.265940\pi$
$283$	−5.16192	−	8.94071i	−0.306844	−	0.531470i	−0.977670	+	0.210145i	$0.932606\pi$
$284$	20.7202	−	35.8885i	1.22952	−	2.12959i
$285$	−5.42738	−	0.256835i	−0.321490	−	0.0152136i
$286$	6.27307	+	10.8653i	0.370934	+	0.642477i
$287$	9.42273	−	16.3207i	0.556206	−	0.963378i
$288$	0.833841	−	6.51201i	0.0491346	−	0.383724i
$289$	−11.1549	−	19.3209i	−0.656172	−	1.13652i
$290$	−10.2607			−0.602527
$291$	−16.0323	+	14.1103i	−0.939828	+	0.827160i
$292$	−19.6369	+	34.0121i	−1.14916	+	1.99041i
$293$	−3.88571	+	6.73025i	−0.227006	+	0.393186i	−0.956919	−	0.290354i	$-0.906227\pi$
$293$	−3.88571	+	6.73025i	−0.227006	+	0.393186i	0.729914	+	0.683539i	$0.239560\pi$
$294$	3.27540	+	16.3153i	0.191025	+	0.951528i
$295$	4.81171	−	8.33413i	0.280149	−	0.485232i
$296$	15.5799			0.905565
$297$	−2.50283	+	5.14403i	−0.145229	+	0.298487i
$298$	−2.96356	−	5.13304i	−0.171674	−	0.297349i
$299$	10.5824			0.611998
$300$	5.74115	+	28.5976i	0.331465	+	1.65108i
$301$	7.65440	+	13.2578i	0.441192	+	0.764167i
$302$	−28.2799	−	48.9823i	−1.62733	−	2.81861i
$303$	5.12174	+	25.5122i	0.294236	+	1.46564i
$304$	−10.9078	+	3.11520i	−0.625603	+	0.178669i
$305$	8.55846			0.490056
$306$	−35.9024	−	27.3472i	−2.05241	−	1.56333i
$307$	−4.92022	+	8.52206i	−0.280812	+	0.486380i	−0.971585	−	0.236692i	$-0.923937\pi$
$307$	−4.92022	+	8.52206i	−0.280812	+	0.486380i	0.690773	+	0.723071i	$0.257270\pi$
$308$	−6.86085	+	11.8833i	−0.390933	+	0.677116i
$309$	0.646077	+	3.21821i	0.0367540	+	0.183078i
$310$	−2.63585			−0.149706
$311$	−12.6580	+	21.9243i	−0.717769	+	1.24321i	0.244112	+	0.969747i	$0.421503\pi$
$311$	−12.6580	+	21.9243i	−0.717769	+	1.24321i	−0.961882	+	0.273466i	$0.911830\pi$
$312$	−26.0373	+	22.9159i	−1.47407	+	1.29736i
$313$	10.3856	−	17.9884i	0.587030	−	1.01677i	−0.407588	−	0.913166i	$-0.633630\pi$
$313$	10.3856	−	17.9884i	0.587030	−	1.01677i	0.994619	−	0.103601i	$-0.0330365\pi$
$314$	8.54638	+	14.8028i	0.482300	+	0.835369i
$315$	−5.69746	−	4.33980i	−0.321015	−	0.244520i
$316$	45.9628			2.58561
$317$	−4.39206	+	7.60726i	−0.246682	+	0.427266i	−0.962603	−	0.270915i	$-0.912674\pi$
$317$	−4.39206	+	7.60726i	−0.246682	+	0.427266i	0.715921	+	0.698181i	$0.246007\pi$
$318$	14.9970	+	5.06115i	0.840988	+	0.283815i
$319$	−6.54167			−0.366263
$320$	3.76241	+	6.51669i	0.210325	+	0.364294i
$321$	3.65583	−	3.21756i	0.204049	−	0.179587i
$322$	8.86744	+	15.3589i	0.494163	+	0.855915i
$323$	6.63974	−	26.5104i	0.369445	−	1.47508i
$324$	−32.7243	−	8.52018i	−1.81802	−	0.473343i
$325$	−10.6437	+	18.4354i	−0.590404	+	1.02261i
$326$	−30.3298			−1.67981
$327$	−1.07975	−	5.37843i	−0.0597105	−	0.297428i
$328$	11.9768	+	20.7445i	0.661311	+	1.14542i
$329$	−0.939568			−0.0518001
$330$	−0.648119	−	3.22839i	−0.0356778	−	0.177717i
$331$	9.59192	+	16.6137i	0.527219	+	0.913171i	0.999497	+	0.0317208i	$0.0100987\pi$
$331$	9.59192	+	16.6137i	0.527219	+	0.913171i	−0.472277	+	0.881450i	$0.656568\pi$
$332$	−18.9764	−	32.8680i	−1.04146	−	1.80387i
$333$	−1.40793	+	10.9954i	−0.0771539	+	0.602546i
$334$	−18.4643			−1.01032
$335$	2.67933	+	4.64074i	0.146388	+	0.253551i
$336$	−14.1678	−	4.78132i	−0.772916	−	0.260842i
$337$	−1.02115	−	1.76869i	−0.0556257	−	0.0963465i	0.836872	−	0.547399i	$-0.184382\pi$
$337$	−1.02115	−	1.76869i	−0.0556257	−	0.0963465i	−0.892497	+	0.451053i	$0.851049\pi$
$338$	−22.9319			−1.24733
$339$	4.72561	+	23.5390i	0.256660	+	1.27846i
$340$	16.9535			0.919434
$341$	−1.68048			−0.0910031
$342$	−4.71478	−	31.0203i	−0.254946	−	1.67739i
$343$	9.93808			0.536606
$344$	−19.4584			−1.04912
$345$	−2.63160	−	0.888108i	−0.141681	−	0.0478141i
$346$	−8.06178			−0.433404
$347$	4.86447	+	8.42551i	0.261138	+	0.452305i	0.966545	−	0.256498i	$-0.0825688\pi$
$347$	4.86447	+	8.42551i	0.261138	+	0.452305i	−0.705406	+	0.708803i	$0.749235\pi$
$348$	−7.61114	−	37.9124i	−0.408000	−	2.03232i
$349$	7.61899	+	13.1965i	0.407835	+	0.706391i	0.994647	−	0.103332i	$-0.0329505\pi$
$349$	7.61899	+	13.1965i	0.407835	+	0.706391i	−0.586812	+	0.809723i	$0.699617\pi$
$350$	−35.6750			−1.90691
$351$	−13.8198	−	20.4465i	−0.737646	−	1.09135i
$352$	1.20463	+	2.08648i	0.0642071	+	0.111210i
$353$	−13.3156	−	23.0632i	−0.708716	−	1.22753i	−0.965334	−	0.261019i	$-0.915941\pi$
$353$	−13.3156	−	23.0632i	−0.708716	−	1.22753i	0.256618	−	0.966513i	$-0.417392\pi$
$354$	52.6549	+	17.7699i	2.79858	+	0.944458i
$355$	−7.93764			−0.421286
$356$	15.9171	+	27.5693i	0.843605	+	1.46117i
$357$	27.0419	−	23.8001i	1.43121	−	1.25963i
$358$	41.6374			2.20060
$359$	−5.98961	+	10.3743i	−0.316119	+	0.547535i	−0.979675	−	0.200592i	$-0.935713\pi$
$359$	−5.98961	+	10.3743i	−0.316119	+	0.547535i	0.663555	+	0.748127i	$0.269047\pi$
$360$	8.39802	−	3.51351i	0.442614	−	0.185178i
$361$	16.1343	−	10.0342i	0.849173	−	0.528114i
$362$	14.0307	+	24.3019i	0.737438	+	1.27728i
$363$	3.33689	+	16.6216i	0.175141	+	0.872407i
$364$	−29.5979	−	51.2651i	−1.55135	−	2.68702i
$365$	7.52265			0.393753
$366$	9.72780	+	48.4558i	0.508480	+	2.53282i
$367$	0.803424	−	1.39157i	0.0419384	−	0.0726394i	−0.844294	−	0.535880i	$-0.819980\pi$
$367$	0.803424	−	1.39157i	0.0419384	−	0.0726394i	0.886233	+	0.463240i	$0.153313\pi$
$368$	−5.79866			−0.302276
$369$	−15.7226	+	6.57794i	−0.818487	+	0.342434i
$370$	−3.19035	−	5.52585i	−0.165858	−	0.287275i
$371$	−6.31690	+	10.9412i	−0.327957	+	0.568038i
$372$	−1.95521	−	9.73925i	−0.101373	−	0.504957i
$373$	4.06344	−	7.03808i	0.210397	−	0.364418i	−0.741442	−	0.671017i	$-0.765858\pi$
$373$	4.06344	−	7.03808i	0.210397	−	0.364418i	0.951839	+	0.306599i	$0.0991910\pi$
$374$	16.5622			0.856411
$375$	8.87259	−	7.80893i	0.458179	−	0.403251i
$376$	0.597123	−	1.03425i	0.0307943	−	0.0533372i
$377$	14.1105	−	24.4401i	0.726727	−	1.25873i
$378$	18.0949	−	37.1903i	0.930703	−	1.91286i
$379$	33.1062			1.70055			0.850277	−	0.526336i	$-0.176435\pi$
$379$	33.1062			1.70055			0.850277	+	0.526336i	$0.176435\pi$
$380$	8.46981	+	8.19662i	0.434492	+	0.420478i
$381$	−15.1653	−	5.11797i	−0.776943	−	0.262201i
$382$	−2.93556	−	5.08454i	−0.150196	−	0.260148i
$383$	−9.84871	−	17.0585i	−0.503246	−	0.871647i	−0.999993	−	0.00375167i	$-0.998806\pi$
$383$	−9.84871	−	17.0585i	−0.503246	−	0.871647i	0.496747	−	0.867895i	$-0.334528\pi$
$384$	−26.9287	+	23.7004i	−1.37420	+	1.20946i
$385$	2.62830			0.133951
$386$	14.8301	+	25.6864i	0.754830	+	1.30740i
$387$	1.75841	−	13.7326i	0.0893852	−	0.698068i
$388$	46.3294			2.35202
$389$	7.97357	−	13.8106i	0.404276	−	0.700227i	−0.589961	−	0.807432i	$-0.700857\pi$
$389$	7.97357	−	13.8106i	0.404276	−	0.700227i	0.994237	+	0.107205i	$0.0341901\pi$
$390$	13.4595	+	4.54228i	0.681547	+	0.230007i
$391$	6.98495	−	12.0983i	0.353244	−	0.611837i
$392$	8.44150	−	14.6211i	0.426360	−	0.738478i
$393$	−11.9247	−	4.02433i	−0.601522	−	0.203000i
$394$	13.3069			0.670392
$395$	−4.40194	−	7.62438i	−0.221486	−	0.383624i
$396$	11.4479	−	4.78950i	0.575279	−	0.240682i
$397$	−12.0149	+	20.8105i	−0.603012	+	1.04445i	0.389351	+	0.921090i	$0.372699\pi$
$397$	−12.0149	+	20.8105i	−0.603012	+	1.04445i	−0.992362	+	0.123357i	$0.960634\pi$
$398$	−23.5775	−	40.8374i	−1.18183	−	2.04699i
$399$	25.0167	+	1.18384i	1.25240	+	0.0592663i
$400$	5.83221	−	10.1017i	0.291611	−	0.505084i
$401$	−1.89136	−	3.27592i	−0.0944498	−	0.163592i	0.814929	−	0.579561i	$-0.196776\pi$
$401$	−1.89136	−	3.27592i	−0.0944498	−	0.163592i	−0.909379	+	0.415969i	$0.863443\pi$
$402$	−23.2293	+	20.4445i	−1.15857	+	1.01968i
$403$	3.62482	−	6.27838i	0.180565	−	0.312748i
$404$	28.2234	−	48.8843i	1.40416	−	2.43208i
$405$	1.72073	+	6.24435i	0.0855036	+	0.310284i
$406$	47.2949			2.34721
$407$	−2.03400	−	3.52300i	−0.100822	−	0.174628i
$408$	9.01246	+	44.8926i	0.446183	+	2.22251i
$409$	−27.1867			−1.34430			−0.672148	−	0.740416i	$-0.734628\pi$
$409$	−27.1867			−1.34430			−0.672148	+	0.740416i	$0.734628\pi$
$410$	4.90507	−	8.49583i	0.242244	−	0.419579i
$411$	−6.28856	−	31.3244i	−0.310192	−	1.54512i
$412$	3.56021	−	6.16646i	0.175399	−	0.303800i
$413$	−22.1789	+	38.4149i	−1.09135	+	1.89027i
$414$	2.03708	−	15.9089i	0.100117	−	0.781880i
$415$	−3.63480	+	6.29566i	−0.178425	+	0.309042i
$416$	−10.3937			−0.509591
$417$	−17.1673	+	15.1092i	−0.840684	+	0.739901i
$418$	8.27431	+	8.00743i	0.404710	+	0.391656i
$419$	2.02350	−	3.50481i	0.0988547	−	0.171221i	−0.812356	−	0.583162i	$-0.801815\pi$
$419$	2.02350	−	3.50481i	0.0988547	−	0.171221i	0.911211	+	0.411940i	$0.135149\pi$
$420$	3.05799	+	15.2324i	0.149215	+	0.743263i
$421$	−6.64463			−0.323839			−0.161920	−	0.986804i	$-0.551769\pi$
$421$	−6.64463			−0.323839			−0.161920	+	0.986804i	$0.551769\pi$
$422$	1.61298	+	2.79376i	0.0785185	+	0.135998i
$423$	0.675952	+	0.514878i	0.0328659	+	0.0250342i
$424$	−8.02915	−	13.9069i	−0.389930	−	0.675379i
$425$	14.0507	+	24.3366i	0.681560	+	1.18050i
$426$	−9.02216	−	44.9409i	−0.437125	−	2.17739i
$427$	−39.4489			−1.90907
$428$	−10.5645			−0.510653
$429$	8.58107	+	2.89592i	0.414298	+	0.139817i
$430$	3.98455	+	6.90144i	0.192152	+	0.332817i
$431$	8.57343	+	14.8496i	0.412967	+	0.715281i	0.995213	−	0.0977326i	$-0.0311590\pi$
$431$	8.57343	+	14.8496i	0.412967	+	0.715281i	−0.582245	+	0.813013i	$0.697826\pi$
$432$	7.57257	+	11.2037i	0.364336	+	0.539038i
$433$	−8.02098	−	13.8927i	−0.385464	−	0.667643i	0.606370	−	0.795183i	$-0.292625\pi$
$433$	−8.02098	−	13.8927i	−0.385464	−	0.667643i	−0.991833	+	0.127540i	$0.959292\pi$
$434$	12.1495			0.583196
$435$	−5.56003	+	4.89348i	−0.266583	+	0.234624i
$436$	−5.94998	+	10.3057i	−0.284952	+	0.493552i
$437$	9.33885	−	2.66713i	0.446738	−	0.127586i
$438$	8.55047	+	42.5913i	0.408557	+	2.03509i
$439$	6.95940			0.332154			0.166077	−	0.986113i	$-0.446890\pi$
$439$	6.95940			0.332154			0.166077	+	0.986113i	$0.446890\pi$
$440$	−1.67036	+	2.89315i	−0.0796314	+	0.137926i
$441$	9.55591	+	7.27882i	0.455043	+	0.346610i
$442$	−35.7249	+	61.8774i	−1.69926	+	2.94321i
$443$	−1.21813	+	2.10986i	−0.0578751	+	0.100243i	−0.893511	−	0.449041i	$-0.851766\pi$
$443$	−1.21813	+	2.10986i	−0.0578751	+	0.100243i	0.835636	+	0.549283i	$0.185099\pi$
$444$	18.0511	−	15.8871i	0.856665	−	0.753966i
$445$	3.04882	−	5.28071i	0.144528	−	0.250330i
$446$	53.1117			2.51491
$447$	−4.05392	−	1.36811i	−0.191744	−	0.0647094i
$448$	−17.3423	−	30.0377i	−0.819345	−	1.41915i
$449$	25.8086			1.21798			0.608991	−	0.793177i	$-0.291575\pi$
$449$	25.8086			1.21798			0.608991	+	0.793177i	$0.291575\pi$
$450$	25.6656	+	19.5497i	1.20989	+	0.921581i
$451$	3.12722	−	5.41651i	0.147255	−	0.255053i
$452$	26.0405	−	45.1034i	1.22484	−	2.12149i
$453$	−38.6847	−	13.0552i	−1.81757	−	0.613389i
$454$	6.32739	+	10.9594i	0.296959	+	0.514348i
$455$	−5.66929	+	9.81950i	−0.265781	+	0.460345i
$456$	−17.2020	+	26.7852i	−0.805555	+	1.25433i
$457$	1.49509	+	2.58957i	0.0699372	+	0.121135i	0.898873	−	0.438208i	$-0.144387\pi$
$457$	1.49509	+	2.58957i	0.0699372	+	0.121135i	−0.828936	+	0.559343i	$0.811053\pi$
$458$	20.0720	−	34.7657i	0.937903	−	1.62450i
$459$	−32.4971	+	2.30363i	−1.51683	+	0.107524i
$460$	3.01246	+	5.21774i	0.140457	+	0.243278i
$461$	−14.1396			−0.658549			−0.329274	−	0.944234i	$-0.606804\pi$
$461$	−14.1396			−0.658549			−0.329274	+	0.944234i	$0.606804\pi$
$462$	2.98741	+	14.8808i	0.138987	+	0.692316i
$463$	−13.8565	+	24.0001i	−0.643964	+	1.11538i	0.340576	+	0.940217i	$0.389378\pi$
$463$	−13.8565	+	24.0001i	−0.643964	+	1.11538i	−0.984540	+	0.175161i	$0.943955\pi$
$464$	−7.73187	+	13.3920i	−0.358943	+	0.621707i
$465$	−1.42831	+	1.25708i	−0.0662362	+	0.0582956i
$466$	−1.56471	+	2.71016i	−0.0724839	+	0.125546i
$467$	27.3728			1.26666			0.633330	−	0.773882i	$-0.281687\pi$
$467$	27.3728			1.26666			0.633330	+	0.773882i	$0.281687\pi$
$468$	−6.79942	+	53.1011i	−0.314303	+	2.45460i
$469$	−12.3500	−	21.3908i	−0.570269	−	0.987734i
$470$	−0.489099			−0.0225605
$471$	11.6908	+	3.94538i	0.538683	+	0.181794i
$472$	−28.1906	−	48.8276i	−1.29758	−	2.24747i
$473$	2.54034	+	4.40001i	0.116805	+	0.202312i
$474$	38.1639	−	33.5887i	1.75293	−	1.54278i
$475$	−4.74655	+	18.9515i	−0.217787	+	0.869554i
$476$	−78.1446			−3.58175
$477$	10.5403	−	4.40978i	0.482606	−	0.201910i
$478$	23.0401	−	39.9067i	1.05383	−	1.82529i
$479$	−16.1621	+	27.9936i	−0.738466	+	1.27906i	0.214720	+	0.976676i	$0.431116\pi$
$479$	−16.1621	+	27.9936i	−0.738466	+	1.27906i	−0.953186	+	0.302385i	$0.902217\pi$
$480$	2.58466	+	0.872265i	0.117973	+	0.0398133i
$481$	17.5495			0.800189
$482$	2.14766	−	3.71985i	0.0978232	−	0.169435i
$483$	12.1300	+	4.09360i	0.551932	+	0.186265i
$484$	18.3879	−	31.8488i	0.835815	−	1.44767i
$485$	−4.43704	−	7.68519i	−0.201476	−	0.348966i
$486$	−33.3981	+	16.8398i	−1.51497	+	0.763870i
$487$	−20.0494			−0.908523			−0.454262	−	0.890868i	$-0.650097\pi$
$487$	−20.0494			−0.908523			−0.454262	+	0.890868i	$0.650097\pi$
$488$	25.0709	−	43.4241i	1.13491	−	1.96572i
$489$	−16.4351	+	14.4648i	−0.743219	+	0.654121i
$490$	−6.91437			−0.312360
$491$	2.34782	+	4.06654i	0.105956	+	0.183521i	0.914128	−	0.405425i	$-0.132877\pi$
$491$	2.34782	+	4.06654i	0.105956	+	0.183521i	−0.808173	+	0.588946i	$0.799543\pi$
$492$	35.0299	+	11.8218i	1.57927	+	0.532970i
$493$	−18.6273	−	32.2634i	−0.838931	−	1.45307i
$494$	−47.7641	+	13.6412i	−2.14901	+	0.613746i
$495$	−1.89088	−	1.44030i	−0.0849885	−	0.0647365i
$496$	−1.98623	+	3.44025i	−0.0891843	+	0.154472i
$497$	36.5873			1.64117
$498$	−39.7758	−	13.4235i	−1.78240	−	0.601520i
$499$	−10.5828	−	18.3300i	−0.473752	−	0.820562i	0.525797	−	0.850610i	$-0.323767\pi$
$499$	−10.5828	−	18.3300i	−0.473752	−	0.820562i	−0.999548	+	0.0300483i	$0.990434\pi$
$500$	−25.6396			−1.14664
$501$	−10.0054	+	8.80594i	−0.447009	+	0.393421i
$502$	7.61493	+	13.1895i	0.339871	+	0.588674i
$503$	12.8870	+	22.3210i	0.574604	+	0.995243i	0.996085	+	0.0884059i	$0.0281773\pi$
$503$	12.8870	+	22.3210i	0.574604	+	0.995243i	−0.421481	+	0.906837i	$0.638489\pi$
$504$	−38.7094	+	16.1950i	−1.72425	+	0.721383i
$505$	−10.8120			−0.481128
$506$	2.94293	+	5.09730i	0.130829	+	0.226603i
$507$	−12.4263	+	10.9366i	−0.551872	+	0.485713i
$508$	17.3601	+	30.0687i	0.770232	+	1.33408i
$509$	−27.1603			−1.20386			−0.601929	−	0.798549i	$-0.705601\pi$
$509$	−27.1603			−1.20386			−0.601929	+	0.798549i	$0.705601\pi$
$510$	14.0769	−	12.3893i	0.623334	−	0.548608i
$511$	−34.6745			−1.53391
$512$	27.6414			1.22159
$513$	−17.3490	−	14.5607i	−0.765975	−	0.642870i
$514$	−57.2161			−2.52369
$515$	−1.36387			−0.0600992
$516$	−22.5447	+	19.8420i	−0.992473	+	0.873494i
$517$	−0.311824			−0.0137140
$518$	14.7054	+	25.4705i	0.646119	+	1.11911i
$519$	−4.36850	+	3.84480i	−0.191756	+	0.168768i
$520$	−7.20600	−	12.4812i	−0.316004	−	0.547335i
$521$	21.0677			0.922994			0.461497	−	0.887142i	$-0.347313\pi$
$521$	21.0677			0.922994			0.461497	+	0.887142i	$0.347313\pi$
$522$	−34.0253	−	25.9174i	−1.48925	−	1.13437i
$523$	4.13511	+	7.16222i	0.180816	+	0.313182i	0.942159	−	0.335167i	$-0.108793\pi$
$523$	4.13511	+	7.16222i	0.180816	+	0.313182i	−0.761343	+	0.648350i	$0.775460\pi$
$524$	13.6505	+	23.6434i	0.596326	+	1.03287i
$525$	−19.3315	+	17.0140i	−0.843695	+	0.742551i
$526$	−10.8706			−0.473979
$527$	−4.78514	−	8.28811i	−0.208444	−	0.361036i
$528$	−4.70201	−	1.58683i	−0.204629	−	0.0690577i
$529$	−18.0354			−0.784147
$530$	−3.28831	+	5.69552i	−0.142835	+	0.247397i
$531$	37.0073	−	15.4829i	1.60598	−	0.671900i
$532$	−39.0403	−	37.7811i	−1.69261	−	1.63802i
$533$	13.4909	+	23.3670i	0.584358	+	1.01214i
$534$	33.3634	+	11.2594i	1.44378	+	0.487243i
$535$	1.01178	+	1.75245i	0.0437430	+	0.0757650i
$536$	31.3951			1.35606
$537$	22.5624	−	19.8576i	0.973639	−	0.856917i
$538$	−5.78967	+	10.0280i	−0.249610	+	0.432338i
$539$	−4.40825			−0.189877
$540$	6.14725	−	12.6344i	0.264536	−	0.543697i
$541$	−13.5852	−	23.5303i	−0.584074	−	1.01165i	−0.994990	−	0.0999732i	$-0.968124\pi$
$541$	−13.5852	−	23.5303i	−0.584074	−	1.01165i	0.410916	−	0.911673i	$-0.365209\pi$
$542$	4.07660	−	7.06088i	0.175105	−	0.303291i
$543$	19.1929	+	6.47719i	0.823647	+	0.277963i
$544$	−6.86035	+	11.8825i	−0.294135	+	0.509457i
$545$	2.27936			0.0976371
$546$	−62.0394	−	20.9369i	−2.65504	−	0.896018i
$547$	−9.42670	+	16.3275i	−0.403056	+	0.698114i	−0.994093	−	0.108530i	$-0.965386\pi$
$547$	−9.42670	+	16.3275i	−0.403056	+	0.698114i	0.591037	+	0.806645i	$0.298719\pi$
$548$	−34.6531	+	60.0210i	−1.48031	+	2.56397i
$549$	28.3807	+	21.6178i	1.21126	+	0.922625i
$550$	−11.8398			−0.504852
$551$	6.29259	−	25.1243i	0.268073	−	1.07033i
$552$	−12.2151	+	10.7507i	−0.519907	+	0.457580i
$553$	20.2901	+	35.1434i	0.862821	+	1.49445i
$554$	19.1574	+	33.1815i	0.813919	+	1.40975i
$555$	−4.36415	−	1.47281i	−0.185248	−	0.0625171i
$556$	49.6092			2.10390
$557$	−4.19140	−	7.25972i	−0.177595	−	0.307604i	0.763461	−	0.645854i	$-0.223498\pi$
$557$	−4.19140	−	7.25972i	−0.177595	−	0.307604i	−0.941056	+	0.338250i	$0.890165\pi$
$558$	−8.74072	−	6.65788i	−0.370024	−	0.281850i
$559$	−21.9183			−0.927044
$560$	3.10650	−	5.38061i	0.131273	−	0.227372i
$561$	8.97469	−	7.89879i	0.378912	−	0.333487i
$562$	9.04522	−	15.6668i	0.381550	−	0.660863i
$563$	−0.809051	+	1.40132i	−0.0340974	+	0.0590585i	−0.882571	−	0.470180i	$-0.844189\pi$
$563$	−0.809051	+	1.40132i	−0.0340974	+	0.0590585i	0.848473	+	0.529239i	$0.177522\pi$
$564$	−0.362803	−	1.80718i	−0.0152768	−	0.0760962i
$565$	−9.97576			−0.419683
$566$	12.3857	+	21.4526i	0.520608	+	0.901720i
$567$	−7.93142	−	28.7824i	−0.333088	−	1.20875i
$568$	−23.2523	+	40.2742i	−0.975646	+	1.68987i
$569$	5.07595	+	8.79180i	0.212795	+	0.368571i	0.952588	−	0.304263i	$-0.0984101\pi$
$569$	5.07595	+	8.79180i	0.212795	+	0.368571i	−0.739793	+	0.672834i	$0.765077\pi$
$570$	13.0226	+	0.616258i	0.545457	+	0.0258122i
$571$	6.06347	−	10.5022i	0.253748	−	0.439505i	−0.710806	−	0.703388i	$-0.751670\pi$
$571$	6.06347	−	10.5022i	0.253748	−	0.439505i	0.964555	+	0.263883i	$0.0850031\pi$
$572$	−9.82298	−	17.0139i	−0.410719	−	0.711387i
$573$	−4.01562	−	1.35518i	−0.167755	−	0.0566136i
$574$	−22.6092	+	39.1602i	−0.943689	+	1.63452i
$575$	−4.99334	+	8.64871i	−0.208236	+	0.360676i
$576$	−3.98397	+	31.1134i	−0.165999	+	1.29639i
$577$	42.8498			1.78386			0.891931	−	0.452171i	$-0.149350\pi$
$577$	42.8498			1.78386			0.891931	+	0.452171i	$0.149350\pi$
$578$	26.7655	+	46.3591i	1.11330	+	1.92829i
$579$	20.2864	+	6.84620i	0.843072	+	0.284518i
$580$	16.0671			0.667151
$581$	16.7541	−	29.0189i	0.695075	−	1.20391i
$582$	38.4683	−	33.8566i	1.59456	−	1.40340i
$583$	−2.09646	+	3.63117i	−0.0868263	+	0.150388i
$584$	22.0366	−	38.1686i	0.911883	−	1.57943i
$585$	9.45969	−	3.95769i	0.391110	−	0.163630i
$586$	9.32349	−	16.1488i	0.385150	−	0.667099i
$587$	11.6113			0.479250			0.239625	−	0.970866i	$-0.422975\pi$
$587$	11.6113			0.479250			0.239625	+	0.970866i	$0.422975\pi$
$588$	−5.12894	−	25.5481i	−0.211514	−	1.05359i
$589$	1.61649	−	6.45416i	0.0666065	−	0.265939i
$590$	−11.5454	+	19.9972i	−0.475315	+	0.823270i
$591$	7.21072	−	6.34629i	0.296609	−	0.261051i
$592$	−9.61629			−0.395227
$593$	3.60159	+	6.23813i	0.147899	+	0.256169i	0.930451	−	0.366417i	$-0.119415\pi$
$593$	3.60159	+	6.23813i	0.147899	+	0.256169i	−0.782551	+	0.622586i	$0.786082\pi$
$594$	6.00536	−	12.3427i	0.246403	−	0.506429i
$595$	7.48405	+	12.9628i	0.306816	+	0.531421i
$596$	4.64063	+	8.03781i	0.190088	+	0.329241i
$597$	−32.2522	−	10.8844i	−1.31999	−	0.445469i
$598$	−25.3918			−1.03835
$599$	−25.0386			−1.02305			−0.511525	−	0.859269i	$-0.670919\pi$
$599$	−25.0386			−1.02305			−0.511525	+	0.859269i	$0.670919\pi$
$600$	−6.44274	−	32.0924i	−0.263024	−	1.31017i
$601$	−17.0803	−	29.5840i	−0.696720	−	1.20675i	−0.969597	−	0.244706i	$-0.921309\pi$
$601$	−17.0803	−	29.5840i	−0.696720	−	1.20675i	0.272877	−	0.962049i	$-0.412025\pi$
$602$	−18.3662	−	31.8111i	−0.748549	−	1.29653i
$603$	−2.83711	+	22.1569i	−0.115536	+	0.902297i
$604$	44.2834	+	76.7011i	1.80187	+	3.12093i
$605$	−7.04418			−0.286386
$606$	−12.2892	−	61.2148i	−0.499216	−	2.48668i
$607$	−0.908746	+	1.57399i	−0.0368849	+	0.0638865i	−0.883879	−	0.467717i	$-0.845077\pi$
$607$	−0.908746	+	1.57399i	−0.0368849	+	0.0638865i	0.846994	+	0.531603i	$0.178410\pi$
$608$	−9.17225	+	2.61955i	−0.371984	+	0.106237i
$609$	25.6281	−	22.5557i	1.03850	−	0.914005i
$610$	−20.5354			−0.831454
$611$	0.672611	−	1.16500i	0.0272109	−	0.0471307i
$612$	56.2195	+	42.8229i	2.27254	+	1.73101i
$613$	−0.633570	+	1.09737i	−0.0255896	+	0.0443225i	−0.878537	−	0.477675i	$-0.841480\pi$
$613$	−0.633570	+	1.09737i	−0.0255896	+	0.0443225i	0.852947	+	0.521998i	$0.174813\pi$
$614$	11.8057	−	20.4481i	0.476439	−	0.825217i
$615$	−1.39385	−	6.94302i	−0.0562056	−	0.279970i
$616$	7.69928	−	13.3355i	0.310213	−	0.537304i
$617$	31.3362			1.26155			0.630774	−	0.775967i	$-0.282738\pi$
$617$	31.3362			1.26155			0.630774	+	0.775967i	$0.282738\pi$
$618$	−1.55021	−	7.72188i	−0.0623588	−	0.310619i
$619$	6.71549	+	11.6316i	0.269918	+	0.467512i	0.968840	−	0.247686i	$-0.0796700\pi$
$619$	6.71549	+	11.6316i	0.269918	+	0.467512i	−0.698922	+	0.715198i	$0.746337\pi$
$620$	4.12746			0.165763
$621$	−6.48337	−	9.59221i	−0.260169	−	0.384922i
$622$	30.3720	−	52.6058i	1.21780	−	2.10930i
$623$	−14.0531	+	24.3406i	−0.563024	+	0.975186i
$624$	16.0708	−	14.1442i	0.643347	−	0.566221i
$625$	−8.74961	−	15.1548i	−0.349984	−	0.606190i
$626$	−24.9196	+	43.1620i	−0.995987	+	1.72510i
$627$	8.30254	+	0.392894i	0.331572	+	0.0156907i
$628$	−13.3828	−	23.1796i	−0.534030	−	0.924967i
$629$	11.5836	−	20.0634i	0.461868	−	0.799978i
$630$	13.6706	+	10.4130i	0.544651	+	0.414866i
$631$	−0.634355	−	1.09874i	−0.0252533	−	0.0437400i	0.853123	−	0.521711i	$-0.174706\pi$
$631$	−0.634355	−	1.09874i	−0.0252533	−	0.0437400i	−0.878376	+	0.477971i	$0.841373\pi$
$632$	−51.5797			−2.05173
$633$	2.20643	+	0.744621i	0.0876976	+	0.0295960i
$634$	10.5384	−	18.2531i	0.418534	−	0.724923i
$635$	3.32522	−	5.75946i	0.131957	−	0.228557i
$636$	−23.4837	−	7.92524i	−0.931189	−	0.314256i
$637$	9.50867	−	16.4695i	0.376747	−	0.652545i
$638$	15.6963			0.621421
$639$	−26.3220	−	20.0497i	−1.04128	−	0.793153i
$640$	−7.45270	−	12.9085i	−0.294594	−	0.510252i
$641$	11.1741			0.441352			0.220676	−	0.975347i	$-0.429174\pi$
$641$	11.1741			0.441352			0.220676	+	0.975347i	$0.429174\pi$
$642$	−8.77191	+	7.72031i	−0.346200	+	0.304697i
$643$	12.3681	+	21.4221i	0.487749	+	0.844805i	0.999901	−	0.0140895i	$-0.00448498\pi$
$643$	12.3681	+	21.4221i	0.487749	+	0.844805i	−0.512152	+	0.858895i	$0.671152\pi$
$644$	−13.8855	−	24.0504i	−0.547165	−	0.947718i
$645$	5.45055	+	1.83944i	0.214615	+	0.0724280i
$646$	−15.9316	+	63.6098i	−0.626819	+	2.50269i
$647$	−22.5664			−0.887177			−0.443589	−	0.896230i	$-0.646295\pi$
$647$	−22.5664			−0.887177			−0.443589	+	0.896230i	$0.646295\pi$
$648$	36.7234	+	9.56139i	1.44263	+	0.375607i
$649$	−7.36073	+	12.7492i	−0.288934	+	0.500448i
$650$	25.5387	−	44.2343i	1.00171	−	1.73501i
$651$	6.58356	−	5.79431i	0.258030	−	0.227097i
$652$	47.4934			1.85998
$653$	8.52063	−	14.7582i	0.333438	−	0.577532i	−0.649745	−	0.760152i	$-0.725125\pi$
$653$	8.52063	−	14.7582i	0.333438	−	0.577532i	0.983184	+	0.182620i	$0.0584579\pi$
$654$	2.59079	+	12.9052i	0.101308	+	0.504631i
$655$	2.61467	−	4.52874i	0.102164	−	0.176953i
$656$	−7.39238	−	12.8040i	−0.288624	−	0.499912i
$657$	24.9458	+	19.0014i	0.973229	+	0.741317i
$658$	2.25443			0.0878867
$659$	5.29586	−	9.17269i	0.206297	−	0.357317i	−0.744248	−	0.667903i	$-0.767192\pi$
$659$	5.29586	−	9.17269i	0.206297	−	0.357317i	0.950545	+	0.310586i	$0.100525\pi$
$660$	1.01489	+	5.05533i	0.0395045	+	0.196778i
$661$	−12.1927			−0.474241			−0.237120	−	0.971480i	$-0.576204\pi$
$661$	−12.1927			−0.474241			−0.237120	+	0.971480i	$0.576204\pi$
$662$	−23.0151	−	39.8634i	−0.894508	−	1.54933i
$663$	10.1518	+	50.5679i	0.394264	+	1.96389i
$664$	21.2954	+	36.8847i	0.826421	+	1.43140i
$665$	−2.52823	+	10.0944i	−0.0980404	+	0.391445i
$666$	3.37822	−	26.3827i	0.130903	−	1.02231i
$667$	6.61975	−	11.4658i	0.256318	−	0.443956i
$668$	28.9132			1.11869
$669$	28.7801	−	25.3298i	1.11270	−	0.979308i
$670$	−6.42887	−	11.1351i	−0.248369	−	0.430187i
$671$	−13.0923			−0.505423
$672$	−11.9136	−	4.02057i	−0.459576	−	0.155097i
$673$	8.59983	+	14.8953i	0.331499	+	0.574173i	0.982806	−	0.184641i	$-0.0591123\pi$
$673$	8.59983	+	14.8953i	0.331499	+	0.574173i	−0.651307	+	0.758814i	$0.725779\pi$
$674$	2.45018	+	4.24384i	0.0943774	+	0.163466i
$675$	23.2312	−	1.64680i	0.894169	−	0.0633852i
$676$	35.9090			1.38112
$677$	9.95754	+	17.2470i	0.382699	+	0.662855i	0.991447	−	0.130509i	$-0.0416611\pi$
$677$	9.95754	+	17.2470i	0.382699	+	0.662855i	−0.608748	+	0.793364i	$0.708328\pi$
$678$	−11.3388	−	56.4802i	−0.435462	−	2.16911i
$679$	20.4519	+	35.4237i	0.784871	+	1.35944i
$680$	−19.0253			−0.729588
$681$	8.65538	+	2.92100i	0.331675	+	0.111933i
$682$	4.03219			0.154401
$683$	−39.6556			−1.51738			−0.758689	−	0.651453i	$-0.774160\pi$
$683$	−39.6556			−1.51738			−0.758689	+	0.651453i	$0.774160\pi$
$684$	7.38287	+	48.5747i	0.282291	+	1.85730i
$685$	13.2752			0.507218
$686$	−23.8457			−0.910433
$687$	−5.70378	−	28.4115i	−0.217613	−	1.08397i
$688$	12.0102			0.457883
$689$	−9.04419	−	15.6650i	−0.344556	−	0.596789i
$690$	6.31434	+	2.13095i	0.240383	+	0.0811239i
$691$	−3.61123	−	6.25483i	−0.137378	−	0.237945i	0.789126	−	0.614232i	$-0.210534\pi$
$691$	−3.61123	−	6.25483i	−0.137378	−	0.237945i	−0.926503	+	0.376287i	$0.877201\pi$
$692$	12.6239			0.479889
$693$	8.71570	+	6.63882i	0.331082	+	0.252188i
$694$	−11.6719	−	20.2164i	−0.443061	−	0.767404i
$695$	−4.75116	−	8.22925i	−0.180222	−	0.312153i
$696$	8.54126	+	42.5454i	0.323756	+	1.61268i
$697$	35.6189			1.34916
$698$	−18.2812	−	31.6640i	−0.691954	−	1.19850i
$699$	0.444638	+	2.21482i	0.0168178	+	0.0837720i
$700$	55.8633			2.11143
$701$	−0.929426	+	1.60981i	−0.0351039	+	0.0608018i	−0.883044	−	0.469291i	$-0.844510\pi$
$701$	−0.929426	+	1.60981i	−0.0351039	+	0.0608018i	0.847940	+	0.530093i	$0.177843\pi$
$702$	33.1596	+	49.0599i	1.25153	+	1.85165i
$703$	15.4872	−	4.42306i	0.584111	−	0.166819i
$704$	−5.75556	−	9.96892i	−0.216921	−	0.375718i
$705$	−0.265032	+	0.233260i	−0.00998169	+	0.00878506i
$706$	31.9497	+	55.3386i	1.20244	+	2.08269i
$707$	49.8362			1.87428
$708$	−82.4521	−	27.8258i	−3.09874	−	1.04576i
$709$	16.6642	−	28.8632i	0.625836	−	1.08398i	−0.362542	−	0.931967i	$-0.618091\pi$
$709$	16.6642	−	28.8632i	0.625836	−	1.08398i	0.988379	−	0.152013i	$-0.0485755\pi$
$710$	19.0458			0.714776
$711$	4.66116	−	36.4020i	0.174807	−	1.36518i
$712$	−17.8623	−	30.9384i	−0.669417	−	1.15946i
$713$	1.70054	−	2.94542i	0.0636857	−	0.110307i
$714$	−64.8852	+	57.1066i	−2.42827	+	2.13716i
$715$	−1.88153	+	3.25890i	−0.0703652	+	0.121876i
$716$	−65.1998			−2.43663
$717$	−6.54722	−	32.6128i	−0.244510	−	1.21795i
$718$	14.3716	−	24.8924i	0.536345	−	0.928976i
$719$	24.4759	−	42.3936i	0.912799	−	1.58101i	0.102706	−	0.994712i	$-0.467250\pi$
$719$	24.4759	−	42.3936i	0.912799	−	1.58101i	0.810093	−	0.586302i	$-0.199417\pi$
$720$	−5.18345	+	2.16862i	−0.193176	+	0.0808198i
$721$	6.28654			0.234123
$722$	−38.7131	+	24.0763i	−1.44075	+	0.896027i
$723$	−0.610291	−	3.03996i	−0.0226970	−	0.113057i
$724$	−21.9706	−	38.0543i	−0.816533	−	1.41428i
$725$	13.3161	+	23.0642i	0.494548	+	0.856582i
$726$	−8.00662	−	39.8823i	−0.297154	−	1.48017i
$727$	−27.7063			−1.02757			−0.513785	−	0.857919i	$-0.671757\pi$
$727$	−27.7063			−1.02757			−0.513785	+	0.857919i	$0.671757\pi$
$728$	33.2150	+	57.5300i	1.23103	+	2.13220i
$729$	−10.0665	+	25.0533i	−0.372834	+	0.927898i
$730$	−18.0501			−0.668062
$731$	−14.4672	+	25.0579i	−0.535088	+	0.926800i
$732$	−15.2327	−	75.8768i	−0.563018	−	2.80449i
$733$	−12.9206	+	22.3791i	−0.477232	+	0.826591i	−0.999660	−	0.0260931i	$-0.991693\pi$
$733$	−12.9206	+	22.3791i	−0.477232	+	0.826591i	0.522427	+	0.852684i	$0.325027\pi$
$734$	−1.92776	+	3.33898i	−0.0711549	+	0.123244i
$735$	−3.74675	+	3.29758i	−0.138201	+	0.121633i
$736$	−4.87605			−0.179734
$737$	−4.09872	−	7.09918i	−0.150978	−	0.261502i
$738$	37.7253	−	15.7833i	1.38869	−	0.580991i
$739$	12.4245	−	21.5199i	0.457044	−	0.791623i	−0.541759	−	0.840534i	$-0.682242\pi$
$739$	12.4245	−	21.5199i	0.457044	−	0.791623i	0.998803	+	0.0489105i	$0.0155749\pi$
$740$	4.99576	+	8.65291i	0.183648	+	0.318087i
$741$	−19.3766	+	30.1713i	−0.711817	+	1.10837i
$742$	15.1570	−	26.2526i	0.556429	−	0.963764i
$743$	4.14105	+	7.17250i	0.151920	+	0.263134i	0.931933	−	0.362630i	$-0.118121\pi$
$743$	4.14105	+	7.17250i	0.151920	+	0.263134i	−0.780013	+	0.625763i	$0.784788\pi$
$744$	2.19415	+	10.9294i	0.0804415	+	0.400693i
$745$	0.888882	−	1.53959i	0.0325661	−	0.0564062i
$746$	−9.74993	+	16.8874i	−0.356970	+	0.618291i
$747$	−27.9555	+	11.6959i	−1.02284	+	0.427930i
$748$	−25.9347			−0.948266
$749$	−4.66363	−	8.07765i	−0.170405	−	0.295151i
$750$	−21.2892	+	18.7370i	−0.777370	+	0.684177i
$751$	−18.8587			−0.688162			−0.344081	−	0.938940i	$-0.611810\pi$
$751$	−18.8587			−0.688162			−0.344081	+	0.938940i	$0.611810\pi$
$752$	−0.368558	+	0.638361i	−0.0134399	+	0.0232786i
$753$	10.4166	+	3.51539i	0.379603	+	0.128108i
$754$	−33.8571	+	58.6423i	−1.23300	+	2.13562i
$755$	8.48220	−	14.6916i	0.308699	−	0.534682i
$756$	−28.3348	+	58.2362i	−1.03053	+	2.11803i
$757$	−2.76509	+	4.78927i	−0.100499	+	0.174069i	−0.911890	−	0.410434i	$-0.865377\pi$
$757$	−2.76509	+	4.78927i	−0.100499	+	0.174069i	0.811391	+	0.584503i	$0.198711\pi$
$758$	−79.4361			−2.88525
$759$	4.02570	+	1.35859i	0.146124	+	0.0493135i
$760$	−9.50486	−	9.19829i	−0.344778	−	0.333657i
$761$	9.58456	−	16.6009i	0.347440	−	0.601784i	−0.638354	−	0.769743i	$-0.720384\pi$
$761$	9.58456	−	16.6009i	0.347440	−	0.601784i	0.985794	+	0.167959i	$0.0537177\pi$
$762$	36.3881	+	12.2802i	1.31820	+	0.444864i
$763$	−10.5064			−0.380356
$764$	4.59678	+	7.96186i	0.166306	+	0.288050i
$765$	1.71928	−	13.4270i	0.0621608	−	0.485454i
$766$	23.6313	+	40.9306i	0.853833	+	1.47888i
$767$	−31.7545	−	55.0003i	−1.14659	−	1.98595i
$768$	37.4242	−	32.9377i	1.35043	−	1.18854i
$769$	−18.1940			−0.656092			−0.328046	−	0.944662i	$-0.606390\pi$
$769$	−18.1940			−0.656092			−0.328046	+	0.944662i	$0.606390\pi$
$770$	−6.30642			−0.227268
$771$	−31.0041	+	27.2873i	−1.11659	+	0.982728i
$772$	−23.2223	−	40.2223i	−0.835790	−	1.44763i
$773$	26.9898	+	46.7476i	0.970754	+	1.68140i	0.693288	+	0.720660i	$0.256161\pi$
$773$	26.9898	+	46.7476i	0.970754	+	1.68140i	0.277466	+	0.960736i	$0.410505\pi$
$774$	−4.21919	+	32.9504i	−0.151656	+	1.18438i
$775$	3.42075	+	5.92492i	0.122877	+	0.212829i
$776$	−51.9911			−1.86637
$777$	20.1159	+	6.78867i	0.721653	+	0.243542i
$778$	−19.1320	+	33.1376i	−0.685916	+	1.18804i
$779$	17.7948	+	17.2209i	0.637566	+	0.617002i
$780$	−21.0762	−	7.11274i	−0.754647	−	0.254677i
$781$	12.1426			0.434497
$782$	−16.7599	+	29.0290i	−0.599333	+	1.03807i
$783$	−30.7980	+	2.18319i	−1.10063	+	0.0780208i
$784$	−5.21029	+	9.02449i	−0.186082	+	0.322303i
$785$	−2.56338	+	4.43990i	−0.0914909	+	0.158467i
$786$	28.6125	+	9.65609i	1.02057	+	0.344421i
$787$	3.16620	−	5.48402i	0.112863	−	0.195484i	−0.804061	−	0.594547i	$-0.797331\pi$
$787$	3.16620	−	5.48402i	0.112863	−	0.195484i	0.916923	+	0.399063i	$0.130665\pi$
$788$	−20.8372			−0.742296
$789$	−5.89052	+	5.18435i	−0.209708	+	0.184568i
$790$	10.5621	+	18.2942i	0.375784	+	0.650877i
$791$	45.9817			1.63492
$792$	−12.8469	+	5.37481i	−0.456494	+	0.190985i
$793$	28.2404	−	48.9137i	1.00284	−	1.73698i
$794$	28.8289	−	49.9332i	1.02310	−	1.77206i
$795$	0.934425	+	4.65453i	0.0331406	+	0.165079i
$796$	36.9199	+	63.9472i	1.30859	+	2.26655i
$797$	−21.3522	+	36.9831i	−0.756334	+	1.31001i	0.188374	+	0.982097i	$0.439678\pi$
$797$	−21.3522	+	36.9831i	−0.756334	+	1.31001i	−0.944708	+	0.327912i	$0.893655\pi$
$798$	−60.0257	−	2.84055i	−2.12489	−	0.100554i
$799$	−0.887915	−	1.53791i	−0.0314122	−	0.0544075i
$800$	4.90426	−	8.49442i	0.173392	−	0.300323i
$801$	23.4487	−	9.81033i	0.828519	−	0.346631i
$802$	4.53817	+	7.86035i	0.160248	+	0.277558i
$803$	−11.5078			−0.406101
$804$	36.3746	−	32.0140i	1.28283	−	1.12905i
$805$	−2.65967	+	4.60669i	−0.0937412	+	0.162365i
$806$	−8.69751	+	15.0645i	−0.306357	+	0.530625i
$807$	1.64523	+	8.19514i	0.0579147	+	0.288483i
$808$	−31.6724	+	54.8582i	−1.11423	+	1.92990i
$809$	−50.3283			−1.76945			−0.884724	−	0.466115i	$-0.845653\pi$
$809$	−50.3283			−1.76945			−0.884724	+	0.466115i	$0.845653\pi$
$810$	−4.12876	−	14.9829i	−0.145070	−	0.526445i
$811$	−17.0518	−	29.5346i	−0.598770	−	1.03710i	−0.993003	−	0.118089i	$-0.962323\pi$
$811$	−17.0518	−	29.5346i	−0.598770	−	1.03710i	0.394233	−	0.919011i	$-0.371010\pi$
$812$	−74.0590			−2.59896
$813$	−1.15843	−	5.77034i	−0.0406279	−	0.202375i
$814$	4.88044	+	8.45318i	0.171059	+	0.296284i
$815$	−4.54852	−	7.87827i	−0.159328	−	0.275964i
$816$	−5.56270	−	27.7087i	−0.194733	−	0.970000i
$817$	−19.3426	+	5.52414i	−0.676710	+	0.193265i
$818$	65.2326			2.28080
$819$	−43.6030	+	18.2424i	−1.52361	+	0.637440i
$820$	−7.68084	+	13.3036i	−0.268226	+	0.464582i
$821$	21.0954	−	36.5383i	0.736234	−	1.27519i	−0.217946	−	0.975961i	$-0.569936\pi$
$821$	21.0954	−	36.5383i	0.736234	−	1.27519i	0.954180	−	0.299233i	$-0.0967309\pi$
$822$	15.0889	+	75.1605i	0.526287	+	2.62152i
$823$	16.8241			0.586451			0.293225	−	0.956043i	$-0.405271\pi$
$823$	16.8241			0.586451			0.293225	+	0.956043i	$0.405271\pi$
$824$	−3.99528	+	6.92003i	−0.139182	+	0.241071i
$825$	−6.41574	+	5.64661i	−0.223367	+	0.196590i
$826$	53.2166	−	92.1738i	1.85164	−	3.20714i
$827$	2.28586	+	3.95922i	0.0794871	+	0.137676i	0.903029	−	0.429580i	$-0.141338\pi$
$827$	2.28586	+	3.95922i	0.0794871	+	0.137676i	−0.823542	+	0.567256i	$0.808005\pi$
$828$	−3.18986	+	24.9117i	−0.110855	+	0.865742i
$829$	11.6422			0.404351			0.202175	−	0.979349i	$-0.435199\pi$
$829$	11.6422			0.404351			0.202175	+	0.979349i	$0.435199\pi$
$830$	8.72144	−	15.1060i	0.302726	−	0.524336i
$831$	26.2058	+	8.84388i	0.909069	+	0.306791i
$832$	49.6594			1.72163
$833$	−12.5524	−	21.7414i	−0.434916	−	0.753296i
$834$	41.1916	−	36.2535i	1.42635	−	1.25535i
$835$	−2.76907	−	4.79617i	−0.0958276	−	0.165978i
$836$	−12.9567	−	12.5388i	−0.448117	−	0.433664i
$837$	−7.91166	+	0.560836i	−0.273467	+	0.0193853i
$838$	−4.85525	+	8.40955i	−0.167722	+	0.290503i
$839$	−15.0350			−0.519065			−0.259532	−	0.965734i	$-0.583568\pi$
$839$	−15.0350			−0.519065			−0.259532	+	0.965734i	$0.583568\pi$
$840$	−3.43169	−	17.0938i	−0.118405	−	0.589794i
$841$	−3.15340	−	5.46185i	−0.108738	−	0.188339i
$842$	15.9433			0.549443
$843$	−2.57034	−	12.8033i	−0.0885273	−	0.440969i
$844$	−2.52576	−	4.37474i	−0.0869401	−	0.150585i
$845$	−3.43907	−	5.95665i	−0.118308	−	0.204915i
$846$	−1.62190	−	1.23541i	−0.0557620	−	0.0424744i
$847$	32.4690			1.11565
$848$	4.95578	+	8.58366i	0.170182	+	0.294764i
$849$	16.9426	+	5.71776i	0.581469	+	0.196233i
$850$	−33.7137	−	58.3939i	−1.15637	−	2.00289i
$851$	8.23313			0.282228
$852$	14.1278	+	70.3728i	0.484010	+	2.41093i
$853$	43.8506			1.50142			0.750708	−	0.660634i	$-0.229712\pi$
$853$	43.8506			1.50142			0.750708	+	0.660634i	$0.229712\pi$
$854$	94.6548			3.23902
$855$	7.35057	−	5.87676i	0.251384	−	0.200981i
$856$	11.8555			0.405213
$857$	2.77105			0.0946574			0.0473287	−	0.998879i	$-0.484929\pi$
$857$	2.77105			0.0946574			0.0473287	+	0.998879i	$0.484929\pi$
$858$	−20.5897	−	6.94856i	−0.702920	−	0.237220i
$859$	40.1989			1.37157			0.685785	−	0.727804i	$-0.259459\pi$
$859$	40.1989			1.37157			0.685785	+	0.727804i	$0.259459\pi$
$860$	−6.23939	−	10.8069i	−0.212762	−	0.368514i
$861$	6.42476	+	32.0028i	0.218955	+	1.09065i
$862$	−20.5713	−	35.6306i	−0.700662	−	1.21358i
$863$	−17.8546			−0.607779			−0.303890	−	0.952707i	$-0.598285\pi$
$863$	−17.8546			−0.607779			−0.303890	+	0.952707i	$0.598285\pi$
$864$	6.36771	+	9.42109i	0.216634	+	0.320512i
$865$	−1.20901	−	2.09407i	−0.0411077	−	0.0712006i
$866$	19.2458	+	33.3346i	0.653998	+	1.13276i
$867$	36.6131	+	12.3561i	1.24344	+	0.419635i
$868$	−19.0249			−0.645747
$869$	6.73387	+	11.6634i	0.228431	+	0.395654i
$870$	13.3409	−	11.7416i	0.452298	−	0.398076i
$871$	35.3640			1.19826
$872$	6.67710	−	11.5651i	0.226115	−	0.391643i
$873$	4.69833	−	36.6923i	0.159014	−	1.24185i
$874$	−22.4079	+	6.39958i	−0.757958	+	0.216469i
$875$	−11.3185	−	19.6042i	−0.382635	−	0.662743i
$876$	−13.3891	−	66.6936i	−0.452377	−	2.25337i
$877$	23.8261	+	41.2680i	0.804550	+	1.39352i	0.916594	+	0.399819i	$0.130927\pi$
$877$	23.8261	+	41.2680i	0.804550	+	1.39352i	−0.112044	+	0.993703i	$0.535740\pi$
$878$	−16.6986			−0.563550
$879$	−2.64942	−	13.1972i	−0.0893626	−	0.445130i
$880$	1.03099	−	1.78572i	0.0347545	−	0.0601966i
$881$	−40.8685			−1.37689			−0.688447	−	0.725287i	$-0.741707\pi$
$881$	−40.8685			−1.37689			−0.688447	+	0.725287i	$0.741707\pi$
$882$	−22.9287	−	17.4650i	−0.772050	−	0.588077i
$883$	10.7098	+	18.5500i	0.360415	+	0.624257i	0.988029	−	0.154268i	$-0.0493018\pi$
$883$	10.7098	+	18.5500i	0.360415	+	0.624257i	−0.627614	+	0.778525i	$0.715968\pi$
$884$	55.9416	−	96.8937i	1.88152	−	3.25889i
$885$	3.28080	+	16.3422i	0.110283	+	0.549337i
$886$	2.92281	−	5.06246i	0.0981939	−	0.170077i
$887$	−22.8598			−0.767558			−0.383779	−	0.923425i	$-0.625378\pi$
$887$	−22.8598			−0.767558			−0.383779	+	0.923425i	$0.625378\pi$
$888$	−20.2570	+	17.8285i	−0.679780	+	0.598287i
$889$	−15.3271	+	26.5473i	−0.514055	+	0.890369i
$890$	−7.31542	+	12.6707i	−0.245214	+	0.424722i
$891$	−2.63228	−	9.55231i	−0.0881848	−	0.320015i
$892$	−83.1674			−2.78465
$893$	0.299951	−	1.19761i	0.0100375	−	0.0400766i
$894$	9.72709	+	3.28268i	0.325323	+	0.109789i
$895$	6.24430	+	10.8154i	0.208724	+	0.361521i
$896$	34.3521	+	59.4996i	1.14762	+	1.98774i
$897$	−13.7593	+	12.1098i	−0.459408	+	0.404334i
$898$	−61.9258			−2.06649
$899$	−4.53496	−	7.85477i	−0.151249	−	0.261971i
$900$	−40.1896	−	30.6128i	−1.33965	−	1.02043i
$901$	−23.8785			−0.795508
$902$	−7.50355	+	12.9965i	−0.249841	+	0.432737i
$903$	−25.1235	−	8.47863i	−0.836058	−	0.282151i
$904$	−29.2227	+	50.6153i	−0.971934	+	1.68344i
$905$	−4.20833	+	7.28905i	−0.139890	+	0.242296i
$906$	92.8212	+	31.3251i	3.08378	+	1.04071i
$907$	−26.6948			−0.886386			−0.443193	−	0.896426i	$-0.646154\pi$
$907$	−26.6948			−0.886386			−0.443193	+	0.896426i	$0.646154\pi$
$908$	−9.90804	−	17.1612i	−0.328810	−	0.569515i
$909$	−35.8536	−	27.3100i	−1.18919	−	0.905815i
$910$	13.6031	−	23.5612i	0.450937	−	0.781046i
$911$	−4.63769	−	8.03271i	−0.153653	−	0.266135i	0.778915	−	0.627130i	$-0.215771\pi$
$911$	−4.63769	−	8.03271i	−0.153653	−	0.266135i	−0.932568	+	0.360995i	$0.882437\pi$
$912$	10.6174	−	16.5324i	0.351579	−	0.547444i
$913$	5.56034	−	9.63080i	0.184021	−	0.318733i
$914$	−3.58735	−	6.21348i	−0.118659	−	0.205524i
$915$	−11.1277	+	9.79368i	−0.367870	+	0.323769i
$916$	−31.4307	+	54.4396i	−1.03850	+	1.79873i
$917$	−12.0519	+	20.8745i	−0.397989	+	0.689338i
$918$	77.9744	−	5.52739i	2.57354	−	0.182431i
$919$	−14.1549			−0.466926			−0.233463	−	0.972366i	$-0.575006\pi$
$919$	−14.1549			−0.466926			−0.233463	+	0.972366i	$0.575006\pi$
$920$	−3.38060	−	5.85537i	−0.111455	−	0.193046i
$921$	−3.35478	−	16.7107i	−0.110544	−	0.550637i
$922$	33.9271			1.11733
$923$	−26.1919	+	45.3656i	−0.862116	+	1.49323i
$924$	−4.67797	−	23.3017i	−0.153894	−	0.766571i
$925$	−8.28076	+	14.3427i	−0.272270	+	0.471585i
$926$	33.2476	−	57.5865i	1.09258	−	1.89241i
$927$	−4.52272	−	3.44499i	−0.148546	−	0.113148i
$928$	−6.50166	+	11.2612i	−0.213428	+	0.369667i
$929$	−8.29371			−0.272108			−0.136054	−	0.990701i	$-0.543442\pi$
$929$	−8.29371			−0.272108			−0.136054	+	0.990701i	$0.543442\pi$
$930$	3.42712	−	3.01627i	0.112380	−	0.0989074i
$931$	4.24040	−	16.9306i	0.138973	−	0.554878i
$932$	2.45018	−	4.24383i	0.0802583	−	0.139011i
$933$	−8.63067	−	42.9908i	−0.282556	−	1.40746i
$934$	−65.6790			−2.14908
$935$	2.48381	+	4.30208i	0.0812293	+	0.140693i
$936$	7.63035	−	59.5904i	0.249406	−	1.94777i
$937$	17.9166	+	31.0324i	0.585310	+	1.01379i	0.994837	+	0.101488i	$0.0323603\pi$
$937$	17.9166	+	31.0324i	0.585310	+	1.01379i	−0.409527	+	0.912298i	$0.634306\pi$
$938$	29.6329	+	51.3256i	0.967548	+	1.67584i
$939$	7.08129	+	35.2731i	0.231089	+	1.15109i
$940$	0.765879			0.0249802
$941$	−43.5237			−1.41883			−0.709416	−	0.704790i	$-0.751041\pi$
$941$	−43.5237			−1.41883			−0.709416	+	0.704790i	$0.751041\pi$
$942$	−28.0512	−	9.46667i	−0.913958	−	0.308441i
$943$	6.32910	+	10.9623i	0.206104	+	0.356982i
$944$	17.3999	+	30.1375i	0.566319	+	0.980893i
$945$	12.3740	−	0.877158i	0.402525	−	0.0285339i
$946$	−6.09537	−	10.5575i	−0.198178	−	0.343254i
$947$	38.7814			1.26022			0.630112	−	0.776504i	$-0.283009\pi$
$947$	38.7814			1.26022			0.630112	+	0.776504i	$0.283009\pi$
$948$	−59.7607	+	52.5965i	−1.94094	+	1.70826i
$949$	24.8225	−	42.9938i	0.805772	−	1.39564i
$950$	11.3890	−	45.4728i	0.369508	−	1.47533i
$951$	−2.99466	−	14.9169i	−0.0971085	−	0.483714i
$952$	87.6943			2.84219
$953$	29.7666	−	51.5572i	0.964234	−	1.67010i	0.252576	−	0.967577i	$-0.418722\pi$
$953$	29.7666	−	51.5572i	0.964234	−	1.67010i	0.711658	−	0.702526i	$-0.247945\pi$
$954$	−25.2906	+	10.5809i	−0.818815	+	0.342571i
$955$	0.880484	−	1.52504i	0.0284918	−	0.0493492i
$956$	−36.0785	+	62.4898i	−1.16686	+	2.02106i
$957$	8.50546	−	7.48581i	0.274943	−	0.241982i
$958$	38.7798	−	67.1687i	1.25292	−	2.17012i
$959$	−61.1898			−1.97592
$960$	−12.3491	−	4.16756i	−0.398566	−	0.134507i
$961$	14.3350	+	24.8290i	0.462420	+	0.800935i
$962$	−42.1088			−1.35764
$963$	−1.07136	+	8.36694i	−0.0345240	+	0.269621i
$964$	−3.36301	+	5.82491i	−0.108315	+	0.187608i
$965$	−4.44809	+	7.70431i	−0.143189	+	0.248011i
$966$	−29.1050	−	9.82229i	−0.936437	−	0.316027i
$967$	−12.7625	−	22.1054i	−0.410416	−	0.710861i	0.584519	−	0.811380i	$-0.301283\pi$
$967$	−12.7625	−	22.1054i	−0.410416	−	0.710861i	−0.994935	+	0.100519i	$0.967950\pi$
$968$	−20.6350	+	35.7409i	−0.663235	+	1.14876i
$969$	21.7036	+	42.0668i	0.697220	+	1.35138i
$970$	10.6464	+	18.4401i	0.341834	+	0.592075i
$971$	−20.7913	+	36.0116i	−0.667226	+	1.15567i	0.311451	+	0.950262i	$0.399185\pi$
$971$	−20.7913	+	36.0116i	−0.667226	+	1.15567i	−0.978677	+	0.205406i	$0.934148\pi$
$972$	52.2980	−	26.3694i	1.67746	−	0.845800i
$973$	21.8997	+	37.9315i	0.702073	+	1.21603i
$974$	48.1070			1.54145
$975$	−7.25723	−	36.1495i	−0.232417	−	1.15771i
$976$	−15.4743	+	26.8024i	−0.495322	+	0.857923i
$977$	−7.20968	+	12.4875i	−0.230658	+	0.399511i	−0.958002	−	0.286762i	$-0.907421\pi$
$977$	−7.20968	+	12.4875i	−0.230658	+	0.399511i	0.727344	+	0.686273i	$0.240755\pi$
$978$	39.4348	−	34.7072i	1.26098	−	1.10982i
$979$	−4.66394	+	8.07818i	−0.149060	+	0.258180i
$980$	10.8272			0.345862
$981$	7.55858	+	5.75743i	0.241327	+	0.183821i
$982$	−5.63343	−	9.75738i	−0.179770	−	0.311371i
$983$	−42.1627			−1.34478			−0.672391	−	0.740196i	$-0.734733\pi$
$983$	−42.1627			−1.34478			−0.672391	+	0.740196i	$0.734733\pi$
$984$	−39.3108	−	13.2665i	−1.25318	−	0.422921i
$985$	1.99562	+	3.45651i	0.0635857	+	0.110134i
$986$	44.6949	+	77.4138i	1.42337	+	2.46536i
$987$	1.22162	−	1.07517i	0.0388847	−	0.0342232i
$988$	74.7936	−	21.3607i	2.37950	−	0.679574i
$989$	−10.2827			−0.326970
$990$	4.53702	+	3.45589i	0.144196	+	0.109835i
$991$	−7.13801	+	12.3634i	−0.226746	+	0.392736i	−0.956842	−	0.290609i	$-0.906142\pi$
$991$	−7.13801	+	12.3634i	−0.226746	+	0.392736i	0.730095	+	0.683345i	$0.239476\pi$
$992$	−1.67020	+	2.89288i	−0.0530290	+	0.0918489i
$993$	−31.4829	−	10.6248i	−0.999079	−	0.337167i
$994$	−87.7887			−2.78449
$995$	7.07177	−	12.2487i	0.224190	−	0.388309i
$996$	62.2848	+	21.0198i	1.97357	+	0.666037i
$997$	−13.2565	+	22.9609i	−0.419836	+	0.727178i	−0.995923	−	0.0902110i	$-0.971246\pi$
$997$	−13.2565	+	22.9609i	−0.419836	+	0.727178i	0.576086	+	0.817389i	$0.304579\pi$
$998$	25.3927	+	43.9814i	0.803792	+	1.39221i
$999$	−10.7518	−	15.9074i	−0.340171	−	0.503287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.h.c.49.3	yes	32
3.2	odd	2		513.2.h.c.334.14		32
9.2	odd	6		513.2.g.c.505.3		32
9.7	even	3		171.2.g.c.106.14	✓	32
19.7	even	3		171.2.g.c.121.14	yes	32
57.26	odd	6		513.2.g.c.64.3		32
171.7	even	3	inner	171.2.h.c.7.3	yes	32
171.83	odd	6		513.2.h.c.235.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.14	✓	32	9.7	even	3
171.2.g.c.121.14	yes	32	19.7	even	3
171.2.h.c.7.3	yes	32	171.7	even	3	inner
171.2.h.c.49.3	yes	32	1.1	even	1	trivial
513.2.g.c.64.3		32	57.26	odd	6
513.2.g.c.505.3		32	9.2	odd	6
513.2.h.c.235.14		32	171.83	odd	6
513.2.h.c.334.14		32	3.2	odd	2

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.39943 q^{2} +(-1.30020 + 1.14433i) q^{3} +3.75726 q^{4} +(-0.359839 - 0.623259i) q^{5} +(3.11973 - 2.74573i) q^{6} +(1.65862 + 2.87282i) q^{7} -4.21641 q^{8} +(0.381029 - 2.97570i) q^{9} +(0.863408 + 1.49547i) q^{10} +(0.550465 + 0.953433i) q^{11} +(-4.88518 + 4.29953i) q^{12} -4.74945 q^{13} +(-3.97975 - 6.89312i) q^{14} +(1.18107 + 0.398587i) q^{15} +2.60247 q^{16} +(-3.13488 + 5.42977i) q^{17} +(-0.914252 + 7.13999i) q^{18} +(-4.19132 + 1.19702i) q^{19} +(-1.35201 - 2.34175i) q^{20} +(-5.44398 - 1.83723i) q^{21} +(-1.32080 - 2.28769i) q^{22} -2.22814 q^{23} +(5.48217 - 4.82496i) q^{24} +(2.24103 - 3.88158i) q^{25} +11.3960 q^{26} +(2.90977 + 4.30503i) q^{27} +(6.23187 + 10.7939i) q^{28} +(-2.97098 + 5.14588i) q^{29} +(-2.83390 - 0.956381i) q^{30} +(-0.763210 + 1.32192i) q^{31} +2.18839 q^{32} +(-1.80675 - 0.609739i) q^{33} +(7.52192 - 13.0283i) q^{34} +(1.19367 - 2.06750i) q^{35} +(1.43162 - 11.1805i) q^{36} -3.69507 q^{37} +(10.0568 - 2.87216i) q^{38} +(6.17522 - 5.43492i) q^{39} +(1.51723 + 2.62792i) q^{40} +(-2.84053 - 4.91994i) q^{41} +(13.0624 + 4.40829i) q^{42} +4.61491 q^{43} +(2.06824 + 3.58229i) q^{44} +(-1.99175 + 0.833295i) q^{45} +5.34627 q^{46} +(-0.141619 + 0.245291i) q^{47} +(-3.38372 + 2.97807i) q^{48} +(-2.00206 + 3.46767i) q^{49} +(-5.37720 + 9.31358i) q^{50} +(-2.13747 - 10.6471i) q^{51} -17.8449 q^{52} +(1.90426 + 3.29828i) q^{53} +(-6.98178 - 10.3296i) q^{54} +(0.396157 - 0.686164i) q^{55} +(-6.99344 - 12.1130i) q^{56} +(4.07976 - 6.35260i) q^{57} +(7.12864 - 12.3472i) q^{58} +(6.68593 + 11.5804i) q^{59} +(4.43760 + 1.49759i) q^{60} +(-5.94603 + 10.2988i) q^{61} +(1.83127 - 3.17185i) q^{62} +(9.18064 - 3.84094i) q^{63} -10.4558 q^{64} +(1.70904 + 2.96014i) q^{65} +(4.33517 + 1.46303i) q^{66} -7.44592 q^{67} +(-11.7785 + 20.4010i) q^{68} +(2.89702 - 2.54972i) q^{69} +(-2.86414 + 4.96083i) q^{70} +(5.51472 - 9.55177i) q^{71} +(-1.60658 + 12.5468i) q^{72} +(-5.22640 + 9.05239i) q^{73} +8.86605 q^{74} +(1.52802 + 7.61130i) q^{75} +(-15.7479 + 4.49751i) q^{76} +(-1.82603 + 3.16277i) q^{77} +(-14.8170 + 13.0407i) q^{78} +12.2331 q^{79} +(-0.936469 - 1.62201i) q^{80} +(-8.70963 - 2.26766i) q^{81} +(6.81565 + 11.8050i) q^{82} +(-5.05059 - 8.74788i) q^{83} +(-20.4544 - 6.90293i) q^{84} +4.51221 q^{85} -11.0731 q^{86} +(-2.02572 - 10.0904i) q^{87} +(-2.32099 - 4.02007i) q^{88} +(4.23637 + 7.33760i) q^{89} +(4.77905 - 1.99943i) q^{90} +(-7.87754 - 13.6443i) q^{91} -8.37170 q^{92} +(-0.520384 - 2.59212i) q^{93} +(0.339804 - 0.588558i) q^{94} +(2.25425 + 2.18154i) q^{95} +(-2.84534 + 2.50424i) q^{96} +12.3306 q^{97} +(4.80380 - 8.32042i) q^{98} +(3.04688 - 1.27473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + q^{3} + 34 q^{4} + 3 q^{5} - 7 q^{6} + q^{7} - 36 q^{8} + 17 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} + 8 q^{13} + q^{14} - 14 q^{15} + 22 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20}+ \cdots - 49 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + q^3 + 34 * q^4 + 3 * q^5 - 7 * q^6 + q^7 - 36 * q^8 + 17 * q^9 - 8 * q^10 + 7 * q^11 - 3 * q^12 + 8 * q^13 + q^14 - 14 * q^15 + 22 * q^16 - 7 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 8 * q^21 - 8 * q^22 - 10 * q^23 - 39 * q^24 - 9 * q^25 - 4 * q^26 - 5 * q^27 - 10 * q^28 + 10 * q^29 - 5 * q^30 - 10 * q^31 - 34 * q^32 + q^33 - 13 * q^34 - 3 * q^35 - 19 * q^36 + 2 * q^37 - 46 * q^38 + 12 * q^40 + 6 * q^41 + 16 * q^42 - 14 * q^43 + 20 * q^44 - 35 * q^45 - 9 * q^47 - 15 * q^48 - 13 * q^49 + q^50 - 10 * q^51 - 38 * q^52 + 16 * q^53 - 40 * q^54 + 15 * q^55 - 6 * q^56 + 69 * q^57 + 37 * q^59 - 19 * q^60 - 12 * q^61 + 54 * q^62 + 21 * q^63 - 64 * q^64 + 54 * q^65 + 37 * q^66 + 22 * q^67 - 2 * q^68 + 3 * q^69 + 24 * q^70 + 9 * q^71 + 15 * q^72 - 10 * q^73 - 12 * q^74 - 76 * q^75 - 40 * q^76 + 46 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 + 17 * q^81 + 7 * q^82 + 3 * q^83 + 12 * q^84 + 54 * q^85 - 34 * q^86 - 9 * q^87 + 9 * q^88 + 30 * q^89 + 133 * q^90 - q^91 + 34 * q^92 + 27 * q^93 - 18 * q^94 + 3 * q^95 - 5 * q^96 + 18 * q^98 - 49 * q^99

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