LMFDB - Embedded newform 546.4.s.d.43.5

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 = [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			43.5
Character	$\chi$	$=$	546.43
Dual form			546.4.s.d.127.5

$q$-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} +11.2847i q^{5} +(-5.19615 + 3.00000i) q^{6} +(6.06218 - 3.50000i) q^{7} -8.00000i q^{8} +(-4.50000 - 7.79423i) q^{9} +(11.2847 - 19.5457i) q^{10} +(-8.19780 - 4.73300i) q^{11} +12.0000 q^{12} +(-43.7434 + 16.8378i) q^{13} -14.0000 q^{14} +(29.3185 + 16.9270i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-4.98929 - 8.64170i) q^{17} +18.0000i q^{18} +(32.1424 - 18.5574i) q^{19} +(-39.0913 + 22.5694i) q^{20} -21.0000i q^{21} +(9.46601 + 16.3956i) q^{22} +(-81.1505 + 140.557i) q^{23} +(-20.7846 - 12.0000i) q^{24} -2.34437 q^{25} +(92.6037 + 14.5795i) q^{26} -27.0000 q^{27} +(24.2487 + 14.0000i) q^{28} +(44.6678 - 77.3669i) q^{29} +(-33.8541 - 58.6370i) q^{30} -43.4154i q^{31} +(27.7128 - 16.0000i) q^{32} +(-24.5934 + 14.1990i) q^{33} +19.9572i q^{34} +(39.4964 + 68.4098i) q^{35} +(18.0000 - 31.1769i) q^{36} +(-70.6662 - 40.7992i) q^{37} -74.2296 q^{38} +(-21.8693 + 138.905i) q^{39} +90.2776 q^{40} +(-373.292 - 215.520i) q^{41} +(-21.0000 + 36.3731i) q^{42} +(-244.664 - 423.770i) q^{43} -37.8640i q^{44} +(87.9555 - 50.7811i) q^{45} +(281.114 - 162.301i) q^{46} -171.074i q^{47} +(24.0000 + 41.5692i) q^{48} +(24.5000 - 42.4352i) q^{49} +(4.06057 + 2.34437i) q^{50} -29.9357 q^{51} +(-145.815 - 117.856i) q^{52} +28.6439 q^{53} +(46.7654 + 27.0000i) q^{54} +(53.4105 - 92.5097i) q^{55} +(-28.0000 - 48.4974i) q^{56} -111.344i q^{57} +(-154.734 + 89.3356i) q^{58} +(-242.440 + 139.973i) q^{59} +135.416i q^{60} +(-108.984 - 188.767i) q^{61} +(-43.4154 + 75.1977i) q^{62} +(-54.5596 - 31.5000i) q^{63} -64.0000 q^{64} +(-190.009 - 493.631i) q^{65} +56.7961 q^{66} +(-215.578 - 124.464i) q^{67} +(19.9572 - 34.5668i) q^{68} +(243.451 + 421.670i) q^{69} -157.986i q^{70} +(-994.059 + 573.920i) q^{71} +(-62.3538 + 36.0000i) q^{72} -557.825i q^{73} +(81.5983 + 141.332i) q^{74} +(-3.51656 + 6.09086i) q^{75} +(128.569 + 74.2296i) q^{76} -66.2621 q^{77} +(176.784 - 218.722i) q^{78} -144.368 q^{79} +(-156.365 - 90.2776i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(431.040 + 746.583i) q^{82} +1167.17i q^{83} +(72.7461 - 42.0000i) q^{84} +(97.5190 - 56.3026i) q^{85} +978.654i q^{86} +(-134.003 - 232.101i) q^{87} +(-37.8640 + 65.5824i) q^{88} +(1383.37 + 798.688i) q^{89} -203.125 q^{90} +(-206.248 + 255.176i) q^{91} -649.204 q^{92} +(-112.796 - 65.1231i) q^{93} +(-171.074 + 296.309i) q^{94} +(209.415 + 362.717i) q^{95} -96.0000i q^{96} +(-525.727 + 303.529i) q^{97} +(-84.8705 + 49.0000i) q^{98} +85.1941i 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$5$			11.2847i			1.00933i	0.863314	+	0.504667i	$0.168385\pi$
$5$			11.2847i			1.00933i	−0.863314	+	0.504667i	$0.831615\pi$
$6$	−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
$10$	11.2847	−	19.5457i	0.356853	−	0.618088i
$11$	−8.19780	−	4.73300i	−0.224703	−	0.129732i	0.383423	−	0.923573i	$-0.374745\pi$
$11$	−8.19780	−	4.73300i	−0.224703	−	0.129732i	−0.608126	+	0.793841i	$0.708078\pi$
$12$	12.0000			0.288675
$13$	−43.7434	+	16.8378i	−0.933250	+	0.359228i
$13$	−43.7434	+	16.8378i	−0.933250	+	0.359228i
$14$	−14.0000			−0.267261
$15$	29.3185	+	16.9270i	0.504667	+	0.291370i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−4.98929	−	8.64170i	−0.0711812	−	0.123289i	0.828238	−	0.560376i	$-0.189344\pi$
$17$	−4.98929	−	8.64170i	−0.0711812	−	0.123289i	−0.899419	+	0.437087i	$0.856010\pi$
$18$			18.0000i			0.235702i
$19$	32.1424	−	18.5574i	0.388103	−	0.224072i	−0.293235	−	0.956040i	$-0.594732\pi$
$19$	32.1424	−	18.5574i	0.388103	−	0.224072i	0.681338	+	0.731969i	$0.261398\pi$
$20$	−39.0913	+	22.5694i	−0.437054	+	0.252333i
$21$		−	21.0000i		−	0.218218i
$22$	9.46601	+	16.3956i	0.0917345	+	0.158889i
$23$	−81.1505	+	140.557i	−0.735698	+	1.27427i	0.218719	+	0.975788i	$0.429812\pi$
$23$	−81.1505	+	140.557i	−0.735698	+	1.27427i	−0.954417	+	0.298478i	$0.903521\pi$
$24$	−20.7846	−	12.0000i	−0.176777	−	0.102062i
$25$	−2.34437			−0.0187550
$26$	92.6037	+	14.5795i	0.698503	+	0.109972i
$27$	−27.0000			−0.192450
$28$	24.2487	+	14.0000i	0.163663	+	0.0944911i
$29$	44.6678	−	77.3669i	0.286021	−	0.495403i	−0.686835	−	0.726813i	$-0.741001\pi$
$29$	44.6678	−	77.3669i	0.286021	−	0.495403i	0.972856	+	0.231410i	$0.0743340\pi$
$30$	−33.8541	−	58.6370i	−0.206029	−	0.356853i
$31$		−	43.4154i		−	0.251537i	−0.992060	−	0.125768i	$-0.959860\pi$
$31$		−	43.4154i		−	0.251537i	0.992060	−	0.125768i	$-0.0401396\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	−24.5934	+	14.1990i	−0.129732	+	0.0749009i
$34$			19.9572i			0.100665i
$35$	39.4964	+	68.4098i	0.190746	+	0.330382i
$36$	18.0000	−	31.1769i	0.0833333	−	0.144338i
$37$	−70.6662	−	40.7992i	−0.313985	−	0.181279i	0.334723	−	0.942317i	$-0.391357\pi$
$37$	−70.6662	−	40.7992i	−0.313985	−	0.181279i	−0.648708	+	0.761037i	$0.724691\pi$
$38$	−74.2296			−0.316885
$39$	−21.8693	+	138.905i	−0.0897920	+	0.570325i
$40$	90.2776			0.356853
$41$	−373.292	−	215.520i	−1.42191	−	0.820941i	−0.425449	−	0.904982i	$-0.639884\pi$
$41$	−373.292	−	215.520i	−1.42191	−	0.820941i	−0.996462	+	0.0840413i	$0.973217\pi$
$42$	−21.0000	+	36.3731i	−0.0771517	+	0.133631i
$43$	−244.664	−	423.770i	−0.867694	−	1.50289i	−0.864347	−	0.502895i	$-0.832268\pi$
$43$	−244.664	−	423.770i	−0.867694	−	1.50289i	−0.00334652	−	0.999994i	$-0.501065\pi$
$44$		−	37.8640i		−	0.129732i
$45$	87.9555	−	50.7811i	0.291370	−	0.168222i
$46$	281.114	−	162.301i	0.901042	−	0.520217i
$47$		−	171.074i		−	0.530930i	−0.964121	−	0.265465i	$-0.914475\pi$
$47$		−	171.074i		−	0.530930i	0.964121	−	0.265465i	$-0.0855255\pi$
$48$	24.0000	+	41.5692i	0.0721688	+	0.125000i
$49$	24.5000	−	42.4352i	0.0714286	−	0.123718i
$50$	4.06057	+	2.34437i	0.0114850	+	0.00663088i
$51$	−29.9357			−0.0821930
$52$	−145.815	−	117.856i	−0.388863	−	0.314302i
$53$	28.6439			0.0742366			0.0371183	−	0.999311i	$-0.488182\pi$
$53$	28.6439			0.0742366			0.0371183	+	0.999311i	$0.488182\pi$
$54$	46.7654	+	27.0000i	0.117851	+	0.0680414i
$55$	53.4105	−	92.5097i	0.130943	−	0.226800i
$56$	−28.0000	−	48.4974i	−0.0668153	−	0.115728i
$57$		−	111.344i		−	0.258736i
$58$	−154.734	+	89.3356i	−0.350302	+	0.202247i
$59$	−242.440	+	139.973i	−0.534967	+	0.308863i	−0.743037	−	0.669251i	$-0.766615\pi$
$59$	−242.440	+	139.973i	−0.534967	+	0.308863i	0.208070	+	0.978114i	$0.433282\pi$
$60$			135.416i			0.291370i
$61$	−108.984	−	188.767i	−0.228755	−	0.396215i	0.728685	−	0.684849i	$-0.240132\pi$
$61$	−108.984	−	188.767i	−0.228755	−	0.396215i	−0.957439	+	0.288635i	$0.906799\pi$
$62$	−43.4154	+	75.1977i	−0.0889316	+	0.154034i
$63$	−54.5596	−	31.5000i	−0.109109	−	0.0629941i
$64$	−64.0000			−0.125000
$65$	−190.009	−	493.631i	−0.362581	−	0.941961i
$66$	56.7961			0.105926
$67$	−215.578	−	124.464i	−0.393091	−	0.226951i	0.290408	−	0.956903i	$-0.406209\pi$
$67$	−215.578	−	124.464i	−0.393091	−	0.226951i	−0.683498	+	0.729952i	$0.739542\pi$
$68$	19.9572	−	34.5668i	0.0355906	−	0.0616447i
$69$	243.451	+	421.670i	0.424755	+	0.735698i
$70$		−	157.986i		−	0.269756i
$71$	−994.059	+	573.920i	−1.66159	+	0.959322i	−0.689639	+	0.724153i	$0.742231\pi$
$71$	−994.059	+	573.920i	−1.66159	+	0.959322i	−0.971955	+	0.235168i	$0.924436\pi$
$72$	−62.3538	+	36.0000i	−0.102062	+	0.0589256i
$73$		−	557.825i		−	0.894363i	−0.894443	−	0.447181i	$-0.852428\pi$
$73$		−	557.825i		−	0.894363i	0.894443	−	0.447181i	$-0.147572\pi$
$74$	81.5983	+	141.332i	0.128184	+	0.222021i
$75$	−3.51656	+	6.09086i	−0.00541409	+	0.00937749i
$76$	128.569	+	74.2296i	0.194052	+	0.112036i
$77$	−66.2621			−0.0980683
$78$	176.784	−	218.722i	0.256627	−	0.317505i
$79$	−144.368			−0.205604			−0.102802	−	0.994702i	$-0.532781\pi$
$79$	−144.368			−0.205604			−0.102802	+	0.994702i	$0.532781\pi$
$80$	−156.365	−	90.2776i	−0.218527	−	0.126167i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	431.040	+	746.583i	0.580493	+	1.00544i
$83$			1167.17i			1.54354i	0.635901	+	0.771771i	$0.280629\pi$
$83$			1167.17i			1.54354i	−0.635901	+	0.771771i	$0.719371\pi$
$84$	72.7461	−	42.0000i	0.0944911	−	0.0545545i
$85$	97.5190	−	56.3026i	0.124440	−	0.0718456i
$86$			978.654i			1.22710i
$87$	−134.003	−	232.101i	−0.165134	−	0.286021i
$88$	−37.8640	+	65.5824i	−0.0458673	+	0.0794444i
$89$	1383.37	+	798.688i	1.64760	+	0.951245i	0.978021	+	0.208508i	$0.0668607\pi$
$89$	1383.37	+	798.688i	1.64760	+	0.951245i	0.669584	+	0.742737i	$0.266473\pi$
$90$	−203.125			−0.237902
$91$	−206.248	+	255.176i	−0.237590	+	0.293953i
$92$	−649.204			−0.735698
$93$	−112.796	−	65.1231i	−0.125768	−	0.0726124i
$94$	−171.074	+	296.309i	−0.187712	+	0.325127i
$95$	209.415	+	362.717i	0.226163	+	0.391726i
$96$		−	96.0000i		−	0.102062i
$97$	−525.727	+	303.529i	−0.550304	+	0.317718i	−0.749245	−	0.662293i	$-0.769583\pi$
$97$	−525.727	+	303.529i	−0.550304	+	0.317718i	0.198940	+	0.980012i	$0.436250\pi$
$98$	−84.8705	+	49.0000i	−0.0874818	+	0.0505076i
$99$			85.1941i			0.0864882i
$100$	−4.68874	−	8.12114i	−0.00468874	−	0.00812114i
$101$	−275.270	+	476.781i	−0.271192	+	0.469718i	−0.969167	−	0.246404i	$-0.920751\pi$
$101$	−275.270	+	476.781i	−0.271192	+	0.469718i	0.697976	+	0.716122i	$0.254084\pi$
$102$	51.8502	+	29.9357i	0.0503327	+	0.0290596i
$103$	−1614.10			−1.54410			−0.772049	−	0.635563i	$-0.780768\pi$
$103$	−1614.10			−1.54410			−0.772049	+	0.635563i	$0.780768\pi$
$104$	134.702	+	349.948i	0.127006	+	0.329954i
$105$	236.979			0.220255
$106$	−49.6126	−	28.6439i	−0.0454604	−	0.0262466i
$107$	247.860	−	429.305i	0.223939	−	0.387874i	−0.732062	−	0.681239i	$-0.761442\pi$
$107$	247.860	−	429.305i	0.223939	−	0.387874i	0.956001	+	0.293365i	$0.0947750\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$			193.644i			0.170162i	0.996374	+	0.0850812i	$0.0271150\pi$
$109$			193.644i			0.170162i	−0.996374	+	0.0850812i	$0.972885\pi$
$110$	−185.019	+	106.821i	−0.160372	+	0.0925908i
$111$	−211.999	+	122.397i	−0.181279	+	0.104662i
$112$			112.000i			0.0944911i
$113$	−966.825	−	1674.59i	−0.804879	−	1.39409i	−0.916373	−	0.400325i	$-0.868897\pi$
$113$	−966.825	−	1674.59i	−0.804879	−	1.39409i	0.111495	−	0.993765i	$-0.464436\pi$
$114$	−111.344	+	192.854i	−0.0914768	+	0.158443i
$115$	−1586.14	−	915.759i	−1.28616	−	0.742565i
$116$	357.342			0.286021
$117$	328.083	+	265.176i	0.259242	+	0.209535i
$118$	559.892			0.436798
$119$	−60.4919	−	34.9250i	−0.0465990	−	0.0269040i
$120$	135.416	−	234.548i	0.103015	−	0.178427i
$121$	−620.697	−	1075.08i	−0.466339	−	0.807723i
$122$			435.938i			0.323508i
$123$	−1119.88	+	646.560i	−0.820941	+	0.473971i
$124$	150.395	−	86.8308i	0.108919	−	0.0628841i
$125$			1384.13i			0.990404i
$126$	63.0000	+	109.119i	0.0445435	+	0.0771517i
$127$	−355.930	+	616.489i	−0.248690	+	0.430745i	−0.963163	−	0.268919i	$-0.913334\pi$
$127$	−355.930	+	616.489i	−0.248690	+	0.430745i	0.714472	+	0.699664i	$0.246667\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	−1467.98			−1.00193
$130$	−164.526	+	1045.00i	−0.110999	+	0.705023i
$131$	−19.8354			−0.0132292			−0.00661462	−	0.999978i	$-0.502106\pi$
$131$	−19.8354			−0.0132292			−0.00661462	+	0.999978i	$0.502106\pi$
$132$	−98.3736	−	56.7961i	−0.0648661	−	0.0374505i
$133$	129.902	−	224.997i	0.0846911	−	0.146689i
$134$	248.928	+	431.156i	0.160479	+	0.277957i
$135$		−	304.687i		−	0.194246i
$136$	−69.1336	+	39.9143i	−0.0435894	+	0.0251664i
$137$	−2114.49	+	1220.80i	−1.31863	+	0.761314i	−0.983509	−	0.180859i	$-0.942112\pi$
$137$	−2114.49	+	1220.80i	−1.31863	+	0.761314i	−0.335126	+	0.942173i	$0.608779\pi$
$138$		−	973.806i		−	0.600695i
$139$	−1433.15	−	2482.29i	−0.874521	−	1.51472i	−0.857272	−	0.514864i	$-0.827842\pi$
$139$	−1433.15	−	2482.29i	−0.874521	−	1.51472i	−0.0172494	−	0.999851i	$-0.505491\pi$
$140$	−157.986	+	273.639i	−0.0953731	+	0.165191i
$141$	−444.463	−	256.611i	−0.265465	−	0.153266i
$142$	2295.68			1.35669
$143$	438.294	+	69.0050i	0.256307	+	0.0403530i
$144$	144.000			0.0833333
$145$	873.062	+	504.063i	0.500027	+	0.288690i
$146$	−557.825	+	966.181i	−0.316205	+	0.547683i
$147$	−73.5000	−	127.306i	−0.0412393	−	0.0714286i
$148$		−	326.393i		−	0.181279i
$149$	126.761	−	73.1857i	0.0696960	−	0.0402390i	−0.464747	−	0.885443i	$-0.653855\pi$
$149$	126.761	−	73.1857i	0.0696960	−	0.0402390i	0.534443	+	0.845205i	$0.320521\pi$
$150$	12.1817	−	7.03311i	0.00663088	−	0.00382834i
$151$		−	2571.20i		−	1.38570i	−0.721081	−	0.692851i	$-0.756355\pi$
$151$		−	2571.20i		−	1.38570i	0.721081	−	0.692851i	$-0.243645\pi$
$152$	−148.459	−	257.139i	−0.0792213	−	0.137215i
$153$	−44.9036	+	77.7753i	−0.0237271	+	0.0410965i
$154$	114.769	+	66.2621i	0.0600544	+	0.0346724i
$155$	489.929			0.253884
$156$	−524.921	+	202.054i	−0.269406	+	0.103700i
$157$	1107.40			0.562929			0.281464	−	0.959572i	$-0.409180\pi$
$157$	1107.40			0.562929			0.281464	+	0.959572i	$0.409180\pi$
$158$	250.053	+	144.368i	0.125906	+	0.0726919i
$159$	42.9658	−	74.4190i	0.0214303	−	0.0371183i
$160$	180.555	+	312.731i	0.0892134	+	0.154522i
$161$			1136.11i			0.556135i
$162$	140.296	−	81.0000i	0.0680414	−	0.0392837i
$163$	−942.370	+	544.077i	−0.452835	+	0.261444i	−0.709027	−	0.705182i	$-0.750865\pi$
$163$	−942.370	+	544.077i	−0.452835	+	0.261444i	0.256192	+	0.966626i	$0.417532\pi$
$164$		−	1724.16i		−	0.820941i
$165$	−160.232	−	277.529i	−0.0756001	−	0.130943i
$166$	1167.17	−	2021.60i	0.545724	−	0.945222i
$167$	60.9254	+	35.1753i	0.0282308	+	0.0162991i	0.514049	−	0.857761i	$-0.328145\pi$
$167$	60.9254	+	35.1753i	0.0282308	+	0.0162991i	−0.485818	+	0.874060i	$0.661478\pi$
$168$	−168.000			−0.0771517
$169$	1629.98	−	1473.09i	0.741910	−	0.670499i
$170$	−225.210			−0.101605
$171$	−289.281	−	167.017i	−0.129368	−	0.0746905i
$172$	978.654	−	1695.08i	0.433847	−	0.751445i
$173$	168.662	+	292.132i	0.0741223	+	0.128384i	0.900704	−	0.434433i	$-0.143051\pi$
$173$	168.662	+	292.132i	0.0741223	+	0.128384i	−0.826582	+	0.562816i	$0.809718\pi$
$174$			536.014i			0.233535i
$175$	−14.2120	+	8.20530i	−0.00613901	+	0.00354436i
$176$	131.165	−	75.7281i	0.0561757	−	0.0324331i
$177$			839.838i			0.356644i
$178$	−1597.38	−	2766.74i	−0.672632	−	1.16503i
$179$	−1867.57	+	3234.72i	−0.779824	+	1.35070i	0.152218	+	0.988347i	$0.451358\pi$
$179$	−1867.57	+	3234.72i	−0.779824	+	1.35070i	−0.932043	+	0.362348i	$0.881975\pi$
$180$	351.822	+	203.125i	0.145685	+	0.0841112i
$181$	−1289.63			−0.529599			−0.264800	−	0.964303i	$-0.585306\pi$
$181$	−1289.63			−0.529599			−0.264800	+	0.964303i	$0.585306\pi$
$182$	612.408	−	235.729i	0.249422	−	0.0960077i
$183$	−653.907			−0.264143
$184$	1124.45	+	649.204i	0.450521	+	0.260108i
$185$	460.406	−	797.447i	0.182972	−	0.316916i
$186$	130.246	+	225.593i	0.0513447	+	0.0889316i
$187$			94.4573i			0.0369380i
$188$	592.618	−	342.148i	0.229899	−	0.132732i
$189$	−163.679	+	94.5000i	−0.0629941	+	0.0363696i
$190$		−	837.658i		−	0.319843i
$191$	−466.503	−	808.007i	−0.176728	−	0.306101i	0.764030	−	0.645181i	$-0.223218\pi$
$191$	−466.503	−	808.007i	−0.176728	−	0.306101i	−0.940758	+	0.339079i	$0.889885\pi$
$192$	−96.0000	+	166.277i	−0.0360844	+	0.0625000i
$193$	3234.44	+	1867.40i	1.20632	+	0.696470i	0.961954	−	0.273213i	$-0.0880864\pi$
$193$	3234.44	+	1867.40i	1.20632	+	0.696470i	0.244367	+	0.969683i	$0.421420\pi$
$194$	1214.12			0.449322
$195$	−1567.51	−	246.788i	−0.575648	−	0.0906301i
$196$	196.000			0.0714286
$197$	1553.29	+	896.794i	0.561764	+	0.324335i	0.753853	−	0.657043i	$-0.228193\pi$
$197$	1553.29	+	896.794i	0.561764	+	0.324335i	−0.192089	+	0.981378i	$0.561526\pi$
$198$	85.1941	−	147.560i	0.0305782	−	0.0529630i
$199$	−317.756	−	550.370i	−0.113192	−	0.196054i	0.803864	−	0.594813i	$-0.202774\pi$
$199$	−317.756	−	550.370i	−0.113192	−	0.196054i	−0.917055	+	0.398760i	$0.869441\pi$
$200$			18.7550i			0.00663088i
$201$	−646.735	+	373.392i	−0.226951	+	0.131030i
$202$	953.562	−	550.539i	0.332141	−	0.191761i
$203$		−	625.349i		−	0.216211i
$204$	−59.8715	−	103.700i	−0.0205482	−	0.0355906i
$205$	2432.08	−	4212.48i	0.828604	−	1.43518i
$206$	2795.70	+	1614.10i	0.945563	+	0.545921i
$207$	1460.71			0.490465
$208$	116.636	−	740.829i	0.0388811	−	0.246958i
$209$	−351.329			−0.116277
$210$	−410.459	−	236.979i	−0.134878	−	0.0778718i
$211$	−20.6387	+	35.7473i	−0.00673377	+	0.0116632i	−0.869373	−	0.494157i	$-0.835477\pi$
$211$	−20.6387	+	35.7473i	−0.00673377	+	0.0116632i	0.862639	+	0.505820i	$0.168810\pi$
$212$	57.2877	+	99.2253i	0.0185591	+	0.0321454i
$213$			3443.52i			1.10773i
$214$	−858.611	+	495.719i	−0.274268	+	0.158349i
$215$	4782.11	−	2760.95i	1.51692	−	0.875793i
$216$			216.000i			0.0680414i
$217$	−151.954	−	263.192i	−0.0475359	−	0.0823347i
$218$	193.644	−	335.401i	0.0601615	−	0.104203i
$219$	−1449.27	−	836.737i	−0.447181	−	0.258180i
$220$	427.284			0.130943
$221$	363.756	+	294.009i	0.110719	+	0.0894896i
$222$	489.590			0.148014
$223$	5654.77	+	3264.78i	1.69808	+	0.980386i	0.947583	+	0.319509i	$0.103518\pi$
$223$	5654.77	+	3264.78i	1.69808	+	0.980386i	0.750495	+	0.660876i	$0.229815\pi$
$224$	112.000	−	193.990i	0.0334077	−	0.0578638i
$225$	10.5497	+	18.2726i	0.00312583	+	0.00541409i
$226$			3867.30i			1.13827i
$227$	−582.612	+	336.371i	−0.170349	+	0.0983512i	−0.582751	−	0.812651i	$-0.698024\pi$
$227$	−582.612	+	336.371i	−0.170349	+	0.0983512i	0.412401	+	0.911002i	$0.364690\pi$
$228$	385.708	−	222.689i	0.112036	−	0.0646839i
$229$		−	5294.01i		−	1.52768i	−0.645407	−	0.763839i	$-0.723312\pi$
$229$		−	5294.01i		−	1.52768i	0.645407	−	0.763839i	$-0.276688\pi$
$230$	1831.52	+	3172.28i	0.525072	+	0.909452i
$231$	−99.3931	+	172.154i	−0.0283099	+	0.0490342i
$232$	−618.935	−	357.342i	−0.175151	−	0.101124i
$233$	1199.40			0.337233			0.168616	−	0.985682i	$-0.446070\pi$
$233$	1199.40			0.337233			0.168616	+	0.985682i	$0.446070\pi$
$234$	−303.080	−	787.382i	−0.0846709	−	0.219969i
$235$	1930.52			0.535886
$236$	−969.761	−	559.892i	−0.267483	−	0.154432i
$237$	−216.552	+	375.080i	−0.0593527	+	0.102802i
$238$	69.8500	+	120.984i	0.0190240	+	0.0329505i
$239$			706.665i			0.191257i	0.995417	+	0.0956283i	$0.0304860\pi$
$239$			706.665i			0.191257i	−0.995417	+	0.0956283i	$0.969514\pi$
$240$	−469.096	+	270.833i	−0.126167	+	0.0728424i
$241$	76.2175	−	44.0042i	0.0203718	−	0.0117617i	−0.489780	−	0.871846i	$-0.662923\pi$
$241$	76.2175	−	44.0042i	0.0203718	−	0.0117617i	0.510151	+	0.860085i	$0.329589\pi$
$242$			2482.79i			0.659503i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	435.938	−	755.066i	0.114377	−	0.198107i
$245$	478.869	+	276.475i	0.124873	+	0.0720953i
$246$	2586.24			0.670296
$247$	−1093.55	+	1352.97i	−0.281705	+	0.348532i
$248$	−347.323			−0.0889316
$249$	3032.41	+	1750.76i	0.771771	+	0.445582i
$250$	1384.13	−	2397.39i	0.350161	−	0.606496i
$251$	−2610.16	−	4520.93i	−0.656382	−	1.13689i	−0.981545	−	0.191229i	$-0.938753\pi$
$251$	−2610.16	−	4520.93i	−0.656382	−	1.13689i	0.325164	−	0.945658i	$-0.394581\pi$
$252$		−	252.000i		−	0.0629941i
$253$	1330.51	−	768.171i	0.330627	−	0.190887i
$254$	1232.98	−	711.860i	0.304582	−	0.175851i
$255$		−	337.816i		−	0.0829601i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1921.47	−	3328.09i	0.466375	−	0.807785i	−0.532888	−	0.846186i	$-0.678893\pi$
$257$	1921.47	−	3328.09i	0.466375	−	0.807785i	0.999262	+	0.0384014i	$0.0122265\pi$
$258$	2542.62	+	1467.98i	0.613552	+	0.354235i
$259$	−571.188			−0.137034
$260$	1329.97	−	1645.47i	0.317236	−	0.392492i
$261$	−804.020			−0.190681
$262$	34.3560	+	19.8354i	0.00810122	+	0.00467724i
$263$	−2203.49	+	3816.55i	−0.516627	+	0.894824i	0.483187	+	0.875517i	$0.339479\pi$
$263$	−2203.49	+	3816.55i	−0.516627	+	0.894824i	−0.999814	+	0.0193068i	$0.993854\pi$
$264$	113.592	+	196.747i	0.0264815	+	0.0458673i
$265$			323.237i			0.0749295i
$266$	−449.993	+	259.804i	−0.103725	+	0.0598856i
$267$	4150.11	−	2396.06i	0.951245	−	0.549201i
$268$		−	995.713i		−	0.226951i
$269$	2369.85	+	4104.71i	0.537147	+	0.930366i	0.999056	+	0.0434389i	$0.0138314\pi$
$269$	2369.85	+	4104.71i	0.537147	+	0.930366i	−0.461909	+	0.886927i	$0.652835\pi$
$270$	−304.687	+	527.733i	−0.0686765	+	0.118951i
$271$	5380.09	+	3106.20i	1.20597	+	0.696266i	0.961876	−	0.273486i	$-0.0881767\pi$
$271$	5380.09	+	3106.20i	1.20597	+	0.696266i	0.244092	+	0.969752i	$0.421510\pi$
$272$	159.657			0.0355906
$273$	353.594	+	918.612i	0.0783900	+	0.203652i
$274$	4883.20			1.07666
$275$	19.2187	+	11.0959i	0.00421429	+	0.00243312i
$276$	−973.806	+	1686.68i	−0.212378	+	0.367849i
$277$	1411.08	+	2444.06i	0.306078	+	0.530143i	0.977501	−	0.210932i	$-0.0676498\pi$
$277$	1411.08	+	2444.06i	0.306078	+	0.530143i	−0.671423	+	0.741075i	$0.734316\pi$
$278$			5732.61i			1.23676i
$279$	−338.389	+	195.369i	−0.0726124	+	0.0419228i
$280$	547.279	−	315.971i	0.116808	−	0.0674390i
$281$		−	6710.08i		−	1.42452i	−0.701916	−	0.712260i	$-0.747672\pi$
$281$		−	6710.08i		−	1.42452i	0.701916	−	0.712260i	$-0.252328\pi$
$282$	513.222	+	888.926i	0.108376	+	0.187712i
$283$	−1451.32	+	2513.75i	−0.304847	+	0.528011i	−0.977227	−	0.212195i	$-0.931939\pi$
$283$	−1451.32	+	2513.75i	−0.304847	+	0.528011i	0.672380	+	0.740206i	$0.265272\pi$
$284$	−3976.24	−	2295.68i	−0.830797	−	0.479661i
$285$	1256.49			0.261151
$286$	−690.142	−	557.814i	−0.142689	−	0.115329i
$287$	−3017.28			−0.620573
$288$	−249.415	−	144.000i	−0.0510310	−	0.0294628i
$289$	2406.71	−	4168.55i	0.489866	−	0.848474i
$290$	−1008.13	−	1746.12i	−0.204135	−	0.353572i
$291$			1821.17i			0.366870i
$292$	1932.36	−	1115.65i	0.387270	−	0.223591i
$293$	−4586.55	+	2648.05i	−0.914503	+	0.527988i	−0.881877	−	0.471479i	$-0.843720\pi$
$293$	−4586.55	+	2648.05i	−0.914503	+	0.527988i	−0.0326257	+	0.999468i	$0.510387\pi$
$294$			294.000i			0.0583212i
$295$	−1579.55	−	2735.86i	−0.311746	−	0.539960i
$296$	−326.393	+	565.330i	−0.0640920	+	0.111011i
$297$	221.341	+	127.791i	0.0432441	+	0.0249670i
$298$	−292.743			−0.0569065
$299$	1183.14	−	7514.83i	0.228838	−	1.45349i
$300$	−28.1325			−0.00541409
$301$	−2966.39	−	1712.64i	−0.568039	−	0.327957i
$302$	−2571.20	+	4453.44i	−0.489919	+	0.848565i
$303$	825.809	+	1430.34i	0.156573	+	0.271192i
$304$			593.837i			0.112036i
$305$	2130.17	−	1229.86i	0.399913	−	0.230890i
$306$	155.551	−	89.8072i	0.0290596	−	0.0167776i
$307$		−	3393.51i		−	0.630873i	−0.948947	−	0.315436i	$-0.897849\pi$
$307$		−	3393.51i		−	0.630873i	0.948947	−	0.315436i	$-0.102151\pi$
$308$	−132.524	−	229.539i	−0.0245171	−	0.0424648i
$309$	−2421.15	+	4193.56i	−0.445743	+	0.772049i
$310$	−848.583	−	489.929i	−0.155472	−	0.0897617i
$311$	3167.85			0.577595			0.288798	−	0.957390i	$-0.406745\pi$
$311$	3167.85			0.577595			0.288798	+	0.957390i	$0.406745\pi$
$312$	1111.24	+	174.954i	0.201640	+	0.0317463i
$313$	−960.774			−0.173502			−0.0867511	−	0.996230i	$-0.527648\pi$
$313$	−960.774			−0.173502			−0.0867511	+	0.996230i	$0.527648\pi$
$314$	−1918.07	−	1107.40i	−0.344722	−	0.199025i
$315$	355.468	−	615.689i	0.0635821	−	0.110127i
$316$	−288.737	−	500.106i	−0.0514009	−	0.0890291i
$317$			639.566i			0.113317i	0.998394	+	0.0566587i	$0.0180447\pi$
$317$			639.566i			0.113317i	−0.998394	+	0.0566587i	$0.981955\pi$
$318$	−148.838	+	85.9316i	−0.0262466	+	0.0151535i
$319$	−732.356	+	422.826i	−0.128539	+	0.0742122i
$320$		−	722.221i		−	0.126167i
$321$	−743.579	−	1287.92i	−0.129291	−	0.223939i
$322$	1136.11	−	1967.79i	0.196623	−	0.340562i
$323$	−320.735	−	185.176i	−0.0552513	−	0.0318994i
$324$	−324.000			−0.0555556
$325$	102.551	−	39.4740i	0.0175031	−	0.00673731i
$326$	2176.31			0.369738
$327$	503.101	+	290.465i	0.0850812	+	0.0491216i
$328$	−1724.16	+	2986.33i	−0.290246	+	0.502722i
$329$	−598.759	−	1037.08i	−0.100336	−	0.173788i
$330$			640.926i			0.106915i
$331$	5401.93	−	3118.81i	0.897031	−	0.517901i	0.0207949	−	0.999784i	$-0.493380\pi$
$331$	5401.93	−	3118.81i	0.897031	−	0.517901i	0.876236	+	0.481883i	$0.160047\pi$
$332$	−4043.21	+	2334.35i	−0.668373	+	0.385885i
$333$			734.385i			0.120853i
$334$	−70.3506	−	121.851i	−0.0115252	−	0.0199622i
$335$	1404.54	−	2432.74i	0.229069	−	0.396760i
$336$	290.985	+	168.000i	0.0472456	+	0.0272772i
$337$	7087.30			1.14561			0.572804	−	0.819692i	$-0.305856\pi$
$337$	7087.30			1.14561			0.572804	+	0.819692i	$0.305856\pi$
$338$	−4296.29	+	921.483i	−0.691383	+	0.148290i
$339$	−5800.95			−0.929394
$340$	390.076	+	225.210i	0.0622201	+	0.0359228i
$341$	−205.485	+	355.911i	−0.0326324	+	0.0565210i
$342$	334.033	+	578.562i	0.0528142	+	0.0914768i
$343$		−	343.000i		−	0.0539949i
$344$	−3390.16	+	1957.31i	−0.531352	+	0.306776i
$345$	−4758.42	+	2747.28i	−0.742565	+	0.428720i
$346$		−	674.649i		−	0.104825i
$347$	−2453.02	−	4248.75i	−0.379496	−	0.657306i	0.611493	−	0.791250i	$-0.290569\pi$
$347$	−2453.02	−	4248.75i	−0.379496	−	0.657306i	−0.990989	+	0.133944i	$0.957236\pi$
$348$	536.014	−	928.403i	0.0825671	−	0.143010i
$349$	−3309.17	−	1910.55i	−0.507553	−	0.293036i	0.224274	−	0.974526i	$-0.427999\pi$
$349$	−3309.17	−	1910.55i	−0.507553	−	0.293036i	−0.731827	+	0.681490i	$0.761332\pi$
$350$	32.8212			0.00501248
$351$	1181.07	−	454.620i	0.179604	−	0.0691335i
$352$	−302.912			−0.0458673
$353$	5134.06	+	2964.15i	0.774103	+	0.446928i	0.834336	−	0.551256i	$-0.185851\pi$
$353$	5134.06	+	2964.15i	0.774103	+	0.446928i	−0.0602335	+	0.998184i	$0.519185\pi$
$354$	839.838	−	1454.64i	0.126093	−	0.218399i
$355$	−6476.52	−	11217.7i	−0.968276	−	1.67710i
$356$			6389.51i			0.951245i
$357$	−181.476	+	104.775i	−0.0269040	+	0.0155330i
$358$	6469.44	−	3735.14i	0.955086	−	0.551419i
$359$		−	5182.90i		−	0.761958i	−0.924584	−	0.380979i	$-0.875587\pi$
$359$		−	5182.90i		−	0.761958i	0.924584	−	0.380979i	$-0.124413\pi$
$360$	−406.249	−	703.644i	−0.0594756	−	0.103015i
$361$	−2740.75	+	4747.11i	−0.399584	+	0.692100i
$362$	2233.71	+	1289.63i	0.324312	+	0.187242i
$363$	−3724.18			−0.538482
$364$	−1296.45	−	204.113i	−0.186683	−	0.0293913i
$365$	6294.89			0.902711
$366$	1132.60	+	653.907i	0.161754	+	0.0933887i
$367$	−2344.64	+	4061.04i	−0.333486	+	0.577615i	−0.983193	−	0.182570i	$-0.941558\pi$
$367$	−2344.64	+	4061.04i	−0.333486	+	0.577615i	0.649707	+	0.760185i	$0.274892\pi$
$368$	−1298.41	−	2248.91i	−0.183924	−	0.318566i
$369$			3879.36i			0.547294i
$370$	−1594.89	+	920.812i	−0.224093	+	0.129380i
$371$	173.644	−	100.254i	0.0242996	−	0.0140294i
$372$		−	520.985i		−	0.0726124i
$373$	349.465	+	605.292i	0.0485111	+	0.0840237i	0.889261	−	0.457399i	$-0.151219\pi$
$373$	349.465	+	605.292i	0.0485111	+	0.0840237i	−0.840750	+	0.541423i	$0.817886\pi$
$374$	94.4573	−	163.605i	0.0130595	−	0.0226198i
$375$	3596.08	+	2076.20i	0.495202	+	0.285905i
$376$	−1368.59			−0.187712
$377$	−651.235	+	4136.40i	−0.0889664	+	0.565081i
$378$	378.000			0.0514344
$379$	6825.81	+	3940.88i	0.925114	+	0.534115i	0.885263	−	0.465091i	$-0.153978\pi$
$379$	6825.81	+	3940.88i	0.925114	+	0.534115i	0.0398508	+	0.999206i	$0.487312\pi$
$380$	−837.658	+	1450.87i	−0.113082	+	0.195863i
$381$	1067.79	+	1849.47i	0.143582	+	0.248690i
$382$			1866.01i			0.249931i
$383$	10430.2	−	6021.85i	1.39153	−	0.803400i	0.398045	−	0.917366i	$-0.369689\pi$
$383$	10430.2	−	6021.85i	1.39153	−	0.803400i	0.993485	+	0.113966i	$0.0363554\pi$
$384$	332.554	−	192.000i	0.0441942	−	0.0255155i
$385$		−	747.747i		−	0.0989837i
$386$	−3734.81	−	6468.88i	−0.492478	−	0.852998i
$387$	−2201.97	+	3813.93i	−0.289231	+	0.500963i
$388$	−2102.91	−	1214.12i	−0.275152	−	0.158859i
$389$	−11162.8			−1.45495			−0.727475	−	0.686134i	$-0.759306\pi$
$389$	−11162.8			−1.45495			−0.727475	+	0.686134i	$0.759306\pi$
$390$	2468.21	+	1994.96i	0.320469	+	0.259022i
$391$	1619.53			0.209471
$392$	−339.482	−	196.000i	−0.0437409	−	0.0252538i
$393$	−29.7532	+	51.5340i	−0.00381895	+	0.00661462i
$394$	−1793.59	−	3106.59i	−0.229339	−	0.397227i
$395$		−	1629.15i		−	0.207523i
$396$	−295.121	+	170.388i	−0.0374505	+	0.0216220i
$397$	−830.645	+	479.573i	−0.105010	+	0.0606274i	−0.551585	−	0.834119i	$-0.685977\pi$
$397$	−830.645	+	479.573i	−0.105010	+	0.0606274i	0.446575	+	0.894746i	$0.352643\pi$
$398$			1271.02i			0.160077i
$399$	−389.705	−	674.990i	−0.0488964	−	0.0846911i
$400$	18.7550	−	32.4846i	0.00234437	−	0.00406057i
$401$	4143.98	+	2392.53i	0.516061	+	0.297948i	0.735321	−	0.677719i	$-0.237031\pi$
$401$	4143.98	+	2392.53i	0.516061	+	0.297948i	−0.219261	+	0.975666i	$0.570365\pi$
$402$	1493.57			0.185305
$403$	731.019	+	1899.14i	0.0903590	+	0.234746i
$404$	−2202.16			−0.271192
$405$	−791.600	−	457.030i	−0.0971232	−	0.0560741i
$406$	−625.349	+	1083.14i	−0.0764423	+	0.132402i
$407$	386.205	+	668.927i	0.0470356	+	0.0814680i
$408$			239.486i			0.0290596i
$409$	−9304.22	+	5371.79i	−1.12485	+	0.649433i	−0.942635	−	0.333826i	$-0.891660\pi$
$409$	−9304.22	+	5371.79i	−1.12485	+	0.649433i	−0.182216	+	0.983259i	$0.558327\pi$
$410$	−8424.97	+	4864.16i	−1.01483	+	0.585911i
$411$			7324.80i			0.879090i
$412$	−3228.20	−	5591.41i	−0.386024	−	0.668614i
$413$	−979.811	+	1697.08i	−0.116739	+	0.202198i
$414$	−2530.02	−	1460.71i	−0.300347	−	0.173406i
$415$	−13171.2			−1.55795
$416$	−942.849	+	1166.52i	−0.111123	+	0.137484i
$417$	−8598.92			−1.00981
$418$	608.520	+	351.329i	0.0712050	+	0.0411102i
$419$	1470.42	−	2546.85i	0.171444	−	0.296949i	−0.767481	−	0.641071i	$-0.778490\pi$
$419$	1470.42	−	2546.85i	0.171444	−	0.296949i	0.938925	+	0.344122i	$0.111824\pi$
$420$	473.957	+	820.918i	0.0550637	+	0.0953731i
$421$			1397.30i			0.161758i	0.996724	+	0.0808791i	$0.0257728\pi$
$421$			1397.30i			0.161758i	−0.996724	+	0.0808791i	$0.974227\pi$
$422$	71.4945	−	41.2774i	0.00824715	−	0.00476150i
$423$	−1333.39	+	769.833i	−0.153266	+	0.0884883i
$424$		−	229.151i		−	0.0262466i
$425$	11.6967	+	20.2594i	0.00133500	+	0.00231229i
$426$	3443.52	−	5964.36i	0.391641	−	0.678343i
$427$	−1321.37	−	762.891i	−0.149755	−	0.0864611i
$428$	1982.88			0.223939
$429$	836.720	−	1035.21i	0.0941661	−	0.116505i
$430$	−11043.8			−1.23856
$431$	−1894.71	−	1093.91i	−0.211752	−	0.122255i	0.390373	−	0.920657i	$-0.372346\pi$
$431$	−1894.71	−	1093.91i	−0.211752	−	0.122255i	−0.602125	+	0.798402i	$0.705679\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	3068.97	+	5315.61i	0.340613	+	0.589958i	0.984547	−	0.175123i	$-0.0560322\pi$
$433$	3068.97	+	5315.61i	0.340613	+	0.589958i	−0.643934	+	0.765081i	$0.722699\pi$
$434$			607.815i			0.0672260i
$435$	2619.19	−	1512.19i	0.288690	−	0.166676i
$436$	−670.801	+	387.287i	−0.0736825	+	0.0425406i
$437$			6023.77i			0.659396i
$438$	1673.47	+	2898.54i	0.182561	+	0.316205i
$439$	5622.87	−	9739.09i	0.611310	−	1.05882i	−0.379710	−	0.925105i	$-0.623976\pi$
$439$	5622.87	−	9739.09i	0.611310	−	1.05882i	0.991020	−	0.133714i	$-0.0426903\pi$
$440$	−740.078	−	427.284i	−0.0801860	−	0.0462954i
$441$	−441.000			−0.0476190
$442$	−336.035	−	872.995i	−0.0361618	−	0.0939460i
$443$	−3184.61			−0.341547			−0.170774	−	0.985310i	$-0.554627\pi$
$443$	−3184.61			−0.341547			−0.170774	+	0.985310i	$0.554627\pi$
$444$	−847.995	−	489.590i	−0.0906397	−	0.0523309i
$445$	−9012.95	+	15610.9i	−0.960124	+	1.66298i
$446$	−6529.57	−	11309.5i	−0.693237	−	1.20072i
$447$		−	439.114i		−	0.0464640i
$448$	−387.979	+	224.000i	−0.0409159	+	0.0236228i
$449$	−9787.92	+	5651.06i	−1.02878	+	0.593964i	−0.916634	−	0.399728i	$-0.869105\pi$
$449$	−9787.92	+	5651.06i	−1.02878	+	0.593964i	−0.112142	+	0.993692i	$0.535771\pi$
$450$		−	42.1987i		−	0.00442059i
$451$	2040.11	+	3533.58i	0.213005	+	0.368936i
$452$	3867.30	−	6698.36i	0.402439	−	0.697045i
$453$	−6680.16	−	3856.79i	−0.692851	−	0.400018i
$454$	1345.48			0.139090
$455$	−2879.58	−	2327.45i	−0.296696	−	0.239808i
$456$	−890.755			−0.0914768
$457$	−2090.20	−	1206.78i	−0.213950	−	0.123524i	0.389196	−	0.921155i	$-0.372753\pi$
$457$	−2090.20	−	1206.78i	−0.213950	−	0.123524i	−0.603146	+	0.797631i	$0.706086\pi$
$458$	−5294.01	+	9169.50i	−0.540116	+	0.935508i
$459$	134.711	+	233.326i	0.0136988	+	0.0237271i
$460$		−	7326.07i		−	0.742565i
$461$	3627.24	−	2094.19i	0.366459	−	0.211575i	−0.305451	−	0.952208i	$-0.598807\pi$
$461$	3627.24	−	2094.19i	0.366459	−	0.211575i	0.671910	+	0.740632i	$0.265474\pi$
$462$	344.308	−	198.786i	0.0346724	−	0.0200181i
$463$			2411.03i			0.242009i	0.992652	+	0.121004i	$0.0386115\pi$
$463$			2411.03i			0.242009i	−0.992652	+	0.121004i	$0.961389\pi$
$464$	714.685	+	1237.87i	0.0715052	+	0.123851i
$465$	734.894	−	1272.87i	0.0732901	−	0.126942i
$466$	−2077.42	−	1199.40i	−0.206512	−	0.119230i
$467$	3591.53			0.355881			0.177940	−	0.984041i	$-0.443057\pi$
$467$	3591.53			0.355881			0.177940	+	0.984041i	$0.443057\pi$
$468$	−262.431	+	1666.87i	−0.0259207	+	0.164639i
$469$	−1742.50			−0.171559
$470$	−3343.76	−	1930.52i	−0.328162	−	0.189464i
$471$	1661.09	−	2877.10i	0.162504	−	0.281464i
$472$	1119.78	+	1939.52i	0.109200	+	0.189139i
$473$			4631.97i			0.450271i
$474$	750.160	−	433.105i	0.0726919	−	0.0419687i
$475$	−75.3536	+	43.5054i	−0.00727887	+	0.00420246i
$476$		−	279.400i		−	0.0269040i
$477$	−128.897	−	223.257i	−0.0123728	−	0.0214303i
$478$	706.665	−	1223.98i	0.0676194	−	0.117120i
$479$	14243.7	+	8223.58i	1.35868	+	0.784436i	0.989446	−	0.144899i	$-0.0462859\pi$
$479$	14243.7	+	8223.58i	1.35868	+	0.784436i	0.369237	+	0.929335i	$0.379619\pi$
$480$	1083.33			0.103015
$481$	3778.15	+	594.832i	0.358147	+	0.0563867i
$482$	−176.017			−0.0166335
$483$	2951.69	+	1704.16i	0.278068	+	0.160542i
$484$	2482.79	−	4300.32i	0.233170	−	0.403862i
$485$	−3425.23	−	5932.67i	−0.320684	−	0.555441i
$486$		−	486.000i		−	0.0453609i
$487$	−17576.4	+	10147.7i	−1.63544	+	0.944223i	−0.653068	+	0.757299i	$0.726518\pi$
$487$	−17576.4	+	10147.7i	−1.63544	+	0.944223i	−0.982374	+	0.186924i	$0.940148\pi$
$488$	−1510.13	+	871.876i	−0.140083	+	0.0808769i
$489$			3264.46i			0.301890i
$490$	−552.950	−	957.738i	−0.0509791	−	0.0882983i
$491$	404.211	−	700.114i	0.0371523	−	0.0643497i	−0.846851	−	0.531830i	$-0.821505\pi$
$491$	404.211	−	700.114i	0.0371523	−	0.0643497i	0.884004	+	0.467480i	$0.154838\pi$
$492$	−4479.50	−	2586.24i	−0.410471	−	0.236985i
$493$	−891.442			−0.0814372
$494$	3247.06	−	1249.86i	0.295733	−	0.113834i
$495$	−961.389			−0.0872954
$496$	601.581	+	347.323i	0.0544593	+	0.0314421i
$497$	−4017.44	+	6958.42i	−0.362589	+	0.628023i
$498$	−3501.52	−	6064.81i	−0.315074	−	0.545724i
$499$			7263.12i			0.651587i	0.945441	+	0.325794i	$0.105631\pi$
$499$			7263.12i			0.651587i	−0.945441	+	0.325794i	$0.894369\pi$
$500$	−4794.77	+	2768.26i	−0.428857	+	0.247601i
$501$	182.776	−	105.526i	0.0162991	−	0.00941028i
$502$			10440.6i			0.928264i
$503$	3287.78	+	5694.60i	0.291441	+	0.504791i	0.974151	−	0.225899i	$-0.0725319\pi$
$503$	3287.78	+	5694.60i	0.291441	+	0.504791i	−0.682710	+	0.730690i	$0.739199\pi$
$504$	−252.000	+	436.477i	−0.0222718	+	0.0385758i
$505$	−5380.33	−	3106.34i	−0.474102	−	0.273723i
$506$	−3072.68			−0.269956
$507$	−1382.22	−	6444.43i	−0.121078	−	0.564512i
$508$	−2847.44			−0.248690
$509$	9847.16	+	5685.26i	0.857500	+	0.495078i	0.863174	−	0.504906i	$-0.168473\pi$
$509$	9847.16	+	5685.26i	0.857500	+	0.495078i	−0.00567432	+	0.999984i	$0.501806\pi$
$510$	−337.816	+	585.114i	−0.0293308	+	0.0508025i
$511$	−1952.39	−	3381.63i	−0.169019	−	0.292749i
$512$			512.000i			0.0441942i
$513$	−867.844	+	501.050i	−0.0746905	+	0.0431226i
$514$	−6656.18	+	3842.95i	−0.571190	+	0.329777i
$515$		−	18214.6i		−	1.55851i
$516$	−2935.96	−	5085.24i	−0.250482	−	0.433847i
$517$	−809.694	+	1402.43i	−0.0688787	+	0.119301i
$518$	989.327	+	571.188i	0.0839161	+	0.0484490i
$519$	1011.97			0.0855890
$520$	−3949.05	+	1520.08i	−0.333033	+	0.128192i
$521$	18802.1			1.58106			0.790531	−	0.612421i	$-0.209804\pi$
$521$	18802.1			1.58106			0.790531	+	0.612421i	$0.209804\pi$
$522$	1392.60	+	804.020i	0.116767	+	0.0674157i
$523$	6071.20	−	10515.6i	0.507600	−	0.879190i	−0.492361	−	0.870391i	$-0.663866\pi$
$523$	6071.20	−	10515.6i	0.507600	−	0.879190i	0.999961	−	0.00879850i	$-0.00280068\pi$
$524$	−39.6709	−	68.7120i	−0.00330731	−	0.00572843i
$525$			49.2318i			0.00409267i
$526$	7633.11	−	4406.98i	0.632736	−	0.365310i
$527$	−375.183	+	216.612i	−0.0310118	+	0.0179047i
$528$		−	454.368i		−	0.0374505i
$529$	−7087.30	−	12275.6i	−0.582502	−	1.00892i
$530$	323.237	−	559.864i	0.0264916	−	0.0458847i
$531$	2181.96	+	1259.76i	0.178322	+	0.102954i
$532$	1039.21			0.0846911
$533$	19957.9	+	3142.18i	1.62190	+	0.255353i
$534$	−9584.26			−0.776688
$535$	4844.58	+	2797.02i	0.391494	+	0.226029i
$536$	−995.713	+	1724.63i	−0.0802393	+	0.138979i
$537$	5602.70	+	9704.17i	0.450232	+	0.779824i
$538$		−	9479.42i		−	0.759641i
$539$	−401.692	+	231.917i	−0.0321004	+	0.0185332i
$540$	1055.47	−	609.374i	0.0841112	−	0.0485616i
$541$			18358.2i			1.45893i	0.684020	+	0.729464i	$0.260230\pi$
$541$			18358.2i			1.45893i	−0.684020	+	0.729464i	$0.739770\pi$
$542$	−6212.40	−	10760.2i	−0.492334	−	0.852748i
$543$	−1934.45	+	3350.56i	−0.152882	+	0.264800i
$544$	−276.534	−	159.657i	−0.0217947	−	0.0125832i
$545$	−2185.21			−0.171751
$546$	306.170	−	1944.68i	0.0239979	−	0.152426i
$547$	−9391.10			−0.734067			−0.367033	−	0.930208i	$-0.619627\pi$
$547$	−9391.10			−0.734067			−0.367033	+	0.930208i	$0.619627\pi$
$548$	−8457.96	−	4883.20i	−0.659317	−	0.380657i
$549$	−980.860	+	1698.90i	−0.0762515	+	0.132072i
$550$	−22.1918	−	38.4374i	−0.00172048	−	0.00297996i
$551$		−	3315.67i		−	0.256356i
$552$	3373.36	−	1947.61i	0.260108	−	0.150174i
$553$	−875.186	+	505.289i	−0.0672996	+	0.0388555i
$554$		−	5644.32i		−	0.432860i
$555$	−1381.22	−	2392.34i	−0.105639	−	0.182972i
$556$	5732.61	−	9929.18i	0.437261	−	0.757358i
$557$	−8997.53	−	5194.72i	−0.684448	−	0.395166i	0.117081	−	0.993122i	$-0.462646\pi$
$557$	−8997.53	−	5194.72i	−0.684448	−	0.395166i	−0.801529	+	0.597956i	$0.795980\pi$
$558$	781.477			0.0592877
$559$	17837.8	+	14417.5i	1.34966	+	1.09087i
$560$	−1263.89			−0.0953731
$561$	245.407	+	141.686i	0.0184690	+	0.0106631i
$562$	−6710.08	+	11622.2i	−0.503644	+	0.872336i
$563$	−8008.66	−	13871.4i	−0.599511	−	1.03838i	−0.992893	−	0.119008i	$-0.962029\pi$
$563$	−8008.66	−	13871.4i	−0.599511	−	1.03838i	0.393382	−	0.919375i	$-0.371305\pi$
$564$		−	2052.89i		−	0.153266i
$565$	18897.2	−	10910.3i	1.40710	−	0.812391i
$566$	5027.51	−	2902.63i	0.373360	−	0.215560i
$567$			567.000i			0.0419961i
$568$	4591.36	+	7952.48i	0.339171	+	0.587462i
$569$	−8297.98	+	14372.5i	−0.611369	+	1.05892i	0.379640	+	0.925134i	$0.376048\pi$
$569$	−8297.98	+	14372.5i	−0.611369	+	1.05892i	−0.991010	+	0.133789i	$0.957286\pi$
$570$	−2176.30	−	1256.49i	−0.159921	−	0.0923307i
$571$	−10491.8			−0.768947			−0.384473	−	0.923136i	$-0.625617\pi$
$571$	−10491.8			−0.768947			−0.384473	+	0.923136i	$0.625617\pi$
$572$	637.547	+	1656.30i	0.0466035	+	0.121073i
$573$	−2799.02			−0.204068
$574$	5226.08	+	3017.28i	0.380022	+	0.219406i
$575$	190.247	−	329.517i	0.0137980	−	0.0238988i
$576$	288.000	+	498.831i	0.0208333	+	0.0360844i
$577$			20425.8i			1.47372i	0.676043	+	0.736862i	$0.263693\pi$
$577$			20425.8i			1.47372i	−0.676043	+	0.736862i	$0.736307\pi$
$578$	−8337.10	+	4813.43i	−0.599961	+	0.346388i
$579$	9703.31	−	5602.21i	0.696470	−	0.402107i
$580$			4032.50i			0.288690i
$581$	4085.11	+	7075.61i	0.291702	+	0.505242i
$582$	1821.17	−	3154.36i	0.129708	−	0.224661i
$583$	−234.817	−	135.572i	−0.0166812	−	0.00963087i
$584$	−4462.60			−0.316205
$585$	−2992.43	+	3702.32i	−0.211490	+	0.261662i
$586$	10592.2			0.746688
$587$	−1526.72	−	881.453i	−0.107350	−	0.0619787i	0.445364	−	0.895350i	$-0.353074\pi$
$587$	−1526.72	−	881.453i	−0.107350	−	0.0619787i	−0.552714	+	0.833371i	$0.686408\pi$
$588$	294.000	−	509.223i	0.0206197	−	0.0357143i
$589$	−805.677	−	1395.47i	−0.0563622	−	0.0976222i
$590$			6318.21i			0.440876i
$591$	4659.88	−	2690.38i	0.324335	−	0.187255i
$592$	1130.66	−	652.787i	0.0784963	−	0.0453199i
$593$		−	11467.3i		−	0.794105i	−0.917796	−	0.397052i	$-0.870033\pi$
$593$		−	11467.3i		−	0.794105i	0.917796	−	0.397052i	$-0.129967\pi$
$594$	−255.582	−	442.681i	−0.0176543	−	0.0305782i
$595$	394.118	−	682.633i	0.0271551	−	0.0470340i
$596$	507.046	+	292.743i	0.0348480	+	0.0201195i
$597$	−1906.54			−0.130702
$598$	−9564.08	+	11832.9i	−0.654021	+	0.809172i
$599$	−12924.2			−0.881585			−0.440792	−	0.897609i	$-0.645303\pi$
$599$	−12924.2			−0.881585			−0.440792	+	0.897609i	$0.645303\pi$
$600$	48.7268	+	28.1325i	0.00331544	+	0.00191417i
$601$	4650.20	−	8054.38i	0.315617	−	0.546664i	−0.663952	−	0.747775i	$-0.731122\pi$
$601$	4650.20	−	8054.38i	0.315617	−	0.546664i	0.979568	+	0.201111i	$0.0644553\pi$
$602$	3425.29	+	5932.77i	0.231901	+	0.401664i
$603$			2240.35i			0.151301i
$604$	8906.88	−	5142.39i	0.600026	−	0.346425i
$605$	12131.9	−	7004.38i	0.815262	−	0.470692i
$606$		−	3303.24i		−	0.221427i
$607$	−6089.57	−	10547.4i	−0.407196	−	0.705284i	0.587378	−	0.809312i	$-0.300160\pi$
$607$	−6089.57	−	10547.4i	−0.407196	−	0.705284i	−0.994574	+	0.104028i	$0.966827\pi$
$608$	593.837	−	1028.56i	0.0396106	−	0.0686076i
$609$	−1624.70	−	938.024i	−0.108106	−	0.0624148i
$610$	−4919.43			−0.326527
$611$	2880.51	+	7483.36i	0.190725	+	0.495490i
$612$	−359.229			−0.0237271
$613$	14009.4	+	8088.35i	0.923060	+	0.532929i	0.884610	−	0.466332i	$-0.154425\pi$
$613$	14009.4	+	8088.35i	0.923060	+	0.532929i	0.0384497	+	0.999261i	$0.487758\pi$
$614$	−3393.51	+	5877.73i	−0.223047	+	0.386329i
$615$	−7296.24	−	12637.5i	−0.478395	−	0.828604i
$616$			530.096i			0.0346724i
$617$	15502.9	−	8950.61i	1.01155	−	0.584016i	0.0999020	−	0.994997i	$-0.468147\pi$
$617$	15502.9	−	8950.61i	1.01155	−	0.584016i	0.911644	+	0.410981i	$0.134814\pi$
$618$	8387.11	−	4842.30i	0.545921	−	0.315188i
$619$		−	5086.82i		−	0.330301i	−0.986268	−	0.165151i	$-0.947189\pi$
$619$		−	5086.82i		−	0.330301i	0.986268	−	0.165151i	$-0.0528111\pi$
$620$	979.859	+	1697.17i	0.0634711	+	0.109935i
$621$	2191.06	−	3795.03i	0.141585	−	0.245233i
$622$	−5486.87	−	3167.85i	−0.353703	−	0.204211i
$623$	11181.6			0.719073
$624$	−1749.78	−	1414.27i	−0.112255	−	0.0907312i
$625$	−15912.6			−1.01840
$626$	1664.11	+	960.774i	0.106248	+	0.0613423i
$627$	−526.993	+	912.780i	−0.0335663	+	0.0581386i
$628$	2214.79	+	3836.13i	0.140732	+	0.243755i
$629$			814.235i			0.0516148i
$630$	−1231.38	+	710.936i	−0.0778718	+	0.0449593i
$631$	7127.82	−	4115.25i	0.449689	−	0.259628i	−0.258010	−	0.966142i	$-0.583067\pi$
$631$	7127.82	−	4115.25i	0.449689	−	0.259628i	0.707699	+	0.706514i	$0.249733\pi$
$632$			1154.95i			0.0726919i
$633$	61.9161	+	107.242i	0.00388774	+	0.00673377i
$634$	639.566	−	1107.76i	0.0400638	−	0.0693925i
$635$	−6956.89	−	4016.56i	−0.434765	−	0.251012i
$636$	343.726			0.0214303
$637$	−357.198	+	2268.79i	−0.0222178	+	0.141119i
$638$	1691.30			0.104952
$639$	8946.53	+	5165.28i	0.553865	+	0.319774i
$640$	−722.221	+	1250.92i	−0.0446067	+	0.0772610i
$641$	−6293.39	−	10900.5i	−0.387791	−	0.671674i	0.604361	−	0.796710i	$-0.293428\pi$
$641$	−6293.39	−	10900.5i	−0.387791	−	0.671674i	−0.992152	+	0.125037i	$0.960095\pi$
$642$			2974.31i			0.182846i
$643$	11212.3	−	6473.44i	0.687669	−	0.397026i	−0.115069	−	0.993357i	$-0.536709\pi$
$643$	11212.3	−	6473.44i	0.687669	−	0.397026i	0.802738	+	0.596332i	$0.203376\pi$
$644$	−3935.59	+	2272.21i	−0.240814	+	0.139034i
$645$		−	16565.7i		−	1.01128i
$646$	370.353	+	641.470i	0.0225563	+	0.0390686i
$647$	8264.88	−	14315.2i	0.502204	−	0.869842i	−0.497793	−	0.867296i	$-0.665856\pi$
$647$	8264.88	−	14315.2i	0.502204	−	0.869842i	0.999997	−	0.00254646i	$-0.000810564\pi$
$648$	561.184	+	324.000i	0.0340207	+	0.0196419i
$649$	2649.97			0.160278
$650$	−217.097	−	34.1798i	−0.0131004	−	0.00206253i
$651$	−911.723			−0.0548898
$652$	−3769.48	−	2176.31i	−0.226417	−	0.130722i
$653$	−13380.2	+	23175.2i	−0.801850	+	1.38884i	0.116548	+	0.993185i	$0.462817\pi$
$653$	−13380.2	+	23175.2i	−0.801850	+	1.38884i	−0.918397	+	0.395659i	$0.870516\pi$
$654$	−580.931	−	1006.20i	−0.0347342	−	0.0601615i
$655$		−	223.837i		−	0.0133527i
$656$	5972.67	−	3448.32i	0.355478	−	0.205235i
$657$	−4347.82	+	2510.21i	−0.258180	+	0.149060i
$658$			2395.04i			0.141897i
$659$	−8583.37	−	14866.8i	−0.507376	−	0.878801i	−0.999964	−	0.00853782i	$-0.997282\pi$
$659$	−8583.37	−	14866.8i	−0.507376	−	0.878801i	0.492588	−	0.870263i	$-0.336051\pi$
$660$	640.926	−	1110.12i	0.0378000	−	0.0654716i
$661$	2209.49	+	1275.65i	0.130014	+	0.0750636i	0.563596	−	0.826050i	$-0.309417\pi$
$661$	2209.49	+	1275.65i	0.130014	+	0.0750636i	−0.433582	+	0.901114i	$0.642751\pi$
$662$	−12475.2			−0.732422
$663$	1309.49	−	504.052i	0.0767066	−	0.0295260i
$664$	9337.39			0.545724
$665$	2539.02	+	1465.90i	0.148058	+	0.0854816i
$666$	734.385	−	1271.99i	0.0427280	−	0.0740070i
$667$	7249.63	+	12556.7i	0.420850	+	0.728933i
$668$			281.402i			0.0162991i
$669$	16964.3	−	9794.35i	0.980386	−	0.566026i
$670$	−4865.47	+	2809.08i	−0.280552	+	0.161976i
$671$			2063.30i			0.118707i
$672$	−336.000	−	581.969i	−0.0192879	−	0.0334077i
$673$	−6263.43	+	10848.6i	−0.358748	+	0.621370i	−0.987752	−	0.156032i	$-0.950130\pi$
$673$	−6263.43	+	10848.6i	−0.358748	+	0.621370i	0.629004	+	0.777402i	$0.283463\pi$
$674$	−12275.6	−	7087.30i	−0.701539	−	0.405034i
$675$	63.2980			0.00360940
$676$	8362.87	+	2700.23i	0.475812	+	0.153632i
$677$	2934.84			0.166610			0.0833049	−	0.996524i	$-0.473452\pi$
$677$	2934.84			0.166610			0.0833049	+	0.996524i	$0.473452\pi$
$678$	10047.5	+	5800.95i	0.569135	+	0.328590i
$679$	−2124.70	+	3680.09i	−0.120086	+	0.207995i
$680$	−450.421	−	780.152i	−0.0254013	−	0.0439963i
$681$			2018.23i			0.113566i
$682$	711.822	−	410.970i	0.0399664	−	0.0230746i
$683$	−16211.2	+	9359.55i	−0.908206	+	0.524353i	−0.879854	−	0.475245i	$-0.842360\pi$
$683$	−16211.2	+	9359.55i	−0.908206	+	0.524353i	−0.0283527	+	0.999598i	$0.509026\pi$
$684$		−	1336.13i		−	0.0746905i
$685$	−13776.4	−	23861.4i	−0.768420	−	1.33094i
$686$	−343.000	+	594.093i	−0.0190901	+	0.0330650i
$687$	−13754.2	−	7941.02i	−0.763839	−	0.441003i
$688$	7829.23			0.433847
$689$	−1252.98	+	482.300i	−0.0692813	+	0.0266679i
$690$	10989.1			0.606301
$691$	15416.2	+	8900.53i	0.848710	+	0.490003i	0.860215	−	0.509931i	$-0.170329\pi$
$691$	15416.2	+	8900.53i	0.848710	+	0.490003i	−0.0115053	+	0.999934i	$0.503662\pi$
$692$	−674.649	+	1168.53i	−0.0370611	+	0.0641918i
$693$	298.179	+	516.462i	0.0163447	+	0.0283099i
$694$			9812.08i			0.536688i
$695$	28011.9	−	16172.7i	1.52885	−	0.882684i
$696$	−1856.81	+	1072.03i	−0.101124	+	0.0583837i
$697$			4301.17i			0.233742i
$698$	3821.10	+	6618.35i	0.207208	+	0.358894i
$699$	1799.10	−	3116.13i	0.0973507	−	0.168616i
$700$	−56.8480	−	32.8212i	−0.00306950	−	0.00177218i
$701$	17729.0			0.955229			0.477615	−	0.878569i	$-0.341502\pi$
$701$	17729.0			0.955229			0.477615	+	0.878569i	$0.341502\pi$
$702$	−2500.30	−	393.647i	−0.134427	−	0.0211642i
$703$	−3028.50			−0.162478
$704$	524.659	+	302.912i	0.0280879	+	0.0162165i
$705$	2895.78	−	5015.63i	0.154697	−	0.267943i
$706$	−5928.30	−	10268.1i	−0.316026	−	0.547373i
$707$			3853.78i			0.205002i
$708$	−2909.28	+	1679.68i	−0.154432	+	0.0891611i
$709$	−11997.4	+	6926.70i	−0.635503	+	0.366908i	−0.782880	−	0.622173i	$-0.786250\pi$
$709$	−11997.4	+	6926.70i	−0.635503	+	0.366908i	0.147377	+	0.989080i	$0.452917\pi$
$710$			25906.1i			1.36935i
$711$	649.657	+	1125.24i	0.0342673	+	0.0593527i
$712$	6389.51	−	11066.9i	0.336316	−	0.582516i
$713$	6102.33	+	3523.18i	0.320524	+	0.185055i
$714$	419.100			0.0219670
$715$	−778.700	+	4946.01i	−0.0407297	+	0.258700i
$716$	−14940.5			−0.779824
$717$	1835.97	+	1060.00i	0.0956283	+	0.0552110i
$718$	−5182.90	+	8977.04i	−0.269393	+	0.466602i
$719$	−8276.99	−	14336.2i	−0.429318	−	0.743600i	0.567495	−	0.823377i	$-0.307913\pi$
$719$	−8276.99	−	14336.2i	−0.429318	−	0.743600i	−0.996813	+	0.0797766i	$0.974579\pi$
$720$			1625.00i			0.0841112i
$721$	−9784.96	+	5649.35i	−0.505425	+	0.291807i
$722$	9494.22	−	5481.49i	0.489388	−	0.282548i
$723$		−	264.025i		−	0.0135812i
$724$	−2579.26	−	4467.41i	−0.132400	−	0.229323i
$725$	−104.718	+	181.377i	−0.00536431	+	0.00929126i
$726$	6450.48	+	3724.18i	0.329752	+	0.190382i
$727$	−6954.06			−0.354762			−0.177381	−	0.984142i	$-0.556762\pi$
$727$	−6954.06			−0.354762			−0.177381	+	0.984142i	$0.556762\pi$
$728$	2041.41	+	1649.99i	0.103928	+	0.0840007i
$729$	729.000			0.0370370
$730$	−10903.1	−	6294.89i	−0.552795	−	0.319156i
$731$	−2441.39	+	4228.62i	−0.123527	+	0.213955i
$732$	−1307.81	−	2265.20i	−0.0660358	−	0.114377i
$733$			22266.8i			1.12202i	0.827809	+	0.561011i	$0.189587\pi$
$733$			22266.8i			1.12202i	−0.827809	+	0.561011i	$0.810413\pi$
$734$	8122.08	−	4689.29i	0.408435	−	0.235810i
$735$	1436.61	−	829.425i	0.0720953	−	0.0416242i
$736$			5193.63i			0.260108i
$737$	1178.18	+	2040.67i	0.0588857	+	0.101993i
$738$	3879.36	−	6719.25i	0.193498	−	0.335148i
$739$	−3672.09	−	2120.08i	−0.182787	−	0.105532i	0.405814	−	0.913956i	$-0.366988\pi$
$739$	−3672.09	−	2120.08i	−0.182787	−	0.105532i	−0.588602	+	0.808423i	$0.700321\pi$
$740$	3683.25			0.182972
$741$	1874.79	+	4870.59i	0.0929450	+	0.241465i
$742$	−401.014			−0.0198406
$743$	−23439.5	−	13532.8i	−1.15735	−	0.668197i	−0.206683	−	0.978408i	$-0.566267\pi$
$743$	−23439.5	−	13532.8i	−1.15735	−	0.668197i	−0.950668	+	0.310211i	$0.899600\pi$
$744$	−520.985	+	902.372i	−0.0256723	+	0.0444658i
$745$	825.879	+	1430.46i	0.0406146	+	0.0703465i
$746$		−	1397.86i		−	0.0686050i
$747$	9097.22	−	5252.28i	0.445582	−	0.257257i
$748$	−327.210	+	188.915i	−0.0159946	+	0.00923450i
$749$		−	3470.03i		−	0.169282i
$750$	−4152.39	−	7192.16i	−0.202165	−	0.350161i
$751$	3950.34	−	6842.20i	0.191944	−	0.332457i	−0.753950	−	0.656931i	$-0.771854\pi$
$751$	3950.34	−	6842.20i	0.191944	−	0.332457i	0.945894	+	0.324474i	$0.105187\pi$
$752$	2370.47	+	1368.59i	0.114950	+	0.0663662i
$753$	−15661.0			−0.757924
$754$	5264.37	−	6513.22i	0.254267	−	0.314586i
$755$	29015.2			1.39864
$756$	−654.715	−	378.000i	−0.0314970	−	0.0181848i
$757$	−15168.4	+	26272.5i	−0.728277	+	1.26141i	0.229333	+	0.973348i	$0.426345\pi$
$757$	−15168.4	+	26272.5i	−0.728277	+	1.26141i	−0.957611	+	0.288065i	$0.906988\pi$
$758$	−7881.76	−	13651.6i	−0.377676	−	0.654154i
$759$		−	4609.03i		−	0.220418i
$760$	2901.73	−	1675.32i	0.138496	−	0.0799607i
$761$	22449.3	−	12961.1i	1.06936	−	0.617398i	0.141357	−	0.989959i	$-0.454854\pi$
$761$	22449.3	−	12961.1i	1.06936	−	0.617398i	0.928008	+	0.372561i	$0.121520\pi$
$762$		−	4271.16i		−	0.203055i
$763$	677.753	+	1173.90i	0.0321577	+	0.0556987i
$764$	1866.01	−	3232.03i	0.0883639	−	0.153051i
$765$	−877.671	−	506.723i	−0.0414801	−	0.0239485i
$766$	−24087.4			−1.13618
$767$	8248.34	−	10205.1i	0.388305	−	0.480422i
$768$	−768.000			−0.0360844
$769$	13569.0	+	7834.05i	0.636293	+	0.367364i	0.783185	−	0.621788i	$-0.213594\pi$
$769$	13569.0	+	7834.05i	0.636293	+	0.367364i	−0.146892	+	0.989153i	$0.546927\pi$
$770$	−747.747	+	1295.14i	−0.0349960	+	0.0606149i
$771$	−5764.42	−	9984.27i	−0.269262	−	0.466375i
$772$			14939.2i			0.696470i
$773$	16621.7	−	9596.53i	0.773403	−	0.446524i	−0.0606843	−	0.998157i	$-0.519328\pi$
$773$	16621.7	−	9596.53i	0.773403	−	0.446524i	0.834087	+	0.551633i	$0.185995\pi$
$774$	7627.85	−	4403.94i	0.354235	−	0.204517i
$775$			101.782i			0.00471756i
$776$	2428.23	+	4205.82i	0.112330	+	0.194562i
$777$	−856.782	+	1483.99i	−0.0395584	+	0.0685172i
$778$	19334.5	+	11162.8i	0.890972	+	0.514403i
$779$	−15998.0			−0.735798
$780$	−2280.11	−	5923.58i	−0.104668	−	0.271921i
$781$	10865.5			0.497820
$782$	−2805.11	−	1619.53i	−0.128274	−	0.0740593i
$783$	−1206.03	+	2088.91i	−0.0550447	+	0.0953403i
$784$	392.000	+	678.964i	0.0178571	+	0.0309295i
$785$			12496.6i			0.568183i
$786$	103.068	−	59.5063i	0.00467724	−	0.00270041i
$787$	−5851.11	+	3378.14i	−0.265019	+	0.153009i	−0.626622	−	0.779324i	$-0.715563\pi$
$787$	−5851.11	+	3378.14i	−0.265019	+	0.153009i	0.361603	+	0.932332i	$0.382230\pi$
$788$			7174.36i			0.324335i
$789$	6610.46	+	11449.7i	0.298275	+	0.516627i
$790$	−1629.15	+	2821.77i	−0.0733704	+	0.127081i
$791$	−11722.1	−	6767.78i	−0.526917	−	0.304215i
$792$	681.553			0.0305782
$793$	7945.77	+	6422.24i	0.355816	+	0.287592i
$794$	1918.29			0.0857401
$795$	839.795	+	484.856i	0.0374647	+	0.0216303i
$796$	1271.02	−	2201.48i	0.0565958	−	0.0980268i
$797$	12013.0	+	20807.1i	0.533904	+	0.924748i	0.999216	+	0.0396015i	$0.0126089\pi$
$797$	12013.0	+	20807.1i	0.533904	+	0.924748i	−0.465312	+	0.885147i	$0.654058\pi$
$798$			1558.82i			0.0691500i
$799$	−1478.37	+	853.538i	−0.0654581	+	0.0377922i
$800$	−64.9691	+	37.5099i	−0.00287126	+	0.00165772i
$801$		−	14376.4i		−	0.634163i
$802$	−4785.05	−	8287.95i	−0.210681	−	0.364910i
$803$	−2640.19	+	4572.94i	−0.116028	+	0.200966i
$804$	−2586.94	−	1493.57i	−0.113476	−	0.0655151i
$805$	−12820.6			−0.561326
$806$	632.976	−	4020.42i	0.0276621	−	0.175699i
$807$	14219.1			0.620244
$808$	3814.25	+	2202.16i	0.166070	+	0.0958807i
$809$	4123.95	−	7142.89i	0.179222	−	0.310421i	−0.762393	−	0.647115i	$-0.775975\pi$
$809$	4123.95	−	7142.89i	0.179222	−	0.310421i	0.941614	+	0.336694i	$0.109309\pi$
$810$	914.060	+	1583.20i	0.0396504	+	0.0686765i
$811$		−	28501.5i		−	1.23406i	−0.786940	−	0.617030i	$-0.788336\pi$
$811$		−	28501.5i		−	1.23406i	0.786940	−	0.617030i	$-0.211664\pi$
$812$	2166.27	−	1250.70i	0.0936223	−	0.0540528i
$813$	16140.3	−	9318.59i	0.696266	−	0.401989i
$814$		−	1544.82i		−	0.0665184i
$815$	−6139.75	−	10634.4i	−0.263885	−	0.457062i
$816$	239.486	−	414.802i	0.0102741	−	0.0177953i
$817$	−15728.1	−	9080.64i	−0.673510	−	0.388851i
$818$	21487.2			0.918437
$819$	2917.02	+	459.255i	0.124455	+	0.0195942i
$820$	19456.6			0.828604
$821$	18701.4	+	10797.3i	0.794987	+	0.458986i	0.841715	−	0.539922i	$-0.181546\pi$
$821$	18701.4	+	10797.3i	0.794987	+	0.458986i	−0.0467283	+	0.998908i	$0.514879\pi$
$822$	7324.80	−	12686.9i	0.310805	−	0.538330i
$823$	9223.98	+	15976.4i	0.390678	+	0.676674i	0.992539	−	0.121927i	$-0.0389073\pi$
$823$	9223.98	+	15976.4i	0.390678	+	0.676674i	−0.601861	+	0.798601i	$0.705574\pi$
$824$			12912.8i			0.545921i
$825$	57.6561	−	33.2878i	0.00243312	−	0.00140476i
$826$	3394.16	−	1959.62i	0.142976	−	0.0825472i
$827$			1551.93i			0.0652552i	0.999468	+	0.0326276i	$0.0103875\pi$
$827$			1551.93i			0.0652552i	−0.999468	+	0.0326276i	$0.989612\pi$
$828$	2921.42	+	5060.04i	0.122616	+	0.212378i
$829$	18027.3	−	31224.2i	0.755264	−	1.30816i	−0.189978	−	0.981788i	$-0.560842\pi$
$829$	18027.3	−	31224.2i	0.755264	−	1.30816i	0.945243	−	0.326368i	$-0.105825\pi$
$830$	22813.2	+	13171.2i	0.954045	+	0.550818i
$831$	8466.49			0.353429
$832$	2799.58	−	1077.62i	0.116656	−	0.0449035i
$833$	−488.950			−0.0203375
$834$	14893.8	+	8598.92i	0.618380	+	0.357022i
$835$	−396.943	+	687.525i	−0.0164512	+	0.0284943i
$836$	−702.658	−	1217.04i	−0.0290693	−	0.0503495i
$837$			1172.22i			0.0484082i
$838$	−5093.69	+	2940.85i	−0.209975	+	0.121229i
$839$	−4964.10	+	2866.03i	−0.204267	+	0.117934i	−0.598644	−	0.801015i	$-0.704294\pi$
$839$	−4964.10	+	2866.03i	−0.204267	+	0.117934i	0.394377	+	0.918949i	$0.370960\pi$
$840$		−	1895.83i		−	0.0778718i
$841$	8204.08	+	14209.9i	0.336384	+	0.582635i
$842$	1397.30	−	2420.19i	0.0571902	−	0.0990563i
$843$	−17433.3	−	10065.1i	−0.712260	−	0.411223i
$844$	−165.109			−0.00673377
$845$	16623.3	+	18393.8i	0.676757	+	0.748835i
$846$	3079.33			0.125141
$847$	−7525.56	−	4344.88i	−0.305291	−	0.176260i
$848$	−229.151	+	396.901i	−0.00927957	+	0.0160727i
$849$	4353.95	+	7541.26i	0.176004	+	0.304847i
$850$		−	46.7870i		−	0.00188798i
$851$	11469.2	−	6621.74i	0.461996	−	0.266734i
$852$	−11928.7	+	6887.05i	−0.479661	+	0.276932i
$853$			16309.6i			0.654667i	0.944909	+	0.327333i	$0.106150\pi$
$853$			16309.6i			0.654667i	−0.944909	+	0.327333i	$0.893850\pi$
$854$	1525.78	+	2642.73i	0.0611372	+	0.105893i
$855$	1884.73	−	3264.45i	0.0753877	−	0.130575i
$856$	−3434.44	−	1982.88i	−0.137134	−	0.0791744i
$857$	−43522.2			−1.73476			−0.867381	−	0.497645i	$-0.834198\pi$
$857$	−43522.2			−1.73476			−0.867381	+	0.497645i	$0.834198\pi$
$858$	−2484.45	+	956.320i	−0.0988553	+	0.0380516i
$859$	−34413.2			−1.36690			−0.683448	−	0.729999i	$-0.739520\pi$
$859$	−34413.2			−1.36690			−0.683448	+	0.729999i	$0.739520\pi$
$860$	19128.4	+	11043.8i	0.758459	+	0.437896i
$861$	−4525.92	+	7839.13i	−0.179144	+	0.310287i
$862$	2187.83	+	3789.42i	0.0864474	+	0.149731i
$863$			29522.3i			1.16448i	0.813016	+	0.582242i	$0.197824\pi$
$863$			29522.3i			1.16448i	−0.813016	+	0.582242i	$0.802176\pi$
$864$	−748.246	+	432.000i	−0.0294628	+	0.0170103i
$865$	−3296.62	+	1903.30i	−0.129582	+	0.0748141i
$866$		−	12275.9i		−	0.481699i
$867$	−7220.14	−	12505.7i	−0.282825	−	0.489866i
$868$	607.815	−	1052.77i	0.0237680	−	0.0411673i
$869$	1183.50	+	683.296i	0.0461998	+	0.0266734i
$870$	−6048.75			−0.235715
$871$	11525.8	+	1814.63i	0.448379	+	0.0705928i
$872$	1549.15			0.0601615
$873$	4731.55	+	2731.76i	0.183435	+	0.105906i
$874$	6023.77	−	10433.5i	0.233132	−	0.403796i
$875$	4844.46	+	8390.85i	0.187169	+	0.324186i
$876$		−	6693.90i		−	0.258180i
$877$	−7477.55	+	4317.17i	−0.287912	+	0.166226i	−0.637000	−	0.770864i	$-0.719825\pi$
$877$	−7477.55	+	4317.17i	−0.287912	+	0.166226i	0.349088	+	0.937090i	$0.386492\pi$
$878$	−19478.2	+	11245.7i	−0.748698	+	0.432261i
$879$			15888.3i			0.609669i
$880$	854.568	+	1480.16i	0.0327358	+	0.0567000i
$881$	−10642.4	+	18433.2i	−0.406984	+	0.704916i	−0.994550	−	0.104260i	$-0.966753\pi$
$881$	−10642.4	+	18433.2i	−0.406984	+	0.704916i	0.587567	+	0.809176i	$0.300086\pi$
$882$	763.834	+	441.000i	0.0291606	+	0.0168359i
$883$	−34454.8			−1.31313			−0.656567	−	0.754267i	$-0.727992\pi$
$883$	−34454.8			−1.31313			−0.656567	+	0.754267i	$0.727992\pi$
$884$	−290.966	+	1848.11i	−0.0110704	+	0.0703151i
$885$	−9477.31			−0.359973
$886$	5515.91	+	3184.61i	0.209154	+	0.120755i
$887$	4536.54	−	7857.52i	0.171727	−	0.297441i	−0.767296	−	0.641293i	$-0.778398\pi$
$887$	4536.54	−	7857.52i	0.171727	−	0.297441i	0.939024	+	0.343852i	$0.111732\pi$
$888$	979.180	+	1695.99i	0.0370035	+	0.0640920i
$889$			4983.02i			0.187992i
$890$	31221.8	−	18025.9i	1.17591	−	0.678910i
$891$	664.022	−	383.373i	0.0249670	−	0.0144147i
$892$			26118.3i			0.980386i
$893$	−3174.69	−	5498.72i	−0.118966	−	0.206056i
$894$	−439.114	+	760.569i	−0.0164275	+	0.0284533i
$895$	−36502.9	−	21074.9i	−1.36330	−	0.787103i
$896$	896.000			0.0334077
$897$	−17749.4	−	14346.1i	−0.660686	−	0.534006i
$898$	22604.2			0.839992
$899$	−3358.91	−	1939.27i	−0.124612	−	0.0719447i
$900$	−42.1987	+	73.0903i	−0.00156291	+	0.00270705i
$901$	−142.913	−	247.532i	−0.00528425	−	0.00915258i
$902$		−	8160.46i		−	0.301235i
$903$	−8899.16	+	5137.93i	−0.327957	+	0.189346i
$904$	−13396.7	+	7734.60i	−0.492885	+	0.284568i
$905$		−	14553.1i		−	0.534542i
$906$	7713.59	+	13360.3i	0.282855	+	0.489919i
$907$	−20577.7	+	35641.6i	−0.753330	+	1.30481i	0.192870	+	0.981224i	$0.438221\pi$
$907$	−20577.7	+	35641.6i	−0.753330	+	1.30481i	−0.946200	+	0.323582i	$0.895113\pi$
$908$	−2330.45	−	1345.48i	−0.0851746	−	0.0491756i
$909$	4954.85			0.180794
$910$	2660.13	+	6910.84i	0.0969039	+	0.251750i
$911$	2374.90			0.0863711			0.0431855	−	0.999067i	$-0.486249\pi$
$911$	2374.90			0.0863711			0.0431855	+	0.999067i	$0.486249\pi$
$912$	1542.83	+	890.755i	0.0560179	+	0.0323419i
$913$	5524.24	−	9568.26i	0.200247	−	0.346838i
$914$	2413.55	+	4180.40i	0.0873449	+	0.151286i
$915$		−	7379.14i		−	0.266608i
$916$	18339.0	−	10588.0i	0.661504	−	0.381919i
$917$	−120.246	+	69.4240i	−0.00433028	+	0.00250009i
$918$		−	538.843i		−	0.0193731i
$919$	−5775.66	−	10003.7i	−0.207314	−	0.359078i	0.743553	−	0.668676i	$-0.233139\pi$
$919$	−5775.66	−	10003.7i	−0.207314	−	0.359078i	−0.950868	+	0.309598i	$0.899806\pi$
$920$	−7326.07	+	12689.1i	−0.262536	+	0.454726i
$921$	−8816.60	−	5090.27i	−0.315436	−	0.182117i
$922$	−8376.76			−0.299213
$923$	33820.0	−	41843.0i	1.20607	−	1.49218i
$924$	−795.145			−0.0283099
$925$	165.668	+	95.6484i	0.00588878	+	0.00339989i
$926$	2411.03	−	4176.02i	0.0855630	−	0.148199i
$927$	7263.45	+	12580.7i	0.257350	+	0.445743i
$928$		−	2858.74i		−	0.101124i
$929$	−4706.85	+	2717.50i	−0.166229	+	0.0959724i	−0.580807	−	0.814042i	$-0.697263\pi$
$929$	−4706.85	+	2717.50i	−0.166229	+	0.0959724i	0.414577	+	0.910014i	$0.363929\pi$
$930$	−2545.75	+	1469.79i	−0.0897617	+	0.0518239i
$931$		−	1818.63i		−	0.0640204i
$932$	2398.80	+	4154.84i	0.0843082	+	0.146026i
$933$	4751.77	−	8230.30i	0.166737	−	0.288798i
$934$	−6220.71	−	3591.53i	−0.217931	−	0.125823i
$935$	−1065.92			−0.0372828
$936$	2121.41	−	2624.66i	0.0740817	−	0.0916558i
$937$	9520.33			0.331927			0.165964	−	0.986132i	$-0.446927\pi$
$937$	9520.33			0.331927			0.165964	+	0.986132i	$0.446927\pi$
$938$	3018.10	+	1742.50i	0.105058	+	0.0606552i
$939$	−1441.16	+	2496.16i	−0.0500858	+	0.0867511i
$940$	3861.04	+	6687.51i	0.133971	+	0.232045i
$941$			28590.3i			0.990456i	0.868763	+	0.495228i	$0.164915\pi$
$941$			28590.3i			0.990456i	−0.868763	+	0.495228i	$0.835085\pi$
$942$	−5754.20	+	3322.19i	−0.199025	+	0.114907i
$943$	60585.6	−	34979.1i	2.09219	−	1.20793i
$944$		−	4479.13i		−	0.154432i
$945$	−1066.40	−	1847.07i	−0.0367091	−	0.0635821i
$946$	4631.97	−	8022.81i	0.159195	−	0.275734i
$947$	−42970.2	−	24808.8i	−1.47449	−	0.851298i	−0.474905	−	0.880037i	$-0.657517\pi$
$947$	−42970.2	−	24808.8i	−1.47449	−	0.851298i	−0.999587	+	0.0287393i	$0.990851\pi$
$948$	−1732.42			−0.0593527
$949$	9392.54	+	24401.2i	0.321280	+	0.834664i
$950$	174.022			0.00594317
$951$	1661.64	+	959.350i	0.0566587	+	0.0327119i
$952$	−279.400	+	483.935i	−0.00951199	+	0.0164752i
$953$	8395.06	+	14540.7i	0.285354	+	0.494248i	0.972695	−	0.232087i	$-0.0745554\pi$
$953$	8395.06	+	14540.7i	0.285354	+	0.494248i	−0.687341	+	0.726335i	$0.741222\pi$
$954$			515.590i			0.0174977i
$955$	9118.12	−	5264.35i	0.308958	−	0.178377i
$956$	−2447.96	+	1413.33i	−0.0828166	+	0.0478142i
$957$			2536.95i			0.0856929i
$958$	−16447.2	−	28487.3i	−0.554680	−	0.960734i
$959$	−8545.60	+	14801.4i	−0.287750	+	0.498397i
$960$	−1876.38	−	1083.33i	−0.0630834	−	0.0364212i
$961$	27906.1			0.936729
$962$	−5949.12	−	4808.43i	−0.199384	−	0.161154i
$963$	−4461.47			−0.149293
$964$	304.870	+	176.017i	0.0101859	+	0.00588083i
$965$	−21073.1	+	36499.7i	−0.702971	+	1.21758i
$966$	−3408.32	−	5903.38i	−0.113521	−	0.196623i
$967$			55038.2i			1.83031i	0.403102	+	0.915155i	$0.367932\pi$
$967$			55038.2i			1.83031i	−0.403102	+	0.915155i	$0.632068\pi$
$968$	−8600.63	+	4965.58i	−0.285573	+	0.164876i
$969$	−962.205	+	555.529i	−0.0318994	+	0.0184171i
$970$			13700.9i			0.453516i
$971$	−2936.42	−	5086.02i	−0.0970484	−	0.168093i	0.813413	−	0.581686i	$-0.197607\pi$
$971$	−2936.42	−	5086.02i	−0.0970484	−	0.168093i	−0.910462	+	0.413593i	$0.864274\pi$
$972$	−486.000	+	841.777i	−0.0160375	+	0.0277778i
$973$	−17376.1	−	10032.1i	−0.572509	−	0.330538i
$974$	40590.8			1.33533
$975$	51.2697	−	325.646i	0.00168405	−	0.0106964i
$976$	3487.50			0.114377
$977$	−36900.7	−	21304.6i	−1.20835	−	0.697641i	−0.245951	−	0.969282i	$-0.579100\pi$
$977$	−36900.7	−	21304.6i	−1.20835	−	0.697641i	−0.962398	+	0.271642i	$0.912433\pi$
$978$	3264.46	−	5654.22i	0.106734	−	0.184869i
$979$	−7560.39	−	13095.0i	−0.246814	−	0.427495i
$980$			2211.80i			0.0720953i
$981$	1509.30	−	871.396i	0.0491216	−	0.0283604i
$982$	−1400.23	+	808.423i	−0.0455021	+	0.0262707i
$983$			8305.07i			0.269472i	0.990882	+	0.134736i	$0.0430186\pi$
$983$			8305.07i			0.269472i	−0.990882	+	0.134736i	$0.956981\pi$
$984$	5172.48	+	8959.00i	0.167574	+	0.290246i
$985$	−10120.1	+	17528.4i	−0.327362	+	0.567008i
$986$	1544.02	+	891.442i	0.0498699	+	0.0287924i
$987$	−3592.55			−0.115858
$988$	−6873.93	−	1082.23i	−0.221345	−	0.0348486i
$989$	79418.2			2.55344
$990$	1665.18	+	961.389i	0.0534573	+	0.0308636i
$991$	8883.00	−	15385.8i	0.284741	−	0.493185i	−0.687806	−	0.725895i	$-0.741426\pi$
$991$	8883.00	−	15385.8i	0.284741	−	0.493185i	0.972546	+	0.232710i	$0.0747592\pi$
$992$	−694.646	−	1203.16i	−0.0222329	−	0.0385085i
$993$		−	18712.8i		−	0.598020i
$994$	13916.8	−	8034.89i	0.444080	−	0.256389i
$995$	6210.75	−	3585.78i	0.197884	−	0.114248i
$996$			14006.1i			0.445582i
$997$	−9474.45	−	16410.2i	−0.300962	−	0.521281i	0.675392	−	0.737459i	$-0.263974\pi$
$997$	−9474.45	−	16410.2i	−0.300962	−	0.521281i	−0.976354	+	0.216178i	$0.930641\pi$
$998$	7263.12	−	12580.1i	0.230371	−	0.399014i
$999$	1907.99	+	1101.58i	0.0604265	+	0.0348873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.s.d.43.5	✓	24
13.10	even	6	inner	546.4.s.d.127.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.s.d.43.5	✓	24	1.1	even	1	trivial
546.4.s.d.127.5	yes	24	13.10	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +11.2847i q^{5} +(-5.19615 + 3.00000i) q^{6} +(6.06218 - 3.50000i) q^{7} -8.00000i q^{8} +(-4.50000 - 7.79423i) q^{9} +(11.2847 - 19.5457i) q^{10} +(-8.19780 - 4.73300i) q^{11} +12.0000 q^{12} +(-43.7434 + 16.8378i) q^{13} -14.0000 q^{14} +(29.3185 + 16.9270i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-4.98929 - 8.64170i) q^{17} +18.0000i q^{18} +(32.1424 - 18.5574i) q^{19} +(-39.0913 + 22.5694i) q^{20} -21.0000i q^{21} +(9.46601 + 16.3956i) q^{22} +(-81.1505 + 140.557i) q^{23} +(-20.7846 - 12.0000i) q^{24} -2.34437 q^{25} +(92.6037 + 14.5795i) q^{26} -27.0000 q^{27} +(24.2487 + 14.0000i) q^{28} +(44.6678 - 77.3669i) q^{29} +(-33.8541 - 58.6370i) q^{30} -43.4154i q^{31} +(27.7128 - 16.0000i) q^{32} +(-24.5934 + 14.1990i) q^{33} +19.9572i q^{34} +(39.4964 + 68.4098i) q^{35} +(18.0000 - 31.1769i) q^{36} +(-70.6662 - 40.7992i) q^{37} -74.2296 q^{38} +(-21.8693 + 138.905i) q^{39} +90.2776 q^{40} +(-373.292 - 215.520i) q^{41} +(-21.0000 + 36.3731i) q^{42} +(-244.664 - 423.770i) q^{43} -37.8640i q^{44} +(87.9555 - 50.7811i) q^{45} +(281.114 - 162.301i) q^{46} -171.074i q^{47} +(24.0000 + 41.5692i) q^{48} +(24.5000 - 42.4352i) q^{49} +(4.06057 + 2.34437i) q^{50} -29.9357 q^{51} +(-145.815 - 117.856i) q^{52} +28.6439 q^{53} +(46.7654 + 27.0000i) q^{54} +(53.4105 - 92.5097i) q^{55} +(-28.0000 - 48.4974i) q^{56} -111.344i q^{57} +(-154.734 + 89.3356i) q^{58} +(-242.440 + 139.973i) q^{59} +135.416i q^{60} +(-108.984 - 188.767i) q^{61} +(-43.4154 + 75.1977i) q^{62} +(-54.5596 - 31.5000i) q^{63} -64.0000 q^{64} +(-190.009 - 493.631i) q^{65} +56.7961 q^{66} +(-215.578 - 124.464i) q^{67} +(19.9572 - 34.5668i) q^{68} +(243.451 + 421.670i) q^{69} -157.986i q^{70} +(-994.059 + 573.920i) q^{71} +(-62.3538 + 36.0000i) q^{72} -557.825i q^{73} +(81.5983 + 141.332i) q^{74} +(-3.51656 + 6.09086i) q^{75} +(128.569 + 74.2296i) q^{76} -66.2621 q^{77} +(176.784 - 218.722i) q^{78} -144.368 q^{79} +(-156.365 - 90.2776i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(431.040 + 746.583i) q^{82} +1167.17i q^{83} +(72.7461 - 42.0000i) q^{84} +(97.5190 - 56.3026i) q^{85} +978.654i q^{86} +(-134.003 - 232.101i) q^{87} +(-37.8640 + 65.5824i) q^{88} +(1383.37 + 798.688i) q^{89} -203.125 q^{90} +(-206.248 + 255.176i) q^{91} -649.204 q^{92} +(-112.796 - 65.1231i) q^{93} +(-171.074 + 296.309i) q^{94} +(209.415 + 362.717i) q^{95} -96.0000i q^{96} +(-525.727 + 303.529i) q^{97} +(-84.8705 + 49.0000i) q^{98} +85.1941i 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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