LMFDB - Embedded newform 546.4.s.d.127.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(43,546)] 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("546.43"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Character	$\chi$	$=$	546.127
Dual form			546.4.s.d.43.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 + 1.00000i) q^{2} +(1.50000 + 2.59808i) q^{3} +(2.00000 - 3.46410i) q^{4} +9.97677i q^{5} +(-5.19615 - 3.00000i) q^{6} +(6.06218 + 3.50000i) q^{7} +8.00000i q^{8} +(-4.50000 + 7.79423i) q^{9} +(-9.97677 - 17.2803i) q^{10} +(9.88228 - 5.70554i) q^{11} +12.0000 q^{12} +(33.7983 - 32.4757i) q^{13} -14.0000 q^{14} +(-25.9204 + 14.9652i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(63.1324 - 109.348i) q^{17} -18.0000i q^{18} +(126.895 + 73.2629i) q^{19} +(34.5605 + 19.9535i) q^{20} +21.0000i q^{21} +(-11.4111 + 19.7646i) q^{22} +(41.3849 + 71.6807i) q^{23} +(-20.7846 + 12.0000i) q^{24} +25.4641 q^{25} +(-26.0647 + 90.0479i) q^{26} -27.0000 q^{27} +(24.2487 - 14.0000i) q^{28} +(-146.853 - 254.356i) q^{29} +(29.9303 - 51.8408i) q^{30} +181.671i q^{31} +(27.7128 + 16.0000i) q^{32} +(29.6468 + 17.1166i) q^{33} +252.530i q^{34} +(-34.9187 + 60.4809i) q^{35} +(18.0000 + 31.1769i) q^{36} +(357.675 - 206.504i) q^{37} -293.052 q^{38} +(135.072 + 39.0970i) q^{39} -79.8142 q^{40} +(-303.985 + 175.506i) q^{41} +(-21.0000 - 36.3731i) q^{42} +(102.806 - 178.065i) q^{43} -45.6443i q^{44} +(-77.7612 - 44.8955i) q^{45} +(-143.361 - 82.7697i) q^{46} -26.1769i q^{47} +(24.0000 - 41.5692i) q^{48} +(24.5000 + 42.4352i) q^{49} +(-44.1051 + 25.4641i) q^{50} +378.794 q^{51} +(-44.9026 - 182.032i) q^{52} +315.764 q^{53} +(46.7654 - 27.0000i) q^{54} +(56.9228 + 98.5932i) q^{55} +(-28.0000 + 48.4974i) q^{56} +439.578i q^{57} +(508.712 + 293.705i) q^{58} +(374.876 + 216.435i) q^{59} +119.721i q^{60} +(-104.285 + 180.626i) q^{61} +(-181.671 - 314.664i) q^{62} +(-54.5596 + 31.5000i) q^{63} -64.0000 q^{64} +(324.003 + 337.198i) q^{65} -68.4665 q^{66} +(93.4865 - 53.9745i) q^{67} +(-252.530 - 437.394i) q^{68} +(-124.155 + 215.042i) q^{69} -139.675i q^{70} +(-840.562 - 485.298i) q^{71} +(-62.3538 - 36.0000i) q^{72} +301.887i q^{73} +(-413.008 + 715.351i) q^{74} +(38.1961 + 66.1576i) q^{75} +(507.581 - 293.052i) q^{76} +79.8775 q^{77} +(-273.048 + 67.3539i) q^{78} -979.292 q^{79} +(138.242 - 79.8142i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(351.012 - 607.970i) q^{82} +521.290i q^{83} +(72.7461 + 42.0000i) q^{84} +(1090.94 + 629.857i) q^{85} +411.224i q^{86} +(440.558 - 763.068i) q^{87} +(45.6443 + 79.0583i) q^{88} +(-55.4447 + 32.0110i) q^{89} +179.582 q^{90} +(318.557 - 78.5795i) q^{91} +331.079 q^{92} +(-471.996 + 272.507i) q^{93} +(26.1769 + 45.3398i) q^{94} +(-730.928 + 1266.00i) q^{95} +96.0000i q^{96} +(264.760 + 152.859i) q^{97} +(-84.8705 - 49.0000i) q^{98} +102.700i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{3} + 48 q^{4} - 108 q^{9} - 24 q^{10} - 174 q^{11} + 288 q^{12} - 96 q^{13} - 336 q^{14} - 90 q^{15} - 192 q^{16} + 140 q^{17} - 60 q^{19} + 120 q^{20} - 128 q^{22} + 34 q^{23} - 1004 q^{25}+ \cdots - 3936 q^{97}+O(q^{100}) $ 24 * q + 36 * q^3 + 48 * q^4 - 108 * q^9 - 24 * q^10 - 174 * q^11 + 288 * q^12 - 96 * q^13 - 336 * q^14 - 90 * q^15 - 192 * q^16 + 140 * q^17 - 60 * q^19 + 120 * q^20 - 128 * q^22 + 34 * q^23 - 1004 * q^25 - 144 * q^26 - 648 * q^27 + 54 * q^29 + 72 * q^30 - 522 * q^33 - 84 * q^35 + 432 * q^36 + 1416 * q^37 + 1056 * q^38 + 108 * q^39 - 192 * q^40 - 942 * q^41 - 504 * q^42 + 762 * q^43 - 270 * q^45 + 636 * q^46 + 576 * q^48 + 588 * q^49 + 720 * q^50 + 840 * q^51 - 528 * q^52 + 184 * q^53 - 256 * q^55 - 672 * q^56 - 2088 * q^58 + 2322 * q^59 - 1274 * q^61 - 232 * q^62 - 1536 * q^64 - 1298 * q^65 - 768 * q^66 - 2472 * q^67 - 560 * q^68 - 102 * q^69 - 2196 * q^71 - 348 * q^74 - 1506 * q^75 - 240 * q^76 + 896 * q^77 - 468 * q^78 - 520 * q^79 + 480 * q^80 - 972 * q^81 - 244 * q^82 + 7974 * q^85 - 162 * q^87 + 512 * q^88 + 1032 * q^89 + 432 * q^90 + 546 * q^91 + 272 * q^92 - 2880 * q^93 - 1104 * q^94 - 2574 * q^95 - 3936 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$			9.97677i			0.892349i	0.894946	+	0.446175i	$0.147214\pi$
$5$			9.97677i			0.892349i	−0.894946	+	0.446175i	$0.852786\pi$
$6$	−5.19615	−	3.00000i	−0.353553	−	0.204124i
$7$	6.06218	+	3.50000i	0.327327	+	0.188982i
$7$	6.06218	+	3.50000i	0.327327	+	0.188982i
$8$			8.00000i			0.353553i
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−9.97677	−	17.2803i	−0.315493	−	0.546450i
$11$	9.88228	−	5.70554i	0.270875	−	0.156389i	−0.358410	−	0.933564i	$-0.616681\pi$
$11$	9.88228	−	5.70554i	0.270875	−	0.156389i	0.629285	+	0.777175i	$0.283348\pi$
$12$	12.0000			0.288675
$13$	33.7983	−	32.4757i	0.721075	−	0.692858i
$13$	33.7983	−	32.4757i	0.721075	−	0.692858i
$14$	−14.0000			−0.267261
$15$	−25.9204	+	14.9652i	−0.446175	+	0.257599i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	63.1324	−	109.348i	0.900697	−	1.56005i	0.0741058	−	0.997250i	$-0.476390\pi$
$17$	63.1324	−	109.348i	0.900697	−	1.56005i	0.826591	−	0.562803i	$-0.190277\pi$
$18$		−	18.0000i		−	0.235702i
$19$	126.895	+	73.2629i	1.53220	+	0.884614i	0.999260	+	0.0384593i	$0.0122450\pi$
$19$	126.895	+	73.2629i	1.53220	+	0.884614i	0.532937	+	0.846155i	$0.321088\pi$
$20$	34.5605	+	19.9535i	0.386399	+	0.223087i
$21$			21.0000i			0.218218i
$22$	−11.4111	+	19.7646i	−0.110584	+	0.191537i
$23$	41.3849	+	71.6807i	0.375189	+	0.649846i	0.990355	−	0.138551i	$-0.0442446\pi$
$23$	41.3849	+	71.6807i	0.375189	+	0.649846i	−0.615166	+	0.788397i	$0.710911\pi$
$24$	−20.7846	+	12.0000i	−0.176777	+	0.102062i
$25$	25.4641			0.203713
$26$	−26.0647	+	90.0479i	−0.196604	+	0.679225i
$27$	−27.0000			−0.192450
$28$	24.2487	−	14.0000i	0.163663	−	0.0944911i
$29$	−146.853	−	254.356i	−0.940339	−	1.62872i	−0.764825	−	0.644238i	$-0.777174\pi$
$29$	−146.853	−	254.356i	−0.940339	−	1.62872i	−0.175514	−	0.984477i	$-0.556159\pi$
$30$	29.9303	−	51.8408i	0.182150	−	0.315493i
$31$			181.671i			1.05255i	0.850314	+	0.526276i	$0.176412\pi$
$31$			181.671i			1.05255i	−0.850314	+	0.526276i	$0.823588\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$	29.6468	+	17.1166i	0.156389	+	0.0902915i
$34$			252.530i			1.27378i
$35$	−34.9187	+	60.4809i	−0.168638	+	0.292090i
$36$	18.0000	+	31.1769i	0.0833333	+	0.144338i
$37$	357.675	−	206.504i	1.58923	−	0.917542i	0.595795	−	0.803137i	$-0.296837\pi$
$37$	357.675	−	206.504i	1.58923	−	0.917542i	0.993434	−	0.114405i	$-0.0364962\pi$
$38$	−293.052			−1.25103
$39$	135.072	+	39.0970i	0.554585	+	0.160527i
$40$	−79.8142			−0.315493
$41$	−303.985	+	175.506i	−1.15791	+	0.668522i	−0.950803	−	0.309796i	$-0.899739\pi$
$41$	−303.985	+	175.506i	−1.15791	+	0.668522i	−0.207111	+	0.978317i	$0.566406\pi$
$42$	−21.0000	−	36.3731i	−0.0771517	−	0.133631i
$43$	102.806	−	178.065i	0.364599	−	0.631505i	−0.624112	−	0.781335i	$-0.714539\pi$
$43$	102.806	−	178.065i	0.364599	−	0.631505i	0.988712	+	0.149830i	$0.0478726\pi$
$44$		−	45.6443i		−	0.156389i
$45$	−77.7612	−	44.8955i	−0.257599	−	0.148725i
$46$	−143.361	−	82.7697i	−0.459511	−	0.265299i
$47$		−	26.1769i		−	0.0812404i	−0.999175	−	0.0406202i	$-0.987067\pi$
$47$		−	26.1769i		−	0.0812404i	0.999175	−	0.0406202i	$-0.0129334\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	24.5000	+	42.4352i	0.0714286	+	0.123718i
$50$	−44.1051	+	25.4641i	−0.124748	+	0.0720233i
$51$	378.794			1.04004
$52$	−44.9026	−	182.032i	−0.119747	−	0.485449i
$53$	315.764			0.818368			0.409184	−	0.912452i	$-0.365813\pi$
$53$	315.764			0.818368			0.409184	+	0.912452i	$0.365813\pi$
$54$	46.7654	−	27.0000i	0.117851	−	0.0680414i
$55$	56.9228	+	98.5932i	0.139554	+	0.241715i
$56$	−28.0000	+	48.4974i	−0.0668153	+	0.115728i
$57$			439.578i			1.02146i
$58$	508.712	+	293.705i	1.15168	+	0.664920i
$59$	374.876	+	216.435i	0.827197	+	0.477583i	0.852892	−	0.522087i	$-0.174846\pi$
$59$	374.876	+	216.435i	0.827197	+	0.477583i	−0.0256947	+	0.999670i	$0.508180\pi$
$60$			119.721i			0.257599i
$61$	−104.285	+	180.626i	−0.218890	+	0.379129i	−0.954469	−	0.298310i	$-0.903577\pi$
$61$	−104.285	+	180.626i	−0.218890	+	0.379129i	0.735579	+	0.677439i	$0.236910\pi$
$62$	−181.671	−	314.664i	−0.372133	−	0.644554i
$63$	−54.5596	+	31.5000i	−0.109109	+	0.0629941i
$64$	−64.0000			−0.125000
$65$	324.003	+	337.198i	0.618271	+	0.643450i
$66$	−68.4665			−0.127691
$67$	93.4865	−	53.9745i	0.170466	−	0.0984184i	−0.412340	−	0.911030i	$-0.635288\pi$
$67$	93.4865	−	53.9745i	0.170466	−	0.0984184i	0.582805	+	0.812612i	$0.301955\pi$
$68$	−252.530	−	437.394i	−0.450349	−	0.780027i
$69$	−124.155	+	215.042i	−0.216615	+	0.375189i
$70$		−	139.675i		−	0.238490i
$71$	−840.562	−	485.298i	−1.40502	−	0.811188i	−0.410116	−	0.912033i	$-0.634512\pi$
$71$	−840.562	−	485.298i	−1.40502	−	0.811188i	−0.994902	+	0.100845i	$0.967845\pi$
$72$	−62.3538	−	36.0000i	−0.102062	−	0.0589256i
$73$			301.887i			0.484016i	0.970274	+	0.242008i	$0.0778060\pi$
$73$			301.887i			0.484016i	−0.970274	+	0.242008i	$0.922194\pi$
$74$	−413.008	+	715.351i	−0.648800	+	1.12375i
$75$	38.1961	+	66.1576i	0.0588068	+	0.101856i
$76$	507.581	−	293.052i	0.766098	−	0.442307i
$77$	79.8775			0.118219
$78$	−273.048	+	67.3539i	−0.396367	+	0.0977734i
$79$	−979.292			−1.39467			−0.697335	−	0.716745i	$-0.745631\pi$
$79$	−979.292			−1.39467			−0.697335	+	0.716745i	$0.745631\pi$
$80$	138.242	−	79.8142i	0.193199	−	0.111544i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	351.012	−	607.970i	0.472716	−	0.818769i
$83$			521.290i			0.689386i	0.938715	+	0.344693i	$0.112017\pi$
$83$			521.290i			0.689386i	−0.938715	+	0.344693i	$0.887983\pi$
$84$	72.7461	+	42.0000i	0.0944911	+	0.0545545i
$85$	1090.94	+	629.857i	1.39211	+	0.803736i
$86$			411.224i			0.515622i
$87$	440.558	−	763.068i	0.542905	−	0.940339i
$88$	45.6443	+	79.0583i	0.0552920	+	0.0957686i
$89$	−55.4447	+	32.0110i	−0.0660351	+	0.0381254i	−0.532654	−	0.846333i	$-0.678805\pi$
$89$	−55.4447	+	32.0110i	−0.0660351	+	0.0381254i	0.466619	+	0.884458i	$0.345472\pi$
$90$	179.582			0.210329
$91$	318.557	−	78.5795i	0.366965	−	0.0905206i
$92$	331.079			0.375189
$93$	−471.996	+	272.507i	−0.526276	+	0.303846i
$94$	26.1769	+	45.3398i	0.0287228	+	0.0497494i
$95$	−730.928	+	1266.00i	−0.789385	+	1.36726i
$96$			96.0000i			0.102062i
$97$	264.760	+	152.859i	0.277137	+	0.160005i	0.632127	−	0.774865i	$-0.282182\pi$
$97$	264.760	+	152.859i	0.277137	+	0.160005i	−0.354989	+	0.934870i	$0.615516\pi$
$98$	−84.8705	−	49.0000i	−0.0874818	−	0.0505076i
$99$			102.700i			0.104260i
$100$	50.9281	−	88.2101i	0.0509281	−	0.0882101i
$101$	659.768	+	1142.75i	0.649994	+	1.12582i	0.983124	+	0.182941i	$0.0585619\pi$
$101$	659.768	+	1142.75i	0.649994	+	1.12582i	−0.333130	+	0.942881i	$0.608105\pi$
$102$	−656.091	+	378.794i	−0.636889	+	0.367708i
$103$	1024.22			0.979804			0.489902	−	0.871778i	$-0.337033\pi$
$103$	1024.22			0.979804			0.489902	+	0.871778i	$0.337033\pi$
$104$	259.806	+	270.387i	0.244962	+	0.254938i
$105$	−209.512			−0.194727
$106$	−546.919	+	315.764i	−0.501146	+	0.289337i
$107$	323.569	+	560.438i	0.292342	+	0.506351i	0.974363	−	0.224981i	$-0.0722321\pi$
$107$	323.569	+	560.438i	0.292342	+	0.506351i	−0.682021	+	0.731332i	$0.738899\pi$
$108$	−54.0000	+	93.5307i	−0.0481125	+	0.0833333i
$109$		−	770.087i		−	0.676706i	−0.941019	−	0.338353i	$-0.890130\pi$
$109$		−	770.087i		−	0.676706i	0.941019	−	0.338353i	$-0.109870\pi$
$110$	−197.186	−	113.846i	−0.170918	−	0.0986796i
$111$	1073.03	+	619.512i	0.917542	+	0.529743i
$112$		−	112.000i		−	0.0944911i
$113$	−568.441	+	984.569i	−0.473225	+	0.819650i	−0.999530	−	0.0306455i	$-0.990244\pi$
$113$	−568.441	+	984.569i	−0.473225	+	0.819650i	0.526305	+	0.850296i	$0.323577\pi$
$114$	−439.578	−	761.371i	−0.361142	−	0.625517i
$115$	−715.142	+	412.887i	−0.579890	+	0.334799i
$116$	−1174.82			−0.940339
$117$	101.031	+	409.573i	0.0798317	+	0.323633i
$118$	−865.738			−0.675404
$119$	765.439	−	441.927i	0.589645	−	0.340431i
$120$	−119.721	−	207.363i	−0.0910750	−	0.157747i
$121$	−600.394	+	1039.91i	−0.451085	+	0.781302i
$122$		−	417.139i		−	0.309557i
$123$	−911.955	−	526.517i	−0.668522	−	0.385971i
$124$	629.327	+	363.342i	0.455768	+	0.263138i
$125$			1501.15i			1.07413i
$126$	63.0000	−	109.119i	0.0445435	−	0.0771517i
$127$	650.749	+	1127.13i	0.454682	+	0.787533i	0.998670	−	0.0515604i	$-0.0164195\pi$
$127$	650.749	+	1127.13i	0.454682	+	0.787533i	−0.543988	+	0.839093i	$0.683086\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$	616.836			0.421003
$130$	−898.388	−	260.041i	−0.606106	−	0.175439i
$131$	−1229.60			−0.820084			−0.410042	−	0.912067i	$-0.634486\pi$
$131$	−1229.60			−0.820084			−0.410042	+	0.912067i	$0.634486\pi$
$132$	118.587	−	68.4665i	0.0781947	−	0.0451458i
$133$	512.841	+	888.266i	0.334353	+	0.579116i
$134$	−107.949	+	186.973i	−0.0695923	+	0.120537i
$135$		−	269.373i		−	0.171733i
$136$	874.788	+	505.059i	0.551562	+	0.318445i
$137$	−1388.34	−	801.560i	−0.865797	−	0.499868i	0.000152478	−	1.00000i	$-0.499951\pi$
$137$	−1388.34	−	801.560i	−0.865797	−	0.499868i	−0.865949	+	0.500132i	$0.833285\pi$
$138$		−	496.618i		−	0.306340i
$139$	161.339	−	279.447i	0.0984500	−	0.170520i	−0.812593	−	0.582831i	$-0.801945\pi$
$139$	161.339	−	279.447i	0.0984500	−	0.170520i	0.911043	+	0.412311i	$0.135278\pi$
$140$	139.675	+	241.924i	0.0843191	+	0.146045i
$141$	68.0097	−	39.2654i	0.0406202	−	0.0234521i
$142$	1941.19			1.14719
$143$	148.713	−	513.772i	0.0869651	−	0.300446i
$144$	144.000			0.0833333
$145$	2537.65	−	1465.11i	1.45338	−	0.839111i
$146$	−301.887	−	522.883i	−0.171125	−	0.296398i
$147$	−73.5000	+	127.306i	−0.0412393	+	0.0714286i
$148$		−	1652.03i		−	0.917542i
$149$	1399.00	+	807.714i	0.769199	+	0.444097i	0.832589	−	0.553892i	$-0.186858\pi$
$149$	1399.00	+	807.714i	0.769199	+	0.444097i	−0.0633898	+	0.997989i	$0.520191\pi$
$150$	−132.315	−	76.3922i	−0.0720233	−	0.0415827i
$151$			728.285i			0.392497i	0.980554	+	0.196248i	$0.0628759\pi$
$151$			728.285i			0.392497i	−0.980554	+	0.196248i	$0.937124\pi$
$152$	−586.104	+	1015.16i	−0.312758	+	0.541713i
$153$	568.191	+	984.136i	0.300232	+	0.520018i
$154$	−138.352	+	79.8775i	−0.0723943	+	0.0417969i
$155$	−1812.49			−0.939244
$156$	405.580	−	389.709i	0.208156	−	0.200011i
$157$	−1721.25			−0.874971			−0.437486	−	0.899225i	$-0.644131\pi$
$157$	−1721.25			−0.874971			−0.437486	+	0.899225i	$0.644131\pi$
$158$	1696.18	−	979.292i	0.854057	−	0.493090i
$159$	473.646	+	820.379i	0.236243	+	0.409184i
$160$	−159.628	+	276.484i	−0.0788733	+	0.136613i
$161$			579.388i			0.283616i
$162$	140.296	+	81.0000i	0.0680414	+	0.0392837i
$163$	1845.18	+	1065.31i	0.886658	+	0.511912i	0.872848	−	0.487992i	$-0.162271\pi$
$163$	1845.18	+	1065.31i	0.886658	+	0.511912i	0.0138103	+	0.999905i	$0.495604\pi$
$164$			1404.05i			0.668522i
$165$	−170.769	+	295.780i	−0.0805716	+	0.139554i
$166$	−521.290	−	902.902i	−0.243735	−	0.422161i
$167$	−1884.65	+	1088.10i	−0.873285	+	0.504191i	−0.868439	−	0.495797i	$-0.834876\pi$
$167$	−1884.65	+	1088.10i	−0.873285	+	0.504191i	−0.00484671	+	0.999988i	$0.501543\pi$
$168$	−168.000			−0.0771517
$169$	87.6535	−	2195.25i	0.0398969	−	0.999204i
$170$	−2519.43			−1.13666
$171$	−1142.06	+	659.367i	−0.510732	+	0.294871i
$172$	−411.224	−	712.261i	−0.182300	−	0.315752i
$173$	2101.32	−	3639.59i	0.923470	−	1.59950i	0.129465	−	0.991584i	$-0.458674\pi$
$173$	2101.32	−	3639.59i	0.923470	−	1.59950i	0.794004	−	0.607912i	$-0.207993\pi$
$174$			1762.23i			0.767784i
$175$	154.368	+	89.1243i	0.0666806	+	0.0384981i
$176$	−158.117	−	91.2886i	−0.0677186	−	0.0390974i
$177$			1298.61i			0.551465i
$178$	64.0220	−	110.889i	0.0269587	−	0.0466939i
$179$	1446.08	+	2504.68i	0.603826	+	1.04586i	0.992236	+	0.124370i	$0.0396911\pi$
$179$	1446.08	+	2504.68i	0.603826	+	1.04586i	−0.388410	+	0.921487i	$0.626976\pi$
$180$	−311.045	+	179.582i	−0.128800	+	0.0743624i
$181$	−410.881			−0.168732			−0.0843662	−	0.996435i	$-0.526887\pi$
$181$	−410.881			−0.168732			−0.0843662	+	0.996435i	$0.526887\pi$
$182$	−473.177	+	454.660i	−0.192715	+	0.185174i
$183$	−625.708			−0.252752
$184$	−573.446	+	331.079i	−0.229755	+	0.132649i
$185$	2060.24	+	3568.44i	0.818768	+	1.41815i
$186$	545.013	−	943.991i	0.214851	−	0.372133i
$187$		−	1440.82i		−	0.563438i
$188$	−90.6796	−	52.3539i	−0.0351781	−	0.0203101i
$189$	−163.679	−	94.5000i	−0.0629941	−	0.0363696i
$190$		−	2923.71i		−	1.11636i
$191$	1445.27	−	2503.29i	0.547520	−	0.948332i	−0.450924	−	0.892562i	$-0.648905\pi$
$191$	1445.27	−	2503.29i	0.547520	−	0.948332i	0.998444	−	0.0557698i	$-0.0177613\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	−831.236	+	479.914i	−0.310019	+	0.178990i	−0.646935	−	0.762545i	$-0.723949\pi$
$193$	−831.236	+	479.914i	−0.310019	+	0.178990i	0.336916	+	0.941535i	$0.390616\pi$
$194$	−611.438			−0.226282
$195$	−390.062	+	1347.58i	−0.143246	+	0.494884i
$196$	196.000			0.0714286
$197$	−125.232	+	72.3026i	−0.0452914	+	0.0261490i	−0.522475	−	0.852655i	$-0.674991\pi$
$197$	−125.232	+	72.3026i	−0.0452914	+	0.0261490i	0.477183	+	0.878804i	$0.341658\pi$
$198$	−102.700	−	177.881i	−0.0368614	−	0.0638457i
$199$	2446.61	−	4237.65i	0.871536	−	1.50954i	0.0111278	−	0.999938i	$-0.496458\pi$
$199$	2446.61	−	4237.65i	0.871536	−	1.50954i	0.860408	−	0.509606i	$-0.170209\pi$
$200$			203.713i			0.0720233i
$201$	280.460	+	161.923i	0.0984184	+	0.0568219i
$202$	−2285.50	−	1319.54i	−0.796077	−	0.459615i
$203$		−	2055.94i		−	0.710830i
$204$	757.589	−	1312.18i	0.260009	−	0.450349i
$205$	−1750.98	−	3032.79i	−0.596555	−	1.03326i
$206$	−1774.01	+	1024.22i	−0.600005	+	0.346413i
$207$	−744.928			−0.250126
$208$	−720.384	−	208.517i	−0.240142	−	0.0695100i
$209$	1672.02			0.553378
$210$	362.886	−	209.512i	0.119245	−	0.0688462i
$211$	−1956.97	−	3389.58i	−0.638501	−	1.10592i	−0.985762	−	0.168147i	$-0.946222\pi$
$211$	−1956.97	−	3389.58i	−0.638501	−	1.10592i	0.347261	−	0.937768i	$-0.387112\pi$
$212$	631.528	−	1093.84i	0.204592	−	0.354364i
$213$		−	2911.79i		−	0.936679i
$214$	−1120.88	−	647.138i	−0.358044	−	0.206717i
$215$	1776.52	+	1025.67i	0.563523	+	0.325350i
$216$		−	216.000i		−	0.0680414i
$217$	−635.849	+	1101.32i	−0.198914	+	0.344528i
$218$	770.087	+	1333.83i	0.239252	+	0.414396i
$219$	−784.324	+	452.830i	−0.242008	+	0.139723i
$220$	455.383			0.139554
$221$	−1417.40	−	5746.07i	−0.431425	−	1.74897i
$222$	−2478.05			−0.749170
$223$	3810.93	−	2200.24i	1.14439	−	0.660713i	0.196875	−	0.980429i	$-0.436921\pi$
$223$	3810.93	−	2200.24i	1.14439	−	0.660713i	0.947514	+	0.319716i	$0.103587\pi$
$224$	112.000	+	193.990i	0.0334077	+	0.0578638i
$225$	−114.588	+	198.473i	−0.0339521	+	0.0588068i
$226$		−	2273.77i		−	0.669242i
$227$	−1649.28	−	952.213i	−0.482232	−	0.278417i	0.239114	−	0.970991i	$-0.423143\pi$
$227$	−1649.28	−	952.213i	−0.482232	−	0.278417i	−0.721346	+	0.692575i	$0.756476\pi$
$228$	1522.74	+	879.155i	0.442307	+	0.255366i
$229$		−	4405.70i		−	1.27134i	−0.771960	−	0.635671i	$-0.780724\pi$
$229$		−	4405.70i		−	1.27134i	0.771960	−	0.635671i	$-0.219276\pi$
$230$	825.775	−	1430.28i	0.236739	−	0.410044i
$231$	119.816	+	207.528i	0.0341270	+	0.0591097i
$232$	2034.85	−	1174.82i	0.575838	−	0.332460i
$233$	−5113.64			−1.43779			−0.718896	−	0.695117i	$-0.755352\pi$
$233$	−5113.64			−1.43779			−0.718896	+	0.695117i	$0.755352\pi$
$234$	−584.563	−	608.370i	−0.163308	−	0.169959i
$235$	261.161			0.0724948
$236$	1499.50	−	865.738i	0.413599	−	0.238791i
$237$	−1468.94	−	2544.27i	−0.402607	−	0.697335i
$238$	−883.853	+	1530.88i	−0.240721	+	0.416942i
$239$			1843.52i			0.498944i	0.968382	+	0.249472i	$0.0802571\pi$
$239$			1843.52i			0.498944i	−0.968382	+	0.249472i	$0.919743\pi$
$240$	414.727	+	239.442i	0.111544	+	0.0643998i
$241$	3611.14	+	2084.89i	0.965203	+	0.557260i	0.897771	−	0.440463i	$-0.145186\pi$
$241$	3611.14	+	2084.89i	0.965203	+	0.557260i	0.0674327	+	0.997724i	$0.478519\pi$
$242$		−	2401.57i		−	0.637930i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	417.139	+	722.506i	0.109445	+	0.189564i
$245$	−423.367	+	244.431i	−0.110400	+	0.0637392i
$246$	2106.07			0.545846
$247$	6668.11	−	1644.85i	1.71774	−	0.423721i
$248$	−1453.37			−0.372133
$249$	−1354.35	+	781.936i	−0.344693	+	0.199009i
$250$	−1501.15	−	2600.06i	−0.379763	−	0.657769i
$251$	−372.593	+	645.351i	−0.0936967	+	0.162288i	−0.909064	−	0.416657i	$-0.863202\pi$
$251$	−372.593	+	645.351i	−0.0936967	+	0.162288i	0.815367	+	0.578944i	$0.196535\pi$
$252$			252.000i			0.0629941i
$253$	817.954	+	472.246i	0.203258	+	0.117351i
$254$	−2254.26	−	1301.50i	−0.556870	−	0.321509i
$255$			3779.14i			0.928075i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2565.23	−	4443.11i	−0.622625	−	1.07842i	−0.988995	−	0.147949i	$-0.952733\pi$
$257$	−2565.23	−	4443.11i	−0.622625	−	1.07842i	0.366369	−	0.930469i	$-0.380601\pi$
$258$	−1068.39	+	616.836i	−0.257811	+	0.148847i
$259$	2891.06			0.693596
$260$	1816.09	−	447.983i	0.433190	−	0.106857i
$261$	2643.35			0.626893
$262$	2129.74	−	1229.60i	0.502197	−	0.289943i
$263$	465.404	+	806.103i	0.109118	+	0.188998i	0.915413	−	0.402515i	$-0.131864\pi$
$263$	465.404	+	806.103i	0.109118	+	0.188998i	−0.806295	+	0.591513i	$0.798531\pi$
$264$	−136.933	+	237.175i	−0.0319229	+	0.0552920i
$265$			3150.30i			0.730270i
$266$	−1776.53	−	1025.68i	−0.409497	−	0.236423i
$267$	−166.334	−	96.0330i	−0.0381254	−	0.0220117i
$268$		−	431.796i		−	0.0984184i
$269$	−1211.73	+	2098.78i	−0.274649	+	0.475707i	−0.970047	−	0.242919i	$-0.921895\pi$
$269$	−1211.73	+	2098.78i	−0.274649	+	0.475707i	0.695397	+	0.718626i	$0.255228\pi$
$270$	269.373	+	466.567i	0.0607167	+	0.105164i
$271$	4123.54	−	2380.73i	0.924307	−	0.533649i	0.0393005	−	0.999227i	$-0.487487\pi$
$271$	4123.54	−	2380.73i	0.924307	−	0.533649i	0.885007	+	0.465579i	$0.154154\pi$
$272$	−2020.24			−0.450349
$273$	681.990	+	709.765i	0.151194	+	0.157351i
$274$	3206.24			0.706920
$275$	251.643	−	145.286i	0.0551806	−	0.0318585i
$276$	496.618	+	860.168i	0.108308	+	0.187594i
$277$	−4046.65	+	7009.00i	−0.877760	+	1.52032i	−0.0239663	+	0.999713i	$0.507629\pi$
$277$	−4046.65	+	7009.00i	−0.877760	+	1.52032i	−0.853794	+	0.520612i	$0.825704\pi$
$278$			645.354i			0.139229i
$279$	−1415.99	−	817.520i	−0.303846	−	0.175425i
$280$	−483.848	−	279.350i	−0.103269	−	0.0596226i
$281$		−	6772.18i		−	1.43770i	−0.695164	−	0.718851i	$-0.744668\pi$
$281$		−	6772.18i		−	1.43770i	0.695164	−	0.718851i	$-0.255332\pi$
$282$	−78.5308	+	136.019i	−0.0165831	+	0.0287228i
$283$	−1314.49	−	2276.76i	−0.276106	−	0.478230i	0.694307	−	0.719679i	$-0.255711\pi$
$283$	−1314.49	−	2276.76i	−0.276106	−	0.478230i	−0.970414	+	0.241448i	$0.922378\pi$
$284$	−3362.25	+	1941.19i	−0.702509	+	0.405594i
$285$	−4385.57			−0.911503
$286$	256.193	+	1038.59i	0.0529687	+	0.214732i
$287$	−2457.08			−0.505355
$288$	−249.415	+	144.000i	−0.0510310	+	0.0294628i
$289$	−5514.89	−	9552.08i	−1.12251	−	1.94425i
$290$	−2930.23	+	5075.30i	−0.593341	+	1.02770i
$291$			917.156i			0.184758i
$292$	1045.77	+	603.773i	0.209585	+	0.121004i
$293$	−5311.63	−	3066.67i	−1.05907	−	0.611457i	−0.133899	−	0.990995i	$-0.542750\pi$
$293$	−5311.63	−	3066.67i	−1.05907	−	0.611457i	−0.925176	+	0.379538i	$0.876083\pi$
$294$		−	294.000i		−	0.0583212i
$295$	−2159.32	+	3740.05i	−0.426171	+	0.738149i
$296$	1652.03	+	2861.40i	0.324400	+	0.561877i
$297$	−266.822	+	154.050i	−0.0521298	+	0.0300972i
$298$	−3230.86			−0.628048
$299$	3726.62	+	1078.68i	0.720790	+	0.208635i
$300$	305.569			0.0588068
$301$	1246.46	−	719.642i	0.238686	−	0.137806i
$302$	−728.285	−	1261.43i	−0.138768	−	0.240354i
$303$	−1979.30	+	3428.26i	−0.375274	+	0.649994i
$304$		−	2344.41i		−	0.442307i
$305$	−1802.07	−	1040.42i	−0.338315	−	0.195326i
$306$	−1968.27	−	1136.38i	−0.367708	−	0.212296i
$307$			2216.10i			0.411985i	0.978554	+	0.205993i	$0.0660423\pi$
$307$			2216.10i			0.411985i	−0.978554	+	0.205993i	$0.933958\pi$
$308$	159.755	−	276.704i	0.0295548	−	0.0511905i
$309$	1536.34	+	2661.01i	0.282845	+	0.489902i
$310$	3139.33	−	1812.49i	0.575167	−	0.332073i
$311$	−1088.59			−0.198482			−0.0992412	−	0.995063i	$-0.531642\pi$
$311$	−1088.59			−0.198482			−0.0992412	+	0.995063i	$0.531642\pi$
$312$	−312.776	+	1080.58i	−0.0567547	+	0.196075i
$313$	−6671.58			−1.20479			−0.602396	−	0.798197i	$-0.705787\pi$
$313$	−6671.58			−1.20479			−0.602396	+	0.798197i	$0.705787\pi$
$314$	2981.29	−	1721.25i	0.535808	−	0.309349i
$315$	−314.268	−	544.329i	−0.0562127	−	0.0973633i
$316$	−1958.58	+	3392.37i	−0.348668	+	0.603910i
$317$		−	3334.75i		−	0.590847i	−0.955366	−	0.295423i	$-0.904539\pi$
$317$		−	3334.75i		−	0.590847i	0.955366	−	0.295423i	$-0.0954607\pi$
$318$	−1640.76	−	947.292i	−0.289337	−	0.167049i
$319$	−2902.48	−	1675.75i	−0.509428	−	0.294118i
$320$		−	638.513i		−	0.111544i
$321$	−970.707	+	1681.31i	−0.168784	+	0.292342i
$322$	−579.388	−	1003.53i	−0.100273	−	0.173679i
$323$	16022.4	−	9250.53i	2.76009	−	1.59354i
$324$	−324.000			−0.0555556
$325$	860.643	−	826.964i	0.146892	−	0.141144i
$326$	−4261.25			−0.723953
$327$	2000.75	−	1155.13i	0.338353	−	0.195348i
$328$	−1404.05	−	2431.88i	−0.236358	−	0.409384i
$329$	91.6193	−	158.689i	0.0153530	−	0.0265922i
$330$		−	683.074i		−	0.113945i
$331$	−1912.27	−	1104.05i	−0.317546	−	0.183336i	0.332752	−	0.943014i	$-0.392023\pi$
$331$	−1912.27	−	1104.05i	−0.317546	−	0.183336i	−0.650298	+	0.759679i	$0.725356\pi$
$332$	1805.80	+	1042.58i	0.298513	+	0.172347i
$333$			3717.07i			0.611694i
$334$	2176.21	−	3769.30i	0.356517	−	0.617506i
$335$	538.491	+	932.693i	0.0878236	+	0.152115i
$336$	290.985	−	168.000i	0.0472456	−	0.0272772i
$337$	8214.45			1.32780			0.663901	−	0.747820i	$-0.268899\pi$
$337$	8214.45			1.32780			0.663901	+	0.747820i	$0.268899\pi$
$338$	2043.43	+	3889.94i	0.328840	+	0.625991i
$339$	−3410.65			−0.546434
$340$	4363.78	−	2519.43i	0.696056	−	0.401868i
$341$	1036.53	+	1795.33i	0.164608	+	0.285109i
$342$	1318.73	−	2284.11i	0.208506	−	0.361142i
$343$			343.000i			0.0539949i
$344$	1424.52	+	822.448i	0.223271	+	0.128905i
$345$	−2145.43	−	1238.66i	−0.334799	−	0.193297i
$346$			8405.27i			1.30598i
$347$	−4660.81	+	8072.75i	−0.721052	+	1.24890i	0.239526	+	0.970890i	$0.423008\pi$
$347$	−4660.81	+	8072.75i	−0.721052	+	1.24890i	−0.960578	+	0.278009i	$0.910325\pi$
$348$	−1762.23	−	3052.27i	−0.271453	−	0.470170i
$349$	−1398.06	+	807.170i	−0.214431	+	0.123802i	−0.603369	−	0.797462i	$-0.706175\pi$
$349$	−1398.06	+	807.170i	−0.214431	+	0.123802i	0.388938	+	0.921264i	$0.372842\pi$
$350$	−356.497			−0.0544445
$351$	−912.555	+	876.845i	−0.138771	+	0.133340i
$352$	365.154			0.0552920
$353$	562.269	−	324.626i	0.0847778	−	0.0489465i	−0.457012	−	0.889461i	$-0.651080\pi$
$353$	562.269	−	324.626i	0.0847778	−	0.0489465i	0.541790	+	0.840514i	$0.317747\pi$
$354$	−1298.61	−	2249.25i	−0.194972	−	0.337702i
$355$	4841.71	−	8386.09i	0.723863	−	1.25377i
$356$			256.088i			0.0381254i
$357$	2296.32	+	1325.78i	0.340431	+	0.196548i
$358$	−5009.35	−	2892.15i	−0.739532	−	0.426969i
$359$			12736.1i			1.87238i	0.351495	+	0.936190i	$0.385673\pi$
$359$			12736.1i			1.87238i	−0.351495	+	0.936190i	$0.614327\pi$
$360$	359.164	−	622.090i	0.0525822	−	0.0910750i
$361$	7305.42	+	12653.4i	1.06509	+	1.84478i
$362$	711.667	−	410.881i	0.103327	−	0.0596559i
$363$	−3602.36			−0.520868
$364$	364.906	−	1260.67i	0.0525446	−	0.181531i
$365$	−3011.85			−0.431911
$366$	1083.76	−	625.708i	0.154779	−	0.0893615i
$367$	−1383.03	−	2395.47i	−0.196712	−	0.340716i	0.750748	−	0.660589i	$-0.229693\pi$
$367$	−1383.03	−	2395.47i	−0.196712	−	0.340716i	−0.947461	+	0.319873i	$0.896360\pi$
$368$	662.158	−	1146.89i	0.0937972	−	0.162462i
$369$		−	3159.10i		−	0.445681i
$370$	−7136.89	−	4120.49i	−1.00278	−	0.578956i
$371$	1914.22	+	1105.17i	0.267874	+	0.154657i
$372$			2180.05i			0.303846i
$373$	−6546.07	+	11338.1i	−0.908694	+	1.57390i	−0.0928137	+	0.995683i	$0.529586\pi$
$373$	−6546.07	+	11338.1i	−0.908694	+	1.57390i	−0.815880	+	0.578221i	$0.803747\pi$
$374$	1440.82	+	2495.57i	0.199206	+	0.345034i
$375$	−3900.09	+	2251.72i	−0.537066	+	0.310075i
$376$	209.416			0.0287228
$377$	−13223.8	−	3827.67i	−1.80652	−	0.522904i
$378$	378.000			0.0514344
$379$	−909.812	+	525.280i	−0.123308	+	0.0711922i	−0.560386	−	0.828232i	$-0.689347\pi$
$379$	−909.812	+	525.280i	−0.123308	+	0.0711922i	0.437077	+	0.899424i	$0.356014\pi$
$380$	2923.71	+	5064.01i	0.394693	+	0.683628i
$381$	−1952.25	+	3381.39i	−0.262511	+	0.454682i
$382$			5781.09i			0.774310i
$383$	−3644.65	−	2104.24i	−0.486248	−	0.280735i	0.236769	−	0.971566i	$-0.423912\pi$
$383$	−3644.65	−	2104.24i	−0.486248	−	0.280735i	−0.723016	+	0.690831i	$0.757245\pi$
$384$	332.554	+	192.000i	0.0441942	+	0.0255155i
$385$			796.920i			0.105493i
$386$	959.828	−	1662.47i	0.126565	−	0.219217i
$387$	925.255	+	1602.59i	0.121533	+	0.210502i
$388$	1059.04	−	611.438i	0.138569	−	0.0800027i
$389$	11993.9			1.56328			0.781638	−	0.623732i	$-0.214384\pi$
$389$	11993.9			1.56328			0.781638	+	0.623732i	$0.214384\pi$
$390$	−671.974	−	2724.14i	−0.0872480	−	0.353698i
$391$	10450.9			1.35173
$392$	−339.482	+	196.000i	−0.0437409	+	0.0252538i
$393$	−1844.41	−	3194.60i	−0.236738	−	0.410042i
$394$	144.605	−	250.464i	0.0184901	−	0.0320258i
$395$		−	9770.17i		−	1.24453i
$396$	355.762	+	205.399i	0.0451458	+	0.0260649i
$397$	1601.70	+	924.741i	0.202486	+	0.116905i	0.597815	−	0.801634i	$-0.296036\pi$
$397$	1601.70	+	924.741i	0.202486	+	0.116905i	−0.395329	+	0.918540i	$0.629369\pi$
$398$			9786.44i			1.23254i
$399$	−1538.52	+	2664.80i	−0.193039	+	0.334353i
$400$	−203.713	−	352.841i	−0.0254641	−	0.0441051i
$401$	6540.88	−	3776.38i	0.814554	−	0.470283i	−0.0339808	−	0.999422i	$-0.510819\pi$
$401$	6540.88	−	3776.38i	0.814554	−	0.470283i	0.848535	+	0.529139i	$0.177485\pi$
$402$	−647.694			−0.0803583
$403$	5899.90	+	6140.18i	0.729268	+	0.758968i
$404$	5278.15			0.649994
$405$	699.851	−	404.059i	0.0858664	−	0.0495750i
$406$	2055.94	+	3560.99i	0.251316	+	0.435292i
$407$	2356.43	−	4081.46i	0.286988	−	0.497077i
$408$			3030.35i			0.367708i
$409$	13316.3	+	7688.19i	1.60990	+	0.929478i	0.989390	+	0.145281i	$0.0464087\pi$
$409$	13316.3	+	7688.19i	1.60990	+	0.929478i	0.620513	+	0.784197i	$0.286925\pi$
$410$	6065.58	+	3501.96i	0.730628	+	0.421828i
$411$		−	4809.36i		−	0.577198i
$412$	2048.45	−	3548.02i	0.244951	−	0.424267i
$413$	1515.04	+	2624.13i	0.180509	+	0.312651i
$414$	1290.25	−	744.928i	0.153170	−	0.0884328i
$415$	−5200.79			−0.615173
$416$	1456.26	−	359.221i	0.171632	−	0.0423371i
$417$	968.031			0.113680
$418$	−2896.02	+	1672.02i	−0.338873	+	0.195649i
$419$	−6801.24	−	11780.1i	−0.792989	−	1.37350i	−0.924108	−	0.382130i	$-0.875190\pi$
$419$	−6801.24	−	11780.1i	−0.792989	−	1.37350i	0.131120	−	0.991367i	$-0.458143\pi$
$420$	−419.024	+	725.771i	−0.0486816	+	0.0843191i
$421$		−	14535.2i		−	1.68266i	−0.540520	−	0.841331i	$-0.681772\pi$
$421$		−	14535.2i		−	1.68266i	0.540520	−	0.841331i	$-0.318228\pi$
$422$	6779.16	+	3913.95i	0.782000	+	0.451488i
$423$	204.029	+	117.796i	0.0234521	+	0.0135401i
$424$			2526.11i			0.289337i
$425$	1607.61	−	2784.46i	0.183483	−	0.317802i
$426$	2911.79	+	5043.37i	0.331166	+	0.573596i
$427$	−1264.39	+	729.993i	−0.143297	+	0.0827327i
$428$	2588.55			0.292342
$429$	1557.89	−	384.290i	0.175328	−	0.0432487i
$430$	−4102.69			−0.460115
$431$	7041.61	−	4065.48i	0.786966	−	0.454355i	−0.0519272	−	0.998651i	$-0.516536\pi$
$431$	7041.61	−	4065.48i	0.786966	−	0.454355i	0.838893	+	0.544296i	$0.183203\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−5615.94	+	9727.09i	−0.623290	+	1.07957i	0.365578	+	0.930781i	$0.380871\pi$
$433$	−5615.94	+	9727.09i	−0.623290	+	1.07957i	−0.988869	+	0.148790i	$0.952462\pi$
$434$		−	2543.40i		−	0.281306i
$435$	7612.96	+	4395.34i	0.839111	+	0.484461i
$436$	−2667.66	−	1540.17i	−0.293022	−	0.169177i
$437$			12127.9i			1.32759i
$438$	905.660	−	1568.65i	0.0987993	−	0.171125i
$439$	1625.42	+	2815.31i	0.176713	+	0.306077i	0.940753	−	0.339093i	$-0.110120\pi$
$439$	1625.42	+	2815.31i	0.176713	+	0.306077i	−0.764039	+	0.645169i	$0.776787\pi$
$440$	−788.746	+	455.383i	−0.0854591	+	0.0493398i
$441$	−441.000			−0.0476190
$442$	8201.08	+	8535.07i	0.882547	+	0.918489i
$443$	−4127.00			−0.442618			−0.221309	−	0.975204i	$-0.571033\pi$
$443$	−4127.00			−0.442618			−0.221309	+	0.975204i	$0.571033\pi$
$444$	4292.10	−	2478.05i	0.458771	−	0.264871i
$445$	−319.366	−	553.159i	−0.0340212	−	0.0589264i
$446$	−4400.48	+	7621.86i	−0.467195	+	0.809205i
$447$			4846.28i			0.512799i
$448$	−387.979	−	224.000i	−0.0409159	−	0.0236228i
$449$	−6048.25	−	3491.96i	−0.635712	−	0.367028i	0.147249	−	0.989099i	$-0.452958\pi$
$449$	−6048.25	−	3491.96i	−0.635712	−	0.367028i	−0.782961	+	0.622071i	$0.786291\pi$
$450$		−	458.353i		−	0.0480155i
$451$	−2002.71	+	3468.80i	−0.209100	+	0.362171i
$452$	2273.77	+	3938.28i	0.236613	+	0.409825i
$453$	−1892.14	+	1092.43i	−0.196248	+	0.113304i
$454$	3808.85			0.393741
$455$	783.970	+	3178.16i	0.0807760	+	0.327461i
$456$	−3516.62			−0.361142
$457$	−3231.33	+	1865.61i	−0.330755	+	0.190962i	−0.656176	−	0.754608i	$-0.727827\pi$
$457$	−3231.33	+	1865.61i	−0.330755	+	0.190962i	0.325421	+	0.945569i	$0.394494\pi$
$458$	4405.70	+	7630.90i	0.449487	+	0.778534i
$459$	−1704.57	+	2952.41i	−0.173339	+	0.300232i
$460$			3303.10i			0.334799i
$461$	9768.35	+	5639.76i	0.986893	+	0.569783i	0.904344	−	0.426804i	$-0.140361\pi$
$461$	9768.35	+	5639.76i	0.986893	+	0.569783i	0.0825486	+	0.996587i	$0.473694\pi$
$462$	−415.056	−	239.633i	−0.0417969	−	0.0241314i
$463$		−	9983.89i		−	1.00214i	−0.865407	−	0.501070i	$-0.832940\pi$
$463$		−	9983.89i		−	1.00214i	0.865407	−	0.501070i	$-0.167060\pi$
$464$	−2349.64	+	4069.70i	−0.235085	+	0.407179i
$465$	−2718.74	−	4708.99i	−0.271136	−	0.469622i
$466$	8857.09	−	5113.64i	0.880465	−	0.508337i
$467$	10388.2			1.02935			0.514676	−	0.857385i	$-0.327912\pi$
$467$	10388.2			1.02935			0.514676	+	0.857385i	$0.327912\pi$
$468$	1620.86	+	469.164i	0.160095	+	0.0463400i
$469$	755.643			0.0743973
$470$	−452.345	+	261.161i	−0.0443938	+	0.0256308i
$471$	−2581.87	−	4471.93i	−0.252583	−	0.437486i
$472$	−1731.48	+	2999.01i	−0.168851	+	0.292458i
$473$		−	2346.26i		−	0.228078i
$474$	5088.55	+	2937.88i	0.493090	+	0.284686i
$475$	3231.27	+	1865.57i	0.312128	+	0.180207i
$476$		−	3535.41i		−	0.340431i
$477$	−1420.94	+	2461.14i	−0.136395	+	0.236243i
$478$	−1843.52	−	3193.08i	−0.176403	−	0.305540i
$479$	−10774.8	+	6220.82i	−1.02779	+	0.593395i	−0.916351	−	0.400376i	$-0.868880\pi$
$479$	−10774.8	+	6220.82i	−1.02779	+	0.593395i	−0.111440	+	0.993771i	$0.535546\pi$
$480$	−957.770			−0.0910750
$481$	5382.46	−	18595.3i	0.510227	−	1.76273i
$482$	−8339.57			−0.788085
$483$	−1505.29	+	869.082i	−0.141808	+	0.0818729i
$484$	2401.57	+	4159.65i	0.225542	+	0.390651i
$485$	−1525.04	+	2641.45i	−0.142781	+	0.247303i
$486$			486.000i			0.0453609i
$487$	−3077.32	−	1776.69i	−0.286338	−	0.165317i	0.349951	−	0.936768i	$-0.386198\pi$
$487$	−3077.32	−	1776.69i	−0.286338	−	0.165317i	−0.636289	+	0.771451i	$0.719531\pi$
$488$	−1445.01	−	834.278i	−0.134042	−	0.0773893i
$489$			6391.88i			0.591105i
$490$	488.862	−	846.733i	0.0450704	−	0.0780643i
$491$	−1870.34	−	3239.53i	−0.171909	−	0.297756i	0.767178	−	0.641434i	$-0.221660\pi$
$491$	−1870.34	−	3239.53i	−0.171909	−	0.297756i	−0.939087	+	0.343679i	$0.888327\pi$
$492$	−3647.82	+	2106.07i	−0.334261	+	0.192986i
$493$	−37084.6			−3.38784
$494$	−9904.66	+	9517.07i	−0.902088	+	0.866788i
$495$	−1024.61			−0.0930360
$496$	2517.31	−	1453.37i	0.227884	−	0.131569i
$497$	−3397.09	−	5883.93i	−0.306600	−	0.531047i
$498$	1563.87	−	2708.70i	0.140720	−	0.243735i
$499$			13949.8i			1.25146i	0.780039	+	0.625731i	$0.215199\pi$
$499$			13949.8i			1.25146i	−0.780039	+	0.625731i	$0.784801\pi$
$500$	5200.12	+	3002.29i	0.465113	+	0.268533i
$501$	−5653.95	−	3264.31i	−0.504191	−	0.291095i
$502$		−	1490.37i		−	0.132507i
$503$	−4644.06	+	8043.75i	−0.411667	+	0.713028i	−0.995072	−	0.0991534i	$-0.968387\pi$
$503$	−4644.06	+	8043.75i	−0.411667	+	0.713028i	0.583405	+	0.812181i	$0.301720\pi$
$504$	−252.000	−	436.477i	−0.0222718	−	0.0385758i
$505$	−11401.0	+	6582.35i	−1.00463	+	0.580022i
$506$	−1888.98			−0.165960
$507$	5834.91	−	3065.15i	0.511119	−	0.268497i
$508$	5205.99			0.454682
$509$	4210.60	−	2430.99i	0.366663	−	0.211693i	−0.305337	−	0.952244i	$-0.598769\pi$
$509$	4210.60	−	2430.99i	0.366663	−	0.211693i	0.672000	+	0.740552i	$0.265436\pi$
$510$	−3779.14	−	6545.67i	−0.328124	−	0.568328i
$511$	−1056.60	+	1830.09i	−0.0914704	+	0.158431i
$512$		−	512.000i		−	0.0441942i
$513$	−3426.17	−	1978.10i	−0.294871	−	0.170244i
$514$	8886.22	+	5130.46i	0.762557	+	0.440263i
$515$			10218.4i			0.874327i
$516$	1233.67	−	2136.78i	0.105251	−	0.182300i
$517$	−149.354	−	258.688i	−0.0127051	−	0.0220060i
$518$	−5007.46	+	2891.06i	−0.424739	+	0.245223i
$519$	12607.9			1.06633
$520$	−2697.58	+	2592.02i	−0.227494	+	0.218592i
$521$	−6202.44			−0.521562			−0.260781	−	0.965398i	$-0.583980\pi$
$521$	−6202.44			−0.521562			−0.260781	+	0.965398i	$0.583980\pi$
$522$	−4578.41	+	2643.35i	−0.383892	+	0.221640i
$523$	4270.04	+	7395.92i	0.357009	+	0.618357i	0.987460	−	0.157872i	$-0.0504633\pi$
$523$	4270.04	+	7395.92i	0.357009	+	0.618357i	−0.630451	+	0.776229i	$0.717130\pi$
$524$	−2459.21	+	4259.47i	−0.205021	+	0.355107i
$525$			534.746i			0.0444537i
$526$	−1612.21	−	930.807i	−0.133642	−	0.0771580i
$527$	19865.5	+	11469.3i	1.64204	+	0.948030i
$528$		−	547.732i		−	0.0451458i
$529$	2658.09	−	4603.94i	0.218467	−	0.378396i
$530$	−3150.30	−	5456.49i	−0.258190	−	0.447197i
$531$	−3373.88	+	1947.91i	−0.275732	+	0.159194i
$532$	4102.72			0.334353
$533$	−4574.50	+	15803.9i	−0.371752	+	1.28432i
$534$	384.132			0.0311293
$535$	−5591.36	+	3228.17i	−0.451842	+	0.260871i
$536$	431.796	+	747.892i	0.0347961	+	0.0602687i
$537$	−4338.23	+	7514.03i	−0.348619	+	0.603826i
$538$		−	4846.93i		−	0.388413i
$539$	484.232	+	279.571i	0.0386964	+	0.0223414i
$540$	−933.135	−	538.746i	−0.0743624	−	0.0429332i
$541$		−	13835.0i		−	1.09947i	−0.835340	−	0.549733i	$-0.814729\pi$
$541$		−	13835.0i		−	1.09947i	0.835340	−	0.549733i	$-0.185271\pi$
$542$	−4761.45	+	8247.08i	−0.377347	+	0.653584i
$543$	−616.322	−	1067.50i	−0.0487088	−	0.0843662i
$544$	3499.15	−	2020.24i	0.275781	−	0.159222i
$545$	7682.98			0.603858
$546$	−1891.01	−	547.358i	−0.148219	−	0.0429025i
$547$	−8946.00			−0.699275			−0.349637	−	0.936885i	$-0.613695\pi$
$547$	−8946.00			−0.699275			−0.349637	+	0.936885i	$0.613695\pi$
$548$	−5553.37	+	3206.24i	−0.432898	+	0.249934i
$549$	−938.563	−	1625.64i	−0.0729634	−	0.126376i
$550$	−290.572	+	503.286i	−0.0225274	+	0.0390185i
$551$		−	43035.4i		−	3.32735i
$552$	−1720.34	−	993.237i	−0.132649	−	0.0765851i
$553$	−5936.64	−	3427.52i	−0.456513	−	0.263568i
$554$		−	16186.6i		−	1.24134i
$555$	−6180.73	+	10705.3i	−0.472716	+	0.818768i
$556$	−645.354	−	1117.79i	−0.0492250	−	0.0852602i
$557$	−3219.70	+	1858.90i	−0.244925	+	0.141407i	−0.617438	−	0.786619i	$-0.711829\pi$
$557$	−3219.70	+	1858.90i	−0.244925	+	0.141407i	0.372513	+	0.928027i	$0.378496\pi$
$558$	3270.08			0.248089
$559$	−2308.13	−	9357.01i	−0.174639	−	0.707978i
$560$	1117.40			0.0843191
$561$	3743.35	−	2161.23i	0.281719	−	0.162651i
$562$	6772.18	+	11729.8i	0.508305	+	0.880410i
$563$	4331.38	−	7502.17i	0.324238	−	0.561597i	−0.657120	−	0.753786i	$-0.728225\pi$
$563$	4331.38	−	7502.17i	0.324238	−	0.561597i	0.981358	+	0.192189i	$0.0615588\pi$
$564$		−	314.123i		−	0.0234521i
$565$	−9822.82	−	5671.21i	−0.731414	−	0.422282i
$566$	4553.51	+	2628.97i	0.338160	+	0.195237i
$567$		−	567.000i		−	0.0419961i
$568$	3882.39	−	6724.49i	0.286798	−	0.496749i
$569$	3554.63	+	6156.81i	0.261895	+	0.453615i	0.966745	−	0.255741i	$-0.0823194\pi$
$569$	3554.63	+	6156.81i	0.261895	+	0.453615i	−0.704851	+	0.709356i	$0.748986\pi$
$570$	7596.02	−	4385.57i	0.558180	−	0.322265i
$571$	−15405.3			−1.12905			−0.564527	−	0.825414i	$-0.690942\pi$
$571$	−15405.3			−1.12905			−0.564527	+	0.825414i	$0.690942\pi$
$572$	−1482.33	−	1542.70i	−0.108356	−	0.112768i
$573$	8671.64			0.632222
$574$	4255.79	−	2457.08i	0.309466	−	0.178670i
$575$	1053.83	+	1825.28i	0.0764307	+	0.132382i
$576$	288.000	−	498.831i	0.0208333	−	0.0360844i
$577$			1770.19i			0.127719i	0.997959	+	0.0638595i	$0.0203410\pi$
$577$			1770.19i			0.127719i	−0.997959	+	0.0638595i	$0.979659\pi$
$578$	19104.2	+	11029.8i	1.37479	+	0.793735i
$579$	−2493.71	−	1439.74i	−0.178990	−	0.103340i
$580$		−	11720.9i		−	0.839111i
$581$	−1824.52	+	3160.16i	−0.130282	+	0.225655i
$582$	−917.156	−	1588.56i	−0.0653219	−	0.113141i
$583$	3120.47	−	1801.60i	0.221675	−	0.127984i
$584$	−2415.09			−0.171125
$585$	−4086.21	+	1007.96i	−0.288793	+	0.0712377i
$586$	12266.7			0.864731
$587$	15410.1	−	8897.01i	1.08355	−	0.625586i	0.151696	−	0.988427i	$-0.451527\pi$
$587$	15410.1	−	8897.01i	1.08355	−	0.625586i	0.931851	+	0.362841i	$0.118193\pi$
$588$	294.000	+	509.223i	0.0206197	+	0.0357143i
$589$	−13309.8	+	23053.2i	−0.931102	+	1.61272i
$590$		−	8637.27i		−	0.602696i
$591$	−375.695	−	216.908i	−0.0261490	−	0.0150971i
$592$	−5722.81	−	3304.06i	−0.397307	−	0.229385i
$593$		−	12121.9i		−	0.839438i	−0.907654	−	0.419719i	$-0.862129\pi$
$593$		−	12121.9i		−	0.839438i	0.907654	−	0.419719i	$-0.137871\pi$
$594$	308.099	−	533.643i	0.0212819	−	0.0368614i
$595$	4409.00	+	7636.61i	0.303784	+	0.526169i
$596$	5596.01	−	3230.86i	0.384600	−	0.222049i
$597$	14679.7			1.00636
$598$	−7533.38	+	1858.29i	−0.515155	+	0.127075i
$599$	23723.4			1.61821			0.809107	−	0.587661i	$-0.199951\pi$
$599$	23723.4			1.61821			0.809107	+	0.587661i	$0.199951\pi$
$600$	−529.261	+	305.569i	−0.0360116	+	0.0207913i
$601$	3781.05	+	6548.97i	0.256626	+	0.444489i	0.965336	−	0.261011i	$-0.0840558\pi$
$601$	3781.05	+	6548.97i	0.256626	+	0.444489i	−0.708710	+	0.705500i	$0.750722\pi$
$602$	−1439.28	+	2492.91i	−0.0974433	+	0.168777i
$603$			971.540i			0.0656122i
$604$	2522.85	+	1456.57i	0.169956	+	0.0981241i
$605$	−10375.0	−	5989.99i	−0.697194	−	0.402525i
$606$		−	7917.22i		−	0.530718i
$607$	−6866.35	+	11892.9i	−0.459138	+	0.795250i	−0.998916	−	0.0465574i	$-0.985175\pi$
$607$	−6866.35	+	11892.9i	−0.459138	+	0.795250i	0.539778	+	0.841808i	$0.318508\pi$
$608$	2344.41	+	4060.64i	0.156379	+	0.270857i
$609$	5341.48	−	3083.90i	0.355415	−	0.205199i
$610$	4161.70			0.276233
$611$	−850.116	−	884.737i	−0.0562880	−	0.0585804i
$612$	4545.53			0.300232
$613$	−18832.3	+	10872.8i	−1.24083	+	0.716392i	−0.969263	−	0.246028i	$-0.920875\pi$
$613$	−18832.3	+	10872.8i	−1.24083	+	0.716392i	−0.271565	+	0.962420i	$0.587541\pi$
$614$	−2216.10	−	3838.40i	−0.145659	−	0.252289i
$615$	5252.94	−	9098.36i	0.344421	−	0.596555i
$616$			639.020i			0.0417969i
$617$	−8105.27	−	4679.58i	−0.528859	−	0.305337i	0.211693	−	0.977336i	$-0.432102\pi$
$617$	−8105.27	−	4679.58i	−0.528859	−	0.305337i	−0.740552	+	0.671999i	$0.765436\pi$
$618$	−5322.02	−	3072.67i	−0.346413	−	0.200002i
$619$			5697.70i			0.369968i	0.982742	+	0.184984i	$0.0592233\pi$
$619$			5697.70i			0.369968i	−0.982742	+	0.184984i	$0.940777\pi$
$620$	−3624.98	+	6278.65i	−0.234811	+	0.406705i
$621$	−1117.39	−	1935.38i	−0.0722051	−	0.125063i
$622$	1885.49	−	1088.59i	0.121545	−	0.0701742i
$623$	−448.154			−0.0288201
$624$	−538.831	−	2184.39i	−0.0345681	−	0.140137i
$625$	−11793.6			−0.754789
$626$	11555.5	−	6671.58i	0.737782	−	0.425959i
$627$	2508.03	+	4344.03i	0.159746	+	0.276689i
$628$	−3442.50	+	5962.58i	−0.218743	+	0.378874i
$629$		−	52148.3i		−	3.30571i
$630$	1088.66	+	628.536i	0.0688462	+	0.0397484i
$631$	−13500.6	−	7794.56i	−0.851742	−	0.491754i	0.00949600	−	0.999955i	$-0.496977\pi$
$631$	−13500.6	−	7794.56i	−0.851742	−	0.491754i	−0.861238	+	0.508201i	$0.830311\pi$
$632$		−	7834.33i		−	0.493090i
$633$	5870.92	−	10168.7i	0.368639	−	0.638501i
$634$	3334.75	+	5775.96i	0.208896	+	0.361818i
$635$	−11245.1	+	6492.38i	−0.702755	+	0.405736i
$636$	3789.17			0.236243
$637$	2206.17	+	638.585i	0.137224	+	0.0397200i
$638$	6702.98			0.415946
$639$	7565.05	−	4367.69i	0.468339	−	0.270396i
$640$	638.513	+	1105.94i	0.0394366	+	0.0683063i
$641$	−11340.9	+	19643.1i	−0.698814	+	1.21038i	0.270064	+	0.962842i	$0.412955\pi$
$641$	−11340.9	+	19643.1i	−0.698814	+	1.21038i	−0.968878	+	0.247539i	$0.920378\pi$
$642$		−	3882.83i		−	0.238696i
$643$	13773.3	+	7952.04i	0.844740	+	0.487711i	0.858873	−	0.512189i	$-0.171165\pi$
$643$	13773.3	+	7952.04i	0.844740	+	0.487711i	−0.0141328	+	0.999900i	$0.504499\pi$
$644$	2007.06	+	1158.78i	0.122809	+	0.0709040i
$645$			6154.03i			0.375682i
$646$	−18501.1	+	32044.8i	−1.12680	+	1.95168i
$647$	−12043.4	−	20859.8i	−0.731803	−	1.26752i	−0.956112	−	0.293001i	$-0.905346\pi$
$647$	−12043.4	−	20859.8i	−0.731803	−	1.26752i	0.224309	−	0.974518i	$-0.427987\pi$
$648$	561.184	−	324.000i	0.0340207	−	0.0196419i
$649$	4939.50			0.298756
$650$	−663.713	+	2292.99i	−0.0400507	+	0.138367i
$651$	−3815.09			−0.229686
$652$	7380.70	−	4261.25i	0.443329	−	0.255956i
$653$	10776.3	+	18665.0i	0.645800	+	1.11856i	0.984116	+	0.177526i	$0.0568095\pi$
$653$	10776.3	+	18665.0i	0.645800	+	1.11856i	−0.338316	+	0.941033i	$0.609857\pi$
$654$	−2310.26	+	4001.49i	−0.138132	+	0.239252i
$655$		−	12267.5i		−	0.731801i
$656$	4863.76	+	2808.09i	0.289478	+	0.167130i
$657$	−2352.97	−	1358.49i	−0.139723	−	0.0806693i
$658$			366.477i			0.0217124i
$659$	6771.92	−	11729.3i	0.400299	−	0.693337i	−0.593463	−	0.804861i	$-0.702240\pi$
$659$	6771.92	−	11729.3i	0.400299	−	0.693337i	0.993762	+	0.111524i	$0.0355731\pi$
$660$	683.074	+	1183.12i	0.0402858	+	0.0697770i
$661$	−9993.41	+	5769.70i	−0.588046	+	0.339509i	−0.764325	−	0.644832i	$-0.776927\pi$
$661$	−9993.41	+	5769.70i	−0.588046	+	0.339509i	0.176278	+	0.984340i	$0.443594\pi$
$662$	4416.20			0.259276
$663$	12802.6	−	12301.6i	0.749943	−	0.720596i
$664$	−4170.32			−0.243735
$665$	−8862.03	+	5116.49i	−0.516774	+	0.298360i
$666$	−3717.07	−	6438.16i	−0.216267	−	0.374585i
$667$	12154.9	−	21053.0i	0.705609	−	1.22215i
$668$			8704.83i			0.504191i
$669$	11432.8	+	6600.72i	0.660713	+	0.381463i
$670$	−1865.39	−	1076.98i	−0.107561	−	0.0621006i
$671$			2380.00i			0.136928i
$672$	−336.000	+	581.969i	−0.0192879	+	0.0334077i
$673$	2223.08	+	3850.49i	0.127330	+	0.220543i	0.922641	−	0.385659i	$-0.126026\pi$
$673$	2223.08	+	3850.49i	0.127330	+	0.220543i	−0.795311	+	0.606202i	$0.792692\pi$
$674$	−14227.8	+	8214.45i	−0.813110	+	0.469449i
$675$	−687.530			−0.0392045
$676$	−7429.26	−	4694.14i	−0.422694	−	0.267077i
$677$	39.2297			0.00222706			0.00111353	−	0.999999i	$-0.499646\pi$
$677$	39.2297			0.00222706			0.00111353	+	0.999999i	$0.499646\pi$
$678$	5907.42	−	3410.65i	0.334621	−	0.193193i
$679$	1070.02	+	1853.32i	0.0604763	+	0.104748i
$680$	−5038.86	+	8727.56i	−0.284164	+	0.492186i
$681$		−	5713.28i		−	0.321488i
$682$	−3590.65	−	2073.06i	−0.201603	−	0.116395i
$683$	−554.498	−	320.139i	−0.0310648	−	0.0179353i	0.484387	−	0.874854i	$-0.339043\pi$
$683$	−554.498	−	320.139i	−0.0310648	−	0.0179353i	−0.515452	+	0.856918i	$0.672376\pi$
$684$			5274.93i			0.294871i
$685$	7996.98	−	13851.2i	0.446057	−	0.772593i
$686$	−343.000	−	594.093i	−0.0190901	−	0.0330650i
$687$	11446.4	−	6608.56i	0.635671	−	0.367005i
$688$	−3289.79			−0.182300
$689$	10672.3	−	10254.7i	0.590104	−	0.567012i
$690$	4954.65			0.273363
$691$	3926.42	−	2266.92i	0.216162	−	0.124801i	−0.388010	−	0.921655i	$-0.626837\pi$
$691$	3926.42	−	2266.92i	0.216162	−	0.124801i	0.604172	+	0.796854i	$0.293504\pi$
$692$	−8405.27	−	14558.4i	−0.461735	−	0.799748i
$693$	−359.449	+	622.584i	−0.0197032	+	0.0341270i
$694$		−	18643.2i		−	1.01972i
$695$	2787.97	+	1609.64i	0.152164	+	0.0878518i
$696$	6104.55	+	3524.46i	0.332460	+	0.191946i
$697$			44320.4i			2.40854i
$698$	1614.34	−	2796.12i	0.0875411	−	0.151626i
$699$	−7670.46	−	13285.6i	−0.415055	−	0.718896i
$700$	617.471	−	356.497i	0.0333403	−	0.0192490i
$701$	−26649.0			−1.43583			−0.717916	−	0.696129i	$-0.754904\pi$
$701$	−26649.0			−1.43583			−0.717916	+	0.696129i	$0.754904\pi$
$702$	703.746	−	2431.29i	0.0378365	−	0.130717i
$703$	60516.4			3.24668
$704$	−632.466	+	365.154i	−0.0338593	+	0.0195487i
$705$	391.742	+	678.517i	0.0209275	+	0.0362474i
$706$	−649.253	+	1124.54i	−0.0346104	+	0.0599470i
$707$			9236.75i			0.491349i
$708$	4498.51	+	2597.21i	0.238791	+	0.137866i
$709$	15247.5	+	8803.18i	0.807664	+	0.466305i	0.846144	−	0.532954i	$-0.178918\pi$
$709$	15247.5	+	8803.18i	0.807664	+	0.466305i	−0.0384801	+	0.999259i	$0.512252\pi$
$710$			19366.8i			1.02370i
$711$	4406.81	−	7632.82i	0.232445	−	0.402607i
$712$	−256.088	−	443.558i	−0.0134794	−	0.0233469i
$713$	−13022.3	+	7518.44i	−0.683997	+	0.394906i
$714$	−5303.12			−0.277961
$715$	5125.78	+	1483.68i	0.268103	+	0.0776033i
$716$	11568.6			0.603826
$717$	−4789.61	+	2765.28i	−0.249472	+	0.144033i
$718$	−12736.1	−	22059.5i	−0.661986	−	1.14659i
$719$	7230.53	−	12523.6i	0.375039	−	0.649587i	−0.615294	−	0.788298i	$-0.710963\pi$
$719$	7230.53	−	12523.6i	0.375039	−	0.649587i	0.990333	+	0.138711i	$0.0442959\pi$
$720$			1436.65i			0.0743624i
$721$	6209.03	+	3584.78i	0.320716	+	0.185165i
$722$	−25306.7	−	14610.8i	−1.30446	−	0.753129i
$723$			12509.4i			0.643469i
$724$	−821.762	+	1423.33i	−0.0421831	+	0.0730633i
$725$	−3739.46	−	6476.94i	−0.191559	−	0.331790i
$726$	6239.47	−	3602.36i	0.318965	−	0.184155i
$727$	33178.9			1.69262			0.846311	−	0.532689i	$-0.178819\pi$
$727$	33178.9			1.69262			0.846311	+	0.532689i	$0.178819\pi$
$728$	628.636	+	2548.45i	0.0320039	+	0.129742i
$729$	729.000			0.0370370
$730$	5216.68	−	3011.85i	0.264490	−	0.152704i
$731$	−12980.8	−	22483.4i	−0.656787	−	1.13759i
$732$	−1251.42	+	2167.52i	−0.0631881	+	0.109445i
$733$		−	6971.16i		−	0.351276i	−0.984455	−	0.175638i	$-0.943801\pi$
$733$		−	6971.16i		−	0.351276i	0.984455	−	0.175638i	$-0.0561989\pi$
$734$	4790.95	+	2766.05i	0.240922	+	0.139097i
$735$	−1270.10	−	733.293i	−0.0637392	−	0.0367999i
$736$			2648.63i			0.132649i
$737$	615.907	−	1066.78i	0.0307832	−	0.0533181i
$738$	3159.10	+	5471.73i	0.157572	+	0.272923i
$739$	−17953.5	+	10365.4i	−0.893679	+	0.515966i	−0.875144	−	0.483862i	$-0.839234\pi$
$739$	−17953.5	+	10365.4i	−0.893679	+	0.515966i	−0.0185351	+	0.999828i	$0.505900\pi$
$740$	16481.9			0.818768
$741$	14275.6	+	14857.0i	0.707729	+	0.736552i
$742$	−4420.69			−0.218718
$743$	22830.6	−	13181.3i	1.12729	−	0.650839i	0.184035	−	0.982920i	$-0.441084\pi$
$743$	22830.6	−	13181.3i	1.12729	−	0.650839i	0.943251	+	0.332081i	$0.107751\pi$
$744$	−2180.05	−	3775.96i	−0.107426	−	0.186067i
$745$	−8058.37	+	13957.5i	−0.396290	+	0.686394i
$746$		−	26184.3i		−	1.28509i
$747$	−4063.06	−	2345.81i	−0.199009	−	0.114898i
$748$	−4991.14	−	2881.63i	−0.243976	−	0.140860i
$749$			4529.96i			0.220990i
$750$	4503.44	−	7800.18i	0.219256	−	0.379763i
$751$	−6647.41	−	11513.6i	−0.322993	−	0.559439i	0.658111	−	0.752920i	$-0.271356\pi$
$751$	−6647.41	−	11513.6i	−0.322993	−	0.559439i	−0.981104	+	0.193481i	$0.938022\pi$
$752$	−362.718	+	209.416i	−0.0175891	+	0.0101551i
$753$	−2235.56			−0.108192
$754$	26731.9	−	6594.06i	1.29114	−	0.318490i
$755$	−7265.93			−0.350244
$756$	−654.715	+	378.000i	−0.0314970	+	0.0181848i
$757$	−10176.6	−	17626.4i	−0.488606	−	0.846291i	0.511308	−	0.859398i	$-0.329161\pi$
$757$	−10176.6	−	17626.4i	−0.488606	−	0.846291i	−0.999914	+	0.0131067i	$0.995828\pi$
$758$	1050.56	−	1819.62i	0.0503405	−	0.0871922i
$759$			2833.48i			0.135505i
$760$	−10128.0	−	5847.42i	−0.483398	−	0.279090i
$761$	9818.40	+	5668.66i	0.467696	+	0.270025i	0.715275	−	0.698843i	$-0.246301\pi$
$761$	9818.40	+	5668.66i	0.467696	+	0.270025i	−0.247579	+	0.968868i	$0.579635\pi$
$762$		−	7808.99i		−	0.371247i
$763$	2695.31	−	4668.41i	0.127885	−	0.221504i
$764$	−5781.09	−	10013.1i	−0.273760	−	0.474166i
$765$	−9818.50	+	5668.71i	−0.464037	+	0.267912i
$766$	8416.96			0.397020
$767$	19699.0	−	4859.24i	0.927368	−	0.228757i
$768$	−768.000			−0.0360844
$769$	−20853.7	+	12039.9i	−0.977898	+	0.564590i	−0.901635	−	0.432498i	$-0.857632\pi$
$769$	−20853.7	+	12039.9i	−0.977898	+	0.564590i	−0.0762632	+	0.997088i	$0.524299\pi$
$770$	−796.920	−	1380.31i	−0.0372974	−	0.0646010i
$771$	7695.69	−	13329.3i	0.359473	−	0.622625i
$772$			3839.31i			0.178990i
$773$	−31994.9	−	18472.3i	−1.48872	−	0.859510i	−0.488798	−	0.872397i	$-0.662565\pi$
$773$	−31994.9	−	18472.3i	−1.48872	−	0.859510i	−0.999917	+	0.0128869i	$0.995898\pi$
$774$	−3205.18	−	1850.51i	−0.148847	−	0.0859369i
$775$			4626.09i			0.214418i
$776$	−1222.88	+	2118.08i	−0.0565704	+	0.0979829i
$777$	4336.58	+	7511.18i	0.200224	+	0.346798i
$778$	−20774.0	+	11993.9i	−0.957308	+	0.552702i
$779$	−51432.3			−2.36554
$780$	3888.03	+	4046.38i	0.178479	+	0.185748i
$781$	−11075.6			−0.507445
$782$	−18101.5	+	10450.9i	−0.827760	+	0.477907i
$783$	3965.02	+	6867.61i	0.180968	+	0.313446i
$784$	392.000	−	678.964i	0.0178571	−	0.0309295i
$785$		−	17172.5i		−	0.780780i
$786$	6389.21	+	3688.81i	0.289943	+	0.167399i
$787$	−33358.0	−	19259.3i	−1.51091	−	0.872323i	−0.999919	−	0.0127357i	$-0.995946\pi$
$787$	−33358.0	−	19259.3i	−1.51091	−	0.872323i	−0.510989	−	0.859587i	$-0.670721\pi$
$788$			578.421i			0.0261490i
$789$	−1396.21	+	2418.31i	−0.0629993	+	0.109118i
$790$	9770.17	+	16922.4i	0.440009	+	0.762118i
$791$	−6891.99	+	3979.09i	−0.309799	+	0.178862i
$792$	−821.597			−0.0368614
$793$	2341.33	+	9491.60i	0.104846	+	0.425040i
$794$	−3698.96			−0.165329
$795$	−8184.73	+	4725.46i	−0.365135	+	0.210811i
$796$	−9786.44	−	16950.6i	−0.435768	−	0.754772i
$797$	−9340.91	+	16178.9i	−0.415147	+	0.719056i	−0.995444	−	0.0953493i	$-0.969603\pi$
$797$	−9340.91	+	16178.9i	−0.415147	+	0.719056i	0.580297	+	0.814405i	$0.302937\pi$
$798$		−	6154.09i		−	0.272998i
$799$	−2862.41	−	1652.61i	−0.126739	−	0.0731730i
$800$	705.681	+	407.425i	0.0311870	+	0.0180058i
$801$		−	576.198i		−	0.0254169i
$802$	−7552.76	+	13081.8i	−0.332540	+	0.575977i
$803$	1722.43	+	2983.33i	0.0756950	+	0.131108i
$804$	1121.84	−	647.694i	0.0492092	−	0.0284109i
$805$	−5780.42			−0.253085
$806$	−16359.1	−	4735.20i	−0.714920	−	0.206936i
$807$	−7270.40			−0.317138
$808$	−9142.02	+	5278.15i	−0.398038	+	0.229808i
$809$	−508.628	−	880.970i	−0.0221043	−	0.0382858i	0.854762	−	0.519021i	$-0.173703\pi$
$809$	−508.628	−	880.970i	−0.0221043	−	0.0382858i	−0.876866	+	0.480735i	$0.840370\pi$
$810$	−808.118	+	1399.70i	−0.0350548	+	0.0607167i
$811$		−	6916.50i		−	0.299471i	−0.988726	−	0.149736i	$-0.952158\pi$
$811$		−	6916.50i		−	0.299471i	0.988726	−	0.149736i	$-0.0478423\pi$
$812$	−7121.97	−	4111.87i	−0.307798	−	0.177707i
$813$	12370.6	+	7142.18i	0.533649	+	0.308102i
$814$			9425.73i			0.405862i
$815$	−10628.4	+	18408.9i	−0.456805	+	0.791209i
$816$	−3030.35	−	5248.73i	−0.130004	−	0.225174i
$817$	26091.2	−	15063.7i	1.11728	−	0.645060i
$818$	−30752.8			−1.31448
$819$	−821.038	+	2836.51i	−0.0350298	+	0.121020i
$820$	−14007.8			−0.596555
$821$	−14741.6	+	8511.05i	−0.626656	+	0.361800i	−0.779456	−	0.626457i	$-0.784504\pi$
$821$	−14741.6	+	8511.05i	−0.626656	+	0.361800i	0.152800	+	0.988257i	$0.451171\pi$
$822$	4809.36	+	8330.06i	0.204070	+	0.353460i
$823$	−1310.48	+	2269.81i	−0.0555047	+	0.0961369i	−0.892443	−	0.451161i	$-0.851010\pi$
$823$	−1310.48	+	2269.81i	−0.0555047	+	0.0961369i	0.836938	+	0.547298i	$0.184343\pi$
$824$			8193.79i			0.346413i
$825$	754.929	+	435.859i	0.0318585	+	0.0183935i
$826$	−5248.26	−	3030.08i	−0.221078	−	0.127639i
$827$			10867.4i			0.456948i	0.973550	+	0.228474i	$0.0733735\pi$
$827$			10867.4i			0.456948i	−0.973550	+	0.228474i	$0.926626\pi$
$828$	−1489.86	+	2580.51i	−0.0625315	+	0.108308i
$829$	−11422.2	−	19783.9i	−0.478541	−	0.828858i	0.521156	−	0.853461i	$-0.325501\pi$
$829$	−11422.2	−	19783.9i	−0.478541	−	0.828858i	−0.999697	+	0.0246038i	$0.992168\pi$
$830$	9008.04	−	5200.79i	0.376715	−	0.217497i
$831$	−24279.9			−1.01355
$832$	−2163.09	+	2078.45i	−0.0901343	+	0.0866072i
$833$	6186.97			0.257342
$834$	−1676.68	+	968.031i	−0.0696147	+	0.0401921i
$835$	−10855.8	−	18802.7i	−0.449915	−	0.779276i
$836$	3344.04	−	5792.04i	0.138344	−	0.239620i
$837$		−	4905.12i		−	0.202564i
$838$	23560.2	+	13602.5i	0.971209	+	0.560728i
$839$	31672.1	+	18285.9i	1.30327	+	0.752443i	0.980963	−	0.194192i	$-0.0622086\pi$
$839$	31672.1	+	18285.9i	1.30327	+	0.752443i	0.322306	+	0.946635i	$0.395542\pi$
$840$		−	1676.10i		−	0.0688462i
$841$	−30936.9	+	53584.2i	−1.26848	+	2.19706i
$842$	14535.2	+	25175.7i	0.594911	+	1.03042i
$843$	17594.6	−	10158.3i	0.718851	−	0.415029i
$844$	−15655.8			−0.638501
$845$	21901.5	+	874.499i	0.891639	+	0.0356020i
$846$	−471.185			−0.0191486
$847$	−7279.39	+	4202.76i	−0.295304	+	0.170494i
$848$	−2526.11	−	4375.35i	−0.102296	−	0.177182i
$849$	3943.46	−	6830.27i	0.159410	−	0.276106i
$850$			6430.43i			0.259485i
$851$	29604.7	+	17092.3i	1.19252	+	0.688503i
$852$	−10086.7	−	5823.58i	−0.405594	−	0.234170i
$853$		−	45283.7i		−	1.81769i	−0.417139	−	0.908843i	$-0.636967\pi$
$853$		−	45283.7i		−	1.81769i	0.417139	−	0.908843i	$-0.363033\pi$
$854$	1459.99	−	2528.77i	0.0585008	−	0.101326i
$855$	−6578.35	−	11394.0i	−0.263128	−	0.455752i
$856$	−4483.50	+	2588.55i	−0.179022	+	0.103358i
$857$	29889.3			1.19136			0.595682	−	0.803220i	$-0.296882\pi$
$857$	29889.3			1.19136			0.595682	+	0.803220i	$0.296882\pi$
$858$	−2314.05	+	2223.50i	−0.0920751	+	0.0884720i
$859$	−4552.09			−0.180810			−0.0904048	−	0.995905i	$-0.528816\pi$
$859$	−4552.09			−0.180810			−0.0904048	+	0.995905i	$0.528816\pi$
$860$	7106.07	−	4102.69i	0.281761	−	0.162675i
$861$	−3685.62	−	6383.68i	−0.145883	−	0.252678i
$862$	−8130.95	+	14083.2i	−0.321278	+	0.556469i
$863$		−	30995.9i		−	1.22261i	−0.791395	−	0.611305i	$-0.790645\pi$
$863$		−	30995.9i		−	1.22261i	0.791395	−	0.611305i	$-0.209355\pi$
$864$	−748.246	−	432.000i	−0.0294628	−	0.0170103i
$865$	36311.3	+	20964.4i	1.42731	+	0.824058i
$866$		−	22463.8i		−	0.881466i
$867$	16544.7	−	28656.2i	0.648082	−	1.12251i
$868$	2543.40	+	4405.29i	0.0994568	+	0.172264i
$869$	−9677.64	+	5587.39i	−0.377781	+	0.218112i
$870$	−17581.4			−0.685131
$871$	1406.83	−	4860.29i	0.0547285	−	0.189075i
$872$	6160.70			0.239252
$873$	−2382.84	+	1375.73i	−0.0923791	+	0.0533351i
$874$	−12127.9	−	21006.2i	−0.469374	−	0.812979i
$875$	−5254.01	+	9100.21i	−0.202992	+	0.351592i
$876$			3622.64i			0.139723i
$877$	29650.6	+	17118.8i	1.14165	+	0.659134i	0.946840	−	0.321706i	$-0.104256\pi$
$877$	29650.6	+	17118.8i	1.14165	+	0.659134i	0.194814	+	0.980840i	$0.437590\pi$
$878$	−5630.63	−	3250.85i	−0.216429	−	0.124955i
$879$		−	18400.0i		−	0.706050i
$880$	910.765	−	1577.49i	0.0348885	−	0.0604287i
$881$	−12958.7	−	22445.1i	−0.495562	−	0.858339i	0.504425	−	0.863456i	$-0.331705\pi$
$881$	−12958.7	−	22445.1i	−0.495562	−	0.858339i	−0.999987	+	0.00511703i	$0.998371\pi$
$882$	763.834	−	441.000i	0.0291606	−	0.0168359i
$883$	−39794.2			−1.51663			−0.758313	−	0.651891i	$-0.773976\pi$
$883$	−39794.2			−1.51663			−0.758313	+	0.651891i	$0.773976\pi$
$884$	−22739.8	−	6582.10i	−0.865182	−	0.250430i
$885$	−12955.9			−0.492099
$886$	7148.17	−	4127.00i	0.271047	−	0.156489i
$887$	13682.6	+	23698.9i	0.517944	+	0.897105i	0.999783	+	0.0208450i	$0.00663566\pi$
$887$	13682.6	+	23698.9i	0.517944	+	0.897105i	−0.481839	+	0.876260i	$0.660031\pi$
$888$	−4956.10	+	8584.21i	−0.187292	+	0.324400i
$889$			9110.49i			0.343708i
$890$	1106.32	+	638.733i	0.0416673	+	0.0240566i
$891$	−800.465	−	462.149i	−0.0300972	−	0.0173766i
$892$		−	17601.9i		−	0.660713i
$893$	1917.80	−	3321.73i	0.0718664	−	0.124476i
$894$	−4846.28	−	8394.01i	−0.181302	−	0.314024i
$895$	−24988.6	+	14427.2i	−0.933270	+	0.538824i
$896$	896.000			0.0334077
$897$	2787.43	+	11300.1i	0.103757	+	0.420623i
$898$	13967.8			0.519057
$899$	46209.2	−	26678.9i	1.71431	−	0.989756i
$900$	458.353	+	793.891i	0.0169760	+	0.0294034i
$901$	19934.9	−	34528.3i	0.737102	−	1.27670i
$902$		−	8010.84i		−	0.295712i
$903$	3739.37	+	2158.93i	0.137806	+	0.0795621i
$904$	−7876.55	−	4547.53i	−0.289790	−	0.167310i
$905$		−	4099.27i		−	0.150568i
$906$	2184.85	−	3784.28i	0.0801180	−	0.138768i
$907$	11490.4	+	19901.9i	0.420652	+	0.728591i	0.996003	−	0.0893154i	$-0.0284679\pi$
$907$	11490.4	+	19901.9i	0.420652	+	0.728591i	−0.575351	+	0.817907i	$0.695135\pi$
$908$	−6597.12	+	3808.85i	−0.241116	+	0.139208i
$909$	−11875.8			−0.433329
$910$	−4536.04	−	4720.77i	−0.165240	−	0.171969i
$911$	46585.6			1.69424			0.847119	−	0.531403i	$-0.178335\pi$
$911$	46585.6			1.69424			0.847119	+	0.531403i	$0.178335\pi$
$912$	6090.97	−	3516.62i	0.221154	−	0.127683i
$913$	2974.24	+	5151.54i	0.107813	+	0.186737i
$914$	3731.22	−	6462.66i	0.135030	−	0.233879i
$915$		−	6242.55i		−	0.225544i
$916$	−15261.8	−	8811.41i	−0.550507	−	0.317835i
$917$	−7454.08	−	4303.61i	−0.268435	−	0.154981i
$918$		−	6818.30i		−	0.245139i
$919$	−17750.2	+	30744.2i	−0.637132	+	1.10354i	0.348928	+	0.937150i	$0.386546\pi$
$919$	−17750.2	+	30744.2i	−0.637132	+	1.10354i	−0.986059	+	0.166395i	$0.946787\pi$
$920$	−3303.10	−	5721.13i	−0.118369	−	0.205022i
$921$	−5757.60	+	3324.15i	−0.205993	+	0.118930i
$922$	−22559.0			−0.805794
$923$	−44170.0	+	10895.6i	−1.57516	+	0.388551i
$924$	958.530			0.0341270
$925$	9107.87	−	5258.43i	0.323746	−	0.186915i
$926$	9983.89	+	17292.6i	0.354310	+	0.613683i
$927$	−4609.01	+	7983.03i	−0.163301	+	0.282845i
$928$		−	9398.56i		−	0.332460i
$929$	−10114.0	−	5839.31i	−0.357189	−	0.206223i	0.310658	−	0.950522i	$-0.399451\pi$
$929$	−10114.0	−	5839.31i	−0.357189	−	0.206223i	−0.667847	+	0.744298i	$0.732784\pi$
$930$	9417.98	+	5437.47i	0.332073	+	0.191722i
$931$			7179.77i			0.252747i
$932$	−10227.3	+	17714.2i	−0.359448	+	0.622583i
$933$	−1632.88	−	2828.23i	−0.0572970	−	0.0992412i
$934$	−17992.9	+	10388.2i	−0.630347	+	0.363931i
$935$	14374.7			0.502784
$936$	−3276.58	+	808.247i	−0.114421	+	0.0282248i
$937$	20853.7			0.727067			0.363534	−	0.931581i	$-0.381570\pi$
$937$	20853.7			0.727067			0.363534	+	0.931581i	$0.381570\pi$
$938$	−1308.81	+	755.643i	−0.0455589	+	0.0263034i
$939$	−10007.4	−	17333.3i	−0.347794	−	0.602396i
$940$	522.323	−	904.689i	0.0181237	−	0.0313912i
$941$		−	3704.28i		−	0.128327i	−0.997939	−	0.0641637i	$-0.979562\pi$
$941$		−	3704.28i		−	0.128327i	0.997939	−	0.0641637i	$-0.0204380\pi$
$942$	8943.87	+	5163.74i	0.309349	+	0.178603i
$943$	−25160.8	−	14526.6i	−0.868873	−	0.501644i
$944$		−	6925.91i		−	0.238791i
$945$	942.805	−	1632.99i	0.0324544	−	0.0562127i
$946$	2346.26	+	4063.83i	0.0806378	+	0.139669i
$947$	−6266.66	+	3618.06i	−0.215036	+	0.124151i	−0.603650	−	0.797250i	$-0.706287\pi$
$947$	−6266.66	+	3618.06i	−0.215036	+	0.124151i	0.388614	+	0.921401i	$0.372954\pi$
$948$	−11751.5			−0.402607
$949$	9803.99	+	10203.3i	0.335354	+	0.349011i
$950$	−7462.29			−0.254851
$951$	8663.94	−	5002.13i	0.295423	−	0.170563i
$952$	3535.41	+	6123.52i	0.120361	+	0.208471i
$953$	9177.25	−	15895.5i	0.311942	−	0.540299i	−0.666841	−	0.745200i	$-0.732354\pi$
$953$	9177.25	−	15895.5i	0.311942	−	0.540299i	0.978783	+	0.204901i	$0.0656873\pi$
$954$		−	5683.75i		−	0.192891i
$955$	24974.7	+	14419.2i	0.846244	+	0.488579i
$956$	6386.15	+	3687.05i	0.216049	+	0.124736i
$957$		−	10054.5i		−	0.339619i
$958$	12441.6	−	21549.5i	0.419594	−	0.726758i
$959$	−5610.92	−	9718.40i	−0.188932	−	0.327240i
$960$	1658.91	−	957.770i	0.0557718	−	0.0321999i
$961$	−3213.41			−0.107865
$962$	9272.56	+	37590.4i	0.310769	+	1.25984i
$963$	−5824.24			−0.194895
$964$	14444.6	−	8339.57i	0.482602	−	0.278630i
$965$	−4787.99	−	8293.05i	−0.159721	−	0.276645i
$966$	1738.16	−	3010.59i	0.0578929	−	0.100273i
$967$			26619.2i			0.885229i	0.896712	+	0.442614i	$0.145949\pi$
$967$			26619.2i			0.885229i	−0.896712	+	0.442614i	$0.854051\pi$
$968$	−8319.30	−	4803.15i	−0.276232	−	0.159483i
$969$	48067.2	+	27751.6i	1.59354	+	0.920030i
$970$		−	6100.17i		−	0.201922i
$971$	−8751.99	+	15158.9i	−0.289253	+	0.501001i	−0.973632	−	0.228126i	$-0.926740\pi$
$971$	−8751.99	+	15158.9i	−0.289253	+	0.501001i	0.684379	+	0.729127i	$0.260074\pi$
$972$	−486.000	−	841.777i	−0.0160375	−	0.0277778i
$973$	1956.13	−	1129.37i	0.0644507	−	0.0372106i
$974$	7106.76			0.233794
$975$	3439.48	+	995.570i	0.112976	+	0.0327013i
$976$	3337.11			0.109445
$977$	456.544	−	263.586i	0.0149500	−	0.00863138i	−0.492506	−	0.870309i	$-0.663919\pi$
$977$	456.544	−	263.586i	0.0149500	−	0.00863138i	0.507456	+	0.861677i	$0.330586\pi$
$978$	−6391.88	−	11071.1i	−0.208987	−	0.361977i
$979$	−365.280	+	632.684i	−0.0119248	+	0.0206544i
$980$			1955.45i			0.0637392i
$981$	6002.24	+	3465.39i	0.195348	+	0.112784i
$982$	6479.06	+	3740.69i	0.210545	+	0.121558i
$983$		−	22948.1i		−	0.744588i	−0.928115	−	0.372294i	$-0.878571\pi$
$983$		−	22948.1i		−	0.744588i	0.928115	−	0.372294i	$-0.121429\pi$
$984$	4212.14	−	7295.64i	0.136461	−	0.236358i
$985$	−721.347	−	1249.41i	−0.0233340	−	0.0404157i
$986$	64232.4	−	37084.6i	2.07462	−	1.19778i
$987$	549.716			0.0177281
$988$	7638.30	−	26388.7i	0.245958	−	0.849734i
$989$	17018.5			0.547175
$990$	1774.68	−	1024.61i	0.0569727	−	0.0328932i
$991$	−24025.3	−	41613.1i	−0.770121	−	1.33389i	−0.937496	−	0.347995i	$-0.886863\pi$
$991$	−24025.3	−	41613.1i	−0.770121	−	1.33389i	0.167375	−	0.985893i	$-0.446471\pi$
$992$	−2906.74	+	5034.62i	−0.0930333	+	0.161138i
$993$		−	6624.30i		−	0.211698i
$994$	11767.9	+	6794.18i	0.375507	+	0.216799i
$995$	42278.1	+	24409.3i	1.34704	+	0.777714i
$996$			6255.49i			0.199009i
$997$	−26509.3	+	45915.4i	−0.842083	+	1.45853i	0.0460474	+	0.998939i	$0.485337\pi$
$997$	−26509.3	+	45915.4i	−0.842083	+	1.45853i	−0.888130	+	0.459591i	$0.847996\pi$
$998$	−13949.8	−	24161.8i	−0.442459	−	0.766361i
$999$	−9657.24	+	5575.61i	−0.305847	+	0.176581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.s.d.127.2	yes	24
13.4	even	6	inner	546.4.s.d.43.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.s.d.43.2	✓	24	13.4	even	6	inner
546.4.s.d.127.2	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(1.50000 + 2.59808i) q^{3} +(2.00000 - 3.46410i) q^{4} +9.97677i q^{5} +(-5.19615 - 3.00000i) q^{6} +(6.06218 + 3.50000i) q^{7} +8.00000i q^{8} +(-4.50000 + 7.79423i) q^{9} +(-9.97677 - 17.2803i) q^{10} +(9.88228 - 5.70554i) q^{11} +12.0000 q^{12} +(33.7983 - 32.4757i) q^{13} -14.0000 q^{14} +(-25.9204 + 14.9652i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(63.1324 - 109.348i) q^{17} -18.0000i q^{18} +(126.895 + 73.2629i) q^{19} +(34.5605 + 19.9535i) q^{20} +21.0000i q^{21} +(-11.4111 + 19.7646i) q^{22} +(41.3849 + 71.6807i) q^{23} +(-20.7846 + 12.0000i) q^{24} +25.4641 q^{25} +(-26.0647 + 90.0479i) q^{26} -27.0000 q^{27} +(24.2487 - 14.0000i) q^{28} +(-146.853 - 254.356i) q^{29} +(29.9303 - 51.8408i) q^{30} +181.671i q^{31} +(27.7128 + 16.0000i) q^{32} +(29.6468 + 17.1166i) q^{33} +252.530i q^{34} +(-34.9187 + 60.4809i) q^{35} +(18.0000 + 31.1769i) q^{36} +(357.675 - 206.504i) q^{37} -293.052 q^{38} +(135.072 + 39.0970i) q^{39} -79.8142 q^{40} +(-303.985 + 175.506i) q^{41} +(-21.0000 - 36.3731i) q^{42} +(102.806 - 178.065i) q^{43} -45.6443i q^{44} +(-77.7612 - 44.8955i) q^{45} +(-143.361 - 82.7697i) q^{46} -26.1769i q^{47} +(24.0000 - 41.5692i) q^{48} +(24.5000 + 42.4352i) q^{49} +(-44.1051 + 25.4641i) q^{50} +378.794 q^{51} +(-44.9026 - 182.032i) q^{52} +315.764 q^{53} +(46.7654 - 27.0000i) q^{54} +(56.9228 + 98.5932i) q^{55} +(-28.0000 + 48.4974i) q^{56} +439.578i q^{57} +(508.712 + 293.705i) q^{58} +(374.876 + 216.435i) q^{59} +119.721i q^{60} +(-104.285 + 180.626i) q^{61} +(-181.671 - 314.664i) q^{62} +(-54.5596 + 31.5000i) q^{63} -64.0000 q^{64} +(324.003 + 337.198i) q^{65} -68.4665 q^{66} +(93.4865 - 53.9745i) q^{67} +(-252.530 - 437.394i) q^{68} +(-124.155 + 215.042i) q^{69} -139.675i q^{70} +(-840.562 - 485.298i) q^{71} +(-62.3538 - 36.0000i) q^{72} +301.887i q^{73} +(-413.008 + 715.351i) q^{74} +(38.1961 + 66.1576i) q^{75} +(507.581 - 293.052i) q^{76} +79.8775 q^{77} +(-273.048 + 67.3539i) q^{78} -979.292 q^{79} +(138.242 - 79.8142i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(351.012 - 607.970i) q^{82} +521.290i q^{83} +(72.7461 + 42.0000i) q^{84} +(1090.94 + 629.857i) q^{85} +411.224i q^{86} +(440.558 - 763.068i) q^{87} +(45.6443 + 79.0583i) q^{88} +(-55.4447 + 32.0110i) q^{89} +179.582 q^{90} +(318.557 - 78.5795i) q^{91} +331.079 q^{92} +(-471.996 + 272.507i) q^{93} +(26.1769 + 45.3398i) q^{94} +(-730.928 + 1266.00i) q^{95} +96.0000i q^{96} +(264.760 + 152.859i) q^{97} +(-84.8705 - 49.0000i) q^{98} +102.700i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{3} + 48 q^{4} - 108 q^{9} - 24 q^{10} - 174 q^{11} + 288 q^{12} - 96 q^{13} - 336 q^{14} - 90 q^{15} - 192 q^{16} + 140 q^{17} - 60 q^{19} + 120 q^{20} - 128 q^{22} + 34 q^{23} - 1004 q^{25}+ \cdots - 3936 q^{97}+O(q^{100}) \) 24 * q + 36 * q^3 + 48 * q^4 - 108 * q^9 - 24 * q^10 - 174 * q^11 + 288 * q^12 - 96 * q^13 - 336 * q^14 - 90 * q^15 - 192 * q^16 + 140 * q^17 - 60 * q^19 + 120 * q^20 - 128 * q^22 + 34 * q^23 - 1004 * q^25 - 144 * q^26 - 648 * q^27 + 54 * q^29 + 72 * q^30 - 522 * q^33 - 84 * q^35 + 432 * q^36 + 1416 * q^37 + 1056 * q^38 + 108 * q^39 - 192 * q^40 - 942 * q^41 - 504 * q^42 + 762 * q^43 - 270 * q^45 + 636 * q^46 + 576 * q^48 + 588 * q^49 + 720 * q^50 + 840 * q^51 - 528 * q^52 + 184 * q^53 - 256 * q^55 - 672 * q^56 - 2088 * q^58 + 2322 * q^59 - 1274 * q^61 - 232 * q^62 - 1536 * q^64 - 1298 * q^65 - 768 * q^66 - 2472 * q^67 - 560 * q^68 - 102 * q^69 - 2196 * q^71 - 348 * q^74 - 1506 * q^75 - 240 * q^76 + 896 * q^77 - 468 * q^78 - 520 * q^79 + 480 * q^80 - 972 * q^81 - 244 * q^82 + 7974 * q^85 - 162 * q^87 + 512 * q^88 + 1032 * q^89 + 432 * q^90 + 546 * q^91 + 272 * q^92 - 2880 * q^93 - 1104 * q^94 - 2574 * q^95 - 3936 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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