LMFDB - Embedded newform 546.4.s.a.127.5

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 = [20,0,-30] 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1388 x^{18} + 806954 x^{16} + 255183238 x^{14} + 47714604791 x^{12} + 5370647791638 x^{10} + \cdots + 42\!\cdots\!84 $ x^20 + 1388x^18 + 806954x^16 + 255183238x^14 + 47714604791x^12 + 5370647791638x^10 + 354442825910071x^8 + 12732087350994070x^6 + 214746587484940741x^4 + 1171569470005573456*x^2 + 422518488802265284
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.5
Root			$16.5747i$ of defining polynomial
Character	$\chi$	$=$	546.127
Dual form			546.4.s.a.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 + 1.00000i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(2.00000 - 3.46410i) q^{4} +17.5747i q^{5} +(5.19615 + 3.00000i) q^{6} +(6.06218 + 3.50000i) q^{7} +8.00000i q^{8} +(-4.50000 + 7.79423i) q^{9} +(-17.5747 - 30.4403i) q^{10} +(-6.24601 + 3.60613i) q^{11} -12.0000 q^{12} +(34.3917 + 31.8466i) q^{13} -14.0000 q^{14} +(45.6604 - 26.3620i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-51.0916 + 88.4932i) q^{17} -18.0000i q^{18} +(50.3531 + 29.0713i) q^{19} +(60.8805 + 35.1494i) q^{20} -21.0000i q^{21} +(7.21227 - 12.4920i) q^{22} +(-3.10875 - 5.38452i) q^{23} +(20.7846 - 12.0000i) q^{24} -183.870 q^{25} +(-91.4149 - 20.7683i) q^{26} +27.0000 q^{27} +(24.2487 - 14.0000i) q^{28} +(40.4407 + 70.0453i) q^{29} +(-52.7241 + 91.3208i) q^{30} -64.8623i q^{31} +(27.7128 + 16.0000i) q^{32} +(18.7380 + 10.8184i) q^{33} -204.366i q^{34} +(-61.5114 + 106.541i) q^{35} +(18.0000 + 31.1769i) q^{36} +(326.257 - 188.364i) q^{37} -116.285 q^{38} +(31.1524 - 137.122i) q^{39} -140.597 q^{40} +(-70.9247 + 40.9484i) q^{41} +(21.0000 + 36.3731i) q^{42} +(186.016 - 322.190i) q^{43} +28.8491i q^{44} +(-136.981 - 79.0861i) q^{45} +(10.7690 + 6.21750i) q^{46} +26.6251i q^{47} +(-24.0000 + 41.5692i) q^{48} +(24.5000 + 42.4352i) q^{49} +(318.472 - 183.870i) q^{50} +306.550 q^{51} +(179.103 - 55.4432i) q^{52} -573.013 q^{53} +(-46.7654 + 27.0000i) q^{54} +(-63.3767 - 109.772i) q^{55} +(-28.0000 + 48.4974i) q^{56} -174.428i q^{57} +(-140.091 - 80.8814i) q^{58} +(-47.3101 - 27.3145i) q^{59} -210.896i q^{60} +(-427.732 + 740.853i) q^{61} +(64.8623 + 112.345i) q^{62} +(-54.5596 + 31.5000i) q^{63} -64.0000 q^{64} +(-559.695 + 604.424i) q^{65} -43.2736 q^{66} +(-288.825 + 166.753i) q^{67} +(204.366 + 353.973i) q^{68} +(-9.32626 + 16.1535i) q^{69} -246.046i q^{70} +(-59.1504 - 34.1505i) q^{71} +(-62.3538 - 36.0000i) q^{72} +367.492i q^{73} +(-376.729 + 652.514i) q^{74} +(275.804 + 477.707i) q^{75} +(201.412 - 116.285i) q^{76} -50.4859 q^{77} +(83.1648 + 268.655i) q^{78} -348.236 q^{79} +(243.522 - 140.597i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(81.8967 - 141.849i) q^{82} +573.119i q^{83} +(-72.7461 - 42.0000i) q^{84} +(-1555.24 - 897.919i) q^{85} +744.065i q^{86} +(121.322 - 210.136i) q^{87} +(-28.8491 - 49.9680i) q^{88} +(-478.182 + 276.078i) q^{89} +316.344 q^{90} +(97.0256 + 313.431i) q^{91} -24.8700 q^{92} +(-168.517 + 97.2935i) q^{93} +(-26.6251 - 46.1161i) q^{94} +(-510.920 + 884.939i) q^{95} -96.0000i q^{96} +(-1063.47 - 613.996i) q^{97} +(-84.8705 - 49.0000i) q^{98} -64.9104i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 40 q^{4} - 90 q^{9} - 24 q^{10} + 18 q^{11} - 240 q^{12} + 28 q^{13} - 280 q^{14} + 18 q^{15} - 160 q^{16} - 106 q^{17} - 60 q^{19} + 24 q^{20} - 24 q^{22} - 450 q^{23} - 304 q^{25} - 60 q^{26}+ \cdots - 1620 q^{97}+O(q^{100}) $ 20 * q - 30 * q^3 + 40 * q^4 - 90 * q^9 - 24 * q^10 + 18 * q^11 - 240 * q^12 + 28 * q^13 - 280 * q^14 + 18 * q^15 - 160 * q^16 - 106 * q^17 - 60 * q^19 + 24 * q^20 - 24 * q^22 - 450 * q^23 - 304 * q^25 - 60 * q^26 + 540 * q^27 + 290 * q^29 - 72 * q^30 - 54 * q^33 - 84 * q^35 + 360 * q^36 + 564 * q^37 + 160 * q^38 + 228 * q^39 - 192 * q^40 - 246 * q^41 + 420 * q^42 - 464 * q^43 - 54 * q^45 - 240 * q^46 - 480 * q^48 + 490 * q^49 + 720 * q^50 + 636 * q^51 + 416 * q^52 - 1528 * q^53 + 1384 * q^55 - 560 * q^56 - 480 * q^58 - 2496 * q^59 - 270 * q^61 - 60 * q^62 - 1280 * q^64 + 3042 * q^65 + 144 * q^66 + 1314 * q^67 + 424 * q^68 - 1350 * q^69 - 516 * q^71 - 540 * q^74 + 456 * q^75 - 240 * q^76 + 168 * q^77 + 1116 * q^78 - 4000 * q^79 + 96 * q^80 - 810 * q^81 - 476 * q^82 - 2730 * q^85 + 870 * q^87 + 96 * q^88 - 1266 * q^89 + 432 * q^90 + 1302 * q^91 - 3600 * q^92 + 1692 * q^93 + 1080 * q^94 - 3798 * q^95 - 1620 * 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
$5$			17.5747i			1.57193i	0.618272	+	0.785964i	$0.287833\pi$
$5$			17.5747i			1.57193i	−0.618272	+	0.785964i	$0.712167\pi$
$6$	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
$10$	−17.5747	−	30.4403i	−0.555760	−	0.962605i
$11$	−6.24601	+	3.60613i	−0.171204	+	0.0988445i	−0.583153	−	0.812362i	$-0.698181\pi$
$11$	−6.24601	+	3.60613i	−0.171204	+	0.0988445i	0.411950	+	0.911207i	$0.364848\pi$
$12$	−12.0000			−0.288675
$13$	34.3917	+	31.8466i	0.733735	+	0.679436i
$13$	34.3917	+	31.8466i	0.733735	+	0.679436i
$14$	−14.0000			−0.267261
$15$	45.6604	−	26.3620i	0.785964	−	0.453776i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−51.0916	+	88.4932i	−0.728914	+	1.26252i	0.228429	+	0.973561i	$0.426641\pi$
$17$	−51.0916	+	88.4932i	−0.728914	+	1.26252i	−0.957343	+	0.288955i	$0.906692\pi$
$18$		−	18.0000i		−	0.235702i
$19$	50.3531	+	29.0713i	0.607989	+	0.351022i	0.772178	−	0.635407i	$-0.219167\pi$
$19$	50.3531	+	29.0713i	0.607989	+	0.351022i	−0.164189	+	0.986429i	$0.552501\pi$
$20$	60.8805	+	35.1494i	0.680665	+	0.392982i
$21$		−	21.0000i		−	0.218218i
$22$	7.21227	−	12.4920i	0.0698936	−	0.121059i
$23$	−3.10875	−	5.38452i	−0.0281835	−	0.0488152i	0.851590	−	0.524209i	$-0.175639\pi$
$23$	−3.10875	−	5.38452i	−0.0281835	−	0.0488152i	−0.879773	+	0.475394i	$0.842306\pi$
$24$	20.7846	−	12.0000i	0.176777	−	0.102062i
$25$	−183.870			−1.47096
$26$	−91.4149	−	20.7683i	−0.689536	−	0.156653i
$27$	27.0000			0.192450
$28$	24.2487	−	14.0000i	0.163663	−	0.0944911i
$29$	40.4407	+	70.0453i	0.258953	+	0.448520i	0.965962	−	0.258685i	$-0.0832890\pi$
$29$	40.4407	+	70.0453i	0.258953	+	0.448520i	−0.707008	+	0.707205i	$0.749956\pi$
$30$	−52.7241	+	91.3208i	−0.320868	+	0.555760i
$31$		−	64.8623i		−	0.375794i	−0.982189	−	0.187897i	$-0.939833\pi$
$31$		−	64.8623i		−	0.375794i	0.982189	−	0.187897i	$-0.0601671\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$	18.7380	+	10.8184i	0.0988445	+	0.0570679i
$34$		−	204.366i		−	1.03084i
$35$	−61.5114	+	106.541i	−0.297066	+	0.514534i
$36$	18.0000	+	31.1769i	0.0833333	+	0.144338i
$37$	326.257	−	188.364i	1.44963	−	0.836944i	0.451170	−	0.892438i	$-0.351007\pi$
$37$	326.257	−	188.364i	1.44963	−	0.836944i	0.998459	+	0.0554938i	$0.0176733\pi$
$38$	−116.285			−0.496421
$39$	31.1524	−	137.122i	0.127907	−	0.563004i
$40$	−140.597			−0.555760
$41$	−70.9247	+	40.9484i	−0.270160	+	0.155977i	−0.628960	−	0.777437i	$-0.716519\pi$
$41$	−70.9247	+	40.9484i	−0.270160	+	0.155977i	0.358800	+	0.933414i	$0.383186\pi$
$42$	21.0000	+	36.3731i	0.0771517	+	0.133631i
$43$	186.016	−	322.190i	0.659703	−	1.14264i	−0.320990	−	0.947083i	$-0.604015\pi$
$43$	186.016	−	322.190i	0.659703	−	1.14264i	0.980692	−	0.195556i	$-0.0626512\pi$
$44$			28.8491i			0.0988445i
$45$	−136.981	−	79.0861i	−0.453776	−	0.261988i
$46$	10.7690	+	6.21750i	0.0345176	+	0.0199287i
$47$			26.6251i			0.0826313i	0.999146	+	0.0413157i	$0.0131549\pi$
$47$			26.6251i			0.0826313i	−0.999146	+	0.0413157i	$0.986845\pi$
$48$	−24.0000	+	41.5692i	−0.0721688	+	0.125000i
$49$	24.5000	+	42.4352i	0.0714286	+	0.123718i
$50$	318.472	−	183.870i	0.900774	−	0.520062i
$51$	306.550			0.841677
$52$	179.103	−	55.4432i	0.477638	−	0.147857i
$53$	−573.013			−1.48508			−0.742541	−	0.669800i	$-0.766380\pi$
$53$	−573.013			−1.48508			−0.742541	+	0.669800i	$0.766380\pi$
$54$	−46.7654	+	27.0000i	−0.117851	+	0.0680414i
$55$	−63.3767	−	109.772i	−0.155376	−	0.269120i
$56$	−28.0000	+	48.4974i	−0.0668153	+	0.115728i
$57$		−	174.428i		−	0.405326i
$58$	−140.091	−	80.8814i	−0.317152	−	0.183108i
$59$	−47.3101	−	27.3145i	−0.104394	−	0.0602720i	0.446894	−	0.894587i	$-0.352530\pi$
$59$	−47.3101	−	27.3145i	−0.104394	−	0.0602720i	−0.551288	+	0.834315i	$0.685863\pi$
$60$		−	210.896i		−	0.453776i
$61$	−427.732	+	740.853i	−0.897794	+	1.55503i	−0.0674869	+	0.997720i	$0.521498\pi$
$61$	−427.732	+	740.853i	−0.897794	+	1.55503i	−0.830308	+	0.557305i	$0.811835\pi$
$62$	64.8623	+	112.345i	0.132863	+	0.230126i
$63$	−54.5596	+	31.5000i	−0.109109	+	0.0629941i
$64$	−64.0000			−0.125000
$65$	−559.695	+	604.424i	−1.06802	+	1.15338i
$66$	−43.2736			−0.0807062
$67$	−288.825	+	166.753i	−0.526651	+	0.304062i	−0.739651	−	0.672990i	$-0.765010\pi$
$67$	−288.825	+	166.753i	−0.526651	+	0.304062i	0.213001	+	0.977052i	$0.431676\pi$
$68$	204.366	+	353.973i	0.364457	+	0.631258i
$69$	−9.32626	+	16.1535i	−0.0162717	+	0.0281835i
$70$		−	246.046i		−	0.420115i
$71$	−59.1504	−	34.1505i	−0.0988713	−	0.0570834i	0.449749	−	0.893155i	$-0.351513\pi$
$71$	−59.1504	−	34.1505i	−0.0988713	−	0.0570834i	−0.548620	+	0.836072i	$0.684847\pi$
$72$	−62.3538	−	36.0000i	−0.102062	−	0.0589256i
$73$			367.492i			0.589200i	0.955621	+	0.294600i	$0.0951865\pi$
$73$			367.492i			0.589200i	−0.955621	+	0.294600i	$0.904814\pi$
$74$	−376.729	+	652.514i	−0.591809	+	1.02504i
$75$	275.804	+	477.707i	0.424629	+	0.735479i
$76$	201.412	−	116.285i	0.303994	−	0.175511i
$77$	−50.4859			−0.0747194
$78$	83.1648	+	268.655i	0.120725	+	0.389990i
$79$	−348.236			−0.495944			−0.247972	−	0.968767i	$-0.579764\pi$
$79$	−348.236			−0.495944			−0.247972	+	0.968767i	$0.579764\pi$
$80$	243.522	−	140.597i	0.340332	−	0.196491i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	81.8967	−	141.849i	0.110292	−	0.191032i
$83$			573.119i			0.757927i	0.925412	+	0.378963i	$0.123719\pi$
$83$			573.119i			0.757927i	−0.925412	+	0.378963i	$0.876281\pi$
$84$	−72.7461	−	42.0000i	−0.0944911	−	0.0545545i
$85$	−1555.24	−	897.919i	−1.98458	−	1.14580i
$86$			744.065i			0.932961i
$87$	121.322	−	210.136i	0.149507	−	0.258953i
$88$	−28.8491	−	49.9680i	−0.0349468	−	0.0605297i
$89$	−478.182	+	276.078i	−0.569519	+	0.328812i	−0.756957	−	0.653465i	$-0.773315\pi$
$89$	−478.182	+	276.078i	−0.569519	+	0.328812i	0.187438	+	0.982276i	$0.439982\pi$
$90$	316.344			0.370507
$91$	97.0256	+	313.431i	0.111770	+	0.361060i
$92$	−24.8700			−0.0281835
$93$	−168.517	+	97.2935i	−0.187897	+	0.108482i
$94$	−26.6251	−	46.1161i	−0.0292146	−	0.0506012i
$95$	−510.920	+	884.939i	−0.551782	+	0.955714i
$96$		−	96.0000i		−	0.102062i
$97$	−1063.47	−	613.996i	−1.11319	−	0.642700i	−0.173535	−	0.984828i	$-0.555519\pi$
$97$	−1063.47	−	613.996i	−1.11319	−	0.642700i	−0.939653	+	0.342128i	$0.888852\pi$
$98$	−84.8705	−	49.0000i	−0.0874818	−	0.0505076i
$99$		−	64.9104i		−	0.0658964i
$100$	−367.739	+	636.943i	−0.367739	+	0.636943i
$101$	55.0834	+	95.4072i	0.0542673	+	0.0939938i	0.891883	−	0.452266i	$-0.149384\pi$
$101$	55.0834	+	95.4072i	0.0542673	+	0.0939938i	−0.837616	+	0.546260i	$0.816051\pi$
$102$	−530.959	+	306.550i	−0.515420	+	0.297578i
$103$	−1346.22			−1.28784			−0.643919	−	0.765093i	$-0.722693\pi$
$103$	−1346.22			−1.28784			−0.643919	+	0.765093i	$0.722693\pi$
$104$	−254.773	+	275.134i	−0.240217	+	0.259414i
$105$	369.068			0.343023
$106$	992.488	−	573.013i	0.909424	−	0.525056i
$107$	525.700	+	910.538i	0.474965	+	0.822664i	0.999589	−	0.0286702i	$-0.00912727\pi$
$107$	525.700	+	910.538i	0.474965	+	0.822664i	−0.524624	+	0.851334i	$0.675794\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$		−	21.9208i		−	0.0192627i	−0.999954	−	0.00963134i	$-0.996934\pi$
$109$		−	21.9208i		−	0.0192627i	0.999954	−	0.00963134i	$-0.00306580\pi$
$110$	219.543	+	126.753i	0.190297	+	0.109868i
$111$	−978.770	−	565.093i	−0.836944	−	0.483210i
$112$		−	112.000i		−	0.0944911i
$113$	617.398	−	1069.37i	0.513982	−	0.890243i	−0.485887	−	0.874022i	$-0.661503\pi$
$113$	617.398	−	1069.37i	0.513982	−	0.890243i	0.999868	−	0.0162209i	$-0.00516349\pi$
$114$	174.428	+	302.118i	0.143304	+	0.248210i
$115$	94.6312	−	54.6353i	0.0767340	−	0.0443024i
$116$	323.526			0.258953
$117$	−402.983	+	124.747i	−0.318425	+	0.0985717i
$118$	109.258			0.0852374
$119$	−619.453	+	357.641i	−0.477186	+	0.275503i
$120$	210.896	+	365.283i	0.160434	+	0.277880i
$121$	−639.492	+	1107.63i	−0.480460	+	0.832180i
$122$		−	1710.93i		−	1.26967i
$123$	212.774	+	122.845i	0.155977	+	0.0900534i
$124$	−224.690	−	129.725i	−0.162724	−	0.0939485i
$125$		−	1034.62i		−	0.740311i
$126$	63.0000	−	109.119i	0.0445435	−	0.0771517i
$127$	−765.806	−	1326.42i	−0.535073	−	0.926774i	−0.999160	−	0.0409845i	$-0.986951\pi$
$127$	−765.806	−	1326.42i	−0.535073	−	0.926774i	0.464086	−	0.885790i	$-0.346383\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$	−1116.10			−0.761759
$130$	364.996	−	1606.59i	0.246248	−	1.08390i
$131$	2733.48			1.82310			0.911548	−	0.411193i	$-0.134888\pi$
$131$	2733.48			1.82310			0.911548	+	0.411193i	$0.134888\pi$
$132$	74.9521	−	43.2736i	0.0494223	−	0.0285340i
$133$	203.499	+	352.471i	0.132674	+	0.229798i
$134$	333.506	−	577.650i	0.215004	−	0.372398i
$135$			474.517i			0.302518i
$136$	−707.946	−	408.733i	−0.446367	−	0.257710i
$137$	−1093.00	−	631.046i	−0.681617	−	0.393532i	0.118847	−	0.992913i	$-0.462080\pi$
$137$	−1093.00	−	631.046i	−0.681617	−	0.393532i	−0.800464	+	0.599381i	$0.795414\pi$
$138$		−	37.3050i		−	0.0230117i
$139$	−320.342	+	554.848i	−0.195475	+	0.338573i	−0.947056	−	0.321068i	$-0.895958\pi$
$139$	−320.342	+	554.848i	−0.195475	+	0.338573i	0.751581	+	0.659641i	$0.229292\pi$
$140$	246.046	+	426.164i	0.148533	+	0.257267i
$141$	69.1741	−	39.9377i	0.0413157	−	0.0238536i
$142$	136.602			0.0807281
$143$	−329.654	−	74.8931i	−0.192777	−	0.0437963i
$144$	144.000			0.0833333
$145$	−1231.03	+	710.733i	−0.705042	+	0.407056i
$146$	−367.492	−	636.514i	−0.208314	−	0.360810i
$147$	73.5000	−	127.306i	0.0412393	−	0.0714286i
$148$		−	1506.92i		−	0.836944i
$149$	−1893.27	−	1093.08i	−1.04096	−	0.600997i	−0.120853	−	0.992670i	$-0.538563\pi$
$149$	−1893.27	−	1093.08i	−1.04096	−	0.600997i	−0.920104	+	0.391674i	$0.871896\pi$
$150$	−955.415	−	551.609i	−0.520062	−	0.300258i
$151$		−	213.418i		−	0.115018i	−0.998345	−	0.0575090i	$-0.981684\pi$
$151$		−	213.418i		−	0.115018i	0.998345	−	0.0575090i	$-0.0183158\pi$
$152$	−232.571	+	402.824i	−0.124105	+	0.214956i
$153$	−459.824	−	796.439i	−0.242971	−	0.420838i
$154$	87.4441	−	50.4859i	0.0457561	−	0.0264173i
$155$	1139.94			0.590721
$156$	−412.701	−	382.160i	−0.211811	−	0.196136i
$157$	−206.908			−0.105179			−0.0525894	−	0.998616i	$-0.516747\pi$
$157$	−206.908			−0.105179			−0.0525894	+	0.998616i	$0.516747\pi$
$158$	603.162	−	348.236i	0.303703	−	0.175343i
$159$	859.519	+	1488.73i	0.428706	+	0.742541i
$160$	−281.195	+	487.044i	−0.138940	+	0.240651i
$161$		−	43.5225i		−	0.0213047i
$162$	140.296	+	81.0000i	0.0680414	+	0.0392837i
$163$	−1116.61	−	644.677i	−0.536564	−	0.309785i	0.207121	−	0.978315i	$-0.433590\pi$
$163$	−1116.61	−	644.677i	−0.536564	−	0.309785i	−0.743685	+	0.668530i	$0.766924\pi$
$164$			327.587i			0.155977i
$165$	−190.130	+	329.315i	−0.0897067	+	0.155376i
$166$	−573.119	−	992.670i	−0.267968	−	0.464134i
$167$	−1682.49	+	971.387i	−0.779611	+	0.450109i	−0.836293	−	0.548283i	$-0.815282\pi$
$167$	−1682.49	+	971.387i	−0.779611	+	0.450109i	0.0566811	+	0.998392i	$0.481948\pi$
$168$	168.000			0.0771517
$169$	168.584	+	2190.52i	0.0767335	+	0.997052i
$170$	3591.67			1.62041
$171$	−453.177	+	261.642i	−0.202663	+	0.117007i
$172$	−744.065	−	1288.76i	−0.329851	−	0.571319i
$173$	−1119.81	+	1939.56i	−0.492123	+	0.852382i	−0.999959	−	0.00907168i	$-0.997112\pi$
$173$	−1119.81	+	1939.56i	−0.492123	+	0.852382i	0.507836	+	0.861454i	$0.330446\pi$
$174$			485.288i			0.211435i
$175$	−1114.65	−	643.544i	−0.481484	−	0.277985i
$176$	99.9361	+	57.6981i	0.0428009	+	0.0247111i
$177$			163.887i			0.0695961i
$178$	552.157	−	956.363i	0.232505	−	0.402711i
$179$	−1364.94	−	2364.14i	−0.569944	−	0.987173i	−0.996571	−	0.0827447i	$-0.973631\pi$
$179$	−1364.94	−	2364.14i	−0.569944	−	0.987173i	0.426626	−	0.904428i	$-0.359702\pi$
$180$	−547.925	+	316.344i	−0.226888	+	0.130994i
$181$	1622.85			0.666440			0.333220	−	0.942849i	$-0.391865\pi$
$181$	1622.85			0.666440			0.333220	+	0.942849i	$0.391865\pi$
$182$	−481.484	−	445.853i	−0.196099	−	0.181587i
$183$	2566.39			1.03668
$184$	43.0761	−	24.8700i	0.0172588	−	0.00996436i
$185$	3310.45	+	5733.86i	1.31562	+	2.27871i
$186$	194.587	−	337.035i	0.0767087	−	0.132863i
$187$		−	736.972i		−	0.288196i
$188$	92.2321	+	53.2502i	0.0357804	+	0.0206578i
$189$	163.679	+	94.5000i	0.0629941	+	0.0363696i
$190$		−	2043.68i		−	0.780337i
$191$	1419.03	−	2457.84i	0.537579	−	0.931114i	−0.461455	−	0.887164i	$-0.652672\pi$
$191$	1419.03	−	2457.84i	0.537579	−	0.931114i	0.999034	−	0.0439503i	$-0.0139943\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	2052.35	−	1184.92i	0.765446	−	0.441930i	−0.0658018	−	0.997833i	$-0.520961\pi$
$193$	2052.35	−	1184.92i	0.765446	−	0.441930i	0.831248	+	0.555902i	$0.187627\pi$
$194$	2455.99			0.908915
$195$	2409.88	+	547.493i	0.885001	+	0.201061i
$196$	196.000			0.0714286
$197$	952.346	−	549.837i	0.344425	−	0.198854i	−0.317802	−	0.948157i	$-0.602945\pi$
$197$	952.346	−	549.837i	0.344425	−	0.198854i	0.662227	+	0.749303i	$0.269611\pi$
$198$	64.9104	+	112.428i	0.0232979	+	0.0403531i
$199$	892.776	−	1546.33i	0.318026	−	0.550838i	−0.662050	−	0.749460i	$-0.730313\pi$
$199$	892.776	−	1546.33i	0.318026	−	0.550838i	0.980076	+	0.198622i	$0.0636466\pi$
$200$		−	1470.96i		−	0.520062i
$201$	866.475	+	500.260i	0.304062	+	0.175550i
$202$	−190.814	−	110.167i	−0.0664637	−	0.0383728i
$203$			566.170i			0.195750i
$204$	613.099	−	1061.92i	0.210419	−	0.364457i
$205$	−719.655	−	1246.48i	−0.245185	−	0.424672i
$206$	2331.73	−	1346.22i	0.788637	−	0.455320i
$207$	55.9575			0.0187890
$208$	166.146	−	731.319i	0.0553854	−	0.243788i
$209$	−419.341			−0.138787
$210$	−639.245	+	369.068i	−0.210058	+	0.121277i
$211$	2533.10	+	4387.47i	0.826474	+	1.43150i	0.900787	+	0.434261i	$0.142990\pi$
$211$	2533.10	+	4387.47i	0.826474	+	1.43150i	−0.0743128	+	0.997235i	$0.523676\pi$
$212$	−1146.03	+	1984.98i	−0.371271	+	0.643060i
$213$			204.903i			0.0659142i
$214$	−1821.08	−	1051.40i	−0.581711	−	0.335851i
$215$	5662.38	+	3269.18i	1.79615	+	1.03701i
$216$			216.000i			0.0680414i
$217$	227.018	−	393.207i	0.0710184	−	0.123007i
$218$	21.9208	+	37.9680i	0.00681039	+	0.0117959i
$219$	954.771	−	551.237i	0.294600	−	0.170088i
$220$	−507.013			−0.155376
$221$	−4575.34	+	1416.34i	−1.39263	+	0.431101i
$222$	2260.37			0.683362
$223$	−1621.56	+	936.208i	−0.486940	+	0.281135i	−0.723304	−	0.690530i	$-0.757378\pi$
$223$	−1621.56	+	936.208i	−0.486940	+	0.281135i	0.236364	+	0.971665i	$0.424044\pi$
$224$	112.000	+	193.990i	0.0334077	+	0.0578638i
$225$	827.413	−	1433.12i	0.245160	−	0.424629i
$226$			2469.59i			0.726880i
$227$	2616.36	+	1510.56i	0.764997	+	0.441671i	0.831087	−	0.556143i	$-0.187719\pi$
$227$	2616.36	+	1510.56i	0.764997	+	0.441671i	−0.0660902	+	0.997814i	$0.521053\pi$
$228$	−604.237	−	348.856i	−0.175511	−	0.101331i
$229$		−	1451.24i		−	0.418780i	−0.977832	−	0.209390i	$-0.932852\pi$
$229$		−	1451.24i		−	0.418780i	0.977832	−	0.209390i	$-0.0671478\pi$
$230$	−109.271	+	189.262i	−0.0313265	+	0.0542591i
$231$	75.7288	+	131.166i	0.0215696	+	0.0373597i
$232$	−560.363	+	323.526i	−0.158576	+	0.0915539i
$233$	1761.09			0.495161			0.247581	−	0.968867i	$-0.420365\pi$
$233$	1761.09			0.495161			0.247581	+	0.968867i	$0.420365\pi$
$234$	573.239	−	619.051i	0.160145	−	0.172943i
$235$	−467.928			−0.129891
$236$	−189.240	+	109.258i	−0.0521971	+	0.0301360i
$237$	522.354	+	904.743i	0.143167	+	0.247972i
$238$	715.282	−	1238.91i	0.194810	−	0.337421i
$239$			2348.98i			0.635746i	0.948133	+	0.317873i	$0.102968\pi$
$239$			2348.98i			0.635746i	−0.948133	+	0.317873i	$0.897032\pi$
$240$	−730.566	−	421.792i	−0.196491	−	0.113444i
$241$	−1437.38	−	829.870i	−0.384189	−	0.221812i	0.295450	−	0.955358i	$-0.404530\pi$
$241$	−1437.38	−	829.870i	−0.384189	−	0.221812i	−0.679639	+	0.733546i	$0.737864\pi$
$242$		−	2557.97i		−	0.679472i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	1710.93	+	2963.41i	0.448897	+	0.777513i
$245$	−745.786	+	430.580i	−0.194476	+	0.112281i
$246$	−491.380			−0.127355
$247$	805.904	+	2603.39i	0.207605	+	0.670647i
$248$	518.899			0.132863
$249$	1489.01	−	859.678i	0.378963	−	0.218795i
$250$	1034.62	+	1792.01i	0.261739	+	0.453346i
$251$	1297.02	−	2246.51i	0.326165	−	0.564934i	−0.655583	−	0.755123i	$-0.727577\pi$
$251$	1297.02	−	2246.51i	0.326165	−	0.564934i	0.981747	+	0.190189i	$0.0609102\pi$
$252$			252.000i			0.0629941i
$253$	38.8346	+	22.4211i	0.00965023	+	0.00557156i
$254$	2652.83	+	1531.61i	0.655329	+	0.378354i
$255$			5387.51i			1.32306i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1774.21	+	3073.03i	0.430632	+	0.745876i	0.996928	−	0.0783257i	$-0.0249574\pi$
$257$	1774.21	+	3073.03i	0.430632	+	0.745876i	−0.566296	+	0.824202i	$0.691624\pi$
$258$	1933.14	−	1116.10i	0.466480	−	0.269323i
$259$	2637.10			0.632670
$260$	974.397	+	3147.69i	0.232421	+	0.750813i
$261$	−727.933			−0.172636
$262$	−4734.53	+	2733.48i	−1.11641	+	0.644562i
$263$	3763.60	+	6518.74i	0.882409	+	1.52838i	0.848655	+	0.528946i	$0.177413\pi$
$263$	3763.60	+	6518.74i	0.882409	+	1.52838i	0.0337533	+	0.999430i	$0.489254\pi$
$264$	−86.5472	+	149.904i	−0.0201766	+	0.0349468i
$265$		−	10070.5i		−	2.33444i
$266$	−704.943	−	406.999i	−0.162492	−	0.0938147i
$267$	1434.55	+	828.235i	0.328812	+	0.189840i
$268$			1334.03i			0.304062i
$269$	3447.51	−	5971.27i	0.781408	−	1.35344i	−0.149714	−	0.988729i	$-0.547835\pi$
$269$	3447.51	−	5971.27i	0.781408	−	1.35344i	0.931122	−	0.364708i	$-0.118831\pi$
$270$	−474.517	−	821.887i	−0.106956	−	0.185253i
$271$	3475.97	−	2006.85i	0.779152	−	0.449844i	−0.0569775	−	0.998375i	$-0.518146\pi$
$271$	3475.97	−	2006.85i	0.779152	−	0.449844i	0.836130	+	0.548532i	$0.184813\pi$
$272$	1634.93			0.364457
$273$	668.779	−	722.227i	0.148265	−	0.160114i
$274$	2524.18			0.556538
$275$	1148.45	−	663.058i	0.251833	−	0.145396i
$276$	37.3050	+	64.6142i	0.00813586	+	0.0140917i
$277$	−4106.97	+	7113.48i	−0.890844	+	1.54299i	−0.0519783	+	0.998648i	$0.516553\pi$
$277$	−4106.97	+	7113.48i	−0.890844	+	1.54299i	−0.838866	+	0.544339i	$0.816781\pi$
$278$		−	1281.37i		−	0.276443i
$279$	505.552	+	291.880i	0.108482	+	0.0626324i
$280$	−852.327	−	492.091i	−0.181915	−	0.105029i
$281$			5067.64i			1.07584i	0.842997	+	0.537918i	$0.180789\pi$
$281$			5067.64i			1.07584i	−0.842997	+	0.537918i	$0.819211\pi$
$282$	−79.8754	+	138.348i	−0.0168671	+	0.0292146i
$283$	−3165.19	−	5482.27i	−0.664845	−	1.15154i	−0.979327	−	0.202281i	$-0.935164\pi$
$283$	−3165.19	−	5482.27i	−0.664845	−	1.15154i	0.314483	−	0.949263i	$-0.398169\pi$
$284$	−236.602	+	136.602i	−0.0494357	+	0.0285417i
$285$	3065.52			0.637143
$286$	645.871	−	199.936i	0.133535	−	0.0413372i
$287$	−573.277			−0.117908
$288$	−249.415	+	144.000i	−0.0510310	+	0.0294628i
$289$	−2764.20	−	4787.74i	−0.562630	−	0.974503i
$290$	1421.47	−	2462.05i	0.287832	−	0.498540i
$291$			3683.98i			0.742126i
$292$	1273.03	+	734.983i	0.255131	+	0.147300i
$293$	−4152.79	−	2397.61i	−0.828015	−	0.478054i	0.0251577	−	0.999683i	$-0.491991\pi$
$293$	−4152.79	−	2397.61i	−0.828015	−	0.478054i	−0.853172	+	0.521629i	$0.825325\pi$
$294$			294.000i			0.0583212i
$295$	480.044	−	831.461i	0.0947432	−	0.164100i
$296$	1506.92	+	2610.05i	0.295904	+	0.512521i
$297$	−168.642	+	97.3656i	−0.0329482	+	0.0190226i
$298$	4372.32			0.849938
$299$	64.5633	−	284.186i	0.0124876	−	0.0549663i
$300$	2206.44			0.424629
$301$	2255.33	−	1302.11i	0.431877	−	0.249344i
$302$	213.418	+	369.651i	0.0406650	+	0.0704338i
$303$	165.250	−	286.222i	0.0313313	−	0.0542673i
$304$		−	930.283i		−	0.175511i
$305$	−13020.3	−	7517.26i	−2.44439	−	1.41127i
$306$	1592.88	+	919.649i	0.297578	+	0.171807i
$307$		−	9176.42i		−	1.70595i	−0.521954	−	0.852974i	$-0.674797\pi$
$307$		−	9176.42i		−	1.70595i	0.521954	−	0.852974i	$-0.325203\pi$
$308$	−100.972	+	174.888i	−0.0186799	+	0.0323545i
$309$	2019.34	+	3497.59i	0.371767	+	0.643919i
$310$	−1974.43	+	1139.94i	−0.361741	+	0.208851i
$311$	−6188.44			−1.12834			−0.564171	−	0.825658i	$-0.690804\pi$
$311$	−6188.44			−1.12834			−0.564171	+	0.825658i	$0.690804\pi$
$312$	1096.98	+	249.219i	0.199052	+	0.0452220i
$313$	6754.96			1.21985			0.609925	−	0.792459i	$-0.291200\pi$
$313$	6754.96			1.21985			0.609925	+	0.792459i	$0.291200\pi$
$314$	358.376	−	206.908i	0.0644086	−	0.0371863i
$315$	−553.603	−	958.868i	−0.0990221	−	0.171511i
$316$	−696.472	+	1206.32i	−0.123986	+	0.214750i
$317$		−	10015.4i		−	1.77452i	−0.461272	−	0.887259i	$-0.652607\pi$
$317$		−	10015.4i		−	1.77452i	0.461272	−	0.887259i	$-0.347393\pi$
$318$	−2977.46	−	1719.04i	−0.525056	−	0.303141i
$319$	−505.186	−	291.669i	−0.0886676	−	0.0511923i
$320$		−	1124.78i		−	0.196491i
$321$	1577.10	−	2731.61i	0.274221	−	0.474965i
$322$	43.5225	+	75.3832i	0.00753235	+	0.0130464i
$323$	−5145.23	+	2970.60i	−0.886342	+	0.511730i
$324$	−324.000			−0.0555556
$325$	−6323.60	−	5855.63i	−1.07929	−	0.999421i
$326$	2578.71			0.438102
$327$	−56.9519	+	32.8812i	−0.00963134	+	0.00556066i
$328$	−327.587	−	567.397i	−0.0551462	−	0.0955161i
$329$	−93.1879	+	161.406i	−0.0156159	+	0.0270475i
$330$		−	760.520i		−	0.126864i
$331$	−4306.33	−	2486.26i	−0.715098	−	0.412862i	0.0978477	−	0.995201i	$-0.468804\pi$
$331$	−4306.33	−	2486.26i	−0.715098	−	0.412862i	−0.812946	+	0.582339i	$0.802138\pi$
$332$	1985.34	+	1146.24i	0.328192	+	0.189482i
$333$			3390.56i			0.557963i
$334$	1942.77	−	3364.98i	0.318275	−	0.551269i
$335$	−2930.64	−	5076.01i	−0.477963	−	0.827857i
$336$	−290.985	+	168.000i	−0.0472456	+	0.0272772i
$337$	3895.77			0.629721			0.314860	−	0.949138i	$-0.398042\pi$
$337$	3895.77			0.629721			0.314860	+	0.949138i	$0.398042\pi$
$338$	−2482.52	−	3625.51i	−0.399500	−	0.583438i
$339$	−3704.39			−0.593495
$340$	−6220.96	+	3591.67i	−0.992291	+	0.572900i
$341$	233.902	+	405.130i	0.0371452	+	0.0643374i
$342$	523.284	−	906.355i	0.0827368	−	0.143304i
$343$			343.000i			0.0539949i
$344$	2577.52	+	1488.13i	0.403984	+	0.233240i
$345$	−283.894	−	163.906i	−0.0443024	−	0.0255780i
$346$		−	4479.23i		−	0.695967i
$347$	−530.519	+	918.886i	−0.0820742	+	0.142157i	−0.904141	−	0.427235i	$-0.859488\pi$
$347$	−530.519	+	918.886i	−0.0820742	+	0.142157i	0.822067	+	0.569391i	$0.192821\pi$
$348$	−485.288	−	840.544i	−0.0747534	−	0.129477i
$349$	6300.80	−	3637.77i	0.966401	−	0.557952i	0.0682637	−	0.997667i	$-0.478254\pi$
$349$	6300.80	−	3637.77i	0.966401	−	0.557952i	0.898137	+	0.439716i	$0.144921\pi$
$350$	2574.17			0.393130
$351$	928.577	+	859.859i	0.141207	+	0.130758i
$352$	−230.792			−0.0349468
$353$	3621.32	−	2090.77i	0.546015	−	0.315242i	−0.201498	−	0.979489i	$-0.564581\pi$
$353$	3621.32	−	2090.77i	0.546015	−	0.315242i	0.747513	+	0.664247i	$0.231248\pi$
$354$	−163.887	−	283.861i	−0.0246059	−	0.0426187i
$355$	600.185	−	1039.55i	0.0897310	−	0.155419i
$356$			2208.63i			0.328812i
$357$	1858.36	+	1072.92i	0.275503	+	0.159062i
$358$	4728.27	+	2729.87i	0.698037	+	0.403012i
$359$			11102.7i			1.63225i	0.577878	+	0.816123i	$0.303881\pi$
$359$			11102.7i			1.63225i	−0.577878	+	0.816123i	$0.696119\pi$
$360$	632.689	−	1095.85i	0.0926267	−	0.160434i
$361$	−1739.21	−	3012.41i	−0.253567	−	0.439190i
$362$	−2810.86	+	1622.85i	−0.408110	+	0.235622i
$363$	3836.95			0.554787
$364$	1279.81	+	290.756i	0.184286	+	0.0418674i
$365$	−6458.55			−0.926181
$366$	−4445.12	+	2566.39i	−0.634837	+	0.366523i
$367$	5412.43	+	9374.60i	0.769827	+	1.33338i	0.937656	+	0.347563i	$0.112991\pi$
$367$	5412.43	+	9374.60i	0.769827	+	1.33338i	−0.167829	+	0.985816i	$0.553676\pi$
$368$	−49.7400	+	86.1523i	−0.00704587	+	0.0122038i
$369$		−	737.071i		−	0.103985i
$370$	−11467.7	−	6620.89i	−1.61129	−	0.930281i
$371$	−3473.71	−	2005.55i	−0.486107	−	0.280654i
$372$			778.348i			0.108482i
$373$	2501.56	−	4332.82i	0.347254	−	0.601461i	−0.638507	−	0.769616i	$-0.720448\pi$
$373$	2501.56	−	4332.82i	0.347254	−	0.601461i	0.985761	+	0.168155i	$0.0537809\pi$
$374$	736.972	+	1276.47i	0.101893	+	0.176484i
$375$	−2688.01	+	1551.92i	−0.370155	+	0.213709i
$376$	−213.001			−0.0292146
$377$	−839.883	+	3696.88i	−0.114738	+	0.505037i
$378$	−378.000			−0.0514344
$379$	1066.69	−	615.852i	0.144570	−	0.0834676i	−0.425970	−	0.904737i	$-0.640067\pi$
$379$	1066.69	−	615.852i	0.144570	−	0.0834676i	0.570540	+	0.821270i	$0.306734\pi$
$380$	2043.68	+	3539.76i	0.275891	+	0.477857i
$381$	−2297.42	+	3979.25i	−0.308925	+	0.535073i
$382$			5676.13i			0.760251i
$383$	1899.29	+	1096.56i	0.253392	+	0.146296i	0.621317	−	0.783560i	$-0.286598\pi$
$383$	1899.29	+	1096.56i	0.253392	+	0.146296i	−0.367924	+	0.929856i	$0.619931\pi$
$384$	−332.554	−	192.000i	−0.0441942	−	0.0255155i
$385$		−	887.273i		−	0.117454i
$386$	−2369.84	+	4104.69i	−0.312492	+	0.541252i
$387$	1674.15	+	2899.71i	0.219901	+	0.380880i
$388$	−4253.89	+	2455.99i	−0.556594	+	0.321350i
$389$	−6664.08			−0.868593			−0.434296	−	0.900770i	$-0.643003\pi$
$389$	−6664.08			−0.868593			−0.434296	+	0.900770i	$0.643003\pi$
$390$	−4721.53	+	1461.60i	−0.613036	+	0.189771i
$391$	635.324			0.0821732
$392$	−339.482	+	196.000i	−0.0437409	+	0.0252538i
$393$	−4100.23	−	7101.80i	−0.526283	−	0.911548i
$394$	−1099.67	+	1904.69i	−0.140611	+	0.243546i
$395$		−	6120.14i		−	0.779589i
$396$	−224.856	−	129.821i	−0.0285340	−	0.0164741i
$397$	6251.46	+	3609.28i	0.790306	+	0.456284i	0.840070	−	0.542477i	$-0.182514\pi$
$397$	6251.46	+	3609.28i	0.790306	+	0.456284i	−0.0497640	+	0.998761i	$0.515847\pi$
$398$			3571.11i			0.449757i
$399$	610.498	−	1057.41i	0.0765994	−	0.132674i
$400$	1470.96	+	2547.77i	0.183870	+	0.318472i
$401$	9986.09	−	5765.47i	1.24360	−	0.717990i	0.273771	−	0.961795i	$-0.411729\pi$
$401$	9986.09	−	5765.47i	1.24360	−	0.717990i	0.969824	+	0.243805i	$0.0783957\pi$
$402$	−2001.04			−0.248265
$403$	2065.65	−	2230.73i	0.255328	−	0.275733i
$404$	440.667			0.0542673
$405$	1232.83	−	711.775i	0.151259	−	0.0873293i
$406$	−566.170	−	980.635i	−0.0692082	−	0.119872i
$407$	−1358.53	+	2353.05i	−0.165455	+	0.286576i
$408$			2452.40i			0.297578i
$409$	9623.77	+	5556.29i	1.16348	+	0.671738i	0.952136	−	0.305673i	$-0.0988815\pi$
$409$	9623.77	+	5556.29i	1.16348	+	0.671738i	0.211347	+	0.977411i	$0.432215\pi$
$410$	2492.96	+	1439.31i	0.300289	+	0.173372i
$411$			3786.28i			0.454412i
$412$	−2692.45	+	4663.46i	−0.321960	+	0.557650i
$413$	−191.202	−	331.171i	−0.0227807	−	0.0394573i
$414$	−96.9213	+	55.9575i	−0.0115059	+	0.00664291i
$415$	−10072.4			−1.19141
$416$	443.546	+	1432.83i	0.0522755	+	0.168871i
$417$	1922.05			0.225715
$418$	726.319	−	419.341i	0.0849891	−	0.0490685i
$419$	1822.72	+	3157.04i	0.212520	+	0.368095i	0.952502	−	0.304531i	$-0.0984997\pi$
$419$	1822.72	+	3157.04i	0.212520	+	0.368095i	−0.739983	+	0.672626i	$0.765166\pi$
$420$	738.137	−	1278.49i	0.0857557	−	0.148533i
$421$			15707.4i			1.81837i	0.416394	+	0.909184i	$0.363294\pi$
$421$			15707.4i			1.81837i	−0.416394	+	0.909184i	$0.636706\pi$
$422$	−8774.93	−	5066.21i	−1.01222	−	0.584406i
$423$	−207.522	−	119.813i	−0.0238536	−	0.0137719i
$424$		−	4584.10i		−	0.525056i
$425$	9394.19	−	16271.2i	1.07220	−	1.85711i
$426$	−204.903	−	354.903i	−0.0233042	−	0.0403641i
$427$	−5185.97	+	2994.12i	−0.587744	+	0.339334i
$428$	4205.60			0.474965
$429$	299.903	+	968.806i	0.0337517	+	0.109031i
$430$	−13076.7			−1.46655
$431$	168.273	−	97.1525i	0.0188061	−	0.0108577i	−0.490567	−	0.871403i	$-0.663210\pi$
$431$	168.273	−	97.1525i	0.0188061	−	0.0108577i	0.509374	+	0.860546i	$0.329877\pi$
$432$	−216.000	−	374.123i	−0.0240563	−	0.0416667i
$433$	−1040.25	+	1801.77i	−0.115453	+	0.199971i	−0.917961	−	0.396671i	$-0.870165\pi$
$433$	−1040.25	+	1801.77i	−0.115453	+	0.199971i	0.802508	+	0.596642i	$0.203499\pi$
$434$			908.073i			0.100435i
$435$	3693.08	+	2132.20i	0.407056	+	0.235014i
$436$	−75.9359	−	43.8416i	−0.00834099	−	0.00481567i
$437$		−	361.502i		−	0.0395721i
$438$	−1102.47	+	1909.54i	−0.120270	+	0.208314i
$439$	−3053.49	−	5288.80i	−0.331971	−	0.574990i	0.650928	−	0.759140i	$-0.274380\pi$
$439$	−3053.49	−	5288.80i	−0.331971	−	0.574990i	−0.982898	+	0.184150i	$0.941047\pi$
$440$	878.173	−	507.013i	0.0951483	−	0.0549339i
$441$	−441.000			−0.0476190
$442$	6508.38	−	7028.51i	0.700389	−	0.756363i
$443$	−15935.0			−1.70902			−0.854509	−	0.519437i	$-0.826142\pi$
$443$	−15935.0			−1.70902			−0.854509	+	0.519437i	$0.826142\pi$
$444$	−3915.08	+	2260.37i	−0.418472	+	0.241605i
$445$	−4851.99	−	8403.89i	−0.516868	−	0.895242i
$446$	1872.42	−	3243.12i	0.198792	−	0.344319i
$447$			6558.48i			0.693971i
$448$	−387.979	−	224.000i	−0.0409159	−	0.0236228i
$449$	−1821.16	−	1051.45i	−0.191416	−	0.110514i	0.401229	−	0.915978i	$-0.368583\pi$
$449$	−1821.16	−	1051.45i	−0.191416	−	0.110514i	−0.592646	+	0.805463i	$0.701916\pi$
$450$			3309.65i			0.346708i
$451$	295.330	−	511.527i	0.0308350	−	0.0534077i
$452$	−2469.59	−	4277.46i	−0.256991	−	0.445121i
$453$	−554.476	+	320.127i	−0.0575090	+	0.0332028i
$454$	−6042.24			−0.624617
$455$	−5508.45	+	1705.19i	−0.567561	+	0.175694i
$456$	1395.42			0.143304
$457$	−11711.7	+	6761.74i	−1.19879	+	0.692124i	−0.960286	−	0.279017i	$-0.909992\pi$
$457$	−11711.7	+	6761.74i	−1.19879	+	0.692124i	−0.238508	+	0.971141i	$0.576658\pi$
$458$	1451.24	+	2513.62i	0.148061	+	0.256449i
$459$	−1379.47	+	2389.32i	−0.140279	+	0.242971i
$460$		−	437.083i		−	0.0443024i
$461$	−5142.89	−	2969.25i	−0.519584	−	0.299982i	0.217180	−	0.976131i	$-0.430314\pi$
$461$	−5142.89	−	2969.25i	−0.519584	−	0.299982i	−0.736764	+	0.676150i	$0.763647\pi$
$462$	−262.332	−	151.458i	−0.0264173	−	0.0152520i
$463$			17985.7i			1.80532i	0.430351	+	0.902661i	$0.358390\pi$
$463$			17985.7i			1.80532i	−0.430351	+	0.902661i	$0.641610\pi$
$464$	647.051	−	1120.73i	0.0647384	−	0.112130i
$465$	−1709.90	−	2961.64i	−0.170527	−	0.295361i
$466$	−3050.29	+	1761.09i	−0.303223	+	0.175066i
$467$	4390.73			0.435072			0.217536	−	0.976052i	$-0.430198\pi$
$467$	4390.73			0.435072			0.217536	+	0.976052i	$0.430198\pi$
$468$	−373.829	+	1645.47i	−0.0369236	+	0.162525i
$469$	−2334.54			−0.229849
$470$	810.475	−	467.928i	0.0795414	−	0.0459232i
$471$	310.362	+	537.563i	0.0303625	+	0.0525894i
$472$	218.516	−	378.481i	0.0213094	−	0.0369089i
$473$			2683.20i			0.260832i
$474$	−1809.49	−	1044.71i	−0.175343	−	0.101234i
$475$	−9258.40	−	5345.34i	−0.894325	−	0.516339i
$476$			2861.13i			0.275503i
$477$	2578.56	−	4466.19i	0.247514	−	0.428706i
$478$	−2348.98	−	4068.56i	−0.224770	−	0.389313i
$479$	5356.77	−	3092.73i	0.510975	−	0.295012i	−0.222259	−	0.974988i	$-0.571343\pi$
$479$	5356.77	−	3092.73i	0.510975	−	0.295012i	0.733234	+	0.679976i	$0.238010\pi$
$480$	1687.17			0.160434
$481$	17219.3	+	3912.00i	1.63229	+	0.370835i
$482$	3319.48			0.313689
$483$	−113.075	+	65.2838i	−0.0106523	+	0.00615014i
$484$	2557.97	+	4430.53i	0.240230	+	0.416090i
$485$	10790.8	−	18690.2i	1.01028	−	1.74985i
$486$		−	486.000i		−	0.0453609i
$487$	−16287.0	−	9403.29i	−1.51547	−	0.874956i	−0.999835	−	0.0181468i	$-0.994223\pi$
$487$	−16287.0	−	9403.29i	−1.51547	−	0.874956i	−0.515633	−	0.856809i	$-0.672443\pi$
$488$	−5926.83	−	3421.86i	−0.549785	−	0.317418i
$489$			3868.06i			0.357709i
$490$	861.160	−	1491.57i	0.0793943	−	0.137515i
$491$	4356.05	+	7544.90i	0.400378	+	0.693476i	0.993771	−	0.111437i	$-0.0355454\pi$
$491$	4356.05	+	7544.90i	0.400378	+	0.693476i	−0.593393	+	0.804913i	$0.702212\pi$
$492$	851.096	−	491.380i	0.0779885	−	0.0450267i
$493$	−8264.72			−0.755019
$494$	−3999.26	−	3703.30i	−0.364241	−	0.337286i
$495$	1140.78			0.103584
$496$	−898.759	+	518.899i	−0.0813618	+	0.0469743i
$497$	−239.054	−	414.053i	−0.0215755	−	0.0373698i
$498$	−1719.36	+	2978.01i	−0.154711	+	0.267968i
$499$			12647.3i			1.13461i	0.823506	+	0.567307i	$0.192015\pi$
$499$			12647.3i			1.13461i	−0.823506	+	0.567307i	$0.807985\pi$
$500$	−3584.01	−	2069.23i	−0.320564	−	0.185078i
$501$	5047.48	+	2914.16i	0.450109	+	0.259870i
$502$			5188.09i			0.461267i
$503$	−8670.76	+	15018.2i	−0.768608	+	1.33127i	0.169709	+	0.985494i	$0.445717\pi$
$503$	−8670.76	+	15018.2i	−0.768608	+	1.33127i	−0.938318	+	0.345775i	$0.887616\pi$
$504$	−252.000	−	436.477i	−0.0222718	−	0.0385758i
$505$	−1676.75	+	968.073i	−0.147751	+	0.0853043i
$506$	−89.6846			−0.00787938
$507$	5438.27	−	3723.78i	0.476375	−	0.326191i
$508$	−6126.45			−0.535073
$509$	15082.1	−	8707.64i	1.31336	−	0.758270i	0.330710	−	0.943732i	$-0.392712\pi$
$509$	15082.1	−	8707.64i	1.31336	−	0.758270i	0.982651	+	0.185463i	$0.0593785\pi$
$510$	−5387.51	−	9331.44i	−0.467771	−	0.810203i
$511$	−1286.22	+	2227.80i	−0.111348	+	0.192861i
$512$		−	512.000i		−	0.0441942i
$513$	1359.53	+	784.926i	0.117007	+	0.0675543i
$514$	−6146.06	−	3548.43i	−0.527414	−	0.304503i
$515$		−	23659.5i		−	2.02439i
$516$	−2232.20	+	3866.28i	−0.190440	+	0.329851i
$517$	−96.0137	−	166.301i	−0.00816766	−	0.0141468i
$518$	−4567.60	+	2637.10i	−0.387430	+	0.223683i
$519$	6718.84			0.568255
$520$	−4835.39	−	4477.56i	−0.407781	−	0.377604i
$521$	−4888.28			−0.411055			−0.205527	−	0.978651i	$-0.565891\pi$
$521$	−4888.28			−0.411055			−0.205527	+	0.978651i	$0.565891\pi$
$522$	1260.82	−	727.933i	0.105717	−	0.0610359i
$523$	3349.99	+	5802.35i	0.280085	+	0.485122i	0.971406	−	0.237426i	$-0.0763039\pi$
$523$	3349.99	+	5802.35i	0.280085	+	0.485122i	−0.691320	+	0.722549i	$0.742971\pi$
$524$	5466.97	−	9469.07i	0.455774	−	0.789424i
$525$			3861.26i			0.320989i
$526$	−13037.5	−	7527.20i	−1.08073	−	0.623957i
$527$	5739.88	+	3313.92i	0.474446	+	0.273921i
$528$		−	346.189i		−	0.0285340i
$529$	6064.17	−	10503.5i	0.498411	−	0.863274i
$530$	10070.5	+	17442.7i	0.825350	+	1.42955i
$531$	425.791	−	245.831i	0.0347980	−	0.0200907i
$532$	1628.00			0.132674
$533$	−3743.29	−	850.426i	−0.304202	−	0.0691108i
$534$	−3312.94			−0.268474
$535$	−16002.4	+	9239.00i	−1.29317	+	0.746611i
$536$	−1334.03	−	2310.60i	−0.107502	−	0.186199i
$537$	−4094.81	+	7092.41i	−0.329058	+	0.569944i
$538$			13790.1i			1.10508i
$539$	−306.054	−	176.701i	−0.0244577	−	0.0141206i
$540$	1643.77	+	949.033i	0.130994	+	0.0756294i
$541$			4061.65i			0.322780i	0.986891	+	0.161390i	$0.0515977\pi$
$541$			4061.65i			0.322780i	−0.986891	+	0.161390i	$0.948402\pi$
$542$	−4013.71	+	6951.94i	−0.318088	+	0.550944i
$543$	−2434.28	−	4216.30i	−0.192385	−	0.333220i
$544$	−2831.78	+	1634.93i	−0.223183	+	0.128855i
$545$	385.251			0.0302795
$546$	−436.133	+	1919.71i	−0.0341846	+	0.150469i
$547$	1288.56			0.100722			0.0503609	−	0.998731i	$-0.483963\pi$
$547$	1288.56			0.100722			0.0503609	+	0.998731i	$0.483963\pi$
$548$	−4372.01	+	2524.18i	−0.340809	+	0.196766i
$549$	−3849.59	−	6667.68i	−0.299265	−	0.518342i
$550$	−1326.12	+	2296.90i	−0.102811	+	0.178073i
$551$			4702.66i			0.363594i
$552$	−129.228	−	74.6101i	−0.00996436	−	0.00575293i
$553$	−2111.07	−	1218.83i	−0.162336	−	0.0937247i
$554$		−	16427.9i		−	1.25984i
$555$	9931.34	−	17201.6i	0.759571	−	1.31562i
$556$	1281.37	+	2219.39i	0.0977375	+	0.169286i
$557$	−19182.6	+	11075.1i	−1.45923	+	0.842487i	−0.998974	−	0.0452983i	$-0.985576\pi$
$557$	−19182.6	+	11075.1i	−1.45923	+	0.842487i	−0.460257	+	0.887786i	$0.652243\pi$
$558$	−1167.52			−0.0885755
$559$	16658.1	−	5156.67i	1.26040	−	0.390168i
$560$	1968.36			0.148533
$561$	−1914.71	+	1105.46i	−0.144098	+	0.0831952i
$562$	−5067.64	−	8777.40i	−0.380365	−	0.658812i
$563$	−1937.23	+	3355.38i	−0.145017	+	0.251177i	−0.929379	−	0.369126i	$-0.879657\pi$
$563$	−1937.23	+	3355.38i	−0.145017	+	0.251177i	0.784362	+	0.620303i	$0.212990\pi$
$564$		−	319.501i		−	0.0238536i
$565$	18793.8	+	10850.6i	1.39940	+	0.807942i
$566$	10964.5	+	6330.38i	0.814265	+	0.470116i
$567$		−	567.000i		−	0.0419961i
$568$	273.204	−	473.203i	0.0201820	−	0.0349563i
$569$	−4331.37	−	7502.14i	−0.319122	−	0.552735i	0.661183	−	0.750224i	$-0.270055\pi$
$569$	−4331.37	−	7502.14i	−0.319122	−	0.552735i	−0.980305	+	0.197489i	$0.936721\pi$
$570$	−5309.63	+	3065.52i	−0.390169	+	0.225264i
$571$	14375.5			1.05358			0.526792	−	0.849994i	$-0.323395\pi$
$571$	14375.5			1.05358			0.526792	+	0.849994i	$0.323395\pi$
$572$	−918.746	+	992.169i	−0.0671585	+	0.0725257i
$573$	−8514.19			−0.620743
$574$	992.945	−	573.277i	0.0722034	−	0.0416866i
$575$	571.605	+	990.049i	0.0414567	+	0.0718050i
$576$	288.000	−	498.831i	0.0208333	−	0.0360844i
$577$			11017.5i			0.794915i	0.917621	+	0.397457i	$0.130107\pi$
$577$			11017.5i			0.794915i	−0.917621	+	0.397457i	$0.869893\pi$
$578$	9575.47	+	5528.40i	0.689078	+	0.397839i
$579$	−6157.04	−	3554.77i	−0.441930	−	0.255149i
$580$			5685.86i			0.407056i
$581$	−2005.91	+	3474.35i	−0.143235	+	0.248090i
$582$	−3683.98	−	6380.84i	−0.262381	−	0.454457i
$583$	3579.04	−	2066.36i	0.254252	−	0.146792i
$584$	−2939.93			−0.208314
$585$	−2192.39	−	7082.30i	−0.154948	−	0.500542i
$586$	9590.45			0.676071
$587$	−12137.0	+	7007.29i	−0.853401	+	0.492711i	−0.861797	−	0.507253i	$-0.830661\pi$
$587$	−12137.0	+	7007.29i	−0.853401	+	0.492711i	0.00839571	+	0.999965i	$0.497328\pi$
$588$	−294.000	−	509.223i	−0.0206197	−	0.0357143i
$589$	1885.64	−	3266.02i	0.131912	−	0.228479i
$590$			1920.18i			0.133987i
$591$	−2857.04	−	1649.51i	−0.198854	−	0.114808i
$592$	−5220.11	−	3013.83i	−0.362407	−	0.209236i
$593$		−	9902.94i		−	0.685776i	−0.939376	−	0.342888i	$-0.888595\pi$
$593$		−	9902.94i		−	0.685776i	0.939376	−	0.342888i	$-0.111405\pi$
$594$	194.731	−	337.284i	0.0134510	−	0.0232979i
$595$	−6285.43	−	10886.7i	−0.433071	−	0.750102i
$596$	−7573.07	+	4372.32i	−0.520479	+	0.300498i
$597$	−5356.66			−0.367225
$598$	172.359	+	556.788i	0.0117864	+	0.0380749i
$599$	6885.68			0.469685			0.234843	−	0.972033i	$-0.424543\pi$
$599$	6885.68			0.469685			0.234843	+	0.972033i	$0.424543\pi$
$600$	−3821.66	+	2206.44i	−0.260031	+	0.150129i
$601$	13313.5	+	23059.6i	0.903609	+	1.56510i	0.822774	+	0.568368i	$0.192425\pi$
$601$	13313.5	+	23059.6i	0.903609	+	1.56510i	0.0808343	+	0.996728i	$0.474242\pi$
$602$	−2604.23	+	4510.66i	−0.176313	+	0.305383i
$603$		−	3001.56i		−	0.202708i
$604$	−739.302	−	426.836i	−0.0498042	−	0.0287545i
$605$	−19466.3	−	11238.9i	−1.30813	−	0.755248i
$606$			661.001i			0.0443091i
$607$	4655.58	−	8063.69i	0.311308	−	0.539201i	−0.667338	−	0.744755i	$-0.732566\pi$
$607$	4655.58	−	8063.69i	0.311308	−	0.539201i	0.978646	+	0.205554i	$0.0658996\pi$
$608$	930.283	+	1611.30i	0.0620526	+	0.107478i
$609$	1470.95	−	849.255i	0.0978752	−	0.0565083i
$610$	30069.0			1.99583
$611$	−847.921	+	915.684i	−0.0561427	+	0.0606295i
$612$	−3678.59			−0.242971
$613$	2964.46	−	1711.53i	0.195323	−	0.112770i	−0.399149	−	0.916886i	$-0.630694\pi$
$613$	2964.46	−	1711.53i	0.195323	−	0.112770i	0.594472	+	0.804116i	$0.297361\pi$
$614$	9176.42	+	15894.0i	0.603144	+	1.04468i
$615$	−2158.96	+	3739.44i	−0.141557	+	0.245185i
$616$		−	403.887i		−	0.0264173i
$617$	−16487.7	−	9519.18i	−1.07580	−	0.621115i	−0.146041	−	0.989278i	$-0.546653\pi$
$617$	−16487.7	−	9519.18i	−1.07580	−	0.621115i	−0.929761	+	0.368164i	$0.879987\pi$
$618$	−6995.18	−	4038.67i	−0.455320	−	0.262879i
$619$		−	22519.8i		−	1.46227i	−0.682231	−	0.731137i	$-0.738990\pi$
$619$		−	22519.8i		−	1.46227i	0.682231	−	0.731137i	$-0.261010\pi$
$620$	2279.87	−	3948.85i	0.147680	−	0.255790i
$621$	−83.9363	−	145.382i	−0.00542391	−	0.00939449i
$622$	10718.7	−	6188.44i	0.690966	−	0.398929i
$623$	−3865.10			−0.248558
$624$	−2149.24	+	665.319i	−0.137882	+	0.0426828i
$625$	−4800.66			−0.307242
$626$	−11699.9	+	6754.96i	−0.747003	+	0.431282i
$627$	629.011	+	1089.48i	0.0400642	+	0.0693933i
$628$	−413.816	+	716.751i	−0.0262947	+	0.0455438i
$629$			38495.4i			2.44024i
$630$	1917.74	+	1107.21i	0.121277	+	0.0700192i
$631$	24840.7	+	14341.8i	1.56718	+	0.904814i	0.996495	+	0.0836467i	$0.0266567\pi$
$631$	24840.7	+	14341.8i	1.56718	+	0.904814i	0.570688	+	0.821167i	$0.306677\pi$
$632$		−	2785.89i		−	0.175343i
$633$	7599.31	−	13162.4i	0.477165	−	0.826474i
$634$	10015.4	+	17347.2i	0.627387	+	1.08667i
$635$	23311.3	−	13458.8i	1.45682	−	0.841097i
$636$	6876.16			0.428706
$637$	−508.822	+	2239.66i	−0.0316488	+	0.139307i
$638$	1166.68			0.0723968
$639$	532.354	−	307.355i	0.0329571	−	0.0190278i
$640$	1124.78	+	1948.18i	0.0694701	+	0.120326i
$641$	11883.3	−	20582.5i	0.732236	−	1.26827i	−0.223689	−	0.974661i	$-0.571810\pi$
$641$	11883.3	−	20582.5i	0.732236	−	1.26827i	0.955925	−	0.293610i	$-0.0948566\pi$
$642$			6308.39i			0.387808i
$643$	11490.6	+	6634.09i	0.704735	+	0.406879i	0.809108	−	0.587659i	$-0.199950\pi$
$643$	11490.6	+	6634.09i	0.704735	+	0.406879i	−0.104374	+	0.994538i	$0.533284\pi$
$644$	−150.766	−	87.0451i	−0.00922520	−	0.00532617i
$645$		−	19615.1i		−	1.19743i
$646$	5941.20	−	10290.5i	0.361848	−	0.626739i
$647$	8165.01	+	14142.2i	0.496135	+	0.859332i	0.999990	−	0.00445669i	$-0.00141861\pi$
$647$	8165.01	+	14142.2i	0.496135	+	0.859332i	−0.503855	+	0.863788i	$0.668085\pi$
$648$	561.184	−	324.000i	0.0340207	−	0.0196419i
$649$	393.999			0.0238302
$650$	16808.4	+	3818.65i	1.01428	+	0.230430i
$651$	−1362.11			−0.0820050
$652$	−4466.45	+	2578.71i	−0.268282	+	0.154893i
$653$	15014.8	+	26006.4i	0.899809	+	1.55851i	0.827738	+	0.561115i	$0.189628\pi$
$653$	15014.8	+	26006.4i	0.899809	+	1.55851i	0.0720712	+	0.997399i	$0.477039\pi$
$654$	65.7624	−	113.904i	0.00393198	−	0.00681039i
$655$			48040.1i			2.86578i
$656$	1134.79	+	655.174i	0.0675401	+	0.0389943i
$657$	−2864.31	−	1653.71i	−0.170088	−	0.0982001i
$658$		−	372.752i		−	0.0220842i
$659$	7396.85	−	12811.7i	0.437239	−	0.757320i	−0.560237	−	0.828333i	$-0.689290\pi$
$659$	7396.85	−	12811.7i	0.437239	−	0.757320i	0.997475	+	0.0710129i	$0.0226232\pi$
$660$	760.520	+	1317.26i	0.0448533	+	0.0776882i
$661$	18326.8	−	10581.0i	1.07841	−	0.622620i	0.147943	−	0.988996i	$-0.452735\pi$
$661$	18326.8	−	10581.0i	1.07841	−	0.622620i	0.930467	+	0.366376i	$0.119402\pi$
$662$	9945.05			0.583875
$663$	10542.8	+	9762.57i	0.617568	+	0.571866i
$664$	−4584.95			−0.267968
$665$	−6194.57	+	3576.44i	−0.361226	+	0.208554i
$666$	−3390.56	−	5872.62i	−0.197270	−	0.341681i
$667$	251.440	−	435.507i	0.0145964	−	0.0252817i
$668$			7771.10i			0.450109i
$669$	4864.68	+	2808.62i	0.281135	+	0.162313i
$670$	10152.0	+	5861.27i	0.585383	+	0.337971i
$671$		−	6169.83i		−	0.354968i
$672$	336.000	−	581.969i	0.0192879	−	0.0334077i
$673$	2086.50	+	3613.93i	0.119508	+	0.206993i	0.919573	−	0.392920i	$-0.128535\pi$
$673$	2086.50	+	3613.93i	0.119508	+	0.206993i	−0.800065	+	0.599913i	$0.795202\pi$
$674$	−6747.66	+	3895.77i	−0.385624	+	0.222640i
$675$	−4964.48			−0.283086
$676$	7925.36	+	3797.05i	0.450919	+	0.216036i
$677$	−24877.8			−1.41231			−0.706153	−	0.708059i	$-0.749571\pi$
$677$	−24877.8			−1.41231			−0.706153	+	0.708059i	$0.749571\pi$
$678$	6416.19	−	3704.39i	0.363440	−	0.209832i
$679$	−4297.97	−	7444.31i	−0.242918	−	0.420746i
$680$	7183.35	−	12441.9i	0.405101	−	0.701656i
$681$		−	9063.35i		−	0.509998i
$682$	−810.261	−	467.804i	−0.0454934	−	0.0262656i
$683$	−22109.7	−	12765.0i	−1.23866	−	0.715139i	−0.269837	−	0.962906i	$-0.586970\pi$
$683$	−22109.7	−	12765.0i	−1.23866	−	0.715139i	−0.968820	+	0.247767i	$0.920303\pi$
$684$			2093.14i			0.117007i
$685$	11090.4	−	19209.2i	0.618604	−	1.07145i
$686$	−343.000	−	594.093i	−0.0190901	−	0.0330650i
$687$	−3770.43	+	2176.86i	−0.209390	+	0.120891i
$688$	−5952.52			−0.329851
$689$	−19706.9	−	18248.5i	−1.08966	−	1.00902i
$690$	655.624			0.0361727
$691$	−14365.4	+	8293.87i	−0.790862	+	0.456605i	−0.840266	−	0.542174i	$-0.817601\pi$
$691$	−14365.4	+	8293.87i	−0.790862	+	0.456605i	0.0494037	+	0.998779i	$0.484268\pi$
$692$	4479.23	+	7758.25i	0.246062	+	0.426191i
$693$	227.186	−	393.498i	0.0124532	−	0.0215696i
$694$		−	2122.08i		−	0.116070i
$695$	−9751.28	−	5629.91i	−0.532212	−	0.307273i
$696$	1681.09	+	970.577i	0.0915539	+	0.0528586i
$697$		−	8368.47i		−	0.454775i
$698$	−7275.53	+	12601.6i	−0.394531	+	0.683349i
$699$	−2641.63	−	4575.43i	−0.142941	−	0.247581i
$700$	−4458.60	+	2574.17i	−0.240742	+	0.138992i
$701$	−7993.62			−0.430692			−0.215346	−	0.976538i	$-0.569088\pi$
$701$	−7993.62			−0.430692			−0.215346	+	0.976538i	$0.569088\pi$
$702$	−2468.20	−	560.743i	−0.132701	−	0.0301480i
$703$	21904.0			1.17514
$704$	399.744	−	230.792i	0.0214005	−	0.0123556i
$705$	701.892	+	1215.71i	0.0374962	+	0.0649453i
$706$	−4181.54	+	7242.64i	−0.222910	+	0.386091i
$707$			771.167i			0.0410223i
$708$	567.721	+	327.774i	0.0301360	+	0.0173990i
$709$	11010.1	+	6356.66i	0.583204	+	0.336713i	0.762406	−	0.647099i	$-0.224018\pi$
$709$	11010.1	+	6356.66i	0.583204	+	0.336713i	−0.179202	+	0.983812i	$0.557351\pi$
$710$			2400.74i			0.126899i
$711$	1567.06	−	2714.23i	0.0826574	−	0.143167i
$712$	−2208.63	−	3825.45i	−0.116253	−	0.201355i
$713$	−349.252	+	201.641i	−0.0183445	+	0.0105912i
$714$	−4291.69			−0.224948
$715$	1316.22	−	5793.57i	0.0688446	−	0.303031i
$716$	−10919.5			−0.569944
$717$	6102.84	−	3523.48i	0.317873	−	0.183524i
$718$	−11102.7	−	19230.4i	−0.577086	−	0.999542i
$719$	−4761.43	+	8247.04i	−0.246970	+	0.427765i	−0.962684	−	0.270629i	$-0.912768\pi$
$719$	−4761.43	+	8247.04i	−0.246970	+	0.427765i	0.715714	+	0.698394i	$0.246102\pi$
$720$			2530.75i			0.130994i
$721$	−8161.05	−	4711.78i	−0.421544	−	0.243379i
$722$	6024.81	+	3478.43i	0.310554	+	0.179299i
$723$			4979.22i			0.256126i
$724$	3245.71	−	5621.73i	0.166610	−	0.288577i
$725$	−7435.82	−	12879.2i	−0.380909	−	0.659754i
$726$	−6645.79	+	3836.95i	−0.339736	+	0.196147i
$727$	−24799.8			−1.26516			−0.632582	−	0.774493i	$-0.718005\pi$
$727$	−24799.8			−1.26516			−0.632582	+	0.774493i	$0.718005\pi$
$728$	−2507.45	+	776.205i	−0.127654	+	0.0395166i
$729$	729.000			0.0370370
$730$	11186.5	−	6458.55i	0.567167	−	0.327454i
$731$	19007.7	+	32922.4i	0.961733	+	1.66577i
$732$	5132.78	−	8890.24i	0.259171	−	0.448897i
$733$			7993.05i			0.402770i	0.979512	+	0.201385i	$0.0645442\pi$
$733$			7993.05i			0.402770i	−0.979512	+	0.201385i	$0.935456\pi$
$734$	−18749.2	−	10824.9i	−0.942842	−	0.544350i
$735$	2237.36	+	1291.74i	0.112281	+	0.0648252i
$736$		−	198.960i		−	0.00996436i
$737$	1202.67	−	2083.08i	0.0601097	−	0.104113i
$738$	737.071	+	1276.64i	0.0367642	+	0.0636774i
$739$	−4367.71	+	2521.70i	−0.217414	+	0.125524i	−0.604752	−	0.796414i	$-0.706728\pi$
$739$	−4367.71	+	2521.70i	−0.217414	+	0.125524i	0.387339	+	0.921938i	$0.373394\pi$
$740$	26483.6			1.31562
$741$	5554.95	−	5998.89i	0.275393	−	0.297402i
$742$	8022.18			0.396905
$743$	32903.4	−	18996.8i	1.62464	−	0.937987i	0.638986	−	0.769218i	$-0.279354\pi$
$743$	32903.4	−	18996.8i	1.62464	−	0.937987i	0.985656	−	0.168769i	$-0.0539792\pi$
$744$	−778.348	−	1348.14i	−0.0383543	−	0.0664316i
$745$	19210.5	−	33273.6i	0.944724	−	1.63631i
$746$			10006.2i			0.491091i
$747$	−4467.02	−	2579.03i	−0.218795	−	0.126321i
$748$	−2552.95	−	1473.94i	−0.124793	−	0.0720491i
$749$			7359.79i			0.359040i
$750$	3103.85	−	5376.02i	0.151115	−	0.261739i
$751$	18106.9	+	31362.1i	0.879802	+	1.52386i	0.851558	+	0.524261i	$0.175658\pi$
$751$	18106.9	+	31362.1i	0.879802	+	1.52386i	0.0282446	+	0.999601i	$0.491008\pi$
$752$	368.929	−	213.001i	0.0178902	−	0.0103289i
$753$	−7782.14			−0.376623
$754$	−2242.16	−	7243.07i	−0.108295	−	0.349837i
$755$	3750.76			0.180800
$756$	654.715	−	378.000i	0.0314970	−	0.0181848i
$757$	−9848.05	−	17057.3i	−0.472832	−	0.818968i	0.526685	−	0.850061i	$-0.323435\pi$
$757$	−9848.05	−	17057.3i	−0.472832	−	0.818968i	−0.999517	+	0.0310922i	$0.990101\pi$
$758$	−1231.70	+	2133.38i	−0.0590205	+	0.102227i
$759$		−	134.527i		−	0.00643349i
$760$	−7079.51	−	4087.36i	−0.337896	−	0.195084i
$761$	25991.4	+	15006.1i	1.23809	+	0.714812i	0.968704	−	0.248220i	$-0.0798454\pi$
$761$	25991.4	+	15006.1i	1.23809	+	0.714812i	0.269387	+	0.963032i	$0.413179\pi$
$762$		−	9189.68i		−	0.436886i
$763$	76.7228	−	132.888i	0.00364031	−	0.00630519i
$764$	−5676.13	−	9831.34i	−0.268789	−	0.465557i
$765$	13997.2	−	8081.27i	0.661528	−	0.381933i
$766$	−4386.23			−0.206894
$767$	−757.202	−	2446.06i	−0.0356467	−	0.115153i
$768$	768.000			0.0360844
$769$	22986.5	−	13271.3i	1.07791	−	0.622333i	0.147580	−	0.989050i	$-0.452852\pi$
$769$	22986.5	−	13271.3i	1.07791	−	0.622333i	0.930332	+	0.366717i	$0.119518\pi$
$770$	887.273	+	1536.80i	0.0415261	+	0.0719253i
$771$	5322.64	−	9219.08i	0.248625	−	0.430632i
$772$		−	9479.38i		−	0.441930i
$773$	−5174.07	−	2987.25i	−0.240748	−	0.138996i	0.374772	−	0.927117i	$-0.377721\pi$
$773$	−5174.07	−	2987.25i	−0.240748	−	0.138996i	−0.615521	+	0.788121i	$0.711054\pi$
$774$	−5799.42	−	3348.29i	−0.269323	−	0.155493i
$775$			11926.2i			0.552777i
$776$	4911.97	−	8507.78i	0.227229	−	0.393572i
$777$	−3955.65	−	6851.39i	−0.182636	−	0.316335i
$778$	11542.5	−	6664.08i	0.531902	−	0.307094i
$779$	−4761.70			−0.219006
$780$	6716.34	−	7253.09i	0.308312	−	0.332952i
$781$	492.605			0.0225695
$782$	−1100.41	+	635.324i	−0.0503206	+	0.0290526i
$783$	1091.90	+	1891.22i	0.0498356	+	0.0863178i
$784$	392.000	−	678.964i	0.0178571	−	0.0309295i
$785$		−	3636.35i		−	0.165333i
$786$	14203.6	+	8200.45i	0.644562	+	0.372138i
$787$	14339.5	+	8278.89i	0.649487	+	0.374982i	0.788260	−	0.615343i	$-0.210982\pi$
$787$	14339.5	+	8278.89i	0.649487	+	0.374982i	−0.138773	+	0.990324i	$0.544316\pi$
$788$		−	4398.70i		−	0.198854i
$789$	11290.8	−	19556.2i	0.509459	−	0.882409i
$790$	6120.14	+	10600.4i	0.275626	+	0.477399i
$791$	7485.56	−	4321.79i	0.336480	−	0.194267i
$792$	519.283			0.0232979
$793$	−38304.1	+	11857.4i	−1.71528	+	0.530983i
$794$	−14437.1			−0.645283
$795$	−26164.0	+	15105.8i	−1.16722	+	0.673896i
$796$	−3571.11	−	6185.34i	−0.159013	−	0.275419i
$797$	422.460	−	731.723i	0.0187758	−	0.0325206i	−0.856485	−	0.516172i	$-0.827356\pi$
$797$	422.460	−	731.723i	0.0187758	−	0.0325206i	0.875261	+	0.483652i	$0.160690\pi$
$798$			2441.99i			0.108328i
$799$	−2356.14	−	1360.32i	−0.104323	−	0.0602311i
$800$	−5095.54	−	2941.91i	−0.225193	−	0.130015i
$801$		−	4969.41i		−	0.219208i
$802$	−11530.9	+	19972.2i	−0.507696	+	0.879355i
$803$	−1325.22	−	2295.35i	−0.0582392	−	0.100873i
$804$	3465.90	−	2001.04i	0.152031	−	0.0877751i
$805$	764.895			0.0334894
$806$	−1347.08	+	5929.38i	−0.0588694	+	0.259124i
$807$	−20685.1			−0.902292
$808$	−763.258	+	440.667i	−0.0332318	+	0.0191864i
$809$	−3877.40	−	6715.86i	−0.168507	−	0.291863i	0.769388	−	0.638782i	$-0.220561\pi$
$809$	−3877.40	−	6715.86i	−0.168507	−	0.291863i	−0.937895	+	0.346919i	$0.887228\pi$
$810$	−1423.55	+	2465.66i	−0.0617512	+	0.106956i
$811$			40923.1i			1.77189i	0.463790	+	0.885945i	$0.346489\pi$
$811$			40923.1i			1.77189i	−0.463790	+	0.885945i	$0.653511\pi$
$812$	1961.27	+	1132.34i	0.0847624	+	0.0489376i
$813$	−10427.9	−	6020.56i	−0.449844	−	0.259717i
$814$		−	5434.14i		−	0.233988i
$815$	11330.0	−	19624.1i	0.486960	−	0.843439i
$816$	−2452.40	−	4247.67i	−0.105210	−	0.182228i
$817$	18733.0	−	10815.5i	0.802184	−	0.463141i
$818$	−22225.1			−0.949981
$819$	−2879.57	−	654.200i	−0.122857	−	0.0279116i
$820$	−5757.24			−0.245185
$821$	−2287.62	+	1320.76i	−0.0972455	+	0.0561447i	−0.547834	−	0.836587i	$-0.684547\pi$
$821$	−2287.62	+	1320.76i	−0.0972455	+	0.0561447i	0.450589	+	0.892732i	$0.351214\pi$
$822$	−3786.28	−	6558.02i	−0.160659	−	0.278269i
$823$	12418.3	−	21509.1i	0.525972	−	0.911011i	−0.473570	−	0.880756i	$-0.657035\pi$
$823$	12418.3	−	21509.1i	0.525972	−	0.911011i	0.999542	−	0.0302544i	$-0.00963174\pi$
$824$		−	10769.8i		−	0.455320i
$825$	−3445.35	−	1989.17i	−0.145396	−	0.0839445i
$826$	662.342	+	382.403i	0.0279005	+	0.0161084i
$827$			20181.4i			0.848579i	0.905526	+	0.424290i	$0.139476\pi$
$827$			20181.4i			0.848579i	−0.905526	+	0.424290i	$0.860524\pi$
$828$	111.915	−	193.843i	0.00469724	−	0.00813586i
$829$	17923.1	+	31043.7i	0.750898	+	1.30059i	0.947388	+	0.320087i	$0.103712\pi$
$829$	17923.1	+	31043.7i	0.750898	+	1.30059i	−0.196490	+	0.980506i	$0.562954\pi$
$830$	17445.9	−	10072.4i	0.729584	−	0.421226i
$831$	24641.8			1.02866
$832$	−2201.07	−	2038.18i	−0.0917169	−	0.0849295i
$833$	−5006.98			−0.208261
$834$	−3329.09	+	1922.05i	−0.138222	+	0.0798023i
$835$	−17071.8	−	29569.3i	−0.707539	−	1.22549i
$836$	−838.681	+	1452.64i	−0.0346966	+	0.0600963i
$837$		−	1751.28i		−	0.0723216i
$838$	−6314.09	−	3645.44i	−0.260282	−	0.150274i
$839$	18460.4	+	10658.1i	0.759621	+	0.438567i	0.829160	−	0.559012i	$-0.188819\pi$
$839$	18460.4	+	10658.1i	0.759621	+	0.438567i	−0.0695386	+	0.997579i	$0.522153\pi$
$840$			2952.55i			0.121277i
$841$	8923.60	−	15456.1i	0.365886	−	0.633734i
$842$	−15707.4	−	27206.1i	−0.642890	−	1.11352i
$843$	13166.1	−	7601.45i	0.537918	−	0.310567i
$844$	20264.8			0.826474
$845$	−38497.7	+	2962.80i	−1.56729	+	0.120620i
$846$	479.252			0.0194764
$847$	−7753.42	+	4476.44i	−0.314535	+	0.181597i
$848$	4584.10	+	7939.90i	0.185635	+	0.321530i
$849$	−9495.57	+	16446.8i	−0.383848	+	0.664845i
$850$			37576.8i			1.51632i
$851$	−2028.50	−	1171.16i	−0.0817112	−	0.0471760i
$852$	709.805	+	409.806i	0.0285417	+	0.0164786i
$853$		−	3660.02i		−	0.146913i	−0.997298	−	0.0734565i	$-0.976597\pi$
$853$		−	3660.02i		−	0.146913i	0.997298	−	0.0734565i	$-0.0234030\pi$
$854$	5988.25	−	10371.9i	0.239946	−	0.415598i
$855$	−4598.28	−	7964.45i	−0.183927	−	0.318571i
$856$	−7284.31	+	4205.60i	−0.290856	+	0.167926i
$857$	−35921.0			−1.43178			−0.715891	−	0.698212i	$-0.753979\pi$
$857$	−35921.0			−1.43178			−0.715891	+	0.698212i	$0.753979\pi$
$858$	−1488.25	−	1378.12i	−0.0592170	−	0.0548347i
$859$	−26502.7			−1.05269			−0.526346	−	0.850271i	$-0.676438\pi$
$859$	−26502.7			−1.05269			−0.526346	+	0.850271i	$0.676438\pi$
$860$	22649.5	−	13076.7i	0.898073	−	0.518503i
$861$	859.916	+	1489.42i	0.0340370	+	0.0589538i
$862$	−194.305	+	336.546i	−0.00767756	+	0.0132979i
$863$		−	15008.1i		−	0.591983i	−0.955191	−	0.295992i	$-0.904350\pi$
$863$		−	15008.1i		−	0.591983i	0.955191	−	0.295992i	$-0.0956500\pi$
$864$	748.246	+	432.000i	0.0294628	+	0.0170103i
$865$	−34087.2	−	19680.2i	−1.33988	−	0.773582i
$866$		−	4161.01i		−	0.163276i
$867$	−8292.60	+	14363.2i	−0.324834	+	0.562630i
$868$	−908.073	−	1572.83i	−0.0355092	−	0.0615037i
$869$	2175.08	−	1255.78i	0.0849075	−	0.0490214i
$870$	−8528.79			−0.332360
$871$	−15243.7	−	3463.17i	−0.593012	−	0.134725i
$872$	175.366			0.00681039
$873$	9571.26	−	5525.97i	0.371063	−	0.214233i
$874$	361.502	+	626.141i	0.0139908	+	0.0242329i
$875$	3621.15	−	6272.02i	0.139906	−	0.242324i
$876$		−	4409.90i		−	0.170088i
$877$	−27113.6	−	15654.0i	−1.04397	−	0.602736i	−0.123014	−	0.992405i	$-0.539256\pi$
$877$	−27113.6	−	15654.0i	−1.04397	−	0.602736i	−0.920955	+	0.389669i	$0.872589\pi$
$878$	10577.6	+	6106.98i	0.406579	+	0.234739i
$879$			14385.7i			0.552010i
$880$	−1014.03	+	1756.35i	−0.0388441	+	0.0672800i
$881$	12204.9	+	21139.5i	0.466734	+	0.808407i	0.999278	−	0.0379954i	$-0.0120972\pi$
$881$	12204.9	+	21139.5i	0.466734	+	0.808407i	−0.532544	+	0.846402i	$0.678764\pi$
$882$	763.834	−	441.000i	0.0291606	−	0.0168359i
$883$	14355.5			0.547113			0.273556	−	0.961856i	$-0.411800\pi$
$883$	14355.5			0.547113			0.273556	+	0.961856i	$0.411800\pi$
$884$	−4244.33	+	18682.1i	−0.161485	+	0.710801i
$885$	−2880.26			−0.109400
$886$	27600.2	−	15935.0i	1.04656	−	0.604229i
$887$	9666.78	+	16743.3i	0.365929	+	0.633807i	0.988925	−	0.148418i	$-0.0474181\pi$
$887$	9666.78	+	16743.3i	0.365929	+	0.633807i	−0.622996	+	0.782225i	$0.714085\pi$
$888$	4520.75	−	7830.16i	0.170840	−	0.295904i
$889$		−	10721.3i		−	0.404478i
$890$	16807.8	+	9703.98i	0.633032	+	0.365481i
$891$	505.926	+	292.097i	0.0190226	+	0.0109827i
$892$			7489.66i			0.281135i
$893$	−774.028	+	1340.66i	−0.0290054	+	0.0502389i
$894$	−6558.48	−	11359.6i	−0.245356	−	0.424969i
$895$	41549.0	−	23988.3i	1.55176	−	0.895912i
$896$	896.000			0.0334077
$897$	−835.182	+	258.539i	−0.0310880	+	0.00962359i
$898$	4205.80			0.156291
$899$	4543.30	−	2623.08i	0.168551	−	0.0973132i
$900$	−3309.65	−	5732.49i	−0.122580	−	0.212314i
$901$	29276.1	−	50707.8i	1.08250	−	1.87494i
$902$			1181.32i			0.0436072i
$903$	−6765.98	−	3906.34i	−0.249344	−	0.143959i
$904$	8554.92	+	4939.19i	0.314748	+	0.181720i
$905$			28521.1i			1.04760i
$906$	640.254	−	1108.95i	0.0234779	−	0.0406650i
$907$	23027.5	+	39884.7i	0.843015	+	1.46014i	0.887334	+	0.461127i	$0.152555\pi$
$907$	23027.5	+	39884.7i	0.843015	+	1.46014i	−0.0443192	+	0.999017i	$0.514112\pi$
$908$	10465.5	−	6042.24i	0.382498	−	0.220836i
$909$	−991.501			−0.0361782
$910$	7835.73	−	8461.94i	0.285442	−	0.308253i
$911$	−22634.7			−0.823186			−0.411593	−	0.911368i	$-0.635027\pi$
$911$	−22634.7			−0.823186			−0.411593	+	0.911368i	$0.635027\pi$
$912$	−2416.95	+	1395.42i	−0.0877556	+	0.0506657i
$913$	−2066.74	−	3579.70i	−0.0749169	−	0.129760i
$914$	13523.5	−	23423.3i	0.489406	−	0.847675i
$915$			45103.5i			1.62959i
$916$	−5027.24	−	2902.48i	−0.181337	−	0.104695i
$917$	16570.9	+	9567.20i	0.596748	+	0.344533i
$918$		−	5517.89i		−	0.198385i
$919$	2607.53	−	4516.38i	0.0935959	−	0.162113i	−0.815426	−	0.578862i	$-0.803497\pi$
$919$	2607.53	−	4516.38i	0.0935959	−	0.162113i	0.909022	+	0.416749i	$0.136831\pi$
$920$	437.083	+	757.050i	0.0156633	+	0.0271295i
$921$	−23841.0	+	13764.6i	−0.852974	+	0.492465i
$922$	11877.0			0.424239
$923$	−946.707	−	3058.24i	−0.0337608	−	0.109061i
$924$	605.830			0.0215696
$925$	−59988.7	+	34634.5i	−2.13234	+	1.23111i
$926$	−17985.7	−	31152.1i	−0.638278	−	1.10553i
$927$	6058.01	−	10492.8i	0.214640	−	0.371767i
$928$			2588.20i			0.0915539i
$929$	1145.97	+	661.626i	0.0404716	+	0.0233663i	0.520099	−	0.854106i	$-0.325895\pi$
$929$	1145.97	+	661.626i	0.0404716	+	0.0233663i	−0.479628	+	0.877472i	$0.659228\pi$
$930$	5923.28	+	3419.81i	0.208851	+	0.120580i
$931$			2848.99i			0.100292i
$932$	3522.17	−	6100.58i	0.123790	−	0.214411i
$933$	9282.66	+	16078.0i	0.325724	+	0.564171i
$934$	−7604.96	+	4390.73i	−0.266426	+	0.153821i
$935$	12952.1			0.453024
$936$	−997.978	−	3223.86i	−0.0348503	−	0.112580i
$937$	31390.0			1.09441			0.547207	−	0.836997i	$-0.315691\pi$
$937$	31390.0			1.09441			0.547207	+	0.836997i	$0.315691\pi$
$938$	4043.55	−	2334.54i	0.140753	−	0.0812640i
$939$	−10132.4	−	17549.9i	−0.352140	−	0.609925i
$940$	−935.856	+	1620.95i	−0.0324726	+	0.0562442i
$941$			16706.7i			0.578772i	0.957213	+	0.289386i	$0.0934510\pi$
$941$			16706.7i			0.578772i	−0.957213	+	0.289386i	$0.906549\pi$
$942$	−1075.13	−	620.725i	−0.0371863	−	0.0214695i
$943$	440.974	+	254.597i	0.0152281	+	0.00879195i
$944$			874.064i			0.0301360i
$945$	−1660.81	+	2876.60i	−0.0571705	+	0.0990221i
$946$	−2683.20	−	4647.44i	−0.0922181	−	0.159726i
$947$	−14971.3	+	8643.71i	−0.513731	+	0.296603i	−0.734366	−	0.678754i	$-0.762520\pi$
$947$	−14971.3	+	8643.71i	−0.513731	+	0.296603i	0.220635	+	0.975356i	$0.429187\pi$
$948$	4178.83			0.143167
$949$	−11703.4	+	12638.7i	−0.400324	+	0.432317i
$950$	21381.4			0.730213
$951$	−26020.8	+	15023.1i	−0.887259	+	0.512259i
$952$	−2861.13	−	4955.62i	−0.0974052	−	0.168711i
$953$	−167.686	+	290.441i	−0.00569978	+	0.00987230i	−0.868861	−	0.495056i	$-0.835148\pi$
$953$	−167.686	+	290.441i	−0.00569978	+	0.00987230i	0.863161	+	0.504928i	$0.168481\pi$
$954$			10314.2i			0.350037i
$955$	43195.7	+	24939.0i	1.46364	+	0.845035i
$956$	8137.12	+	4697.97i	0.275286	+	0.158936i
$957$			1750.01i			0.0591117i
$958$	−6185.47	+	10713.5i	−0.208605	+	0.361314i
$959$	−4417.32	−	7651.02i	−0.148741	−	0.257627i
$960$	−2922.26	+	1687.17i	−0.0982455	+	0.0567221i
$961$	25583.9			0.858779
$962$	−33736.7	+	10443.5i	−1.13068	+	0.350013i
$963$	−9462.59			−0.316644
$964$	−5749.51	+	3319.48i	−0.192095	+	0.110906i
$965$	20824.6	+	36069.3i	0.694683	+	1.20323i
$966$	130.568	−	226.150i	0.00434880	−	0.00753235i
$967$			53133.2i			1.76696i	0.468469	+	0.883480i	$0.344806\pi$
$967$			53133.2i			1.76696i	−0.468469	+	0.883480i	$0.655194\pi$
$968$	−8861.06	−	5115.93i	−0.294220	−	0.169868i
$969$	15435.7	+	8911.81i	0.511730	+	0.295447i
$970$			43163.2i			1.42875i
$971$	1537.20	−	2662.50i	0.0508044	−	0.0879957i	−0.839505	−	0.543352i	$-0.817155\pi$
$971$	1537.20	−	2662.50i	0.0508044	−	0.0879957i	0.890309	+	0.455356i	$0.150488\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	−3883.94	+	2242.39i	−0.127968	+	0.0738826i
$974$	37613.2			1.23737
$975$	−5727.98	+	25212.6i	−0.188146	+	0.828154i
$976$	13687.4			0.448897
$977$	−17037.0	+	9836.32i	−0.557894	+	0.322100i	−0.752300	−	0.658821i	$-0.771055\pi$
$977$	−17037.0	+	9836.32i	−0.557894	+	0.322100i	0.194406	+	0.980921i	$0.437722\pi$
$978$	−3868.06	−	6699.68i	−0.126469	−	0.219051i
$979$	1991.15	−	3448.77i	0.0650025	−	0.112588i
$980$			3444.64i			0.112281i
$981$	170.856	+	98.6436i	0.00556066	+	0.00321045i
$982$	−15089.8	−	8712.10i	−0.490361	−	0.283110i
$983$		−	23309.7i		−	0.756321i	−0.925740	−	0.378161i	$-0.876557\pi$
$983$		−	23309.7i		−	0.756321i	0.925740	−	0.378161i	$-0.123443\pi$
$984$	−982.761	+	1702.19i	−0.0318387	+	0.0551462i
$985$	9663.21	+	16737.2i	0.312584	+	0.541412i
$986$	14314.9	−	8264.72i	0.462353	−	0.266939i
$987$	559.128			0.0180316
$988$	10630.2	+	2415.04i	0.342300	+	0.0777660i
$989$	−2313.11			−0.0743708
$990$	−1975.89	+	1140.78i	−0.0634322	+	0.0366226i
$991$	24719.3	+	42815.0i	0.792365	+	1.37242i	0.924499	+	0.381184i	$0.124484\pi$
$991$	24719.3	+	42815.0i	0.792365	+	1.37242i	−0.132134	+	0.991232i	$0.542183\pi$
$992$	1037.80	−	1797.52i	0.0332158	−	0.0575315i
$993$			14917.6i			0.476732i
$994$	828.106	+	478.107i	0.0264245	+	0.0152562i
$995$	27176.3	+	15690.3i	0.865877	+	0.499914i
$996$		−	6877.42i		−	0.218795i
$997$	−15937.2	+	27604.0i	−0.506254	+	0.876858i	0.493719	+	0.869621i	$0.335637\pi$
$997$	−15937.2	+	27604.0i	−0.506254	+	0.876858i	−0.999974	+	0.00723706i	$0.997696\pi$
$998$	−12647.3	−	21905.8i	−0.401147	−	0.694806i
$999$	8808.93	−	5085.84i	0.278981	−	0.161070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.s.a.127.5	yes	20
13.4	even	6	inner	546.4.s.a.43.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.s.a.43.1	✓	20	13.4	even	6	inner
546.4.s.a.127.5	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +17.5747i q^{5} +(5.19615 + 3.00000i) q^{6} +(6.06218 + 3.50000i) q^{7} +8.00000i q^{8} +(-4.50000 + 7.79423i) q^{9} +(-17.5747 - 30.4403i) q^{10} +(-6.24601 + 3.60613i) q^{11} -12.0000 q^{12} +(34.3917 + 31.8466i) q^{13} -14.0000 q^{14} +(45.6604 - 26.3620i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-51.0916 + 88.4932i) q^{17} -18.0000i q^{18} +(50.3531 + 29.0713i) q^{19} +(60.8805 + 35.1494i) q^{20} -21.0000i q^{21} +(7.21227 - 12.4920i) q^{22} +(-3.10875 - 5.38452i) q^{23} +(20.7846 - 12.0000i) q^{24} -183.870 q^{25} +(-91.4149 - 20.7683i) q^{26} +27.0000 q^{27} +(24.2487 - 14.0000i) q^{28} +(40.4407 + 70.0453i) q^{29} +(-52.7241 + 91.3208i) q^{30} -64.8623i q^{31} +(27.7128 + 16.0000i) q^{32} +(18.7380 + 10.8184i) q^{33} -204.366i q^{34} +(-61.5114 + 106.541i) q^{35} +(18.0000 + 31.1769i) q^{36} +(326.257 - 188.364i) q^{37} -116.285 q^{38} +(31.1524 - 137.122i) q^{39} -140.597 q^{40} +(-70.9247 + 40.9484i) q^{41} +(21.0000 + 36.3731i) q^{42} +(186.016 - 322.190i) q^{43} +28.8491i q^{44} +(-136.981 - 79.0861i) q^{45} +(10.7690 + 6.21750i) q^{46} +26.6251i q^{47} +(-24.0000 + 41.5692i) q^{48} +(24.5000 + 42.4352i) q^{49} +(318.472 - 183.870i) q^{50} +306.550 q^{51} +(179.103 - 55.4432i) q^{52} -573.013 q^{53} +(-46.7654 + 27.0000i) q^{54} +(-63.3767 - 109.772i) q^{55} +(-28.0000 + 48.4974i) q^{56} -174.428i q^{57} +(-140.091 - 80.8814i) q^{58} +(-47.3101 - 27.3145i) q^{59} -210.896i q^{60} +(-427.732 + 740.853i) q^{61} +(64.8623 + 112.345i) q^{62} +(-54.5596 + 31.5000i) q^{63} -64.0000 q^{64} +(-559.695 + 604.424i) q^{65} -43.2736 q^{66} +(-288.825 + 166.753i) q^{67} +(204.366 + 353.973i) q^{68} +(-9.32626 + 16.1535i) q^{69} -246.046i q^{70} +(-59.1504 - 34.1505i) q^{71} +(-62.3538 - 36.0000i) q^{72} +367.492i q^{73} +(-376.729 + 652.514i) q^{74} +(275.804 + 477.707i) q^{75} +(201.412 - 116.285i) q^{76} -50.4859 q^{77} +(83.1648 + 268.655i) q^{78} -348.236 q^{79} +(243.522 - 140.597i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(81.8967 - 141.849i) q^{82} +573.119i q^{83} +(-72.7461 - 42.0000i) q^{84} +(-1555.24 - 897.919i) q^{85} +744.065i q^{86} +(121.322 - 210.136i) q^{87} +(-28.8491 - 49.9680i) q^{88} +(-478.182 + 276.078i) q^{89} +316.344 q^{90} +(97.0256 + 313.431i) q^{91} -24.8700 q^{92} +(-168.517 + 97.2935i) q^{93} +(-26.6251 - 46.1161i) q^{94} +(-510.920 + 884.939i) q^{95} -96.0000i q^{96} +(-1063.47 - 613.996i) q^{97} +(-84.8705 - 49.0000i) q^{98} -64.9104i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 40 q^{4} - 90 q^{9} - 24 q^{10} + 18 q^{11} - 240 q^{12} + 28 q^{13} - 280 q^{14} + 18 q^{15} - 160 q^{16} - 106 q^{17} - 60 q^{19} + 24 q^{20} - 24 q^{22} - 450 q^{23} - 304 q^{25} - 60 q^{26}+ \cdots - 1620 q^{97}+O(q^{100}) \) 20 * q - 30 * q^3 + 40 * q^4 - 90 * q^9 - 24 * q^10 + 18 * q^11 - 240 * q^12 + 28 * q^13 - 280 * q^14 + 18 * q^15 - 160 * q^16 - 106 * q^17 - 60 * q^19 + 24 * q^20 - 24 * q^22 - 450 * q^23 - 304 * q^25 - 60 * q^26 + 540 * q^27 + 290 * q^29 - 72 * q^30 - 54 * q^33 - 84 * q^35 + 360 * q^36 + 564 * q^37 + 160 * q^38 + 228 * q^39 - 192 * q^40 - 246 * q^41 + 420 * q^42 - 464 * q^43 - 54 * q^45 - 240 * q^46 - 480 * q^48 + 490 * q^49 + 720 * q^50 + 636 * q^51 + 416 * q^52 - 1528 * q^53 + 1384 * q^55 - 560 * q^56 - 480 * q^58 - 2496 * q^59 - 270 * q^61 - 60 * q^62 - 1280 * q^64 + 3042 * q^65 + 144 * q^66 + 1314 * q^67 + 424 * q^68 - 1350 * q^69 - 516 * q^71 - 540 * q^74 + 456 * q^75 - 240 * q^76 + 168 * q^77 + 1116 * q^78 - 4000 * q^79 + 96 * q^80 - 810 * q^81 - 476 * q^82 - 2730 * q^85 + 870 * q^87 + 96 * q^88 - 1266 * q^89 + 432 * q^90 + 1302 * q^91 - 3600 * q^92 + 1692 * q^93 + 1080 * q^94 - 3798 * q^95 - 1620 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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