LMFDB - Embedded newform 253.3.g.a.24.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,3,Mod(24,253)] 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("253.24"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	253.g (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			24.10
Character	$\chi$	$=$	253.24
Dual form			253.3.g.a.116.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.51750 - 0.817984i) q^{2} +(1.62027 - 1.17720i) q^{3} +(2.43262 + 1.76740i) q^{4} +(2.85518 + 8.78734i) q^{5} +(-5.04196 + 1.63823i) q^{6} +(3.48178 - 4.79226i) q^{7} +(1.54518 + 2.12676i) q^{8} +(-1.54166 + 4.74475i) q^{9} -24.4576i q^{10} +(-2.35696 + 10.7445i) q^{11} +6.02210 q^{12} +(-16.5137 - 5.36564i) q^{13} +(-12.6854 + 9.21645i) q^{14} +(14.9706 + 10.8768i) q^{15} +(-5.86705 - 18.0569i) q^{16} +(-31.6380 + 10.2798i) q^{17} +(7.76226 - 10.6838i) q^{18} +(-1.25540 - 1.72791i) q^{19} +(-8.58521 + 26.4225i) q^{20} -11.8635i q^{21} +(14.7225 - 25.1213i) q^{22} -4.79583 q^{23} +(5.00723 + 1.62695i) q^{24} +(-48.8398 + 35.4842i) q^{25} +(37.1842 + 27.0159i) q^{26} +(8.65759 + 26.6453i) q^{27} +(16.9397 - 5.50405i) q^{28} +(23.5271 - 32.3823i) q^{29} +(-28.7914 - 39.6280i) q^{30} +(1.09334 - 3.36495i) q^{31} +39.7421i q^{32} +(8.82949 + 20.1837i) q^{33} +88.0573 q^{34} +(52.0523 + 16.9128i) q^{35} +(-12.1362 + 8.81745i) q^{36} +(13.7174 + 9.96630i) q^{37} +(1.74706 + 5.37691i) q^{38} +(-33.0731 + 10.7461i) q^{39} +(-14.2768 + 19.6503i) q^{40} +(-2.08561 - 2.87059i) q^{41} +(-9.70416 + 29.8663i) q^{42} +51.0107i q^{43} +(-24.7235 + 21.9717i) q^{44} -46.0954 q^{45} +(12.0735 + 3.92291i) q^{46} +(-1.23883 + 0.900063i) q^{47} +(-30.7628 - 22.3505i) q^{48} +(4.29888 + 13.2306i) q^{49} +(151.980 - 49.3812i) q^{50} +(-39.1608 + 53.9003i) q^{51} +(-30.6884 - 42.2390i) q^{52} +(-10.5596 + 32.4992i) q^{53} -74.1613i q^{54} +(-101.145 + 9.96609i) q^{55} +15.5720 q^{56} +(-4.06818 - 1.32183i) q^{57} +(-85.7176 + 62.2775i) q^{58} +(35.8678 + 26.0594i) q^{59} +(17.1942 + 52.9182i) q^{60} +(57.7758 - 18.7725i) q^{61} +(-5.50495 + 7.57692i) q^{62} +(17.3703 + 23.9082i) q^{63} +(9.04024 - 27.8230i) q^{64} -160.432i q^{65} +(-5.71830 - 58.0347i) q^{66} +25.4784 q^{67} +(-95.1320 - 30.9103i) q^{68} +(-7.77055 + 5.64564i) q^{69} +(-117.207 - 85.1559i) q^{70} +(-26.5354 - 81.6675i) q^{71} +(-12.4731 + 4.05275i) q^{72} +(46.5102 - 64.0157i) q^{73} +(-26.3813 - 36.3108i) q^{74} +(-37.3619 + 114.988i) q^{75} -6.42216i q^{76} +(43.2841 + 48.7052i) q^{77} +92.0517 q^{78} +(67.6540 + 21.9821i) q^{79} +(141.921 - 103.112i) q^{80} +(9.06934 + 6.58926i) q^{81} +(2.90241 + 8.93271i) q^{82} +(-59.3250 + 19.2759i) q^{83} +(20.9676 - 28.8594i) q^{84} +(-180.664 - 248.663i) q^{85} +(41.7259 - 128.419i) q^{86} -80.1641i q^{87} +(-26.4929 + 11.5895i) q^{88} +48.1862 q^{89} +(116.045 + 37.7053i) q^{90} +(-83.2107 + 60.4561i) q^{91} +(-11.6665 - 8.47617i) q^{92} +(-2.18970 - 6.73921i) q^{93} +(3.85499 - 1.25256i) q^{94} +(11.5993 - 15.9651i) q^{95} +(46.7843 + 64.3931i) q^{96} +(-13.2508 + 40.7819i) q^{97} -36.8244i q^{98} +(-47.3464 - 27.7476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 8 q^{3} + 88 q^{4} - 40 q^{6} - 120 q^{9} - 8 q^{14} - 12 q^{15} - 272 q^{16} - 80 q^{17} + 80 q^{18} - 60 q^{19} + 40 q^{20} + 136 q^{22} - 60 q^{24} - 268 q^{25} + 40 q^{26} + 148 q^{27} - 240 q^{28}+ \cdots - 414 q^{99}+O(q^{100}) $ 176 * q - 8 * q^3 + 88 * q^4 - 40 * q^6 - 120 * q^9 - 8 * q^14 - 12 * q^15 - 272 * q^16 - 80 * q^17 + 80 * q^18 - 60 * q^19 + 40 * q^20 + 136 * q^22 - 60 * q^24 - 268 * q^25 + 40 * q^26 + 148 * q^27 - 240 * q^28 + 160 * q^29 + 240 * q^30 + 108 * q^31 - 160 * q^33 - 420 * q^34 + 150 * q^35 + 32 * q^36 + 96 * q^37 + 70 * q^38 - 320 * q^39 + 270 * q^40 - 362 * q^42 + 174 * q^44 + 180 * q^45 - 138 * q^47 - 182 * q^48 + 464 * q^49 + 410 * q^50 + 500 * q^51 - 70 * q^52 - 130 * q^53 + 88 * q^55 + 472 * q^56 - 100 * q^57 + 468 * q^58 - 126 * q^59 - 376 * q^60 - 570 * q^62 - 160 * q^63 + 1096 * q^64 - 562 * q^66 - 472 * q^67 - 480 * q^68 + 380 * q^70 - 264 * q^71 + 1050 * q^72 - 840 * q^73 + 530 * q^74 - 64 * q^75 + 326 * q^77 - 576 * q^78 + 90 * q^79 + 274 * q^80 - 276 * q^81 - 132 * q^82 + 180 * q^83 - 1120 * q^84 + 360 * q^85 - 704 * q^86 + 272 * q^88 + 340 * q^89 + 1600 * q^90 + 514 * q^91 - 838 * q^93 - 690 * q^94 - 520 * q^95 - 1240 * q^96 + 832 * q^97 - 414 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.51750	−	0.817984i	−1.25875	−	0.408992i	−0.397700	−	0.917515i	$-0.630192\pi$
$2$	−2.51750	−	0.817984i	−1.25875	−	0.408992i	−0.861048	+	0.508523i	$0.830192\pi$
$3$	1.62027	−	1.17720i	0.540091	−	0.392399i	−0.284028	−	0.958816i	$-0.591671\pi$
$3$	1.62027	−	1.17720i	0.540091	−	0.392399i	0.824119	+	0.566417i	$0.191671\pi$
$4$	2.43262	+	1.76740i	0.608156	+	0.441851i
$5$	2.85518	+	8.78734i	0.571036	+	1.75747i	0.649297	+	0.760535i	$0.275063\pi$
$5$	2.85518	+	8.78734i	0.571036	+	1.75747i	−0.0782613	+	0.996933i	$0.524937\pi$
$6$	−5.04196	+	1.63823i	−0.840327	+	0.273039i
$7$	3.48178	−	4.79226i	0.497397	−	0.684608i	−0.484334	−	0.874883i	$-0.660938\pi$
$7$	3.48178	−	4.79226i	0.497397	−	0.684608i	0.981731	+	0.190275i	$0.0609379\pi$
$8$	1.54518	+	2.12676i	0.193148	+	0.265845i
$9$	−1.54166	+	4.74475i	−0.171296	+	0.527194i
$10$		−	24.4576i		−	2.44576i
$11$	−2.35696	+	10.7445i	−0.214269	+	0.976775i
$11$	−2.35696	+	10.7445i	−0.214269	+	0.976775i
$12$	6.02210			0.501841
$13$	−16.5137	−	5.36564i	−1.27029	−	0.412741i	−0.405138	−	0.914256i	$-0.632776\pi$
$13$	−16.5137	−	5.36564i	−1.27029	−	0.412741i	−0.865149	+	0.501515i	$0.832776\pi$
$14$	−12.6854	+	9.21645i	−0.906097	+	0.658318i
$15$	14.9706	+	10.8768i	0.998040	+	0.725118i
$16$	−5.86705	−	18.0569i	−0.366691	−	1.12856i
$17$	−31.6380	+	10.2798i	−1.86106	+	0.604695i	−0.866675	+	0.498874i	$0.833747\pi$
$17$	−31.6380	+	10.2798i	−1.86106	+	0.604695i	−0.994385	+	0.105821i	$0.966253\pi$
$18$	7.76226	−	10.6838i	0.431237	−	0.593546i
$19$	−1.25540	−	1.72791i	−0.0660737	−	0.0909427i	0.774701	−	0.632327i	$-0.217900\pi$
$19$	−1.25540	−	1.72791i	−0.0660737	−	0.0909427i	−0.840775	+	0.541385i	$0.817900\pi$
$20$	−8.58521	+	26.4225i	−0.429260	+	1.32113i
$21$		−	11.8635i		−	0.564929i
$22$	14.7225	−	25.1213i	0.669204	−	1.14188i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$	5.00723	+	1.62695i	0.208635	+	0.0677895i
$25$	−48.8398	+	35.4842i	−1.95359	+	1.41937i
$26$	37.1842	+	27.0159i	1.43016	+	1.03907i
$27$	8.65759	+	26.6453i	0.320652	+	0.986864i
$28$	16.9397	−	5.50405i	0.604990	−	0.196573i
$29$	23.5271	−	32.3823i	0.811279	−	1.11663i	−0.179846	−	0.983695i	$-0.557560\pi$
$29$	23.5271	−	32.3823i	0.811279	−	1.11663i	0.991125	−	0.132935i	$-0.0424402\pi$
$30$	−28.7914	−	39.6280i	−0.959713	−	1.32093i
$31$	1.09334	−	3.36495i	0.0352690	−	0.108547i	−0.931872	−	0.362787i	$-0.881825\pi$
$31$	1.09334	−	3.36495i	0.0352690	−	0.108547i	0.967141	+	0.254240i	$0.0818253\pi$
$32$			39.7421i			1.24194i
$33$	8.82949	+	20.1837i	0.267560	+	0.611626i
$34$	88.0573			2.58992
$35$	52.0523	+	16.9128i	1.48721	+	0.483223i
$36$	−12.1362	+	8.81745i	−0.337116	+	0.244929i
$37$	13.7174	+	9.96630i	0.370741	+	0.269359i	0.757518	−	0.652814i	$-0.226412\pi$
$37$	13.7174	+	9.96630i	0.370741	+	0.269359i	−0.386777	+	0.922173i	$0.626412\pi$
$38$	1.74706	+	5.37691i	0.0459753	+	0.141498i
$39$	−33.0731	+	10.7461i	−0.848029	+	0.275541i
$40$	−14.2768	+	19.6503i	−0.356920	+	0.491258i
$41$	−2.08561	−	2.87059i	−0.0508685	−	0.0700145i	0.782825	−	0.622242i	$-0.213778\pi$
$41$	−2.08561	−	2.87059i	−0.0508685	−	0.0700145i	−0.833693	+	0.552227i	$0.813778\pi$
$42$	−9.70416	+	29.8663i	−0.231051	+	0.711103i
$43$			51.0107i			1.18629i	0.805094	+	0.593147i	$0.202115\pi$
$43$			51.0107i			1.18629i	−0.805094	+	0.593147i	$0.797885\pi$
$44$	−24.7235	+	21.9717i	−0.561898	+	0.499356i
$45$	−46.0954			−1.02434
$46$	12.0735	+	3.92291i	0.262467	+	0.0852808i
$47$	−1.23883	+	0.900063i	−0.0263581	+	0.0191503i	−0.600886	−	0.799335i	$-0.705186\pi$
$47$	−1.23883	+	0.900063i	−0.0263581	+	0.0191503i	0.574528	+	0.818485i	$0.305186\pi$
$48$	−30.7628	−	22.3505i	−0.640891	−	0.465635i
$49$	4.29888	+	13.2306i	0.0877322	+	0.270012i
$50$	151.980	−	49.3812i	3.03959	−	0.987624i
$51$	−39.1608	+	53.9003i	−0.767860	+	1.05687i
$52$	−30.6884	−	42.2390i	−0.590162	−	0.812289i
$53$	−10.5596	+	32.4992i	−0.199238	+	0.613192i	0.800663	+	0.599115i	$0.204481\pi$
$53$	−10.5596	+	32.4992i	−0.199238	+	0.613192i	−0.999901	+	0.0140767i	$0.995519\pi$
$54$		−	74.1613i		−	1.37336i
$55$	−101.145	+	9.96609i	−1.83901	+	0.181202i
$56$	15.5720			0.278071
$57$	−4.06818	−	1.32183i	−0.0713716	−	0.0231900i
$58$	−85.7176	+	62.2775i	−1.47789	+	1.07375i
$59$	35.8678	+	26.0594i	0.607928	+	0.441686i	0.848684	−	0.528900i	$-0.177395\pi$
$59$	35.8678	+	26.0594i	0.607928	+	0.441686i	−0.240756	+	0.970586i	$0.577395\pi$
$60$	17.1942	+	52.9182i	0.286569	+	0.881970i
$61$	57.7758	−	18.7725i	0.947145	−	0.307746i	0.205590	−	0.978638i	$-0.434089\pi$
$61$	57.7758	−	18.7725i	0.947145	−	0.307746i	0.741555	+	0.670892i	$0.234089\pi$
$62$	−5.50495	+	7.57692i	−0.0887896	+	0.122208i
$63$	17.3703	+	23.9082i	0.275720	+	0.379495i
$64$	9.04024	−	27.8230i	0.141254	−	0.434734i
$65$		−	160.432i		−	2.46818i
$66$	−5.71830	−	58.0347i	−0.0866409	−	0.879314i
$67$	25.4784			0.380275			0.190138	−	0.981757i	$-0.439107\pi$
$67$	25.4784			0.380275			0.190138	+	0.981757i	$0.439107\pi$
$68$	−95.1320	−	30.9103i	−1.39900	−	0.454563i
$69$	−7.77055	+	5.64564i	−0.112617	+	0.0818208i
$70$	−117.207	−	85.1559i	−1.67439	−	1.21651i
$71$	−26.5354	−	81.6675i	−0.373738	−	1.15025i	−0.944326	−	0.329010i	$-0.893285\pi$
$71$	−26.5354	−	81.6675i	−0.373738	−	1.15025i	0.570589	−	0.821236i	$-0.306715\pi$
$72$	−12.4731	+	4.05275i	−0.173237	+	0.0562882i
$73$	46.5102	−	64.0157i	0.637125	−	0.876928i	−0.361333	−	0.932437i	$-0.617678\pi$
$73$	46.5102	−	64.0157i	0.637125	−	0.876928i	0.998458	+	0.0555090i	$0.0176781\pi$
$74$	−26.3813	−	36.3108i	−0.356504	−	0.490686i
$75$	−37.3619	+	114.988i	−0.498159	+	1.53318i
$76$		−	6.42216i		−	0.0845021i
$77$	43.2841	+	48.7052i	0.562131	+	0.632536i
$78$	92.0517			1.18015
$79$	67.6540	+	21.9821i	0.856379	+	0.278255i	0.704116	−	0.710085i	$-0.251344\pi$
$79$	67.6540	+	21.9821i	0.856379	+	0.278255i	0.152264	+	0.988340i	$0.451344\pi$
$80$	141.921	−	103.112i	1.77401	−	1.28889i
$81$	9.06934	+	6.58926i	0.111967	+	0.0813489i
$82$	2.90241	+	8.93271i	0.0353953	+	0.108935i
$83$	−59.3250	+	19.2759i	−0.714759	+	0.232239i	−0.643749	−	0.765236i	$-0.722622\pi$
$83$	−59.3250	+	19.2759i	−0.714759	+	0.232239i	−0.0710096	+	0.997476i	$0.522622\pi$
$84$	20.9676	−	28.8594i	0.249614	−	0.343565i
$85$	−180.664	−	248.663i	−2.12546	−	2.92545i
$86$	41.7259	−	128.419i	0.485185	−	1.49325i
$87$		−	80.1641i		−	0.921427i
$88$	−26.4929	+	11.5895i	−0.301056	+	0.131699i
$89$	48.1862			0.541418			0.270709	−	0.962661i	$-0.412742\pi$
$89$	48.1862			0.541418			0.270709	+	0.962661i	$0.412742\pi$
$90$	116.045	+	37.7053i	1.28939	+	0.418948i
$91$	−83.2107	+	60.4561i	−0.914403	+	0.664353i
$92$	−11.6665	−	8.47617i	−0.126809	−	0.0921323i
$93$	−2.18970	−	6.73921i	−0.0235452	−	0.0724647i
$94$	3.85499	−	1.25256i	0.0410105	−	0.0133251i
$95$	11.5993	−	15.9651i	0.122098	−	0.168054i
$96$	46.7843	+	64.3931i	0.487337	+	0.670761i
$97$	−13.2508	+	40.7819i	−0.136607	+	0.420432i	−0.995836	−	0.0911577i	$-0.970943\pi$
$97$	−13.2508	+	40.7819i	−0.136607	+	0.420432i	0.859230	+	0.511590i	$0.170943\pi$
$98$		−	36.8244i		−	0.375759i
$99$	−47.3464	−	27.7476i	−0.478247	−	0.280279i
$100$	−181.524			−1.81524
$101$	130.702	+	42.4676i	1.29408	+	0.420471i	0.873517	−	0.486793i	$-0.161833\pi$
$101$	130.702	+	42.4676i	1.29408	+	0.420471i	0.420561	+	0.907264i	$0.361833\pi$
$102$	142.677	−	103.661i	1.39879	−	1.01628i
$103$	−49.6714	−	36.0884i	−0.482247	−	0.350373i	0.319948	−	0.947435i	$-0.396334\pi$
$103$	−49.6714	−	36.0884i	−0.482247	−	0.350373i	−0.802195	+	0.597062i	$0.796334\pi$
$104$	−14.1053	−	43.4116i	−0.135628	−	0.417419i
$105$	104.249	−	33.8724i	0.992844	−	0.322595i
$106$	53.1676	−	73.1790i	0.501581	−	0.690368i
$107$	121.333	+	167.001i	1.13396	+	1.56076i	0.780328	+	0.625371i	$0.215052\pi$
$107$	121.333	+	167.001i	1.13396	+	1.56076i	0.353629	+	0.935386i	$0.384948\pi$
$108$	−26.0324	+	80.1195i	−0.241041	+	0.741847i
$109$			48.8119i			0.447816i	0.974610	+	0.223908i	$0.0718815\pi$
$109$			48.8119i			0.447816i	−0.974610	+	0.223908i	$0.928118\pi$
$110$	262.785	+	57.6457i	2.38896	+	0.524051i
$111$	33.9583			0.305930
$112$	−106.961	−	34.7538i	−0.955011	−	0.310302i
$113$	−91.0103	+	66.1228i	−0.805401	+	0.585158i	−0.912493	−	0.409091i	$-0.865846\pi$
$113$	−91.0103	+	66.1228i	−0.805401	+	0.585158i	0.107093	+	0.994249i	$0.465846\pi$
$114$	9.16040	+	6.65542i	0.0803544	+	0.0583809i
$115$	−13.6930	−	42.1426i	−0.119069	−	0.366457i
$116$	114.465	−	37.1920i	0.986768	−	0.320621i
$117$	50.9172	−	70.0815i	0.435190	−	0.598987i
$118$	−68.9807	−	94.9438i	−0.584583	−	0.804609i
$119$	−60.8931	+	187.410i	−0.511706	+	1.57487i
$120$			48.6454i			0.405379i
$121$	−109.889	−	50.6489i	−0.908177	−	0.418586i
$122$	−160.806			−1.31808
$123$	−6.75851	−	2.19597i	−0.0549472	−	0.0178534i
$124$	8.60691	−	6.25329i	0.0694106	−	0.0504297i
$125$	−264.384	−	192.087i	−2.11508	−	1.53669i
$126$	−24.1732	−	74.3975i	−0.191851	−	0.590456i
$127$	−95.7391	+	31.1075i	−0.753851	+	0.244941i	−0.660638	−	0.750705i	$-0.729714\pi$
$127$	−95.7391	+	31.1075i	−0.753851	+	0.244941i	−0.0932137	+	0.995646i	$0.529714\pi$
$128$	47.9218	−	65.9587i	0.374389	−	0.515303i
$129$	60.0496	+	82.6512i	0.465501	+	0.640707i
$130$	−131.230	+	403.886i	−1.00947	+	3.10681i
$131$		−	22.2278i		−	0.169678i	−0.996395	−	0.0848388i	$-0.972962\pi$
$131$		−	22.2278i		−	0.169678i	0.996395	−	0.0848388i	$-0.0270375\pi$
$132$	−14.1939	+	64.7045i	−0.107529	+	0.490186i
$133$	−12.6516			−0.0951250
$134$	−64.1419	−	20.8410i	−0.478671	−	0.155529i
$135$	−209.423	+	152.154i	−1.55128	+	1.12707i
$136$	−70.7492	−	51.4023i	−0.520214	−	0.377958i
$137$	50.1411	+	154.318i	0.365993	+	1.12641i	0.949357	+	0.314200i	$0.101736\pi$
$137$	50.1411	+	154.318i	0.365993	+	1.12641i	−0.583364	+	0.812211i	$0.698264\pi$
$138$	24.1804	−	7.85668i	0.175220	−	0.0569325i
$139$	77.1675	−	106.212i	0.555162	−	0.764115i	−0.435539	−	0.900170i	$-0.643442\pi$
$139$	77.1675	−	106.212i	0.555162	−	0.764115i	0.990701	+	0.136055i	$0.0434424\pi$
$140$	96.7319	+	133.140i	0.690942	+	0.951000i
$141$	−0.947691	+	2.91669i	−0.00672122	+	0.0206858i
$142$			227.303i			1.60073i
$143$	96.5734	−	164.785i	0.675339	−	1.15235i
$144$	94.7206			0.657782
$145$	351.728	+	114.283i	2.42571	+	0.788161i
$146$	−169.453	+	123.115i	−1.16064	+	0.843252i
$147$	22.5404	+	16.3765i	0.153336	+	0.111405i
$148$	15.7549	+	48.4885i	0.106452	+	0.327625i
$149$	−137.485	+	44.6717i	−0.922720	+	0.299810i	−0.731582	−	0.681753i	$-0.761218\pi$
$149$	−137.485	+	44.6717i	−0.922720	+	0.299810i	−0.191138	+	0.981563i	$0.561218\pi$
$150$	188.117	−	258.921i	1.25411	−	1.72614i
$151$	111.443	+	153.389i	0.738036	+	1.01582i	0.998729	+	0.0503979i	$0.0160489\pi$
$151$	111.443	+	153.389i	0.738036	+	1.01582i	−0.260693	+	0.965422i	$0.583951\pi$
$152$	1.73503	−	5.33987i	0.0114147	−	0.0351307i
$153$		−	165.962i		−	1.08472i
$154$	−69.1274	−	158.021i	−0.448880	−	1.02611i
$155$	32.6906			0.210907
$156$	−99.4473	−	32.3124i	−0.637482	−	0.207131i
$157$	163.252	−	118.609i	1.03982	−	0.755474i	0.0695705	−	0.997577i	$-0.477837\pi$
$157$	163.252	−	118.609i	1.03982	−	0.755474i	0.970251	+	0.242103i	$0.0778371\pi$
$158$	−152.338	−	110.680i	−0.964162	−	0.700505i
$159$	21.1485	+	65.0883i	0.133009	+	0.409360i
$160$	−349.228	+	113.471i	−2.18267	+	0.709193i
$161$	−16.6980	+	22.9829i	−0.103714	+	0.142751i
$162$	−17.4421	−	24.0070i	−0.107667	−	0.148191i
$163$	47.6979	−	146.799i	0.292625	−	0.900607i	−0.691384	−	0.722488i	$-0.742999\pi$
$163$	47.6979	−	146.799i	0.292625	−	0.900607i	0.984009	−	0.178119i	$-0.0570013\pi$
$164$		−	10.6692i		−	0.0650560i
$165$	−152.151	+	135.216i	−0.922127	+	0.819489i
$166$	165.118			0.994686
$167$	95.5093	+	31.0329i	0.571912	+	0.185825i	0.580674	−	0.814136i	$-0.302789\pi$
$167$	95.5093	+	31.0329i	0.571912	+	0.185825i	−0.00876206	+	0.999962i	$0.502789\pi$
$168$	25.2308	−	18.3313i	0.150183	−	0.109115i
$169$	107.189	+	77.8776i	0.634256	+	0.460814i
$170$	251.419	+	773.790i	1.47894	+	4.55170i
$171$	10.1339	−	3.29271i	0.0592626	−	0.0192556i
$172$	−90.1565	+	124.090i	−0.524165	+	0.721452i
$173$	−73.8209	−	101.606i	−0.426710	−	0.587316i	0.540484	−	0.841354i	$-0.318241\pi$
$173$	−73.8209	−	101.606i	−0.426710	−	0.587316i	−0.967194	+	0.254038i	$0.918241\pi$
$174$	−65.5730	+	201.813i	−0.376856	+	1.15984i
$175$			357.601i			2.04344i
$176$	207.841	−	20.4791i	1.18092	−	0.116359i
$177$	88.7926			0.501653
$178$	−121.309	−	39.4155i	−0.681509	−	0.221436i
$179$	117.308	−	85.2289i	0.655350	−	0.476139i	−0.209740	−	0.977757i	$-0.567262\pi$
$179$	117.308	−	85.2289i	0.655350	−	0.476139i	0.865089	+	0.501618i	$0.167262\pi$
$180$	−112.133	−	81.4693i	−0.622960	−	0.452607i
$181$	101.348	+	311.917i	0.559934	+	1.72330i	0.682543	+	0.730846i	$0.260874\pi$
$181$	101.348	+	311.917i	0.559934	+	1.72330i	−0.122609	+	0.992455i	$0.539126\pi$
$182$	258.935	−	84.1330i	1.42272	−	0.462269i
$183$	71.5137	−	98.4301i	0.390785	−	0.537870i
$184$	−7.41043	−	10.1996i	−0.0402741	−	0.0554325i
$185$	−48.4115	+	148.995i	−0.261684	+	0.805380i
$186$			18.7571i			0.100845i
$187$	−35.8820	−	364.164i	−0.191882	−	1.94740i
$188$	−4.60438			−0.0244914
$189$	157.835	+	51.2837i	0.835107	+	0.271343i
$190$	−42.2605	+	30.7041i	−0.222424	+	0.161600i
$191$	169.121	+	122.873i	0.885448	+	0.643316i	0.934687	−	0.355471i	$-0.115680\pi$
$191$	169.121	+	122.873i	0.885448	+	0.643316i	−0.0492393	+	0.998787i	$0.515680\pi$
$192$	−18.1055	−	55.7230i	−0.0942994	−	0.290224i
$193$	−247.689	+	80.4790i	−1.28336	+	0.416989i	−0.869763	−	0.493470i	$-0.835728\pi$
$193$	−247.689	+	80.4790i	−1.28336	+	0.416989i	−0.413599	+	0.910459i	$0.635728\pi$
$194$	66.7179	−	91.8293i	0.343907	−	0.473347i
$195$	−188.860	−	259.943i	−0.968510	−	1.33304i
$196$	−12.9263	+	39.7829i	−0.0659503	+	0.202974i
$197$			186.574i			0.947078i	0.880773	+	0.473539i	$0.157024\pi$
$197$			186.574i			0.947078i	−0.880773	+	0.473539i	$0.842976\pi$
$198$	96.4973	+	108.583i	0.487360	+	0.548400i
$199$	125.274			0.629519			0.314760	−	0.949171i	$-0.398076\pi$
$199$	125.274			0.629519			0.314760	+	0.949171i	$0.398076\pi$
$200$	−150.933	−	49.0410i	−0.754664	−	0.245205i
$201$	41.2820	−	29.9931i	0.205383	−	0.149220i
$202$	−294.304	−	213.824i	−1.45695	−	1.05854i
$203$	−73.2680	−	225.496i	−0.360926	−	1.11082i
$204$	−190.527	+	61.9060i	−0.933957	+	0.303461i
$205$	19.2701	−	26.5230i	0.0940004	−	0.129381i
$206$	95.5279	+	131.483i	0.463728	+	0.638266i
$207$	7.39355	−	22.7550i	0.0357176	−	0.109928i
$208$			329.668i			1.58494i
$209$	21.5245	−	9.41605i	0.102988	−	0.0450529i
$210$	−290.153			−1.38168
$211$	−203.349	−	66.0720i	−0.963739	−	0.313138i	−0.215453	−	0.976514i	$-0.569123\pi$
$211$	−203.349	−	66.0720i	−0.963739	−	0.313138i	−0.748286	+	0.663377i	$0.769123\pi$
$212$	−83.1268	+	60.3952i	−0.392108	+	0.284883i
$213$	−139.133	−	101.086i	−0.653207	−	0.474583i
$214$	−168.852	−	519.673i	−0.789028	−	2.42838i
$215$	−448.248	+	145.645i	−2.08487	+	0.677417i
$216$	−43.2906	+	59.5845i	−0.200420	+	0.275854i
$217$	−12.3190	−	16.9556i	−0.0567694	−	0.0781363i
$218$	39.9274	−	122.884i	0.183153	−	0.563688i
$219$		−	158.475i		−	0.723628i
$220$	−263.663	−	154.521i	−1.19847	−	0.702368i
$221$	577.619			2.61366
$222$	−85.4898	−	27.7773i	−0.385089	−	0.125123i
$223$	151.183	−	109.841i	0.677950	−	0.492560i	−0.194727	−	0.980858i	$-0.562382\pi$
$223$	151.183	−	109.841i	0.677950	−	0.492560i	0.872677	+	0.488298i	$0.162382\pi$
$224$	190.455	+	138.373i	0.850244	+	0.617738i
$225$	−93.0692	−	286.437i	−0.413641	−	1.27306i
$226$	283.205	−	92.0190i	1.25312	−	0.407164i
$227$	140.685	−	193.636i	0.619758	−	0.853024i	−0.377577	−	0.925978i	$-0.623243\pi$
$227$	140.685	−	193.636i	0.619758	−	0.853024i	0.997335	+	0.0729540i	$0.0232426\pi$
$228$	−7.56014	−	10.4056i	−0.0331585	−	0.0456388i
$229$	92.0657	−	283.349i	0.402034	−	1.23733i	−0.521313	−	0.853366i	$-0.674558\pi$
$229$	92.0657	−	283.349i	0.402034	−	1.23733i	0.923347	−	0.383967i	$-0.125442\pi$
$230$			117.294i			0.509976i
$231$	127.468	+	27.9619i	0.551808	+	0.121047i
$232$	105.223			0.453547
$233$	−187.823	−	61.0276i	−0.806109	−	0.261921i	−0.123160	−	0.992387i	$-0.539303\pi$
$233$	−187.823	−	61.0276i	−0.806109	−	0.261921i	−0.682949	+	0.730466i	$0.739303\pi$
$234$	−185.509	+	134.780i	−0.792775	+	0.575985i
$235$	−11.4462	−	8.31618i	−0.0487074	−	0.0353880i
$236$	41.1952	+	126.786i	0.174556	+	0.537227i
$237$	135.495	−	44.0250i	0.571710	−	0.185760i
$238$	306.596	−	421.994i	1.28822	−	1.77308i
$239$	−199.013	−	273.917i	−0.832689	−	1.14610i	−0.987417	−	0.158141i	$-0.949450\pi$
$239$	−199.013	−	273.917i	−0.832689	−	1.14610i	0.154728	−	0.987957i	$-0.450550\pi$
$240$	108.568	−	334.138i	0.452366	−	1.39224i
$241$		−	37.2582i		−	0.154598i	−0.997008	−	0.0772992i	$-0.975370\pi$
$241$		−	37.2582i		−	0.154598i	0.997008	−	0.0772992i	$-0.0246297\pi$
$242$	235.216	+	217.396i	0.971968	+	0.898332i
$243$	−229.697			−0.945257
$244$	173.726	+	56.4468i	0.711990	+	0.231339i
$245$	−103.988	+	75.5514i	−0.424439	+	0.308373i
$246$	15.2183	+	11.0567i	0.0618628	+	0.0449460i
$247$	11.4600	+	35.2703i	0.0463968	+	0.142795i
$248$	8.84585	−	2.87419i	0.0356687	−	0.0115895i
$249$	−73.4312	+	101.069i	−0.294904	+	0.405901i
$250$	508.463	+	699.840i	2.03385	+	2.79936i
$251$	−36.3147	+	111.765i	−0.144680	+	0.445279i	−0.996970	−	0.0777908i	$-0.975213\pi$
$251$	−36.3147	+	111.765i	−0.144680	+	0.445279i	0.852290	+	0.523070i	$0.175213\pi$
$252$			88.8601i			0.352619i
$253$	11.3036	−	51.5289i	0.0446783	−	0.203672i
$254$	266.468			1.04909
$255$	−585.451	−	190.225i	−2.29589	−	0.745979i
$256$	−269.267	+	195.634i	−1.05182	+	0.764195i
$257$	96.1029	+	69.8228i	0.373941	+	0.271684i	0.758843	−	0.651273i	$-0.225765\pi$
$257$	96.1029	+	69.8228i	0.373941	+	0.271684i	−0.384902	+	0.922957i	$0.625765\pi$
$258$	−83.5673	−	257.194i	−0.323904	−	0.996875i
$259$	95.5221	−	31.0370i	0.368811	−	0.119834i
$260$	283.547	−	390.270i	1.09057	−	1.50104i
$261$	117.375	+	161.553i	0.449712	+	0.618976i
$262$	−18.1820	+	55.9584i	−0.0693968	+	0.213581i
$263$		−	281.621i		−	1.07080i	−0.844598	−	0.535401i	$-0.820160\pi$
$263$		−	281.621i		−	1.07080i	0.844598	−	0.535401i	$-0.179840\pi$
$264$	−29.2826	+	49.9656i	−0.110919	+	0.189264i
$265$	−315.731			−1.19144
$266$	31.8504	+	10.3488i	0.119738	+	0.0389054i
$267$	78.0748	−	56.7246i	0.292415	−	0.212452i
$268$	61.9794	+	45.0307i	0.231267	+	0.168025i
$269$	88.0167	+	270.888i	0.327200	+	1.00702i	0.970438	+	0.241351i	$0.0775905\pi$
$269$	88.0167	+	270.888i	0.327200	+	1.00702i	−0.643238	+	0.765666i	$0.722410\pi$
$270$	651.680	−	211.744i	2.41363	−	0.784236i
$271$	−197.768	+	272.205i	−0.729772	+	1.00444i	0.269370	+	0.963037i	$0.413184\pi$
$271$	−197.768	+	272.205i	−0.729772	+	1.00444i	−0.999142	+	0.0414081i	$0.986816\pi$
$272$	371.244	+	510.973i	1.36487	+	1.87858i
$273$	−63.6552	+	195.911i	−0.233169	+	0.717622i
$274$		−	429.511i		−	1.56756i
$275$	−266.147	−	608.396i	−0.967808	−	2.21235i
$276$	−28.8810			−0.104641
$277$	−459.575	−	149.325i	−1.65911	−	0.539079i	−0.678429	−	0.734666i	$-0.737339\pi$
$277$	−459.575	−	149.325i	−1.65911	−	0.539079i	−0.980686	+	0.195587i	$0.937339\pi$
$278$	−281.149	+	204.266i	−1.01133	+	0.734771i
$279$	14.2803	+	10.3752i	0.0511838	+	0.0371872i
$280$	44.4607	+	136.836i	0.158788	+	0.488700i
$281$	−35.6929	+	11.5973i	−0.127021	+	0.0412716i	−0.371838	−	0.928298i	$-0.621272\pi$
$281$	−35.6929	+	11.5973i	−0.127021	+	0.0412716i	0.244817	+	0.969569i	$0.421272\pi$
$282$	4.77162	−	6.56757i	0.0169206	−	0.0232893i
$283$	−206.201	−	283.811i	−0.728625	−	1.00287i	−0.999193	−	0.0401656i	$-0.987211\pi$
$283$	−206.201	−	283.811i	−0.728625	−	1.00287i	0.270568	−	0.962701i	$-0.412789\pi$
$284$	79.7889	−	245.565i	0.280947	−	0.864665i
$285$		−	39.5226i		−	0.138676i
$286$	−377.915	+	335.851i	−1.32138	+	1.17431i
$287$	−21.0183			−0.0732343
$288$	−188.566	−	61.2690i	−0.654745	−	0.212739i
$289$	661.484	−	480.596i	2.28887	−	1.66296i
$290$	−791.992	−	575.416i	−2.73101	−	1.98419i
$291$	26.5384	+	81.6767i	0.0911971	+	0.280676i
$292$	226.283	−	73.5239i	0.774943	−	0.251794i
$293$	−65.0619	+	89.5500i	−0.222054	+	0.305631i	−0.905480	−	0.424388i	$-0.860489\pi$
$293$	−65.0619	+	89.5500i	−0.222054	+	0.305631i	0.683426	+	0.730020i	$0.260489\pi$
$294$	−43.3496	−	59.6655i	−0.147447	−	0.202944i
$295$	−126.584	+	389.586i	−0.429099	+	1.32063i
$296$			44.5734i			0.150586i
$297$	−306.697	+	30.2196i	−1.03265	+	0.101749i
$298$	382.660			1.28409
$299$	79.1971	+	25.7327i	0.264873	+	0.0860625i
$300$	−294.118	+	213.689i	−0.980394	+	0.712298i
$301$	244.456	+	177.608i	0.812147	+	0.590059i
$302$	−155.089	−	477.315i	−0.513540	−	1.58051i
$303$	261.765	−	85.0527i	0.863912	−	0.280702i
$304$	−23.8353	+	32.8064i	−0.0784054	+	0.107916i
$305$	329.921	+	454.097i	1.08171	+	1.48884i
$306$	−135.755	+	417.810i	−0.443643	+	1.36539i
$307$			313.780i			1.02209i	0.859555	+	0.511043i	$0.170741\pi$
$307$			313.780i			1.02209i	−0.859555	+	0.511043i	$0.829259\pi$
$308$	19.2121	+	194.982i	0.0623768	+	0.633059i
$309$	−122.964			−0.397943
$310$	−82.2986	−	26.7404i	−0.265479	−	0.0862595i
$311$	−56.2620	+	40.8767i	−0.180907	+	0.131436i	−0.674553	−	0.738226i	$-0.735664\pi$
$311$	−56.2620	+	40.8767i	−0.180907	+	0.131436i	0.493647	+	0.869663i	$0.335664\pi$
$312$	−73.9584	−	53.7339i	−0.237046	−	0.172224i
$313$	−16.0069	−	49.2642i	−0.0511403	−	0.157394i	0.922225	−	0.386654i	$-0.126369\pi$
$313$	−16.0069	−	49.2642i	−0.0511403	−	0.157394i	−0.973365	+	0.229260i	$0.926369\pi$
$314$	−508.007	+	165.061i	−1.61786	+	0.525673i
$315$	−160.494	+	220.901i	−0.509505	+	0.701274i
$316$	125.725	+	173.046i	0.397865	+	0.547614i
$317$	106.883	−	328.951i	0.337169	−	1.03770i	−0.628474	−	0.777830i	$-0.716320\pi$
$317$	106.883	−	328.951i	0.337169	−	1.03770i	0.965644	−	0.259870i	$-0.0836797\pi$
$318$		−	181.159i		−	0.569681i
$319$	292.479	+	329.111i	0.916863	+	1.03170i
$320$	270.302			0.844692
$321$	393.186	+	127.754i	1.22488	+	0.397987i
$322$	60.8369	−	44.2006i	0.188934	−	0.137269i
$323$	57.4810	+	41.7624i	0.177960	+	0.129295i
$324$	10.4164	+	32.0584i	0.0321494	+	0.0989456i
$325$	996.923	−	323.920i	3.06746	−	0.996677i
$326$	−240.158	+	330.550i	−0.736682	+	1.01396i
$327$	57.4613	+	79.0886i	0.175723	+	0.241861i
$328$	2.88242	−	8.87117i	0.00878786	−	0.0270463i
$329$			9.07062i			0.0275703i
$330$	493.644	−	215.948i	1.49589	−	0.654388i
$331$	81.9538			0.247595			0.123797	−	0.992308i	$-0.460493\pi$
$331$	81.9538			0.247595			0.123797	+	0.992308i	$0.460493\pi$
$332$	−178.384	−	57.9604i	−0.537300	−	0.174579i
$333$	−68.4352	+	49.7211i	−0.205511	+	0.149313i
$334$	−215.060	−	156.250i	−0.643892	−	0.467815i
$335$	72.7455	+	223.888i	0.217151	+	0.668321i
$336$	−214.218	+	69.6038i	−0.637555	+	0.207154i
$337$	−110.309	+	151.827i	−0.327326	+	0.450526i	−0.940686	−	0.339277i	$-0.889817\pi$
$337$	−110.309	+	151.827i	−0.327326	+	0.450526i	0.613360	+	0.789803i	$0.289817\pi$
$338$	−206.146	−	283.736i	−0.609899	−	0.839455i
$339$	−69.6218	+	214.274i	−0.205374	+	0.632077i
$340$		−	924.211i		−	2.71827i
$341$	33.5778	+	19.6785i	0.0984687	+	0.0577081i
$342$	−28.2055			−0.0824721
$343$	354.420	+	115.158i	1.03330	+	0.335738i
$344$	−108.487	+	78.8207i	−0.315370	+	0.229130i
$345$	−71.7965	−	52.1632i	−0.208106	−	0.151198i
$346$	102.732	+	316.176i	0.296913	+	0.913804i
$347$	−338.135	+	109.867i	−0.974453	+	0.316619i	−0.752612	−	0.658464i	$-0.771207\pi$
$347$	−338.135	+	109.867i	−0.974453	+	0.316619i	−0.221841	+	0.975083i	$0.571207\pi$
$348$	141.682	−	195.009i	0.407133	−	0.560371i
$349$	117.193	+	161.302i	0.335796	+	0.462183i	0.943208	−	0.332204i	$-0.107792\pi$
$349$	117.193	+	161.302i	0.335796	+	0.462183i	−0.607412	+	0.794387i	$0.707792\pi$
$350$	292.512	−	900.260i	0.835750	−	2.57217i
$351$		−	486.467i		−	1.38595i
$352$	−427.010	−	93.6708i	−1.21310	−	0.266110i
$353$	370.540			1.04969			0.524845	−	0.851198i	$-0.324123\pi$
$353$	370.540			1.04969			0.524845	+	0.851198i	$0.324123\pi$
$354$	−223.535	−	72.6310i	−0.631455	−	0.205172i
$355$	641.876	−	466.350i	1.80810	−	1.31366i
$356$	117.219	+	85.1645i	0.329267	+	0.239226i
$357$	121.955	+	375.338i	0.341610	+	1.05137i
$358$	−365.037	+	118.608i	−1.01966	+	0.331307i
$359$	−227.986	+	313.796i	−0.635058	+	0.874083i	−0.998340	−	0.0575965i	$-0.981656\pi$
$359$	−227.986	+	313.796i	−0.635058	+	0.874083i	0.363282	+	0.931679i	$0.381656\pi$
$360$	−71.2258	−	98.0339i	−0.197849	−	0.272316i
$361$	110.145	−	338.993i	0.305112	−	0.939039i
$362$		−	868.152i		−	2.39821i
$363$	−237.675	+	47.2965i	−0.654751	+	0.130293i
$364$	−309.271			−0.849645
$365$	695.323	+	225.924i	1.90499	+	0.618970i
$366$	−260.550	+	189.300i	−0.711885	+	0.517214i
$367$	132.623	+	96.3562i	0.361370	+	0.262551i	0.753623	−	0.657306i	$-0.228304\pi$
$367$	132.623	+	96.3562i	0.361370	+	0.262551i	−0.392253	+	0.919857i	$0.628304\pi$
$368$	28.1374	+	86.5980i	0.0764603	+	0.235321i
$369$	16.8355	−	5.47020i	0.0456248	−	0.0148244i
$370$	243.752	−	335.495i	0.658788	−	0.906744i
$371$	118.978	+	163.759i	0.320696	+	0.441400i
$372$	6.58419	−	20.2641i	0.0176994	−	0.0544733i
$373$		−	484.414i		−	1.29870i	−0.760491	−	0.649348i	$-0.775042\pi$
$373$		−	484.414i		−	1.29870i	0.760491	−	0.649348i	$-0.224958\pi$
$374$	−207.548	+	946.134i	−0.554941	+	2.52977i
$375$	−654.499			−1.74533
$376$	−3.82843	−	1.24393i	−0.0101820	−	0.00330833i
$377$	−562.271	+	408.514i	−1.49144	+	1.08359i
$378$	−355.400	−	258.213i	−0.940212	−	0.683104i
$379$	25.1052	+	77.2660i	0.0662407	+	0.203868i	0.978698	−	0.205303i	$-0.0658180\pi$
$379$	25.1052	+	77.2660i	0.0662407	+	0.203868i	−0.912458	+	0.409171i	$0.865818\pi$
$380$	56.4337	−	18.3364i	0.148510	−	0.0482537i
$381$	−118.504	+	163.106i	−0.311034	+	0.428101i
$382$	−325.252	−	447.671i	−0.851445	−	1.17191i
$383$	−87.6290	+	269.694i	−0.228796	+	0.704163i	0.769088	+	0.639143i	$0.220711\pi$
$383$	−87.6290	+	269.694i	−0.228796	+	0.704163i	−0.997884	+	0.0650193i	$0.979289\pi$
$384$		−	163.285i		−	0.425220i
$385$	−304.406	+	519.414i	−0.790664	+	1.34913i
$386$	689.386			1.78597
$387$	−242.033	−	78.6412i	−0.625408	−	0.203207i
$388$	−104.312	+	75.7874i	−0.268847	+	0.195328i
$389$	−400.135	−	290.715i	−1.02862	−	0.747339i	−0.0605915	−	0.998163i	$-0.519299\pi$
$389$	−400.135	−	290.715i	−1.02862	−	0.747339i	−0.968033	+	0.250823i	$0.919299\pi$
$390$	262.824	+	808.889i	0.673908	+	2.07408i
$391$	151.731	−	49.3003i	0.388058	−	0.126088i
$392$	−21.4957	+	29.5863i	−0.0548361	+	0.0754754i
$393$	−26.1665	−	36.0151i	−0.0665813	−	0.0916414i
$394$	152.615	−	469.700i	0.387347	−	1.19213i
$395$			657.261i			1.66395i
$396$	−66.1347	−	151.180i	−0.167007	−	0.381767i
$397$	−101.009			−0.254431			−0.127216	−	0.991875i	$-0.540604\pi$
$397$	−101.009			−0.254431			−0.127216	+	0.991875i	$0.540604\pi$
$398$	−315.378	−	102.472i	−0.792406	−	0.257468i
$399$	−20.4991	+	14.8935i	−0.0513761	+	0.0373269i
$400$	927.282	+	673.710i	2.31820	+	1.68427i
$401$	29.1144	+	89.6050i	0.0726046	+	0.223454i	0.980773	−	0.195150i	$-0.0625195\pi$
$401$	29.1144	+	89.6050i	0.0726046	+	0.223454i	−0.908169	+	0.418604i	$0.862519\pi$
$402$	−128.461	+	41.7396i	−0.319555	+	0.103830i
$403$	−36.1102	+	49.7014i	−0.0896035	+	0.123329i
$404$	242.891	+	334.311i	0.601215	+	0.827502i
$405$	−32.0075	+	98.5089i	−0.0790308	+	0.243232i
$406$			627.617i			1.54586i
$407$	−139.415	+	123.897i	−0.342542	+	0.304415i
$408$	−175.143			−0.429273
$409$	−115.172	−	37.4216i	−0.281594	−	0.0914954i	0.164815	−	0.986325i	$-0.447297\pi$
$409$	−115.172	−	37.4216i	−0.281594	−	0.0914954i	−0.446409	+	0.894829i	$0.647297\pi$
$410$	−70.2078	+	51.0090i	−0.171239	+	0.124412i
$411$	262.905	+	191.012i	0.639672	+	0.464749i
$412$	−57.0491	−	175.579i	−0.138469	−	0.426162i
$413$	249.767	−	81.1543i	0.604763	−	0.196500i
$414$	−37.2265	+	51.2379i	−0.0899191	+	0.123763i
$415$	−338.767	−	466.273i	−0.816306	−	1.12355i
$416$	213.242	−	656.291i	0.512600	−	1.57762i
$417$		−	262.934i		−	0.630536i
$418$	−61.8901	+	6.09818i	−0.148062	+	0.0145889i
$419$	−445.868			−1.06412			−0.532062	−	0.846705i	$-0.678583\pi$
$419$	−445.868			−1.06412			−0.532062	+	0.846705i	$0.678583\pi$
$420$	313.464	+	101.851i	0.746343	+	0.242502i
$421$	230.597	−	167.538i	0.547736	−	0.397953i	−0.279214	−	0.960229i	$-0.590074\pi$
$421$	230.597	−	167.538i	0.547736	−	0.397953i	0.826950	+	0.562276i	$0.190074\pi$
$422$	457.884	+	332.672i	1.08503	+	0.788323i
$423$	−2.36071	−	7.26553i	−0.00558088	−	0.0171762i
$424$	−85.4345	+	27.7593i	−0.201496	+	0.0654701i
$425$	1180.42	−	1624.71i	2.77747	−	3.82286i
$426$	267.580	+	368.293i	0.628123	+	0.864537i
$427$	111.200	−	342.239i	0.260422	−	0.801495i
$428$			620.696i			1.45022i
$429$	−37.5097	−	380.683i	−0.0874351	−	0.887374i
$430$	1247.60			2.90139
$431$	157.011	+	51.0160i	0.364295	+	0.118367i	0.485444	−	0.874268i	$-0.338658\pi$
$431$	157.011	+	51.0160i	0.364295	+	0.118367i	−0.121149	+	0.992634i	$0.538658\pi$
$432$	430.338	−	312.659i	0.996153	−	0.723748i
$433$	−571.219	−	415.015i	−1.31921	−	0.958464i	−0.999942	−	0.0108005i	$-0.996562\pi$
$433$	−571.219	−	415.015i	−1.31921	−	0.958464i	−0.319271	−	0.947663i	$-0.603438\pi$
$434$	17.1435	+	52.7623i	0.0395012	+	0.121572i
$435$	704.429	−	228.883i	1.61938	−	0.526168i
$436$	−86.2705	+	118.741i	−0.197868	+	0.272342i
$437$	6.02069	+	8.28677i	0.0137773	+	0.0189629i
$438$	−129.630	+	398.959i	−0.295958	+	0.910866i
$439$			569.746i			1.29783i	0.760862	+	0.648914i	$0.224776\pi$
$439$			569.746i			1.29783i	−0.760862	+	0.648914i	$0.775224\pi$
$440$	−177.483	−	199.712i	−0.403371	−	0.453891i
$441$	−69.4033			−0.157377
$442$	−1454.15	−	472.484i	−3.28994	−	1.06897i
$443$	164.278	−	119.355i	0.370830	−	0.269424i	−0.386725	−	0.922195i	$-0.626394\pi$
$443$	164.278	−	119.355i	0.370830	−	0.269424i	0.757555	+	0.652771i	$0.226394\pi$
$444$	82.6077	+	60.0180i	0.186053	+	0.135176i
$445$	137.580	+	423.428i	0.309169	+	0.951524i
$446$	−470.451	+	152.859i	−1.05482	+	0.342732i
$447$	−170.176	+	234.228i	−0.380708	+	0.523999i
$448$	−101.859	−	140.197i	−0.227363	−	0.312939i
$449$	211.390	−	650.591i	0.470801	−	1.44898i	−0.380737	−	0.924683i	$-0.624330\pi$
$449$	211.390	−	650.591i	0.470801	−	1.44898i	0.851538	−	0.524293i	$-0.175670\pi$
$450$			797.235i			1.77163i
$451$	35.7589	−	15.6430i	0.0792879	−	0.0346851i
$452$	−338.260			−0.748362
$453$	361.138	+	117.341i	0.797213	+	0.259030i
$454$	−512.566	+	372.401i	−1.12900	+	0.820267i
$455$	−768.830	−	558.587i	−1.68974	−	1.22766i
$456$	−3.47486	−	10.6945i	−0.00762030	−	0.0234529i
$457$	100.819	−	32.7582i	0.220611	−	0.0716809i	−0.196626	−	0.980479i	$-0.562998\pi$
$457$	100.819	−	32.7582i	0.220611	−	0.0716809i	0.417237	+	0.908798i	$0.362998\pi$
$458$	−463.550	+	638.022i	−1.01212	+	1.39306i
$459$	−547.818	−	754.007i	−1.19350	−	1.64272i
$460$	41.1732	−	126.718i	0.0895070	−	0.275474i
$461$			72.7431i			0.157794i	0.996883	+	0.0788971i	$0.0251398\pi$
$461$			72.7431i			0.157794i	−0.996883	+	0.0788971i	$0.974860\pi$
$462$	−298.027	−	174.660i	−0.645080	−	0.378053i
$463$	−155.196			−0.335196			−0.167598	−	0.985855i	$-0.553601\pi$
$463$	−155.196			−0.335196			−0.167598	+	0.985855i	$0.553601\pi$
$464$	−722.759	−	234.839i	−1.55767	−	0.506118i
$465$	52.9678	−	38.4833i	0.113909	−	0.0827598i
$466$	422.925	+	307.273i	0.907565	+	0.659385i
$467$	182.292	+	561.037i	0.390347	+	1.20136i	0.932527	+	0.361101i	$0.117599\pi$
$467$	182.292	+	561.037i	0.390347	+	1.20136i	−0.542180	+	0.840262i	$0.682401\pi$
$468$	247.725	−	80.4906i	0.529326	−	0.171989i
$469$	88.7103	−	122.099i	0.189148	−	0.260339i
$470$	22.0134	+	30.2988i	0.0468369	+	0.0644655i
$471$	124.886	−	384.359i	0.265151	−	0.816050i
$472$			116.549i			0.246925i
$473$	−548.085	−	120.230i	−1.15874	−	0.254187i
$474$	−377.120			−0.795613
$475$	122.627	+	39.8440i	0.258162	+	0.0838820i
$476$	−479.359	+	348.274i	−1.00706	+	0.731669i
$477$	−137.921	−	100.206i	−0.289143	−	0.210074i
$478$	276.954	+	852.375i	0.579401	+	1.78321i
$479$	−166.294	+	54.0321i	−0.347168	+	0.112802i	−0.477410	−	0.878680i	$-0.658425\pi$
$479$	−166.294	+	54.0321i	−0.347168	+	0.112802i	0.130242	+	0.991482i	$0.458425\pi$
$480$	−432.266	+	594.963i	−0.900555	+	1.23951i
$481$	−173.050	−	238.183i	−0.359772	−	0.495184i
$482$	−30.4766	+	93.7975i	−0.0632296	+	0.194601i
$483$			56.8954i			0.117796i
$484$	−177.803	−	317.429i	−0.367361	−	0.655845i
$485$	−396.198			−0.816903
$486$	578.262	+	187.889i	1.18984	+	0.386603i
$487$	−389.893	+	283.274i	−0.800602	+	0.581672i	−0.911091	−	0.412206i	$-0.864759\pi$
$487$	−389.893	+	283.274i	−0.800602	+	0.581672i	0.110488	+	0.993877i	$0.464759\pi$
$488$	129.199	+	93.8684i	0.264752	+	0.192353i
$489$	−95.5277	−	294.004i	−0.195353	−	0.601235i
$490$	323.588	−	105.140i	0.660384	−	0.214572i
$491$	123.243	−	169.630i	0.251005	−	0.345478i	−0.664858	−	0.746970i	$-0.731508\pi$
$491$	123.243	−	169.630i	0.251005	−	0.345478i	0.915863	+	0.401491i	$0.131508\pi$
$492$	−12.5597	−	17.2870i	−0.0255279	−	0.0351362i
$493$	−411.467	+	1266.36i	−0.834618	+	2.56869i
$494$		−	98.1669i		−	0.198718i
$495$	108.645	−	495.273i	0.219485	−	1.00055i
$496$	−67.1754			−0.135434
$497$	−483.762	−	157.184i	−0.973364	−	0.316265i
$498$	267.536	−	194.376i	0.537221	−	0.390314i
$499$	658.357	+	478.324i	1.31935	+	0.958565i	0.999940	+	0.0109494i	$0.00348536\pi$
$499$	658.357	+	478.324i	1.31935	+	0.958565i	0.319412	+	0.947616i	$0.396515\pi$
$500$	−303.653	−	934.549i	−0.607307	−	1.86910i
$501$	191.283	−	62.1516i	0.381802	−	0.124055i
$502$	182.844	−	251.663i	0.364231	−	0.501321i
$503$	268.029	+	368.910i	0.532860	+	0.733419i	0.987563	−	0.157224i	$-0.0502545\pi$
$503$	268.029	+	368.910i	0.532860	+	0.733419i	−0.454703	+	0.890643i	$0.650255\pi$
$504$	−24.0067	+	73.8850i	−0.0476323	+	0.146597i
$505$			1269.77i			2.51440i
$506$	−70.6066	+	120.478i	−0.139539	+	0.238098i
$507$	265.353			0.523379
$508$	−287.877	−	93.5368i	−0.566687	−	0.184128i
$509$	−2.17568	+	1.58073i	−0.00427442	+	0.00310555i	−0.589920	−	0.807461i	$-0.700841\pi$
$509$	−2.17568	+	1.58073i	−0.00427442	+	0.00310555i	0.585646	+	0.810567i	$0.300841\pi$
$510$	1318.27	+	957.780i	2.58484	+	1.87800i
$511$	−144.842	−	445.777i	−0.283448	−	0.872363i
$512$	527.747	−	171.475i	1.03076	−	0.334913i
$513$	35.1720	−	48.4101i	0.0685614	−	0.0943667i
$514$	−184.825	−	254.389i	−0.359581	−	0.494921i
$515$	175.300	−	539.518i	0.340389	−	1.04761i
$516$			307.191i			0.595332i
$517$	−6.75087	−	15.4321i	−0.0130578	−	0.0298492i
$518$	−265.865			−0.513252
$519$	−239.220	−	77.7272i	−0.460925	−	0.149763i
$520$	341.199	−	247.896i	0.656152	−	0.476723i
$521$	413.253	+	300.246i	0.793192	+	0.576287i	0.908909	−	0.416995i	$-0.136917\pi$
$521$	413.253	+	300.246i	0.793192	+	0.576287i	−0.115717	+	0.993282i	$0.536917\pi$
$522$	−163.343	−	502.719i	−0.312918	−	0.963064i
$523$	383.148	−	124.492i	0.732596	−	0.238035i	0.0811201	−	0.996704i	$-0.474150\pi$
$523$	383.148	−	124.492i	0.732596	−	0.238035i	0.651476	+	0.758670i	$0.274150\pi$
$524$	39.2855	−	54.0718i	0.0749723	−	0.103190i
$525$	420.967	+	579.412i	0.801842	+	1.10364i
$526$	−230.362	+	708.980i	−0.437950	+	1.34787i
$527$			117.700i			0.223339i
$528$	312.652	−	277.852i	0.592144	−	0.526235i
$529$	23.0000			0.0434783
$530$	794.852	+	258.263i	1.49972	+	0.487289i
$531$	−178.942	+	130.009i	−0.336990	+	0.244837i
$532$	−30.7766	−	22.3605i	−0.0578508	−	0.0420311i
$533$	19.0386	+	58.5948i	0.0357197	+	0.109934i
$534$	−242.953	+	78.9402i	−0.454968	+	0.147828i
$535$	−1121.07	+	1543.01i	−2.09545	+	2.88414i
$536$	39.3688	+	54.1865i	0.0734492	+	0.101094i
$537$	89.7390	−	276.188i	0.167112	−	0.514317i
$538$		−	753.955i		−	1.40140i
$539$	−152.289	+	15.0054i	−0.282539	+	0.0278393i
$540$	−778.365			−1.44142
$541$	195.931	+	63.6617i	0.362164	+	0.117674i	0.484446	−	0.874821i	$-0.339021\pi$
$541$	195.931	+	63.6617i	0.362164	+	0.117674i	−0.122282	+	0.992495i	$0.539021\pi$
$542$	720.540	−	523.503i	1.32941	−	0.965872i
$543$	531.400	+	386.085i	0.978637	+	0.711021i
$544$	−408.542	−	1257.36i	−0.750996	−	2.31133i
$545$	−428.927	+	139.367i	−0.787022	+	0.255719i
$546$	320.504	−	441.136i	0.587003	−	0.807941i
$547$	145.337	+	200.039i	0.265699	+	0.365703i	0.920932	−	0.389724i	$-0.127430\pi$
$547$	145.337	+	200.039i	0.265699	+	0.365703i	−0.655233	+	0.755427i	$0.727430\pi$
$548$	−150.769	+	464.018i	−0.275125	+	0.846748i
$549$			303.073i			0.552045i
$550$	172.367	+	1749.34i	0.313394	+	3.18062i
$551$	−85.4896			−0.155154
$552$	−24.0138	−	7.80256i	−0.0435033	−	0.0141351i
$553$	340.900	−	247.678i	0.616456	−	0.447882i
$554$	1034.83	+	751.850i	1.86793	+	1.35713i
$555$	96.9570	+	298.403i	0.174697	+	0.537663i
$556$	375.439	−	121.988i	0.675250	−	0.219402i
$557$	196.099	−	269.907i	0.352063	−	0.484573i	−0.595853	−	0.803094i	$-0.703186\pi$
$557$	196.099	−	269.907i	0.352063	−	0.484573i	0.947916	+	0.318520i	$0.103186\pi$
$558$	−27.4638	−	37.8007i	−0.0492183	−	0.0677432i
$559$	273.705	−	842.376i	0.489632	−	1.50693i
$560$		−	1039.13i		−	1.85559i
$561$	−486.832	−	547.805i	−0.867793	−	0.976480i
$562$	99.3432			0.176767
$563$	−739.125	−	240.156i	−1.31283	−	0.426565i	−0.432805	−	0.901488i	$-0.642476\pi$
$563$	−739.125	−	240.156i	−1.31283	−	0.426565i	−0.880028	+	0.474922i	$0.842476\pi$
$564$	−7.46036	+	5.42027i	−0.0132276	+	0.00961040i
$565$	−840.894	−	610.945i	−1.48831	−	1.08132i
$566$	286.957	+	883.163i	0.506991	+	1.56036i
$567$	63.1549	−	20.5203i	0.111384	−	0.0361909i
$568$	132.685	−	182.625i	0.233600	−	0.321523i
$569$	306.913	+	422.430i	0.539391	+	0.742408i	0.988525	−	0.151056i	$-0.0482675\pi$
$569$	306.913	+	422.430i	0.539391	+	0.742408i	−0.449134	+	0.893464i	$0.648267\pi$
$570$	−32.3288	+	99.4979i	−0.0567173	+	0.174558i
$571$			46.7964i			0.0819552i	0.999160	+	0.0409776i	$0.0130472\pi$
$571$			46.7964i			0.0819552i	−0.999160	+	0.0409776i	$0.986953\pi$
$572$	526.169	−	230.177i	0.919877	−	0.402407i
$573$	418.667			0.730659
$574$	52.9134	+	17.1926i	0.0921836	+	0.0299523i
$575$	234.228	−	170.176i	0.407352	−	0.295959i
$576$	118.076	+	85.7873i	0.204993	+	0.148936i
$577$	235.385	+	724.441i	0.407946	+	1.25553i	0.918410	+	0.395630i	$0.129474\pi$
$577$	235.385	+	724.441i	0.407946	+	1.25553i	−0.510463	+	0.859899i	$0.670526\pi$
$578$	−2058.40	+	668.816i	−3.56125	+	1.15712i
$579$	−306.584	+	421.976i	−0.529506	+	0.728802i
$580$	653.637	+	899.654i	1.12696	+	1.55113i
$581$	−114.182	+	351.415i	−0.196526	+	0.604845i
$582$		−	227.329i		−	0.390599i
$583$	−324.299	−	190.057i	−0.556260	−	0.325999i
$584$	208.013			0.356186
$585$	761.207	+	247.331i	1.30121	+	0.422789i
$586$	237.044	−	172.222i	0.404511	−	0.293895i
$587$	284.714	+	206.857i	0.485032	+	0.352396i	0.803271	−	0.595614i	$-0.203091\pi$
$587$	284.714	+	206.857i	0.485032	+	0.352396i	−0.318239	+	0.948011i	$0.603091\pi$
$588$	25.8883	+	79.6759i	0.0440277	+	0.135503i
$589$	−7.18691	+	2.33517i	−0.0122019	+	0.00396463i
$590$	637.351	−	877.239i	1.08026	−	1.48685i
$591$	219.635	+	302.301i	0.371632	+	0.511508i
$592$	99.4798	−	306.167i	0.168040	−	0.517175i
$593$		−	348.217i		−	0.587213i	−0.955926	−	0.293606i	$-0.905145\pi$
$593$		−	348.217i		−	0.587213i	0.955926	−	0.293606i	$-0.0948555\pi$
$594$	796.828	+	174.796i	1.34146	+	0.294269i
$595$	−1820.69			−3.05999
$596$	−413.403	−	134.323i	−0.693629	−	0.225374i
$597$	202.978	−	147.473i	0.339997	−	0.247023i
$598$	−178.329	−	129.564i	−0.298210	−	0.216662i
$599$	−78.5834	−	241.855i	−0.131191	−	0.403765i	0.863787	−	0.503857i	$-0.168086\pi$
$599$	−78.5834	−	241.855i	−0.131191	−	0.403765i	−0.994978	+	0.100092i	$0.968086\pi$
$600$	−302.283	+	98.2178i	−0.503805	+	0.163696i
$601$	416.645	−	573.463i	0.693254	−	0.954182i	−0.306743	−	0.951792i	$-0.599239\pi$
$601$	416.645	−	573.463i	0.693254	−	0.954182i	0.999997	−	0.00238962i	$-0.000760639\pi$
$602$	−470.137	−	647.089i	−0.780959	−	1.07490i
$603$	−39.2791	+	120.889i	−0.0651395	+	0.200479i
$604$			570.103i			0.943879i
$605$	131.315	−	1110.25i	0.217049	−	1.83512i
$606$	−728.565			−1.20225
$607$	922.291	+	299.671i	1.51943	+	0.493691i	0.945613	−	0.325295i	$-0.105464\pi$
$607$	922.291	+	299.671i	1.51943	+	0.493691i	0.573813	+	0.818986i	$0.305464\pi$
$608$	68.6709	−	49.8923i	0.112945	−	0.0820597i
$609$	−384.167	−	279.114i	−0.630816	−	0.458315i
$610$	−459.130	−	1413.06i	−0.752673	−	2.31649i
$611$	25.2871	−	8.21628i	0.0413864	−	0.0134473i
$612$	293.323	−	403.724i	0.479286	−	0.659680i
$613$	−80.1540	−	110.323i	−0.130757	−	0.179971i	0.738618	−	0.674124i	$-0.235479\pi$
$613$	−80.1540	−	110.323i	−0.130757	−	0.179971i	−0.869375	+	0.494152i	$0.835479\pi$
$614$	256.667	−	789.941i	0.418025	−	1.28655i
$615$		−	65.6592i		−	0.106763i
$616$	−36.7025	+	167.313i	−0.0595821	+	0.271612i
$617$	326.540			0.529239			0.264619	−	0.964353i	$-0.414754\pi$
$617$	326.540			0.529239			0.264619	+	0.964353i	$0.414754\pi$
$618$	309.562	+	100.583i	0.500910	+	0.162756i
$619$	−724.871	+	526.650i	−1.17104	+	0.850808i	−0.991133	−	0.132877i	$-0.957579\pi$
$619$	−724.871	+	526.650i	−1.17104	+	0.850808i	−0.179904	+	0.983684i	$0.557579\pi$
$620$	79.5240	+	57.7776i	0.128265	+	0.0931897i
$621$	−41.5204	−	127.787i	−0.0668605	−	0.205775i
$622$	175.076	−	56.8856i	0.281472	−	0.0914559i
$623$	167.774	−	230.921i	0.269300	−	0.370659i
$624$	388.084	+	534.151i	0.621929	+	0.856012i
$625$	466.686	−	1436.31i	0.746697	−	2.29810i
$626$			137.116i			0.219035i
$627$	23.7910	−	40.5952i	0.0379442	−	0.0647451i
$628$	606.761			0.966181
$629$	−536.444	−	174.301i	−0.852852	−	0.277108i
$630$	584.737	−	424.837i	0.928154	−	0.674344i
$631$	−523.497	−	380.343i	−0.829630	−	0.602762i	0.0898244	−	0.995958i	$-0.471369\pi$
$631$	−523.497	−	380.343i	−0.829630	−	0.602762i	−0.919455	+	0.393196i	$0.871369\pi$
$632$	57.7870	+	177.850i	0.0914351	+	0.281408i
$633$	−407.260	+	132.327i	−0.643381	+	0.209047i
$634$	−538.154	+	740.705i	−0.848823	+	1.16830i
$635$	−546.705	−	752.474i	−0.860952	−	1.18500i
$636$	−63.5911	+	195.713i	−0.0999860	+	0.307725i
$637$		−	241.553i		−	0.379203i
$638$	−467.108	−	1067.78i	−0.732145	−	1.67364i
$639$	428.400			0.670423
$640$	716.427	+	232.781i	1.11942	+	0.363721i
$641$	751.861	−	546.259i	1.17295	−	0.852198i	0.181591	−	0.983374i	$-0.441875\pi$
$641$	751.861	−	546.259i	1.17295	−	0.852198i	0.991359	+	0.131176i	$0.0418754\pi$
$642$	−885.344	−	643.240i	−1.37904	−	1.00193i
$643$	−309.180	−	951.557i	−0.480839	−	1.47987i	−0.837918	−	0.545797i	$-0.816227\pi$
$643$	−309.180	−	951.557i	−0.480839	−	1.47987i	0.357078	−	0.934074i	$-0.383773\pi$
$644$	−81.2400	+	26.3965i	−0.126149	+	0.0409883i
$645$	−554.831	+	763.660i	−0.860204	+	1.18397i
$646$	−110.547	−	152.155i	−0.171126	−	0.235534i
$647$	−278.684	+	857.703i	−0.430733	+	1.32566i	0.466663	+	0.884435i	$0.345456\pi$
$647$	−278.684	+	857.703i	−0.430733	+	1.32566i	−0.897396	+	0.441226i	$0.854544\pi$
$648$			29.4699i			0.0454782i
$649$	−364.535	+	323.961i	−0.561688	+	0.499169i
$650$	−2774.71			−4.26879
$651$	−39.9201	−	12.9708i	−0.0613212	−	0.0199245i
$652$	375.484	−	272.805i	0.575896	−	0.418413i
$653$	816.817	+	593.452i	1.25087	+	0.908809i	0.998272	−	0.0587633i	$-0.0187157\pi$
$653$	816.817	+	593.452i	1.25087	+	0.908809i	0.252596	+	0.967572i	$0.418716\pi$
$654$	−79.9653	−	246.108i	−0.122271	−	0.376312i
$655$	195.323	−	63.4643i	0.298203	−	0.0968920i
$656$	−39.5977	+	54.5016i	−0.0603624	+	0.0830817i
$657$	232.036	+	319.370i	0.353175	+	0.486103i
$658$	7.41962	−	22.8352i	0.0112760	−	0.0347040i
$659$			741.747i			1.12556i	0.826605	+	0.562782i	$0.190269\pi$
$659$			741.747i			1.12556i	−0.826605	+	0.562782i	$0.809731\pi$
$660$	−609.107	+	60.0168i	−0.922889	+	0.0909345i
$661$	558.290			0.844615			0.422307	−	0.906453i	$-0.361220\pi$
$661$	558.290			0.844615			0.422307	+	0.906453i	$0.361220\pi$
$662$	−206.319	−	67.0370i	−0.311659	−	0.101264i
$663$	935.901	−	679.972i	1.41161	−	1.02560i
$664$	−132.663	−	96.3853i	−0.199794	−	0.145159i
$665$	−36.1227	−	111.174i	−0.0543198	−	0.167179i
$666$	212.957	−	69.1938i	0.319755	−	0.103895i
$667$	−112.832	+	155.300i	−0.169163	+	0.232833i
$668$	177.491	+	244.295i	0.265704	+	0.365711i
$669$	115.653	−	355.944i	0.172875	−	0.532054i
$670$		−	623.141i		−	0.930061i
$671$	65.5260	+	665.020i	0.0976543	+	0.991088i
$672$	471.481			0.701609
$673$	734.726	+	238.727i	1.09172	+	0.354720i	0.798910	−	0.601451i	$-0.205411\pi$
$673$	734.726	+	238.727i	1.09172	+	0.354720i	0.292807	+	0.956171i	$0.405411\pi$
$674$	401.895	−	291.994i	0.596283	−	0.433225i
$675$	−1368.32	−	994.146i	−2.02715	−	1.47281i
$676$	123.110	+	378.894i	0.182115	+	0.560494i
$677$	331.563	−	107.731i	0.489753	−	0.159131i	−0.0537214	−	0.998556i	$-0.517108\pi$
$677$	331.563	−	107.731i	0.489753	−	0.159131i	0.543475	+	0.839425i	$0.317108\pi$
$678$	350.546	−	482.485i	0.517029	−	0.711629i
$679$	149.301	+	205.495i	0.219884	+	0.302644i
$680$	249.688	−	768.459i	0.367188	−	1.13009i
$681$		−	479.358i		−	0.703903i
$682$	−68.4354	−	77.0066i	−0.100345	−	0.112913i
$683$	−440.602			−0.645098			−0.322549	−	0.946553i	$-0.604540\pi$
$683$	−440.602			−0.645098			−0.322549	+	0.946553i	$0.604540\pi$
$684$	30.4715	+	9.90080i	0.0445490	+	0.0144749i
$685$	−1212.89	+	881.213i	−1.77064	+	1.28644i
$686$	−798.055	−	579.821i	−1.16335	−	0.845220i
$687$	−184.386	−	567.482i	−0.268393	−	0.826030i
$688$	921.096	−	299.282i	1.33880	−	0.435003i
$689$	348.757	−	480.024i	0.506179	−	0.696696i
$690$	138.079	+	190.049i	0.200114	+	0.275433i
$691$	−307.466	+	946.283i	−0.444958	+	1.36944i	0.437571	+	0.899184i	$0.355839\pi$
$691$	−307.466	+	946.283i	−0.444958	+	1.36944i	−0.882530	+	0.470257i	$0.844161\pi$
$692$		−	377.640i		−	0.545722i
$693$	−297.824	+	130.285i	−0.429760	+	0.188002i
$694$	941.124			1.35609
$695$	1153.65	+	374.843i	1.65992	+	0.539342i
$696$	170.490	−	123.868i	0.244957	−	0.177971i
$697$	95.4937	+	69.3802i	0.137007	+	0.0995412i
$698$	−163.090	−	501.939i	−0.233653	−	0.719111i
$699$	−376.167	+	122.224i	−0.538150	+	0.174855i
$700$	−632.026	+	869.910i	−0.902895	+	1.24273i
$701$	144.784	+	199.278i	0.206539	+	0.284276i	0.899702	−	0.436504i	$-0.143784\pi$
$701$	144.784	+	199.278i	0.206539	+	0.284276i	−0.693163	+	0.720781i	$0.743784\pi$
$702$	−397.923	+	1224.68i	−0.566841	+	1.74456i
$703$		−	36.2142i		−	0.0515138i
$704$	277.637	+	162.711i	0.394371	+	0.231123i
$705$	−28.3358			−0.0401926
$706$	−932.834	−	303.096i	−1.32129	−	0.429315i
$707$	658.591	−	478.494i	0.931529	−	0.676795i
$708$	215.999	+	156.933i	0.305083	+	0.221656i
$709$	−386.875	−	1190.68i	−0.545664	−	1.67938i	−0.719407	−	0.694589i	$-0.755586\pi$
$709$	−386.875	−	1190.68i	−0.545664	−	1.67938i	0.173744	−	0.984791i	$-0.444414\pi$
$710$	−1997.39	+	648.991i	−2.81322	+	0.914072i
$711$	−208.599	+	287.112i	−0.293388	+	0.403815i
$712$	74.4564	+	102.480i	0.104574	+	0.143933i
$713$	−5.24347	+	16.1377i	−0.00735409	+	0.0226336i
$714$		−	1044.67i		−	1.46312i
$715$	1723.76	+	378.131i	2.41085	+	0.528855i
$716$	435.999			0.608937
$717$	−644.909	−	209.544i	−0.899455	−	0.292251i
$718$	830.634	−	603.491i	1.15687	−	0.840517i
$719$	−430.269	−	312.609i	−0.598427	−	0.434783i	0.246893	−	0.969043i	$-0.420590\pi$
$719$	−430.269	−	312.609i	−0.598427	−	0.434783i	−0.845320	+	0.534260i	$0.820590\pi$
$720$	270.444	+	832.342i	0.375617	+	1.15603i
$721$	−345.890	+	112.386i	−0.479736	+	0.155876i
$722$	−554.582	+	763.316i	−0.768119	+	1.05722i
$723$	−43.8603	−	60.3685i	−0.0606643	−	0.0834972i
$724$	−304.742	+	937.901i	−0.420915	+	1.29544i
$725$			2416.39i			3.33295i
$726$	637.033	+	75.3453i	0.877456	+	0.103781i
$727$	277.747			0.382045			0.191022	−	0.981586i	$-0.438820\pi$
$727$	277.747			0.382045			0.191022	+	0.981586i	$0.438820\pi$
$728$	−257.151	−	83.5535i	−0.353230	−	0.114771i
$729$	−453.796	+	329.702i	−0.622492	+	0.452267i
$730$	−1565.67	−	1137.53i	−2.14475	−	1.55826i
$731$	−524.380	−	1613.88i	−0.717346	−	2.20776i
$732$	347.932	−	113.050i	0.475317	−	0.154440i
$733$	62.3667	−	85.8404i	0.0850842	−	0.117108i	−0.764353	−	0.644798i	$-0.776942\pi$
$733$	62.3667	−	85.8404i	0.0850842	−	0.117108i	0.849437	+	0.527690i	$0.176942\pi$
$734$	−255.060	−	351.060i	−0.347493	−	0.478283i
$735$	−79.5494	+	244.828i	−0.108230	+	0.333099i
$736$		−	190.597i		−	0.258963i
$737$	−60.0517	+	273.753i	−0.0814813	+	0.371443i
$738$	−46.8580			−0.0634932
$739$	−1182.94	−	384.360i	−1.60073	−	0.520108i	−0.633440	−	0.773792i	$-0.718358\pi$
$739$	−1182.94	−	384.360i	−1.60073	−	0.520108i	−0.967287	+	0.253684i	$0.918358\pi$
$740$	−381.102	+	276.887i	−0.515003	+	0.374171i
$741$	60.0884	+	43.6568i	0.0810909	+	0.0589160i
$742$	−165.575	−	509.586i	−0.223146	−	0.686774i
$743$	156.053	−	50.7047i	0.210031	−	0.0682433i	−0.202112	−	0.979362i	$-0.564780\pi$
$743$	156.053	−	50.7047i	0.210031	−	0.0682433i	0.412143	+	0.911119i	$0.364780\pi$
$744$	10.9492	−	15.0703i	0.0147167	−	0.0202557i
$745$	−785.091	−	1080.58i	−1.05381	−	1.45045i
$746$	−396.243	+	1219.51i	−0.531157	+	1.63473i
$747$		−	311.199i		−	0.416599i
$748$	556.339	−	949.293i	0.743768	−	1.26911i
$749$	1222.77			1.63253
$750$	1647.70	+	535.370i	2.19693	+	0.713826i
$751$	−445.483	+	323.662i	−0.593186	+	0.430975i	−0.843454	−	0.537202i	$-0.819481\pi$
$751$	−445.483	+	323.662i	−0.593186	+	0.430975i	0.250268	+	0.968177i	$0.419481\pi$
$752$	23.5206	+	17.0888i	0.0312775	+	0.0227244i
$753$	72.7298	+	223.839i	0.0965868	+	0.297263i
$754$	1749.67	−	568.504i	2.32052	−	0.753984i
$755$	−1029.69	+	1417.24i	−1.36382	+	1.87714i
$756$	293.314	+	403.713i	0.387982	+	0.534011i
$757$	−269.221	+	828.576i	−0.355642	+	1.09455i	0.599995	+	0.800004i	$0.295169\pi$
$757$	−269.221	+	828.576i	−0.355642	+	1.09455i	−0.955637	+	0.294548i	$0.904831\pi$
$758$		−	215.053i		−	0.283711i
$759$	−42.3448	−	96.7974i	−0.0557902	−	0.127533i
$760$	51.8771			0.0682593
$761$	549.879	+	178.667i	0.722575	+	0.234779i	0.647139	−	0.762372i	$-0.275965\pi$
$761$	549.879	+	178.667i	0.722575	+	0.234779i	0.0754356	+	0.997151i	$0.475965\pi$
$762$	431.751	−	313.686i	0.566603	−	0.411661i
$763$	233.919	+	169.952i	0.306579	+	0.222742i
$764$	194.240	+	597.809i	0.254241	+	0.782472i
$765$	1458.37	−	473.853i	1.90636	−	0.619415i
$766$	441.211	−	607.275i	0.575994	−	0.792788i
$767$	−452.485	−	622.792i	−0.589941	−	0.811984i
$768$	−205.986	+	633.960i	−0.268211	+	0.825469i
$769$			970.786i			1.26240i	0.775620	+	0.631201i	$0.217438\pi$
$769$			970.786i			1.26240i	−0.775620	+	0.631201i	$0.782562\pi$
$770$	1191.21	−	1058.62i	1.54703	−	1.37484i
$771$	237.908			0.308571
$772$	−744.772	−	241.991i	−0.964731	−	0.313460i
$773$	−653.398	+	474.722i	−0.845276	+	0.614129i	−0.923839	−	0.382780i	$-0.874967\pi$
$773$	−653.398	+	474.722i	−0.845276	+	0.614129i	0.0785636	+	0.996909i	$0.474967\pi$
$774$	544.989	+	395.958i	0.704121	+	0.511574i
$775$	66.0042	+	203.140i	0.0851667	+	0.262116i
$776$	−107.208	+	34.8341i	−0.138155	+	0.0448893i
$777$	118.235	−	162.737i	0.152169	−	0.209443i
$778$	769.538	+	1059.18i	0.989123	+	1.36141i
$779$	−2.34186	+	7.20749i	−0.00300623	+	0.00925223i
$780$		−	966.134i		−	1.23863i
$781$	940.021	−	92.6225i	1.20361	−	0.118595i
$782$	−422.308			−0.540036
$783$	1066.52	+	346.535i	1.36210	+	0.442573i
$784$	213.682	−	155.249i	0.272554	−	0.198022i
$785$	1508.38	+	1095.90i	1.92150	+	1.39605i
$786$	36.4143	+	112.072i	0.0463286	+	0.142585i
$787$	856.413	−	278.265i	1.08820	−	0.353577i	0.290649	−	0.956830i	$-0.406129\pi$
$787$	856.413	−	278.265i	1.08820	−	0.353577i	0.797550	+	0.603252i	$0.206129\pi$
$788$	−329.752	+	453.865i	−0.418468	+	0.575971i
$789$	−331.523	−	456.303i	−0.420182	−	0.578331i
$790$	537.629	−	1654.65i	0.680544	−	2.09450i
$791$			666.370i			0.842440i
$792$	−14.1463	−	143.570i	−0.0178614	−	0.181275i
$793$	−1054.82			−1.33017
$794$	254.290	+	82.6240i	0.320265	+	0.104060i
$795$	−511.570	+	371.677i	−0.643484	+	0.467519i
$796$	304.745	+	221.410i	0.382846	+	0.278154i
$797$	−310.640	−	956.052i	−0.389762	−	1.19956i	−0.932967	−	0.359963i	$-0.882789\pi$
$797$	−310.640	−	956.052i	−0.389762	−	1.19956i	0.543205	−	0.839600i	$-0.317211\pi$
$798$	63.7890	−	20.7263i	0.0799361	−	0.0259728i
$799$	29.9417	−	41.2111i	0.0374739	−	0.0515784i
$800$	−1410.22	−	1941.00i	−1.76277	−	2.42625i
$801$	−74.2868	+	228.631i	−0.0927426	+	0.285432i
$802$		−	249.396i		−	0.310967i
$803$	578.196	+	650.612i	0.720044	+	0.810227i
$804$	153.434			0.190838
$805$	−249.634	−	81.1110i	−0.310104	−	0.100759i
$806$	131.562	−	95.5856i	0.163229	−	0.118593i
$807$	461.499	+	335.299i	0.571870	+	0.415488i
$808$	111.640	+	343.592i	0.138168	+	0.425237i
$809$	−587.785	+	190.983i	−0.726557	+	0.236073i	−0.648864	−	0.760905i	$-0.724756\pi$
$809$	−587.785	+	190.983i	−0.726557	+	0.236073i	−0.0776934	+	0.996977i	$0.524756\pi$
$810$	161.157	−	221.814i	0.198960	−	0.273845i
$811$	−362.579	−	499.047i	−0.447076	−	0.615347i	0.524690	−	0.851293i	$-0.324181\pi$
$811$	−362.579	−	499.047i	−0.447076	−	0.615347i	−0.971766	+	0.235946i	$0.924181\pi$
$812$	220.309	−	678.041i	0.271316	−	0.835026i
$813$			673.858i			0.828853i
$814$	452.322	−	197.871i	0.555678	−	0.243085i
$815$	1426.16			1.74989
$816$	1203.03	+	390.889i	1.47430	+	0.479030i
$817$	88.1418	−	64.0388i	0.107885	−	0.0783829i
$818$	259.335	+	188.418i	0.317035	+	0.230339i
$819$	−158.566	−	488.017i	−0.193610	−	0.595869i
$820$	93.7538	−	30.4624i	0.114334	−	0.0371493i
$821$	−401.585	+	552.734i	−0.489141	+	0.673245i	−0.980229	−	0.197865i	$-0.936599\pi$
$821$	−401.585	+	552.734i	−0.489141	+	0.673245i	0.491088	+	0.871110i	$0.336599\pi$
$822$	−505.618	−	695.924i	−0.615108	−	0.846623i
$823$	−263.903	+	812.210i	−0.320660	+	0.986890i	0.652702	+	0.757615i	$0.273635\pi$
$823$	−263.903	+	812.210i	−0.320660	+	0.986890i	−0.973362	+	0.229275i	$0.926365\pi$
$824$		−	161.402i		−	0.195876i
$825$	−1147.43	−	672.459i	−1.39083	−	0.815102i
$826$	−695.171			−0.841612
$827$	−543.155	−	176.482i	−0.656777	−	0.213400i	−0.0383772	−	0.999263i	$-0.512219\pi$
$827$	−543.155	−	176.482i	−0.656777	−	0.213400i	−0.618400	+	0.785863i	$0.712219\pi$
$828$	58.2031	−	42.2870i	0.0702935	−	0.0510712i
$829$	−657.886	−	477.982i	−0.793590	−	0.576577i	0.115437	−	0.993315i	$-0.463173\pi$
$829$	−657.886	−	477.982i	−0.793590	−	0.576577i	−0.909027	+	0.416738i	$0.863173\pi$
$830$	471.441	+	1450.95i	0.568001	+	1.74813i
$831$	−920.421	+	299.063i	−1.10761	+	0.359883i
$832$	−298.576	+	410.955i	−0.358865	+	0.493936i
$833$	−272.016	−	374.398i	−0.326550	−	0.449457i
$834$	−215.076	+	661.935i	−0.257884	+	0.793687i
$835$			927.877i			1.11123i
$836$	69.0030	+	15.1368i	0.0825395	+	0.0181062i
$837$	99.1259			0.118430
$838$	1122.47	+	364.713i	1.33947	+	0.435219i
$839$	150.463	−	109.318i	0.179336	−	0.130295i	−0.494496	−	0.869180i	$-0.664647\pi$
$839$	150.463	−	109.318i	0.179336	−	0.130295i	0.673832	+	0.738885i	$0.264647\pi$
$840$	233.122	+	169.373i	0.277526	+	0.201634i
$841$	−235.204	−	723.883i	−0.279672	−	0.860741i
$842$	−717.570	+	233.153i	−0.852221	+	0.276903i
$843$	−44.1799	+	60.8084i	−0.0524079	+	0.0721333i
$844$	−377.895	−	520.128i	−0.447743	−	0.616266i
$845$	−378.292	+	1164.26i	−0.447683	+	1.37783i
$846$			20.2220i			0.0239030i
$847$	−625.333	+	350.270i	−0.738292	+	0.413542i
$848$	648.789			0.765082
$849$	−668.203	−	217.112i	−0.787048	−	0.255727i
$850$	−4300.71	+	3124.65i	−5.05965	+	3.67605i
$851$	−65.7865	−	47.7967i	−0.0773049	−	0.0561653i
$852$	−159.799	−	491.809i	−0.187557	−	0.577241i
$853$	−92.9049	+	30.1866i	−0.108915	+	0.0353888i	−0.362968	−	0.931802i	$-0.618236\pi$
$853$	−92.9049	+	30.1866i	−0.108915	+	0.0353888i	0.254052	+	0.967190i	$0.418236\pi$
$854$	−559.891	+	770.624i	−0.655611	+	0.902371i
$855$	57.8682	+	79.6488i	0.0676821	+	0.0931565i
$856$	−167.689	+	516.093i	−0.195898	+	0.602913i
$857$		−	234.944i		−	0.274147i	−0.990561	−	0.137073i	$-0.956230\pi$
$857$		−	234.944i		−	0.274147i	0.990561	−	0.137073i	$-0.0437696\pi$
$858$	−216.963	+	989.051i	−0.252870	+	1.15274i
$859$	1634.64			1.90295			0.951477	−	0.307720i	$-0.0995659\pi$
$859$	1634.64			1.90295			0.951477	+	0.307720i	$0.0995659\pi$
$860$	−1347.83	−	437.937i	−1.56725	−	0.509229i
$861$	−34.0553	+	24.7426i	−0.0395532	+	0.0287371i
$862$	−353.545	−	256.865i	−0.410145	−	0.297988i
$863$	345.191	+	1062.39i	0.399989	+	1.23104i	0.925007	+	0.379949i	$0.124059\pi$
$863$	345.191	+	1062.39i	0.399989	+	1.23104i	−0.525018	+	0.851091i	$0.675941\pi$
$864$	−1058.94	+	344.071i	−1.22563	+	0.398231i
$865$	682.072	−	938.791i	0.788522	−	1.08531i
$866$	1098.57	+	1512.05i	1.26855	+	1.74601i
$867$	506.028	−	1557.39i	0.583654	−	1.79630i
$868$		−	63.0191i		−	0.0726027i
$869$	−395.645	+	675.099i	−0.455288	+	0.776868i
$870$	−1960.62			−2.25359
$871$	−420.744	−	136.708i	−0.483058	−	0.156955i
$872$	−103.811	+	75.4233i	−0.119050	+	0.0864946i
$873$	−173.072	−	125.744i	−0.198249	−	0.144037i
$874$	−8.37862	−	25.7867i	−0.00958652	−	0.0295043i
$875$	−1841.06	+	598.196i	−2.10407	+	0.683652i
$876$	280.089	−	385.509i	0.319736	−	0.440079i
$877$	263.765	+	363.041i	0.300758	+	0.413958i	0.932471	−	0.361244i	$-0.117648\pi$
$877$	263.765	+	363.041i	0.300758	+	0.413958i	−0.631713	+	0.775202i	$0.717648\pi$
$878$	466.044	−	1434.33i	0.530801	−	1.63364i
$879$			221.686i			0.252203i
$880$	773.382	+	1767.90i	0.878843	+	2.00898i
$881$	−293.246			−0.332856			−0.166428	−	0.986054i	$-0.553223\pi$
$881$	−293.246			−0.332856			−0.166428	+	0.986054i	$0.553223\pi$
$882$	174.722	+	56.7708i	0.198098	+	0.0643660i
$883$	1178.66	−	856.343i	1.33483	−	0.969811i	0.335213	−	0.942142i	$-0.391192\pi$
$883$	1178.66	−	856.343i	1.33483	−	0.969811i	0.999617	−	0.0276688i	$-0.00880838\pi$
$884$	1405.13	+	1020.89i	1.58951	+	1.15485i
$885$	253.519	+	780.251i	0.286462	+	0.881640i
$886$	−511.199	+	166.098i	−0.576974	+	0.187470i
$887$	6.87029	−	9.45614i	0.00774553	−	0.0106608i	−0.805127	−	0.593103i	$-0.797903\pi$
$887$	6.87029	−	9.45614i	0.00774553	−	0.0106608i	0.812872	+	0.582442i	$0.197903\pi$
$888$	52.4717	+	72.2211i	0.0590897	+	0.0813300i
$889$	−184.267	+	567.116i	−0.207275	+	0.637926i
$890$		−	1178.52i		−	1.32418i
$891$	−92.1745	+	81.9150i	−0.103451	+	0.0919361i
$892$	561.904			0.629938
$893$	3.11046	+	1.01065i	0.00348315	+	0.00113175i
$894$	620.013	−	450.466i	0.693527	−	0.503877i
$895$	1083.87	+	787.477i	1.21103	+	0.879863i
$896$	−149.238	−	459.308i	−0.166560	−	0.512620i
$897$	158.613	−	51.5366i	0.176826	−	0.0574544i
$898$	−1064.35	+	1464.95i	−1.18524	+	1.63134i
$899$	−83.2417	−	114.572i	−0.0925936	−	0.127444i
$900$	279.849	−	861.286i	0.310943	−	0.956984i
$901$		−	1136.76i		−	1.26167i
$902$	−102.819	+	10.1310i	−0.113989	+	0.0112317i
$903$	605.165			0.670172
$904$	−281.255	−	91.3852i	−0.311122	−	0.101090i
$905$	−2451.56	+	1781.16i	−2.70890	+	1.96813i
$906$	−813.180	−	590.810i	−0.897549	−	0.652108i
$907$	−426.743	−	1313.38i	−0.470499	−	1.44805i	−0.851932	−	0.523652i	$-0.824569\pi$
$907$	−426.743	−	1313.38i	−0.470499	−	1.44805i	0.381433	−	0.924396i	$-0.375431\pi$
$908$	684.468	−	222.397i	0.753819	−	0.244931i
$909$	−402.996	+	554.677i	−0.443340	+	0.610206i
$910$	1478.61	+	2035.13i	1.62485	+	2.23641i
$911$	323.623	−	996.008i	0.355239	−	1.09331i	−0.600632	−	0.799526i	$-0.705084\pi$
$911$	323.623	−	996.008i	0.355239	−	1.09331i	0.955871	−	0.293787i	$-0.0949157\pi$
$912$			81.2141i			0.0890506i
$913$	−67.2830	−	682.851i	−0.0736944	−	0.747920i
$914$	−280.608			−0.307011
$915$	1069.12	+	347.379i	1.16844	+	0.379649i
$916$	724.754	−	526.565i	0.791216	−	0.574852i
$917$	−106.521	−	77.3922i	−0.116163	−	0.0843972i
$918$	762.364	+	2346.32i	0.830462	+	2.55590i
$919$	1597.90	−	519.190i	1.73874	−	0.564951i	0.744075	−	0.668096i	$-0.232890\pi$
$919$	1597.90	−	519.190i	1.73874	−	0.564951i	0.994666	+	0.103144i	$0.0328903\pi$
$920$	68.4690	−	94.2396i	0.0744229	−	0.102434i
$921$	369.381	+	508.410i	0.401065	+	0.552019i
$922$	59.5027	−	183.131i	0.0645366	−	0.198623i
$923$			1491.01i			1.61540i
$924$	260.661	+	293.308i	0.282101	+	0.317433i
$925$	−1023.60			−1.10660
$926$	390.705	+	126.948i	0.421928	+	0.137093i
$927$	247.807	−	180.042i	0.267321	−	0.194220i
$928$	1286.94	+	935.017i	1.38679	+	1.00756i
$929$	−53.5145	−	164.701i	−0.0576044	−	0.177288i	0.918114	−	0.396316i	$-0.129711\pi$
$929$	−53.5145	−	164.701i	−0.0576044	−	0.177288i	−0.975719	+	0.219028i	$0.929711\pi$
$930$	−164.825	+	53.5549i	−0.177231	+	0.0575859i
$931$	17.4645	−	24.0378i	0.0187588	−	0.0258193i
$932$	−349.044	−	480.417i	−0.374510	−	0.515469i
$933$	−43.0398	+	132.463i	−0.0461305	+	0.141975i
$934$		−	1561.52i		−	1.67186i
$935$	3097.59	−	1355.06i	3.31293	−	1.44926i
$936$	227.723			0.243293
$937$	−393.775	−	127.945i	−0.420250	−	0.136548i	0.0912553	−	0.995828i	$-0.470912\pi$
$937$	−393.775	−	127.945i	−0.420250	−	0.136548i	−0.511506	+	0.859280i	$0.670912\pi$
$938$	−323.203	+	234.821i	−0.344566	+	0.250342i
$939$	−83.9292	−	60.9781i	−0.0893814	−	0.0649394i
$940$	−13.1463	−	40.4603i	−0.0139855	−	0.0430428i
$941$	963.305	−	312.997i	1.02370	−	0.332621i	0.251405	−	0.967882i	$-0.419107\pi$
$941$	963.305	−	312.997i	1.02370	−	0.332621i	0.772298	+	0.635261i	$0.219107\pi$
$942$	−628.800	+	865.469i	−0.667516	+	0.918757i
$943$	10.0022	+	13.7669i	0.0106068	+	0.0145990i
$944$	260.116	−	800.553i	0.275546	−	0.848044i
$945$			1533.38i			1.62262i
$946$	1281.46	+	751.004i	1.35460	+	0.793873i
$947$	−202.649			−0.213991			−0.106995	−	0.994260i	$-0.534123\pi$
$947$	−202.649			−0.213991			−0.106995	+	0.994260i	$0.534123\pi$
$948$	407.419	+	132.378i	0.429767	+	0.139640i
$949$	−1111.54	+	807.582i	−1.17128	+	0.850982i
$950$	−276.122	−	200.614i	−0.290654	−	0.211173i
$951$	−214.061	−	658.812i	−0.225091	−	0.692757i
$952$	−492.666	+	160.077i	−0.517506	+	0.168148i
$953$	−159.167	+	219.074i	−0.167017	+	0.229879i	−0.884319	−	0.466883i	$-0.845377\pi$
$953$	−159.167	+	219.074i	−0.167017	+	0.229879i	0.717302	+	0.696762i	$0.245377\pi$
$954$	265.249	+	365.084i	0.278039	+	0.382688i
$955$	−596.859	+	1836.94i	−0.624984	+	1.92350i
$956$		−	1018.07i		−	1.06493i
$957$	861.325	+	188.944i	0.900026	+	0.197434i
$958$	462.841			0.483133
$959$	914.114	+	297.013i	0.953195	+	0.309712i
$960$	437.962	−	318.198i	0.456211	−	0.331456i
$961$	767.338	+	557.504i	0.798478	+	0.580129i
$962$	240.824	+	741.179i	0.250336	+	0.770456i
$963$	−979.433	+	318.237i	−1.01706	+	0.330464i
$964$	65.8504	−	90.6352i	0.0683095	−	0.0940200i
$965$	−1414.39	−	1946.74i	−1.46569	−	2.01735i
$966$	46.5395	−	143.234i	0.0481776	−	0.148275i
$967$		−	742.893i		−	0.768245i	−0.923282	−	0.384123i	$-0.874504\pi$
$967$		−	742.893i		−	0.768245i	0.923282	−	0.384123i	$-0.125496\pi$
$968$	−62.0811	−	311.970i	−0.0641333	−	0.322283i
$969$	142.297			0.146850
$970$	997.427	+	324.084i	1.02828	+	0.334107i
$971$	95.6811	−	69.5164i	0.0985387	−	0.0715925i	−0.537425	−	0.843312i	$-0.680603\pi$
$971$	95.6811	−	69.5164i	0.0985387	−	0.0715925i	0.635964	+	0.771719i	$0.280603\pi$
$972$	−558.767	−	405.968i	−0.574863	−	0.417663i
$973$	−240.315	−	739.613i	−0.246983	−	0.760137i
$974$	1213.27	−	394.215i	1.24566	−	0.404738i
$975$	1233.97	−	1698.41i	1.26561	−	1.74196i
$976$	−677.948	−	933.115i	−0.694618	−	0.956060i
$977$	−238.820	+	735.013i	−0.244442	+	0.752317i	0.751285	+	0.659978i	$0.229434\pi$
$977$	−238.820	+	735.013i	−0.244442	+	0.752317i	−0.995728	+	0.0923389i	$0.970566\pi$
$978$			818.294i			0.836702i
$979$	−113.573	+	517.738i	−0.116009	+	0.528843i
$980$	−386.493			−0.394380
$981$	−231.600	−	75.2515i	−0.236086	−	0.0767090i
$982$	−449.019	+	326.232i	−0.457250	+	0.332211i
$983$	−248.204	−	180.330i	−0.252496	−	0.183449i	0.454336	−	0.890830i	$-0.349876\pi$
$983$	−248.204	−	180.330i	−0.252496	−	0.183449i	−0.706832	+	0.707381i	$0.749876\pi$
$984$	−5.77281	−	17.7669i	−0.00586668	−	0.0180558i
$985$	−1639.49	+	532.703i	−1.66446	+	0.540816i
$986$	2071.73	−	2851.50i	2.10115	−	2.89198i
$987$	10.6779	+	14.6969i	0.0108185	+	0.0148904i
$988$	−34.4590	+	106.054i	−0.0348775	+	0.107342i
$989$		−	244.638i		−	0.247359i
$990$	−678.640	+	1157.98i	−0.685495	+	1.16968i
$991$	−1135.22			−1.14553			−0.572765	−	0.819719i	$-0.694129\pi$
$991$	−1135.22			−1.14553			−0.572765	+	0.819719i	$0.694129\pi$
$992$	133.730	+	43.4516i	0.134809	+	0.0438020i
$993$	132.788	−	96.4758i	0.133724	−	0.0971559i
$994$	1089.30	+	791.419i	1.09587	+	0.796196i
$995$	357.681	+	1100.83i	0.359478	+	1.10636i
$996$	−357.261	+	116.081i	−0.358696	+	0.116547i
$997$	−205.767	+	283.214i	−0.206386	+	0.284066i	−0.899645	−	0.436623i	$-0.856174\pi$
$997$	−205.767	+	283.214i	−0.206386	+	0.284066i	0.693259	+	0.720689i	$0.256174\pi$
$998$	−1266.15	−	1742.70i	−1.26869	−	1.74620i
$999$	−146.795	+	451.790i	−0.146942	+	0.452242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.g.a.24.10	✓	176
11.6	odd	10	inner	253.3.g.a.116.10	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.g.a.24.10	✓	176	1.1	even	1	trivial
253.3.g.a.116.10	yes	176	11.6	odd	10	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:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.51750 - 0.817984i) q^{2} +(1.62027 - 1.17720i) q^{3} +(2.43262 + 1.76740i) q^{4} +(2.85518 + 8.78734i) q^{5} +(-5.04196 + 1.63823i) q^{6} +(3.48178 - 4.79226i) q^{7} +(1.54518 + 2.12676i) q^{8} +(-1.54166 + 4.74475i) q^{9} -24.4576i q^{10} +(-2.35696 + 10.7445i) q^{11} +6.02210 q^{12} +(-16.5137 - 5.36564i) q^{13} +(-12.6854 + 9.21645i) q^{14} +(14.9706 + 10.8768i) q^{15} +(-5.86705 - 18.0569i) q^{16} +(-31.6380 + 10.2798i) q^{17} +(7.76226 - 10.6838i) q^{18} +(-1.25540 - 1.72791i) q^{19} +(-8.58521 + 26.4225i) q^{20} -11.8635i q^{21} +(14.7225 - 25.1213i) q^{22} -4.79583 q^{23} +(5.00723 + 1.62695i) q^{24} +(-48.8398 + 35.4842i) q^{25} +(37.1842 + 27.0159i) q^{26} +(8.65759 + 26.6453i) q^{27} +(16.9397 - 5.50405i) q^{28} +(23.5271 - 32.3823i) q^{29} +(-28.7914 - 39.6280i) q^{30} +(1.09334 - 3.36495i) q^{31} +39.7421i q^{32} +(8.82949 + 20.1837i) q^{33} +88.0573 q^{34} +(52.0523 + 16.9128i) q^{35} +(-12.1362 + 8.81745i) q^{36} +(13.7174 + 9.96630i) q^{37} +(1.74706 + 5.37691i) q^{38} +(-33.0731 + 10.7461i) q^{39} +(-14.2768 + 19.6503i) q^{40} +(-2.08561 - 2.87059i) q^{41} +(-9.70416 + 29.8663i) q^{42} +51.0107i q^{43} +(-24.7235 + 21.9717i) q^{44} -46.0954 q^{45} +(12.0735 + 3.92291i) q^{46} +(-1.23883 + 0.900063i) q^{47} +(-30.7628 - 22.3505i) q^{48} +(4.29888 + 13.2306i) q^{49} +(151.980 - 49.3812i) q^{50} +(-39.1608 + 53.9003i) q^{51} +(-30.6884 - 42.2390i) q^{52} +(-10.5596 + 32.4992i) q^{53} -74.1613i q^{54} +(-101.145 + 9.96609i) q^{55} +15.5720 q^{56} +(-4.06818 - 1.32183i) q^{57} +(-85.7176 + 62.2775i) q^{58} +(35.8678 + 26.0594i) q^{59} +(17.1942 + 52.9182i) q^{60} +(57.7758 - 18.7725i) q^{61} +(-5.50495 + 7.57692i) q^{62} +(17.3703 + 23.9082i) q^{63} +(9.04024 - 27.8230i) q^{64} -160.432i q^{65} +(-5.71830 - 58.0347i) q^{66} +25.4784 q^{67} +(-95.1320 - 30.9103i) q^{68} +(-7.77055 + 5.64564i) q^{69} +(-117.207 - 85.1559i) q^{70} +(-26.5354 - 81.6675i) q^{71} +(-12.4731 + 4.05275i) q^{72} +(46.5102 - 64.0157i) q^{73} +(-26.3813 - 36.3108i) q^{74} +(-37.3619 + 114.988i) q^{75} -6.42216i q^{76} +(43.2841 + 48.7052i) q^{77} +92.0517 q^{78} +(67.6540 + 21.9821i) q^{79} +(141.921 - 103.112i) q^{80} +(9.06934 + 6.58926i) q^{81} +(2.90241 + 8.93271i) q^{82} +(-59.3250 + 19.2759i) q^{83} +(20.9676 - 28.8594i) q^{84} +(-180.664 - 248.663i) q^{85} +(41.7259 - 128.419i) q^{86} -80.1641i q^{87} +(-26.4929 + 11.5895i) q^{88} +48.1862 q^{89} +(116.045 + 37.7053i) q^{90} +(-83.2107 + 60.4561i) q^{91} +(-11.6665 - 8.47617i) q^{92} +(-2.18970 - 6.73921i) q^{93} +(3.85499 - 1.25256i) q^{94} +(11.5993 - 15.9651i) q^{95} +(46.7843 + 64.3931i) q^{96} +(-13.2508 + 40.7819i) q^{97} -36.8244i q^{98} +(-47.3464 - 27.7476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 8 q^{3} + 88 q^{4} - 40 q^{6} - 120 q^{9} - 8 q^{14} - 12 q^{15} - 272 q^{16} - 80 q^{17} + 80 q^{18} - 60 q^{19} + 40 q^{20} + 136 q^{22} - 60 q^{24} - 268 q^{25} + 40 q^{26} + 148 q^{27} - 240 q^{28}+ \cdots - 414 q^{99}+O(q^{100}) \) 176 * q - 8 * q^3 + 88 * q^4 - 40 * q^6 - 120 * q^9 - 8 * q^14 - 12 * q^15 - 272 * q^16 - 80 * q^17 + 80 * q^18 - 60 * q^19 + 40 * q^20 + 136 * q^22 - 60 * q^24 - 268 * q^25 + 40 * q^26 + 148 * q^27 - 240 * q^28 + 160 * q^29 + 240 * q^30 + 108 * q^31 - 160 * q^33 - 420 * q^34 + 150 * q^35 + 32 * q^36 + 96 * q^37 + 70 * q^38 - 320 * q^39 + 270 * q^40 - 362 * q^42 + 174 * q^44 + 180 * q^45 - 138 * q^47 - 182 * q^48 + 464 * q^49 + 410 * q^50 + 500 * q^51 - 70 * q^52 - 130 * q^53 + 88 * q^55 + 472 * q^56 - 100 * q^57 + 468 * q^58 - 126 * q^59 - 376 * q^60 - 570 * q^62 - 160 * q^63 + 1096 * q^64 - 562 * q^66 - 472 * q^67 - 480 * q^68 + 380 * q^70 - 264 * q^71 + 1050 * q^72 - 840 * q^73 + 530 * q^74 - 64 * q^75 + 326 * q^77 - 576 * q^78 + 90 * q^79 + 274 * q^80 - 276 * q^81 - 132 * q^82 + 180 * q^83 - 1120 * q^84 + 360 * q^85 - 704 * q^86 + 272 * q^88 + 340 * q^89 + 1600 * q^90 + 514 * q^91 - 838 * q^93 - 690 * q^94 - 520 * q^95 - 1240 * q^96 + 832 * q^97 - 414 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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