LMFDB - Embedded newform 253.3.g.a.24.7

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			24.7
Character	$\chi$	$=$	253.24
Dual form			253.3.g.a.116.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.81261 - 0.913872i) q^{2} +(-3.21219 + 2.33380i) q^{3} +(3.83953 + 2.78958i) q^{4} +(1.38144 + 4.25163i) q^{5} +(11.1674 - 3.62852i) q^{6} +(3.16567 - 4.35717i) q^{7} +(-1.29663 - 1.78466i) q^{8} +(2.09044 - 6.43370i) q^{9} -13.2206i q^{10} +(8.08764 - 7.45587i) q^{11} -18.8436 q^{12} +(-16.0373 - 5.21085i) q^{13} +(-12.8857 + 9.36199i) q^{14} +(-14.3599 - 10.4331i) q^{15} +(-3.85032 - 11.8501i) q^{16} +(15.0653 - 4.89502i) q^{17} +(-11.7592 + 16.1851i) q^{18} +(18.5930 + 25.5910i) q^{19} +(-6.55621 + 20.1779i) q^{20} +21.3841i q^{21} +(-29.5611 + 13.5794i) q^{22} +4.79583 q^{23} +(8.33006 + 2.70660i) q^{24} +(4.05741 - 2.94788i) q^{25} +(40.3447 + 29.3121i) q^{26} +(-2.74248 - 8.44049i) q^{27} +(24.3094 - 7.89859i) q^{28} +(17.8747 - 24.6024i) q^{29} +(30.8543 + 42.4673i) q^{30} +(-13.7301 + 42.2568i) q^{31} +45.6721i q^{32} +(-8.57860 + 42.8246i) q^{33} -46.8463 q^{34} +(22.8983 + 7.44009i) q^{35} +(25.9737 - 18.8710i) q^{36} +(-4.03303 - 2.93017i) q^{37} +(-28.9078 - 88.9691i) q^{38} +(63.6761 - 20.6896i) q^{39} +(5.79650 - 7.97820i) q^{40} +(41.3552 + 56.9206i) q^{41} +(19.5423 - 60.1450i) q^{42} +54.5033i q^{43} +(51.8516 - 6.06591i) q^{44} +30.2416 q^{45} +(-13.4888 - 4.38277i) q^{46} +(-9.04879 + 6.57433i) q^{47} +(40.0236 + 29.0789i) q^{48} +(6.17838 + 19.0151i) q^{49} +(-14.1059 + 4.58328i) q^{50} +(-36.9688 + 50.8832i) q^{51} +(-47.0398 - 64.7447i) q^{52} +(6.48502 - 19.9588i) q^{53} +26.2461i q^{54} +(42.8722 + 24.0859i) q^{55} -11.8808 q^{56} +(-119.448 - 38.8111i) q^{57} +(-72.7580 + 52.8618i) q^{58} +(-59.2291 - 43.0324i) q^{59} +(-26.0314 - 80.1163i) q^{60} +(30.6668 - 9.96425i) q^{61} +(77.2346 - 106.304i) q^{62} +(-21.4151 - 29.4753i) q^{63} +(26.3372 - 81.0575i) q^{64} -75.3834i q^{65} +(63.2644 - 112.609i) q^{66} -66.0953 q^{67} +(71.4989 + 23.2314i) q^{68} +(-15.4051 + 11.1925i) q^{69} +(-57.6045 - 41.8521i) q^{70} +(22.6368 + 69.6688i) q^{71} +(-14.1925 + 4.61142i) q^{72} +(-77.8206 + 107.111i) q^{73} +(8.66554 + 11.9271i) q^{74} +(-6.15344 + 18.9383i) q^{75} +150.124i q^{76} +(-6.88369 - 58.8420i) q^{77} -198.004 q^{78} +(-15.1025 - 4.90710i) q^{79} +(45.0632 - 32.7403i) q^{80} +(77.7633 + 56.4983i) q^{81} +(-64.2979 - 197.889i) q^{82} +(6.22289 - 2.02194i) q^{83} +(-59.6527 + 82.1049i) q^{84} +(41.6237 + 57.2901i) q^{85} +(49.8090 - 153.296i) q^{86} +120.744i q^{87} +(-23.7929 - 4.76617i) q^{88} +52.0498 q^{89} +(-85.0577 - 27.6369i) q^{90} +(-73.4734 + 53.3816i) q^{91} +(18.4138 + 13.3784i) q^{92} +(-54.5151 - 167.780i) q^{93} +(31.4588 - 10.2216i) q^{94} +(-83.1186 + 114.403i) q^{95} +(-106.589 - 146.708i) q^{96} +(-4.28031 + 13.1734i) q^{97} -59.1283i q^{98} +(-31.0622 - 67.6195i) 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 $

$2$	−2.81261	−	0.913872i	−1.40630	−	0.456936i	−0.495080	−	0.868847i	$-0.664861\pi$
$2$	−2.81261	−	0.913872i	−1.40630	−	0.456936i	−0.911224	+	0.411912i	$0.864861\pi$
$3$	−3.21219	+	2.33380i	−1.07073	+	0.777932i	−0.976044	−	0.217575i	$-0.930185\pi$
$3$	−3.21219	+	2.33380i	−1.07073	+	0.777932i	−0.0946879	+	0.995507i	$0.530185\pi$
$4$	3.83953	+	2.78958i	0.959883	+	0.697396i
$5$	1.38144	+	4.25163i	0.276288	+	0.850327i	0.988876	+	0.148744i	$0.0475230\pi$
$5$	1.38144	+	4.25163i	0.276288	+	0.850327i	−0.712588	+	0.701583i	$0.752477\pi$
$6$	11.1674	−	3.62852i	1.86124	−	0.604753i
$7$	3.16567	−	4.35717i	0.452238	−	0.622452i	−0.520638	−	0.853777i	$-0.674306\pi$
$7$	3.16567	−	4.35717i	0.452238	−	0.622452i	0.972877	+	0.231325i	$0.0743060\pi$
$8$	−1.29663	−	1.78466i	−0.162079	−	0.223082i
$9$	2.09044	−	6.43370i	0.232271	−	0.714856i
$10$		−	13.2206i		−	1.32206i
$11$	8.08764	−	7.45587i	0.735240	−	0.677807i
$11$	8.08764	−	7.45587i	0.735240	−	0.677807i
$12$	−18.8436			−1.57030
$13$	−16.0373	−	5.21085i	−1.23364	−	0.400834i	−0.381609	−	0.924324i	$-0.624630\pi$
$13$	−16.0373	−	5.21085i	−1.23364	−	0.400834i	−0.852032	+	0.523489i	$0.824630\pi$
$14$	−12.8857	+	9.36199i	−0.920405	+	0.668713i
$15$	−14.3599	−	10.4331i	−0.957327	−	0.695538i
$16$	−3.85032	−	11.8501i	−0.240645	−	0.740629i
$17$	15.0653	−	4.89502i	0.886196	−	0.287942i	0.169668	−	0.985501i	$-0.445730\pi$
$17$	15.0653	−	4.89502i	0.886196	−	0.287942i	0.716528	+	0.697559i	$0.245730\pi$
$18$	−11.7592	+	16.1851i	−0.653287	+	0.899172i
$19$	18.5930	+	25.5910i	0.978577	+	1.34690i	0.937592	+	0.347736i	$0.113049\pi$
$19$	18.5930	+	25.5910i	0.978577	+	1.34690i	0.0409846	+	0.999160i	$0.486951\pi$
$20$	−6.55621	+	20.1779i	−0.327810	+	1.00890i
$21$			21.3841i			1.01829i
$22$	−29.5611	+	13.5794i	−1.34369	+	0.617244i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$	8.33006	+	2.70660i	0.347086	+	0.112775i
$25$	4.05741	−	2.94788i	0.162296	−	0.117915i
$26$	40.3447	+	29.3121i	1.55172	+	1.12739i
$27$	−2.74248	−	8.44049i	−0.101573	−	0.312611i
$28$	24.3094	−	7.89859i	0.868192	−	0.282093i
$29$	17.8747	−	24.6024i	0.616369	−	0.848360i	−0.380713	−	0.924693i	$-0.624321\pi$
$29$	17.8747	−	24.6024i	0.616369	−	0.848360i	0.997082	+	0.0763337i	$0.0243214\pi$
$30$	30.8543	+	42.4673i	1.02848	+	1.41558i
$31$	−13.7301	+	42.2568i	−0.442905	+	1.36312i	0.441859	+	0.897084i	$0.354319\pi$
$31$	−13.7301	+	42.2568i	−0.442905	+	1.36312i	−0.884765	+	0.466038i	$0.845681\pi$
$32$			45.6721i			1.42725i
$33$	−8.57860	+	42.8246i	−0.259958	+	1.29772i
$34$	−46.8463			−1.37783
$35$	22.8983	+	7.44009i	0.654236	+	0.212574i
$36$	25.9737	−	18.8710i	0.721491	−	0.524194i
$37$	−4.03303	−	2.93017i	−0.109001	−	0.0791938i	0.531950	−	0.846776i	$-0.321460\pi$
$37$	−4.03303	−	2.93017i	−0.109001	−	0.0791938i	−0.640950	+	0.767582i	$0.721460\pi$
$38$	−28.9078	−	88.9691i	−0.760732	−	2.34129i
$39$	63.6761	−	20.6896i	1.63272	−	0.530503i
$40$	5.79650	−	7.97820i	0.144913	−	0.199455i
$41$	41.3552	+	56.9206i	1.00866	+	1.38831i	0.919855	+	0.392258i	$0.128306\pi$
$41$	41.3552	+	56.9206i	1.00866	+	1.38831i	0.0888088	+	0.996049i	$0.471694\pi$
$42$	19.5423	−	60.1450i	0.465293	−	1.43202i
$43$			54.5033i			1.26752i	0.773531	+	0.633759i	$0.218489\pi$
$43$			54.5033i			1.26752i	−0.773531	+	0.633759i	$0.781511\pi$
$44$	51.8516	−	6.06591i	1.17844	−	0.137861i
$45$	30.2416			0.672035
$46$	−13.4888	−	4.38277i	−0.293235	−	0.0952777i
$47$	−9.04879	+	6.57433i	−0.192528	+	0.139879i	−0.679873	−	0.733330i	$-0.737965\pi$
$47$	−9.04879	+	6.57433i	−0.192528	+	0.139879i	0.487346	+	0.873209i	$0.337965\pi$
$48$	40.0236	+	29.0789i	0.833825	+	0.605810i
$49$	6.17838	+	19.0151i	0.126089	+	0.388063i
$50$	−14.1059	+	4.58328i	−0.282118	+	0.0916656i
$51$	−36.9688	+	50.8832i	−0.724878	+	0.997709i
$52$	−47.0398	−	64.7447i	−0.904612	−	1.24509i
$53$	6.48502	−	19.9588i	0.122359	−	0.376582i	−0.871052	−	0.491191i	$-0.836562\pi$
$53$	6.48502	−	19.9588i	0.122359	−	0.376582i	0.993411	+	0.114609i	$0.0365616\pi$
$54$			26.2461i			0.486038i
$55$	42.8722	+	24.0859i	0.779495	+	0.437925i
$56$	−11.8808			−0.212156
$57$	−119.448	−	38.8111i	−2.09559	−	0.680897i
$58$	−72.7580	+	52.8618i	−1.25445	+	0.911410i
$59$	−59.2291	−	43.0324i	−1.00388	−	0.729363i	−0.0409653	−	0.999161i	$-0.513043\pi$
$59$	−59.2291	−	43.0324i	−1.00388	−	0.729363i	−0.962917	+	0.269797i	$0.913043\pi$
$60$	−26.0314	−	80.1163i	−0.433856	−	1.33527i
$61$	30.6668	−	9.96425i	0.502735	−	0.163348i	−0.0466609	−	0.998911i	$-0.514858\pi$
$61$	30.6668	−	9.96425i	0.502735	−	0.163348i	0.549396	+	0.835562i	$0.314858\pi$
$62$	77.2346	−	106.304i	1.24572	−	1.71459i
$63$	−21.4151	−	29.4753i	−0.339922	−	0.467863i
$64$	26.3372	−	81.0575i	0.411519	−	1.26652i
$65$		−	75.3834i		−	1.15974i
$66$	63.2644	−	112.609i	0.958552	−	1.70620i
$67$	−66.0953			−0.986497			−0.493248	−	0.869888i	$-0.664191\pi$
$67$	−66.0953			−0.986497			−0.493248	+	0.869888i	$0.664191\pi$
$68$	71.4989	+	23.2314i	1.05145	+	0.341638i
$69$	−15.4051	+	11.1925i	−0.223263	+	0.162210i
$70$	−57.6045	−	41.8521i	−0.822922	−	0.597888i
$71$	22.6368	+	69.6688i	0.318828	+	0.981251i	0.974150	+	0.225901i	$0.0725327\pi$
$71$	22.6368	+	69.6688i	0.318828	+	0.981251i	−0.655323	+	0.755349i	$0.727467\pi$
$72$	−14.1925	+	4.61142i	−0.197118	+	0.0640475i
$73$	−77.8206	+	107.111i	−1.06604	+	1.46727i	−0.192010	+	0.981393i	$0.561501\pi$
$73$	−77.8206	+	107.111i	−1.06604	+	1.46727i	−0.874026	+	0.485880i	$0.838499\pi$
$74$	8.66554	+	11.9271i	0.117102	+	0.161177i
$75$	−6.15344	+	18.9383i	−0.0820458	+	0.252511i
$76$			150.124i			1.97532i
$77$	−6.88369	−	58.8420i	−0.0893986	−	0.764182i
$78$	−198.004			−2.53851
$79$	−15.1025	−	4.90710i	−0.191171	−	0.0621151i	0.211867	−	0.977299i	$-0.432046\pi$
$79$	−15.1025	−	4.90710i	−0.191171	−	0.0621151i	−0.403038	+	0.915183i	$0.632046\pi$
$80$	45.0632	−	32.7403i	0.563290	−	0.409254i
$81$	77.7633	+	56.4983i	0.960040	+	0.697510i
$82$	−64.2979	−	197.889i	−0.784121	−	2.41328i
$83$	6.22289	−	2.02194i	0.0749745	−	0.0243607i	−0.271290	−	0.962498i	$-0.587450\pi$
$83$	6.22289	−	2.02194i	0.0749745	−	0.0243607i	0.346264	+	0.938137i	$0.387450\pi$
$84$	−59.6527	+	82.1049i	−0.710151	+	0.977439i
$85$	41.6237	+	57.2901i	0.489690	+	0.674001i
$86$	49.8090	−	153.296i	0.579174	−	1.78252i
$87$			120.744i			1.38786i
$88$	−23.7929	−	4.76617i	−0.270374	−	0.0541611i
$89$	52.0498			0.584829			0.292414	−	0.956292i	$-0.405541\pi$
$89$	52.0498			0.584829			0.292414	+	0.956292i	$0.405541\pi$
$90$	−85.0577	−	27.6369i	−0.945085	−	0.307077i
$91$	−73.4734	+	53.3816i	−0.807400	+	0.586611i
$92$	18.4138	+	13.3784i	0.200150	+	0.145417i
$93$	−54.5151	−	167.780i	−0.586184	−	1.80409i
$94$	31.4588	−	10.2216i	0.334668	−	0.108740i
$95$	−83.1186	+	114.403i	−0.874933	+	1.20424i
$96$	−106.589	−	146.708i	−1.11031	−	1.52821i
$97$	−4.28031	+	13.1734i	−0.0441269	+	0.135809i	−0.970693	−	0.240324i	$-0.922746\pi$
$97$	−4.28031	+	13.1734i	−0.0441269	+	0.135809i	0.926566	+	0.376133i	$0.122746\pi$
$98$		−	59.1283i		−	0.603350i
$99$	−31.0622	−	67.6195i	−0.313759	−	0.683026i
$100$	23.8019			0.238019
$101$	104.529	+	33.9636i	1.03494	+	0.336274i	0.776743	−	0.629818i	$-0.216870\pi$
$101$	104.529	+	33.9636i	1.03494	+	0.336274i	0.258201	+	0.966091i	$0.416870\pi$
$102$	150.479	−	109.330i	1.47529	−	1.07186i
$103$	54.3534	+	39.4901i	0.527703	+	0.383399i	0.819498	−	0.573082i	$-0.194252\pi$
$103$	54.3534	+	39.4901i	0.527703	+	0.383399i	−0.291795	+	0.956481i	$0.594252\pi$
$104$	11.4949	+	35.3777i	0.110528	+	0.340171i
$105$	−90.9173	+	29.5408i	−0.865879	+	0.281341i
$106$	−36.4797	+	50.2099i	−0.344148	+	0.473679i
$107$	−52.7743	−	72.6375i	−0.493217	−	0.678855i	0.487760	−	0.872978i	$-0.337814\pi$
$107$	−52.7743	−	72.6375i	−0.493217	−	0.678855i	−0.980977	+	0.194122i	$0.937814\pi$
$108$	13.0156	−	40.0579i	0.120515	−	0.370907i
$109$		−	118.103i		−	1.08351i	−0.840536	−	0.541756i	$-0.817760\pi$
$109$		−	118.103i		−	1.08351i	0.840536	−	0.541756i	$-0.182240\pi$
$110$	−98.5714	−	106.924i	−0.896103	−	0.972035i
$111$	19.7933			0.178318
$112$	−63.8215	−	20.7369i	−0.569835	−	0.185151i
$113$	92.4933	−	67.2003i	0.818525	−	0.594693i	−0.0977645	−	0.995210i	$-0.531169\pi$
$113$	92.4933	−	67.2003i	0.818525	−	0.594693i	0.916290	+	0.400516i	$0.131169\pi$
$114$	300.493	+	218.321i	2.63591	+	1.91510i
$115$	6.62515	+	20.3901i	0.0576100	+	0.177305i
$116$	137.261	−	44.5988i	1.18329	−	0.384473i
$117$	−67.0501	+	92.2866i	−0.573078	+	0.788774i
$118$	127.262	+	175.161i	1.07849	+	1.48442i
$119$	26.3634	−	81.1381i	0.221541	−	0.681833i
$120$			39.1554i			0.326295i
$121$	9.81996	−	120.601i	0.0811567	−	0.996701i
$122$	−95.3598			−0.781637
$123$	−265.682	−	86.3253i	−2.16002	−	0.701832i
$124$	−170.596	+	123.945i	−1.37577	+	0.999558i
$125$	108.555	+	78.8697i	0.868438	+	0.630957i
$126$	33.2956	+	102.473i	0.264251	+	0.813280i
$127$	53.5796	−	17.4091i	0.421886	−	0.137079i	−0.0903769	−	0.995908i	$-0.528807\pi$
$127$	53.5796	−	17.4091i	0.421886	−	0.137079i	0.512263	+	0.858828i	$0.328807\pi$
$128$	−40.7707	+	56.1161i	−0.318521	+	0.438407i
$129$	−127.200	−	175.075i	−0.986043	−	1.35717i
$130$	−68.8907	+	212.024i	−0.529929	+	1.63095i
$131$			192.045i			1.46599i	0.680233	+	0.732996i	$0.261879\pi$
$131$			192.045i			1.46599i	−0.680233	+	0.732996i	$0.738121\pi$
$132$	−152.401	+	140.496i	−1.15455	+	1.06436i
$133$	170.363			1.28093
$134$	185.900	+	60.4026i	1.38731	+	0.450766i
$135$	32.0973	−	23.3200i	0.237758	−	0.172741i
$136$	−28.2701	−	20.5394i	−0.207868	−	0.151025i
$137$	73.9022	+	227.448i	0.539432	+	1.66020i	0.733873	+	0.679287i	$0.237711\pi$
$137$	73.9022	+	227.448i	0.539432	+	1.66020i	−0.194441	+	0.980914i	$0.562289\pi$
$138$	53.5571	−	17.4018i	0.388095	−	0.126100i
$139$	−19.5524	+	26.9115i	−0.140665	+	0.193608i	−0.873537	−	0.486758i	$-0.838179\pi$
$139$	−19.5524	+	26.9115i	−0.140665	+	0.193608i	0.732872	+	0.680366i	$0.238179\pi$
$140$	67.1638	+	92.4431i	0.479742	+	0.660308i
$141$	13.7233	−	42.2361i	0.0973286	−	0.299547i
$142$		−	216.638i		−	1.52562i
$143$	−168.556	+	77.4289i	−1.17871	+	0.541461i
$144$	−84.2887			−0.585338
$145$	129.293	+	42.0100i	0.891678	+	0.289724i
$146$	316.765	−	230.143i	2.16962	−	1.57632i
$147$	−64.2235	−	46.6611i	−0.436895	−	0.317423i
$148$	−7.31101	−	22.5010i	−0.0493987	−	0.152034i
$149$	197.755	−	64.2546i	1.32722	−	0.431239i	0.442250	−	0.896892i	$-0.354180\pi$
$149$	197.755	−	64.2546i	1.32722	−	0.431239i	0.884967	+	0.465653i	$0.154180\pi$
$150$	34.6144	−	47.6427i	0.230763	−	0.317618i
$151$	134.274	+	184.813i	0.889233	+	1.22392i	0.973777	+	0.227505i	$0.0730567\pi$
$151$	134.274	+	184.813i	0.889233	+	1.22392i	−0.0845439	+	0.996420i	$0.526943\pi$
$152$	21.5630	−	66.3642i	0.141862	−	0.436607i
$153$		−	107.159i		−	0.700383i
$154$	−34.4129	+	171.790i	−0.223461	+	1.11552i
$155$	−198.628			−1.28147
$156$	302.202	+	98.1914i	1.93719	+	0.629432i
$157$	78.7453	−	57.2118i	0.501562	−	0.364406i	−0.308051	−	0.951370i	$-0.599677\pi$
$157$	78.7453	−	57.2118i	0.501562	−	0.364406i	0.809613	+	0.586963i	$0.199677\pi$
$158$	37.9929	+	27.6035i	0.240461	+	0.174706i
$159$	25.7487	+	79.2464i	0.161942	+	0.498405i
$160$	−194.181	+	63.0933i	−1.21363	+	0.394333i
$161$	15.1820	−	20.8962i	0.0942982	−	0.129790i
$162$	−167.085	−	229.973i	−1.03139	−	1.41959i
$163$	39.7909	−	122.464i	0.244116	−	0.751312i	−0.751664	−	0.659546i	$-0.770749\pi$
$163$	39.7909	−	122.464i	0.244116	−	0.751312i	0.995781	−	0.0917665i	$-0.0292513\pi$
$164$			333.912i			2.03605i
$165$	−193.925	+	22.6866i	−1.17531	+	0.137494i
$166$	−19.3503			−0.116568
$167$	−14.9710	−	4.86438i	−0.0896469	−	0.0291280i	0.263850	−	0.964564i	$-0.415008\pi$
$167$	−14.9710	−	4.86438i	−0.0896469	−	0.0291280i	−0.353497	+	0.935436i	$0.615008\pi$
$168$	38.1633	−	27.7273i	0.227163	−	0.165043i
$169$	93.3195	+	67.8006i	0.552187	+	0.401187i
$170$	−64.7153	−	199.173i	−0.380678	−	1.17161i
$171$	203.512	−	66.1252i	1.19013	−	0.386697i
$172$	−152.041	+	209.267i	−0.883962	+	1.21667i
$173$	25.6721	+	35.3346i	0.148394	+	0.204246i	0.876742	−	0.480960i	$-0.159712\pi$
$173$	25.6721	+	35.3346i	0.148394	+	0.204246i	−0.728349	+	0.685207i	$0.759712\pi$
$174$	110.344	−	339.605i	0.634162	−	1.95175i
$175$		−	27.0108i		−	0.154348i
$176$	−119.493	−	67.1316i	−0.678935	−	0.381430i
$177$	290.684			1.64228
$178$	−146.396	−	47.5668i	−0.822447	−	0.267229i
$179$	−160.824	+	116.845i	−0.898456	+	0.652766i	−0.938069	−	0.346449i	$-0.887387\pi$
$179$	−160.824	+	116.845i	−0.898456	+	0.652766i	0.0396133	+	0.999215i	$0.487387\pi$
$180$	116.114	+	84.3614i	0.645075	+	0.468674i
$181$	−89.1917	−	274.504i	−0.492772	−	1.51660i	−0.820401	−	0.571789i	$-0.806250\pi$
$181$	−89.1917	−	274.504i	−0.492772	−	1.51660i	0.327629	−	0.944806i	$-0.393750\pi$
$182$	255.436	−	82.9961i	1.40349	−	0.456023i
$183$	−75.2532	+	103.577i	−0.411220	+	0.565996i
$184$	−6.21842	−	8.55893i	−0.0337958	−	0.0465159i
$185$	6.88662	−	21.1948i	0.0372250	−	0.114567i
$186$			521.720i			2.80494i
$187$	85.3463	−	151.914i	0.456398	−	0.812376i
$188$	−53.0828			−0.282355
$189$	−45.4584	−	14.7703i	−0.240521	−	0.0781499i
$190$	338.330	−	245.811i	1.78068	−	1.29374i
$191$	36.4388	+	26.4744i	0.190779	+	0.138609i	0.679075	−	0.734069i	$-0.262381\pi$
$191$	36.4388	+	26.4744i	0.190779	+	0.138609i	−0.488296	+	0.872678i	$0.662381\pi$
$192$	104.572	+	321.838i	0.544644	+	1.67624i
$193$	−360.288	+	117.065i	−1.86678	+	0.606553i	−0.874103	+	0.485741i	$0.838550\pi$
$193$	−360.288	+	117.065i	−1.86678	+	0.606553i	−0.992675	+	0.120812i	$0.961450\pi$
$194$	24.0777	−	33.1401i	0.124112	−	0.170825i
$195$	175.929	+	242.146i	0.902202	+	1.24177i
$196$	−29.3221	+	90.2442i	−0.149603	+	0.460430i
$197$		−	58.0679i		−	0.294761i	−0.989080	−	0.147381i	$-0.952916\pi$
$197$		−	58.0679i		−	0.294761i	0.989080	−	0.147381i	$-0.0470842\pi$
$198$	25.5701	+	218.574i	0.129142	+	1.10391i
$199$	−51.1908			−0.257240			−0.128620	−	0.991694i	$-0.541055\pi$
$199$	−51.1908			−0.257240			−0.128620	+	0.991694i	$0.541055\pi$
$200$	−10.5219	−	3.41878i	−0.0526096	−	0.0170939i
$201$	212.311	−	154.253i	1.05627	−	0.767427i
$202$	−262.962	−	191.053i	−1.30179	−	0.945806i
$203$	−50.6115	−	155.766i	−0.249318	−	0.767321i
$204$	−283.886	+	92.2401i	−1.39160	+	0.452157i
$205$	−184.876	+	254.460i	−0.901833	+	1.24127i
$206$	−116.786	−	160.742i	−0.566922	−	0.780301i
$207$	10.0254	−	30.8550i	0.0484318	−	0.149058i
$208$			210.107i			1.01013i
$209$	341.177	+	68.3443i	1.63242	+	0.327006i
$210$	282.711			1.34624
$211$	−1.90272	−	0.618230i	−0.00901761	−	0.00293000i	0.304505	−	0.952511i	$-0.401509\pi$
$211$	−1.90272	−	0.618230i	−0.00901761	−	0.00293000i	−0.313522	+	0.949581i	$0.601509\pi$
$212$	80.5764	−	58.5422i	0.380077	−	0.276142i
$213$	−235.306	−	170.960i	−1.10472	−	0.802630i
$214$	82.0519	+	252.530i	0.383420	+	1.18005i
$215$	−231.728	+	75.2930i	−1.07780	+	0.350200i
$216$	−11.5074	+	15.8386i	−0.0532750	+	0.0733268i
$217$	140.655	+	193.595i	0.648180	+	0.892143i
$218$	−107.931	+	332.177i	−0.495095	+	1.52375i
$219$		−	525.679i		−	2.40036i
$220$	97.4198	+	212.074i	0.442817	+	0.963974i
$221$	−267.115			−1.20867
$222$	−55.6708	−	18.0885i	−0.250769	−	0.0814799i
$223$	−259.341	+	188.422i	−1.16296	+	0.844943i	−0.990150	−	0.140011i	$-0.955286\pi$
$223$	−259.341	+	188.422i	−1.16296	+	0.844943i	−0.172815	+	0.984954i	$0.555286\pi$
$224$	199.001	+	144.583i	0.888398	+	0.645459i
$225$	−10.4840	−	32.2665i	−0.0465957	−	0.143407i
$226$	−321.560	+	104.481i	−1.42283	+	0.462306i
$227$	−13.5830	+	18.6954i	−0.0598369	+	0.0823584i	−0.837887	−	0.545844i	$-0.816209\pi$
$227$	−13.5830	+	18.6954i	−0.0598369	+	0.0823584i	0.778050	+	0.628203i	$0.216209\pi$
$228$	−350.359	−	482.228i	−1.53666	−	2.11504i
$229$	84.4741	−	259.984i	0.368882	−	1.13530i	−0.578632	−	0.815589i	$-0.696413\pi$
$229$	84.4741	−	259.984i	0.368882	−	1.13530i	0.947514	−	0.319714i	$-0.103587\pi$
$230$		−	63.4039i		−	0.275669i
$231$	159.437	+	172.947i	0.690203	+	0.748688i
$232$	−67.0839			−0.289155
$233$	342.171	+	111.178i	1.46854	+	0.477159i	0.930668	−	0.365866i	$-0.119227\pi$
$233$	342.171	+	111.178i	1.46854	+	0.477159i	0.537875	+	0.843024i	$0.319227\pi$
$234$	272.924	−	198.291i	1.16634	−	0.847396i
$235$	−40.4520	−	29.3901i	−0.172136	−	0.125064i
$236$	−107.369	−	330.449i	−0.454955	−	1.40021i
$237$	59.9643	−	19.4836i	0.253014	−	0.0822092i
$238$	−148.300	+	204.117i	−0.623108	+	0.857635i
$239$	61.7471	+	84.9876i	0.258356	+	0.355597i	0.918416	−	0.395616i	$-0.129469\pi$
$239$	61.7471	+	84.9876i	0.258356	+	0.355597i	−0.660060	+	0.751213i	$0.729469\pi$
$240$	−68.3425	+	210.336i	−0.284760	+	0.876402i
$241$		−	205.175i		−	0.851349i	−0.904876	−	0.425675i	$-0.860037\pi$
$241$		−	205.175i		−	0.851349i	0.904876	−	0.425675i	$-0.139963\pi$
$242$	−137.833	+	330.229i	−0.569560	+	1.36458i
$243$	−301.773			−1.24186
$244$	145.542	+	47.2896i	0.596485	+	0.193810i
$245$	−72.3102	+	52.5364i	−0.295144	+	0.214434i
$246$	668.369	+	485.599i	2.71695	+	1.97398i
$247$	−164.831	−	507.297i	−0.667331	−	2.05383i
$248$	93.2168	−	30.2880i	0.375874	−	0.122129i
$249$	−15.2703	+	21.0178i	−0.0613266	+	0.0844089i
$250$	−233.245	−	321.035i	−0.932981	−	1.28414i
$251$	32.4947	−	100.008i	0.129461	−	0.398440i	−0.865227	−	0.501381i	$-0.832825\pi$
$251$	32.4947	−	100.008i	0.129461	−	0.398440i	0.994687	+	0.102942i	$0.0328255\pi$
$252$		−	172.911i		−	0.686154i
$253$	38.7870	−	35.7571i	0.153308	−	0.141332i
$254$	−166.608			−0.655937
$255$	−267.407	−	86.8857i	−1.04865	−	0.340728i
$256$	−109.852	+	79.8119i	−0.429108	+	0.311765i
$257$	−6.56632	−	4.77071i	−0.0255499	−	0.0185631i	0.574937	−	0.818198i	$-0.305027\pi$
$257$	−6.56632	−	4.77071i	−0.0255499	−	0.0185631i	−0.600487	+	0.799635i	$0.705027\pi$
$258$	197.766	+	608.662i	0.766536	+	2.35915i
$259$	−25.5345	+	8.29666i	−0.0985887	+	0.0320334i
$260$	210.288	−	289.437i	0.808801	−	1.11322i
$261$	−120.919	−	166.430i	−0.463290	−	0.637664i
$262$	175.504	−	540.147i	0.669864	−	2.06163i
$263$		−	289.471i		−	1.10065i	−0.834950	−	0.550326i	$-0.814504\pi$
$263$		−	289.471i		−	1.10065i	0.834950	−	0.550326i	$-0.185496\pi$
$264$	87.5506	−	40.2178i	0.331631	−	0.152340i
$265$	93.8164			0.354024
$266$	−479.166	−	155.690i	−1.80137	−	0.585302i
$267$	−167.194	+	121.474i	−0.626195	+	0.454957i
$268$	−253.775	−	184.378i	−0.946922	−	0.687979i
$269$	63.1755	+	194.434i	0.234853	+	0.722803i	0.997141	+	0.0755651i	$0.0240761\pi$
$269$	63.1755	+	194.434i	0.234853	+	0.722803i	−0.762288	+	0.647238i	$0.775924\pi$
$270$	−111.589	+	36.2573i	−0.413291	+	0.134286i
$271$	49.7005	−	68.4068i	0.183397	−	0.252424i	−0.707413	−	0.706800i	$-0.750138\pi$
$271$	49.7005	−	68.4068i	0.183397	−	0.252424i	0.890810	+	0.454377i	$0.150138\pi$
$272$	−116.013	−	159.678i	−0.426517	−	0.587051i
$273$	111.429	−	342.944i	0.408166	−	1.25620i
$274$		−	707.258i		−	2.58123i
$275$	10.8359	−	54.0929i	0.0394031	−	0.196702i
$276$	−90.3710			−0.327431
$277$	45.8734	+	14.9052i	0.165608	+	0.0538092i	0.390647	−	0.920540i	$-0.372251\pi$
$277$	45.8734	+	14.9052i	0.165608	+	0.0538092i	−0.225040	+	0.974350i	$0.572251\pi$
$278$	79.5869	−	57.8233i	0.286284	−	0.207997i
$279$	243.166	+	176.670i	0.871562	+	0.633227i
$280$	−16.4126	−	50.5126i	−0.0586163	−	0.180402i
$281$	57.1182	−	18.5588i	0.203268	−	0.0660457i	−0.205614	−	0.978633i	$-0.565919\pi$
$281$	57.1182	−	18.5588i	0.203268	−	0.0660457i	0.408881	+	0.912588i	$0.365919\pi$
$282$	−77.1967	+	106.252i	−0.273747	+	0.376781i
$283$	124.271	+	171.044i	0.439119	+	0.604396i	0.970016	−	0.243041i	$-0.0781449\pi$
$283$	124.271	+	171.044i	0.439119	+	0.604396i	−0.530897	+	0.847436i	$0.678145\pi$
$284$	−107.432	+	330.643i	−0.378283	+	1.16424i
$285$		−	561.466i		−	1.97006i
$286$	544.841	−	63.7388i	1.90504	−	0.222863i
$287$	378.929			1.32031
$288$	293.841	+	95.4747i	1.02028	+	0.331509i
$289$	−30.8031	+	22.3798i	−0.106585	+	0.0774386i
$290$	−325.260	−	236.315i	−1.12159	−	0.814879i
$291$	−16.9949	−	52.3051i	−0.0584019	−	0.179742i
$292$	−597.590	+	194.169i	−2.04654	+	0.664961i
$293$	−171.436	+	235.962i	−0.585107	+	0.805331i	−0.994244	−	0.107142i	$-0.965830\pi$
$293$	−171.436	+	235.962i	−0.585107	+	0.805331i	0.409137	+	0.912473i	$0.365830\pi$
$294$	137.993	+	189.931i	0.469365	+	0.646025i
$295$	101.137	−	311.267i	0.342837	−	1.05514i
$296$			10.9969i			0.0371518i
$297$	−85.1114	−	47.8161i	−0.286570	−	0.160997i
$298$	−614.929			−2.06352
$299$	−76.9124	−	24.9904i	−0.257232	−	0.0835798i
$300$	−76.4564	+	55.5488i	−0.254855	+	0.185163i
$301$	237.480	+	172.539i	0.788970	+	0.573220i
$302$	−208.766	−	642.515i	−0.691277	−	2.12753i
$303$	−415.033	+	134.852i	−1.36975	+	0.445057i
$304$	231.666	−	318.862i	0.762061	−	1.04889i
$305$	84.7287	+	116.619i	0.277799	+	0.382358i
$306$	−97.9292	+	301.395i	−0.320030	+	0.984951i
$307$			230.529i			0.750909i	0.926841	+	0.375455i	$0.122513\pi$
$307$			230.529i			0.750909i	−0.926841	+	0.375455i	$0.877487\pi$
$308$	137.715	−	245.129i	0.447125	−	0.795872i
$309$	−266.755			−0.863286
$310$	558.662	+	181.520i	1.80213	+	0.585549i
$311$	−78.1953	+	56.8122i	−0.251432	+	0.182676i	−0.706361	−	0.707852i	$-0.749665\pi$
$311$	−78.1953	+	56.8122i	−0.251432	+	0.182676i	0.454929	+	0.890528i	$0.349665\pi$
$312$	−119.488	−	86.8134i	−0.382976	−	0.278248i
$313$	−56.2288	−	173.054i	−0.179645	−	0.552890i	0.820170	−	0.572119i	$-0.193879\pi$
$313$	−56.2288	−	173.054i	−0.179645	−	0.552890i	−0.999815	+	0.0192297i	$0.993879\pi$
$314$	−273.764	+	88.9513i	−0.871859	+	0.283284i
$315$	95.7347	−	131.768i	0.303920	−	0.418310i
$316$	−44.2977	−	60.9706i	−0.140183	−	0.192945i
$317$	14.7594	−	45.4246i	0.0465595	−	0.143295i	−0.925074	−	0.379787i	$-0.875997\pi$
$317$	14.7594	−	45.4246i	0.0465595	−	0.143295i	0.971634	+	0.236491i	$0.0759974\pi$
$318$		−	246.420i		−	0.774906i
$319$	−38.8683	−	332.247i	−0.121844	−	1.04153i
$320$	381.010			1.19066
$321$	339.042	+	110.162i	1.05621	+	0.343182i
$322$	−61.7975	+	44.8985i	−0.191918	+	0.139436i
$323$	405.378	+	294.524i	1.25504	+	0.911839i
$324$	140.968	+	433.854i	0.435086	+	1.33906i
$325$	−80.4310	+	26.1336i	−0.247480	+	0.0804112i
$326$	−223.833	+	308.079i	−0.686603	+	0.945028i
$327$	275.628	+	379.369i	0.842898	+	1.16015i
$328$	47.9614	−	147.610i	0.146224	−	0.450030i
$329$			60.2392i			0.183098i
$330$	566.169	+	113.415i	1.71566	+	0.343681i
$331$	131.460			0.397162			0.198581	−	0.980085i	$-0.436367\pi$
$331$	131.460			0.397162			0.198581	+	0.980085i	$0.436367\pi$
$332$	29.5333	+	9.59597i	0.0889559	+	0.0289035i
$333$	−27.2827	+	19.8220i	−0.0819299	+	0.0595256i
$334$	37.6622	+	27.3632i	0.112761	+	0.0819258i
$335$	−91.3066	−	281.013i	−0.272557	−	0.838845i
$336$	253.403	−	82.3356i	0.754175	−	0.245046i
$337$	325.720	−	448.314i	0.966527	−	1.33031i	0.0227449	−	0.999741i	$-0.492759\pi$
$337$	325.720	−	448.314i	0.966527	−	1.33031i	0.943782	−	0.330569i	$-0.107241\pi$
$338$	−200.510	−	275.979i	−0.593225	−	0.816505i
$339$	−140.275	+	431.721i	−0.413790	+	1.27351i
$340$			336.080i			0.988470i
$341$	204.017	+	444.128i	0.598291	+	1.30243i
$342$	−632.831			−1.85038
$343$	353.396	+	114.825i	1.03031	+	0.334768i
$344$	97.2698	−	70.6706i	0.282761	−	0.205438i
$345$	−68.8677	−	50.0353i	−0.199616	−	0.145030i
$346$	−39.9142	−	122.843i	−0.115359	−	0.355039i
$347$	262.195	−	85.1922i	0.755604	−	0.245511i	0.0942130	−	0.995552i	$-0.469967\pi$
$347$	262.195	−	85.1922i	0.755604	−	0.245511i	0.661391	+	0.750041i	$0.269967\pi$
$348$	−336.825	+	463.600i	−0.967887	+	1.33218i
$349$	180.192	+	248.013i	0.516309	+	0.710639i	0.984967	−	0.172741i	$-0.0552624\pi$
$349$	180.192	+	248.013i	0.516309	+	0.710639i	−0.468658	+	0.883380i	$0.655262\pi$
$350$	−24.6844	+	75.9708i	−0.0705269	+	0.217060i
$351$			149.654i			0.426364i
$352$	340.526	+	369.380i	0.967402	+	1.04937i
$353$	80.0285			0.226710			0.113355	−	0.993555i	$-0.463840\pi$
$353$	80.0285			0.226710			0.113355	+	0.993555i	$0.463840\pi$
$354$	−817.581	−	265.648i	−2.30955	−	0.750418i
$355$	−264.935	+	192.486i	−0.746295	+	0.542215i
$356$	199.847	+	145.197i	0.561368	+	0.407857i
$357$	104.676	+	322.158i	0.293209	+	0.902404i
$358$	559.115	−	181.667i	1.56177	−	0.507451i
$359$	158.405	−	218.026i	0.441239	−	0.607313i	−0.529248	−	0.848467i	$-0.677526\pi$
$359$	158.405	−	218.026i	0.441239	−	0.607313i	0.970487	+	0.241154i	$0.0775258\pi$
$360$	−39.2122	−	53.9709i	−0.108923	−	0.149919i
$361$	−197.647	+	608.294i	−0.547498	+	1.68503i
$362$			853.581i			2.35796i
$363$	249.914	+	410.311i	0.688469	+	1.13033i
$364$	−431.016			−1.18411
$365$	−562.901	−	182.898i	−1.54219	−	0.501089i
$366$	306.314	−	222.550i	0.836924	−	0.608061i
$367$	124.636	+	90.5537i	0.339609	+	0.246740i	0.744497	−	0.667626i	$-0.232689\pi$
$367$	124.636	+	90.5537i	0.339609	+	0.246740i	−0.404888	+	0.914366i	$0.632689\pi$
$368$	−18.4655	−	56.8309i	−0.0501780	−	0.154432i
$369$	452.661	−	147.078i	1.22672	−	0.398586i
$370$	−38.7387	+	53.3193i	−0.104699	+	0.144106i
$371$	−66.4346	−	91.4394i	−0.179069	−	0.246467i
$372$	258.725	−	796.272i	0.695496	−	2.14052i
$373$		−	467.828i		−	1.25423i	−0.778927	−	0.627115i	$-0.784236\pi$
$373$		−	467.828i		−	1.25423i	0.778927	−	0.627115i	$-0.215764\pi$
$374$	−378.876	+	349.280i	−1.01304	+	0.933903i
$375$	−532.765			−1.42071
$376$	23.4659	+	7.62453i	0.0624093	+	0.0202780i
$377$	−414.862	+	301.415i	−1.10043	+	0.799510i
$378$	114.358	+	83.0863i	0.302536	+	0.219805i
$379$	66.1895	+	203.710i	0.174643	+	0.537495i	0.999617	−	0.0276755i	$-0.00881052\pi$
$379$	66.1895	+	203.710i	0.174643	+	0.537495i	−0.824974	+	0.565170i	$0.808811\pi$
$380$	−638.273	+	207.388i	−1.67967	+	0.545757i
$381$	−131.479	+	180.965i	−0.345089	+	0.474974i
$382$	−78.2940	−	107.762i	−0.204958	−	0.282101i
$383$	57.9235	−	178.270i	0.151236	−	0.465457i	−0.846524	−	0.532351i	$-0.821309\pi$
$383$	57.9235	−	178.270i	0.151236	−	0.465457i	0.997760	+	0.0668935i	$0.0213088\pi$
$384$		−	275.406i		−	0.717204i
$385$	240.665	−	110.554i	0.625105	−	0.287152i
$386$	1120.33			2.90241
$387$	350.658	+	113.936i	0.906093	+	0.294407i
$388$	−53.1829	+	38.6396i	−0.137069	+	0.0995866i
$389$	−490.410	−	356.304i	−1.26070	−	0.915949i	−0.261904	−	0.965094i	$-0.584350\pi$
$389$	−490.410	−	356.304i	−1.26070	−	0.915949i	−0.998792	+	0.0491453i	$0.984350\pi$
$390$	−273.530	−	841.839i	−0.701359	−	2.15856i
$391$	72.2508	−	23.4757i	0.184785	−	0.0600401i
$392$	25.9244	−	35.6819i	0.0661337	−	0.0910252i
$393$	−448.194	−	616.886i	−1.14044	−	1.56968i
$394$	−53.0666	+	163.322i	−0.134687	+	0.414524i
$395$		−	70.9891i		−	0.179719i
$396$	69.3662	−	346.278i	0.175167	−	0.874439i
$397$	523.412			1.31842			0.659209	−	0.751960i	$-0.270891\pi$
$397$	523.412			1.31842			0.659209	+	0.751960i	$0.270891\pi$
$398$	143.980	+	46.7819i	0.361758	+	0.117542i
$399$	−547.241	+	397.594i	−1.37153	+	0.996475i
$400$	−50.5549	−	36.7303i	−0.126387	−	0.0918257i
$401$	49.5796	+	152.590i	0.123640	+	0.380524i	0.993651	−	0.112508i	$-0.0358884\pi$
$401$	49.5796	+	152.590i	0.123640	+	0.380524i	−0.870011	+	0.493032i	$0.835888\pi$
$402$	−738.115	+	239.828i	−1.83611	+	0.596587i
$403$	440.388	−	606.141i	1.09277	−	1.50407i
$404$	306.599	+	421.998i	0.758910	+	1.04455i
$405$	−132.785	+	408.670i	−0.327864	+	1.00906i
$406$			484.362i			1.19301i
$407$	−54.4647	+	6.37161i	−0.133820	+	0.0156551i
$408$	138.744			0.340059
$409$	264.094	+	85.8092i	0.645706	+	0.209803i	0.613520	−	0.789679i	$-0.289753\pi$
$409$	264.094	+	85.8092i	0.645706	+	0.209803i	0.0321861	+	0.999482i	$0.489753\pi$
$410$	752.526	−	546.742i	1.83543	−	1.33352i
$411$	−768.204	−	558.133i	−1.86911	−	1.35799i
$412$	98.5308	+	303.247i	0.239153	+	0.736036i
$413$	−374.999	+	121.845i	−0.907988	+	0.295023i
$414$	−56.3950	+	77.6210i	−0.136220	+	0.187490i
$415$	17.1931	+	23.6642i	0.0414291	+	0.0570223i
$416$	237.991	−	732.460i	0.572093	−	1.76072i
$417$		−	132.076i		−	0.316730i
$418$	−897.138	−	504.017i	−2.14626	−	1.20578i
$419$	−391.790			−0.935059			−0.467530	−	0.883977i	$-0.654856\pi$
$419$	−391.790			−0.935059			−0.467530	+	0.883977i	$0.654856\pi$
$420$	−431.487	−	140.199i	−1.02735	−	0.333806i
$421$	−485.511	+	352.744i	−1.15323	+	0.837873i	−0.988907	−	0.148533i	$-0.952545\pi$
$421$	−485.511	+	352.744i	−1.15323	+	0.837873i	−0.164326	+	0.986406i	$0.552545\pi$
$422$	4.78661	+	3.47768i	0.0113427	+	0.00824094i
$423$	23.3814	+	71.9605i	0.0552751	+	0.170119i
$424$	−44.0284	+	14.3057i	−0.103841	+	0.0337399i
$425$	46.6963	−	64.2719i	0.109874	−	0.151228i
$426$	505.589	+	695.884i	1.18683	+	1.63353i
$427$	53.6650	−	165.164i	0.125679	−	0.386801i
$428$		−	426.112i		−	0.995590i
$429$	360.731	−	642.091i	0.840864	−	1.49672i
$430$	720.568			1.67574
$431$	495.342	+	160.946i	1.14929	+	0.373426i	0.820874	−	0.571109i	$-0.193487\pi$
$431$	495.342	+	160.946i	1.14929	+	0.373426i	0.328411	+	0.944535i	$0.393487\pi$
$432$	−89.4609	+	64.9972i	−0.207085	+	0.150456i
$433$	−237.516	−	172.566i	−0.548537	−	0.398535i	0.278709	−	0.960376i	$-0.410093\pi$
$433$	−237.516	−	172.566i	−0.548537	−	0.398535i	−0.827246	+	0.561840i	$0.810093\pi$
$434$	−218.686	−	673.048i	−0.503886	−	1.55080i
$435$	−513.358	+	166.800i	−1.18013	+	0.383449i
$436$	329.458	−	453.460i	0.755637	−	1.04004i
$437$	89.1687	+	122.730i	0.204047	+	0.280847i
$438$	−480.403	+	1478.53i	−1.09681	+	3.37563i
$439$			657.233i			1.49711i	0.663070	+	0.748557i	$0.269253\pi$
$439$			657.233i			1.49711i	−0.663070	+	0.748557i	$0.730747\pi$
$440$	−12.6044	−	107.743i	−0.0286464	−	0.244870i
$441$	135.253			0.306696
$442$	751.290	+	244.109i	1.69975	+	0.552282i
$443$	38.5631	−	28.0177i	0.0870498	−	0.0632454i	−0.543409	−	0.839468i	$-0.682867\pi$
$443$	38.5631	−	28.0177i	0.0870498	−	0.0632454i	0.630459	+	0.776223i	$0.282867\pi$
$444$	75.9971	+	55.2151i	0.171165	+	0.124358i
$445$	71.9036	+	221.297i	0.161581	+	0.497296i
$446$	901.619	−	292.954i	2.02157	−	0.656847i
$447$	−485.272	+	667.919i	−1.08562	+	1.49423i
$448$	−269.806	−	371.357i	−0.602246	−	0.828921i
$449$	−8.30087	+	25.5474i	−0.0184875	+	0.0568985i	−0.959875	−	0.280429i	$-0.909523\pi$
$449$	−8.30087	+	25.5474i	−0.0184875	+	0.0568985i	0.941387	+	0.337328i	$0.109523\pi$
$450$			100.334i			0.222965i
$451$	758.859	+	152.014i	1.68261	+	0.337060i
$452$	542.592			1.20043
$453$	−862.630	−	280.285i	−1.90426	−	0.618731i
$454$	55.2887	−	40.1696i	0.121781	−	0.0884793i
$455$	−328.458	−	238.639i	−0.721886	−	0.524481i
$456$	85.6159	+	263.499i	0.187754	+	0.577848i
$457$	−142.268	+	46.2257i	−0.311309	+	0.101150i	−0.460505	−	0.887657i	$-0.652332\pi$
$457$	−142.268	+	46.2257i	−0.311309	+	0.101150i	0.149196	+	0.988808i	$0.452332\pi$
$458$	−475.185	+	654.036i	−1.03752	+	1.42803i
$459$	−82.6327	−	113.734i	−0.180028	−	0.247787i
$460$	−31.4425	+	96.7700i	−0.0683532	+	0.210369i
$461$		−	743.262i		−	1.61228i	−0.591724	−	0.806141i	$-0.701553\pi$
$461$		−	743.262i		−	1.61228i	0.591724	−	0.806141i	$-0.298447\pi$
$462$	−290.383	−	632.137i	−0.628534	−	1.36826i
$463$	127.196			0.274721			0.137360	−	0.990521i	$-0.456138\pi$
$463$	127.196			0.274721			0.137360	+	0.990521i	$0.456138\pi$
$464$	−360.364	−	117.089i	−0.776646	−	0.252348i
$465$	638.031	−	463.556i	1.37211	−	0.996896i
$466$	−860.789	−	625.400i	−1.84719	−	1.34206i
$467$	−1.16856	−	3.59646i	−0.00250227	−	0.00770120i	0.949798	−	0.312865i	$-0.101289\pi$
$467$	−1.16856	−	3.59646i	−0.00250227	−	0.00770120i	−0.952300	+	0.305164i	$0.901289\pi$
$468$	−514.882	+	167.295i	−1.10018	+	0.357469i
$469$	−209.236	+	287.988i	−0.446131	+	0.614047i
$470$	86.9169	+	119.631i	0.184930	+	0.254534i
$471$	−119.425	+	367.551i	−0.253555	+	0.780363i
$472$			161.501i			0.342163i
$473$	406.369	+	440.803i	0.859132	+	0.931930i
$474$	−186.461			−0.393379
$475$	150.879	+	49.0234i	0.317639	+	0.103207i
$476$	327.565	−	237.990i	0.688161	−	0.499978i
$477$	−114.853	−	83.4454i	−0.240782	−	0.174938i
$478$	−96.0026	−	295.466i	−0.200842	−	0.618129i
$479$	−729.629	+	237.071i	−1.52323	+	0.494929i	−0.946693	−	0.322138i	$-0.895598\pi$
$479$	−729.629	+	237.071i	−1.52323	+	0.494929i	−0.576542	+	0.817067i	$0.695598\pi$
$480$	476.501	−	655.847i	0.992710	−	1.36635i
$481$	49.4105	+	68.0077i	0.102724	+	0.141388i
$482$	−187.504	+	577.077i	−0.389012	+	1.19726i
$483$			102.554i			0.212328i
$484$	374.130	−	435.657i	0.772997	−	0.900119i
$485$	−61.9217			−0.127674
$486$	848.768	+	275.781i	1.74644	+	0.567452i
$487$	−270.751	+	196.712i	−0.555956	+	0.403926i	−0.829977	−	0.557798i	$-0.811646\pi$
$487$	−270.751	+	196.712i	−0.555956	+	0.403926i	0.274020	+	0.961724i	$0.411646\pi$
$488$	−57.5463	−	41.8099i	−0.117923	−	0.0856759i
$489$	157.990	+	486.242i	0.323087	+	0.994360i
$490$	251.392	−	81.6821i	0.513044	−	0.166698i
$491$	186.552	−	256.766i	0.379942	−	0.522946i	−0.575627	−	0.817712i	$-0.695242\pi$
$491$	186.552	−	256.766i	0.379942	−	0.522946i	0.955569	+	0.294767i	$0.0952420\pi$
$492$	−779.283	−	1072.59i	−1.58391	−	2.18006i
$493$	148.859	−	458.141i	0.301945	−	0.929291i
$494$			1577.46i			3.19324i
$495$	244.583	−	225.477i	0.494107	−	0.455510i
$496$	553.611			1.11615
$497$	375.219	+	121.916i	0.754968	+	0.245304i
$498$	62.1570	−	45.1597i	0.124813	−	0.0906822i
$499$	−534.614	−	388.420i	−1.07137	−	0.778397i	−0.0952131	−	0.995457i	$-0.530353\pi$
$499$	−534.614	−	388.420i	−1.07137	−	0.778397i	−0.976158	+	0.217060i	$0.930353\pi$
$500$	196.786	+	605.645i	0.393572	+	1.21129i
$501$	59.4423	−	19.3140i	0.118647	−	0.0385509i
$502$	−182.790	+	251.588i	−0.364123	+	0.501172i
$503$	27.9939	+	38.5303i	0.0556539	+	0.0766010i	0.835937	−	0.548826i	$-0.184925\pi$
$503$	27.9939	+	38.5303i	0.0556539	+	0.0766010i	−0.780283	+	0.625427i	$0.784925\pi$
$504$	−24.8360	+	76.4373i	−0.0492777	+	0.151661i
$505$			491.339i			0.972949i
$506$	−141.770	+	65.1244i	−0.280178	+	0.128704i
$507$	−457.993			−0.903340
$508$	254.285	+	82.6221i	0.500560	+	0.162642i
$509$	544.939	−	395.921i	1.07061	−	0.777841i	0.0945853	−	0.995517i	$-0.469847\pi$
$509$	544.939	−	395.921i	1.07061	−	0.777841i	0.976021	+	0.217676i	$0.0698475\pi$
$510$	672.708	+	488.751i	1.31903	+	0.958335i
$511$	220.346	+	678.155i	0.431205	+	1.32711i
$512$	645.781	−	209.827i	1.26129	−	0.409818i
$513$	165.010	−	227.117i	0.321657	−	0.442722i
$514$	14.1087	+	19.4189i	0.0274488	+	0.0377800i
$515$	−92.8113	+	285.644i	−0.180216	+	0.554648i
$516$		−	1027.04i		−	1.99039i
$517$	−24.1660	+	120.637i	−0.0467428	+	0.233341i
$518$	79.4006			0.153283
$519$	−164.927	−	53.5882i	−0.317779	−	0.103253i
$520$	−134.534	+	97.7444i	−0.258719	+	0.187970i
$521$	−631.457	−	458.780i	−1.21201	−	0.880576i	−0.216597	−	0.976261i	$-0.569496\pi$
$521$	−631.457	−	458.780i	−1.21201	−	0.880576i	−0.995412	+	0.0956849i	$0.969496\pi$
$522$	188.001	+	578.608i	0.360155	+	1.10844i
$523$	755.717	−	245.547i	1.44497	−	0.469498i	0.521524	−	0.853237i	$-0.325364\pi$
$523$	755.717	−	245.547i	1.44497	−	0.469498i	0.923442	+	0.383739i	$0.125364\pi$
$524$	−535.726	+	737.363i	−1.02238	+	1.40718i
$525$	63.0377	+	86.7640i	0.120072	+	0.165265i
$526$	−264.540	+	814.169i	−0.502927	+	1.54785i
$527$			703.821i			1.33552i
$528$	540.505	−	63.2315i	1.02368	−	0.119757i
$529$	23.0000			0.0434783
$530$	−263.869	−	85.7361i	−0.497865	−	0.161766i
$531$	−400.673	+	291.106i	−0.754562	+	0.548222i
$532$	654.116	+	475.243i	1.22954	+	0.893314i
$533$	−366.623	−	1128.35i	−0.687849	−	2.11698i
$534$	581.262	−	188.864i	1.08851	−	0.353677i
$535$	235.924	−	324.721i	0.440979	−	0.606955i
$536$	85.7012	+	117.958i	0.159890	+	0.220070i
$537$	243.904	−	750.659i	0.454197	−	1.39787i
$538$		−	604.601i		−	1.12379i
$539$	191.743	+	107.722i	0.355738	+	0.199856i
$540$	188.292			0.348689
$541$	−457.069	−	148.511i	−0.844859	−	0.274511i	−0.145568	−	0.989348i	$-0.546501\pi$
$541$	−457.069	−	148.511i	−0.844859	−	0.274511i	−0.699291	+	0.714837i	$0.746501\pi$
$542$	−202.303	+	146.982i	−0.373253	+	0.271184i
$543$	927.137	+	673.604i	1.70743	+	1.24052i
$544$	223.566	+	688.066i	0.410967	+	1.26483i
$545$	502.130	−	163.152i	0.921339	−	0.299361i
$546$	−626.813	+	862.735i	−1.14801	+	1.58010i
$547$	−51.9228	−	71.4656i	−0.0949229	−	0.130650i	0.758914	−	0.651191i	$-0.225730\pi$
$547$	−51.9228	−	71.4656i	−0.0949229	−	0.130650i	−0.853837	+	0.520541i	$0.825730\pi$
$548$	−350.734	+	1079.45i	−0.640026	+	1.96980i
$549$		−	218.131i		−	0.397324i
$550$	−79.9110	+	142.240i	−0.145293	+	0.258618i
$551$	961.945			1.74582
$552$	39.9496	+	12.9804i	0.0723724	+	0.0235152i
$553$	−69.1905	+	50.2698i	−0.125118	+	0.0909038i
$554$	−115.402	−	83.8447i	−0.208307	−	0.151344i
$555$	27.3433	+	84.1539i	0.0492671	+	0.151629i
$556$	−150.144	+	48.7848i	−0.270043	+	0.0877424i
$557$	−381.186	+	524.657i	−0.684355	+	0.941933i	−0.999976	−	0.00695189i	$-0.997787\pi$
$557$	−381.186	+	524.657i	−0.684355	+	0.941933i	0.315621	+	0.948885i	$0.397787\pi$
$558$	−522.476	−	719.127i	−0.936337	−	1.28876i
$559$	284.008	−	874.088i	0.508065	−	1.56366i
$560$		−	299.993i		−	0.535701i
$561$	80.3880	+	687.159i	0.143294	+	1.22488i
$562$	−177.611			−0.316035
$563$	921.688	+	299.475i	1.63710	+	0.531927i	0.975888	−	0.218271i	$-0.0700417\pi$
$563$	921.688	+	299.475i	1.63710	+	0.531927i	0.661214	+	0.750198i	$0.270042\pi$
$564$	170.512	−	123.884i	0.302327	−	0.219653i
$565$	413.485	+	300.415i	0.731832	+	0.531707i
$566$	−193.213	−	594.647i	−0.341365	−	1.05061i
$567$	492.345	−	159.973i	0.868334	−	0.282139i
$568$	94.9835	−	130.734i	0.167225	−	0.230165i
$569$	−573.739	−	789.684i	−1.00833	−	1.38784i	−0.920073	−	0.391747i	$-0.871871\pi$
$569$	−573.739	−	789.684i	−1.00833	−	1.38784i	−0.0882550	−	0.996098i	$-0.528129\pi$
$570$	−513.108	+	1579.18i	−0.900190	+	2.77050i
$571$			407.498i			0.713656i	0.934170	+	0.356828i	$0.116142\pi$
$571$			407.498i			0.713656i	−0.934170	+	0.356828i	$0.883858\pi$
$572$	−863.170	−	172.910i	−1.50904	−	0.302290i
$573$	−178.834			−0.312102
$574$	−1065.78	−	346.293i	−1.85676	−	0.603297i
$575$	19.4587	−	14.1375i	0.0338411	−	0.0245870i
$576$	−466.444	−	338.891i	−0.809799	−	0.588353i
$577$	−206.820	−	636.526i	−0.358440	−	1.10316i	−0.953988	−	0.299845i	$-0.903065\pi$
$577$	−206.820	−	636.526i	−0.358440	−	1.10316i	0.595548	−	0.803320i	$-0.296935\pi$
$578$	107.089	−	34.7954i	0.185275	−	0.0601997i
$579$	884.111	−	1216.87i	1.52696	−	2.10168i
$580$	379.236	+	521.973i	0.653855	+	0.899954i
$581$	10.8897	−	33.5149i	0.0187430	−	0.0576849i
$582$			162.645i			0.279458i
$583$	−96.3621	−	209.772i	−0.165287	−	0.359814i
$584$	292.061			0.500105
$585$	−484.994	−	157.584i	−0.829050	−	0.269375i
$586$	697.822	−	506.998i	1.19082	−	0.865183i
$587$	−841.713	−	611.540i	−1.43392	−	1.04181i	−0.989269	−	0.146103i	$-0.953327\pi$
$587$	−841.713	−	611.540i	−1.43392	−	1.04181i	−0.444653	−	0.895703i	$-0.646673\pi$
$588$	−116.423	−	358.314i	−0.197999	−	0.609377i
$589$	−1336.68	+	434.313i	−2.26940	+	0.737373i
$590$	−568.916	+	783.046i	−0.964265	+	1.32720i
$591$	135.519	+	186.525i	0.229304	+	0.315610i
$592$	−19.1942	+	59.0738i	−0.0324227	+	0.0997869i
$593$			480.589i			0.810437i	0.914220	+	0.405218i	$0.132804\pi$
$593$			480.589i			0.810437i	−0.914220	+	0.405218i	$0.867196\pi$
$594$	195.687	+	212.269i	0.329440	+	0.357355i
$595$	381.389			0.640990
$596$	938.532	+	304.948i	1.57472	+	0.511657i
$597$	164.435	−	119.469i	0.275435	−	0.200116i
$598$	193.486	+	140.576i	0.323556	+	0.235077i
$599$	−329.234	−	1013.28i	−0.549639	−	1.69162i	−0.709696	−	0.704508i	$-0.751168\pi$
$599$	−329.234	−	1013.28i	−0.549639	−	1.69162i	0.160057	−	0.987108i	$-0.448832\pi$
$600$	41.7772	−	13.5742i	0.0696287	−	0.0226237i
$601$	−244.094	+	335.966i	−0.406146	+	0.559012i	−0.962273	−	0.272085i	$-0.912287\pi$
$601$	−244.094	+	335.966i	−0.406146	+	0.559012i	0.556127	+	0.831097i	$0.312287\pi$
$602$	−510.259	−	702.311i	−0.847606	−	1.16663i
$603$	−138.168	+	425.238i	−0.229134	+	0.705203i
$604$			1084.16i			1.79497i
$605$	526.316	−	124.852i	0.869944	−	0.206367i
$606$	1290.56			2.12964
$607$	919.268	+	298.688i	1.51444	+	0.492073i	0.944192	−	0.329396i	$-0.106845\pi$
$607$	919.268	+	298.688i	1.51444	+	0.492073i	0.570253	+	0.821469i	$0.306845\pi$
$608$	−1168.80	+	849.180i	−1.92236	+	1.39668i
$609$	526.100	+	382.234i	0.863876	+	0.627643i
$610$	−131.734	−	405.435i	−0.215957	−	0.664647i
$611$	179.376	−	58.2829i	0.293578	−	0.0953894i
$612$	298.928	−	411.439i	0.488444	−	0.672286i
$613$	−443.080	−	609.848i	−0.722807	−	0.994858i	−0.999426	−	0.0338783i	$-0.989214\pi$
$613$	−443.080	−	609.848i	−0.722807	−	0.994858i	0.276619	−	0.960980i	$-0.410786\pi$
$614$	210.674	−	648.388i	0.343117	−	1.05601i
$615$		−	1248.84i		−	2.03063i
$616$	−96.0873	+	88.5814i	−0.155986	+	0.143801i
$617$	−746.108			−1.20925			−0.604625	−	0.796510i	$-0.706677\pi$
$617$	−746.108			−1.20925			−0.604625	+	0.796510i	$0.706677\pi$
$618$	750.278	+	243.780i	1.21404	+	0.394466i
$619$	−91.2707	+	66.3121i	−0.147449	+	0.107128i	−0.659064	−	0.752087i	$-0.729047\pi$
$619$	−91.2707	+	66.3121i	−0.147449	+	0.107128i	0.511615	+	0.859215i	$0.329047\pi$
$620$	−762.638	−	554.089i	−1.23006	−	0.893691i
$621$	−13.1525	−	40.4792i	−0.0211795	−	0.0651838i
$622$	271.852	−	88.3300i	0.437061	−	0.142010i
$623$	164.772	−	226.790i	0.264482	−	0.364028i
$624$	−490.347	−	674.905i	−0.785812	−	1.08158i
$625$	−146.618	+	451.245i	−0.234589	+	0.721991i
$626$			538.120i			0.859617i
$627$	−1255.43	+	576.701i	−2.00228	+	0.919779i
$628$	461.942			0.735577
$629$	−75.1022	−	24.4022i	−0.119399	−	0.0387952i
$630$	−389.683	+	283.121i	−0.618544	+	0.449399i
$631$	−237.194	−	172.332i	−0.375903	−	0.273109i	0.383752	−	0.923436i	$-0.374632\pi$
$631$	−237.194	−	172.332i	−0.375903	−	0.273109i	−0.759654	+	0.650327i	$0.774632\pi$
$632$	10.8249	+	33.3155i	0.0171279	+	0.0527144i
$633$	7.55471	−	2.45468i	0.0119348	−	0.00387784i
$634$	−83.0245	+	114.273i	−0.130954	+	0.180242i
$635$	148.034	+	203.751i	0.233124	+	0.320868i
$636$	−122.202	+	376.098i	−0.192141	+	0.591348i
$637$		−	337.146i		−	0.529272i
$638$	−194.310	+	970.002i	−0.304561	+	1.52038i
$639$	495.549			0.775507
$640$	−294.907	−	95.8212i	−0.460793	−	0.149721i
$641$	−73.8661	+	53.6669i	−0.115236	+	0.0837237i	−0.643911	−	0.765101i	$-0.722689\pi$
$641$	−73.8661	+	53.6669i	−0.115236	+	0.0837237i	0.528675	+	0.848824i	$0.322689\pi$
$642$	−852.920	−	619.682i	−1.32854	−	0.965237i
$643$	156.894	+	482.869i	0.244003	+	0.750963i	0.995799	+	0.0915676i	$0.0291878\pi$
$643$	156.894	+	482.869i	0.244003	+	0.750963i	−0.751796	+	0.659396i	$0.770812\pi$
$644$	116.584	−	37.8803i	0.181030	−	0.0588204i
$645$	568.637	−	782.662i	0.881608	−	1.21343i
$646$	−871.011	−	1198.84i	−1.34831	−	1.85580i
$647$	46.5506	−	143.268i	0.0719483	−	0.221434i	−0.908616	−	0.417633i	$-0.862860\pi$
$647$	46.5506	−	143.268i	0.0719483	−	0.221434i	0.980564	+	0.196199i	$0.0628598\pi$
$648$		−	212.038i		−	0.327220i
$649$	−799.868	+	93.5733i	−1.23246	+	0.144181i
$650$	250.104			0.384775
$651$	−903.623	−	293.605i	−1.38805	−	0.451006i
$652$	494.402	−	359.204i	0.758285	−	0.550927i
$653$	644.561	+	468.301i	0.987076	+	0.717153i	0.959279	−	0.282461i	$-0.0911507\pi$
$653$	644.561	+	468.301i	0.987076	+	0.717153i	0.0277973	+	0.999614i	$0.491151\pi$
$654$	−428.538	−	1318.90i	−0.655257	−	2.01667i
$655$	−816.505	+	265.299i	−1.24657	+	0.405036i
$656$	515.282	−	709.225i	0.785491	−	1.08114i
$657$	526.441	+	724.584i	0.801280	+	1.10287i
$658$	55.0509	−	169.429i	0.0836640	−	0.257491i
$659$			450.496i			0.683605i	0.939772	+	0.341803i	$0.111037\pi$
$659$			450.496i			0.683605i	−0.939772	+	0.341803i	$0.888963\pi$
$660$	−807.869	−	453.866i	−1.22404	−	0.687675i
$661$	−583.434			−0.882654			−0.441327	−	0.897346i	$-0.645492\pi$
$661$	−583.434			−0.882654			−0.441327	+	0.897346i	$0.645492\pi$
$662$	−369.747	−	120.138i	−0.558530	−	0.181477i
$663$	858.025	−	623.392i	1.29416	−	0.940259i
$664$	−11.6773	−	8.48402i	−0.0175862	−	0.0127771i
$665$	235.347	+	724.323i	0.353905	+	1.08921i
$666$	94.8502	−	30.8187i	0.142418	−	0.0462743i
$667$	85.7241	−	117.989i	0.128522	−	0.176895i
$668$	−43.9122	−	60.4399i	−0.0657368	−	0.0904789i
$669$	393.315	−	1210.50i	0.587914	−	1.80941i
$670$			873.822i			1.30421i
$671$	173.730	−	309.235i	0.258912	−	0.460857i
$672$	−976.657			−1.45336
$673$	608.216	+	197.622i	0.903739	+	0.293643i	0.723779	−	0.690031i	$-0.242403\pi$
$673$	608.216	+	197.622i	0.903739	+	0.293643i	0.179960	+	0.983674i	$0.442403\pi$
$674$	−1325.82	+	963.267i	−1.96710	+	1.42918i
$675$	−36.0089	−	26.1620i	−0.0533465	−	0.0387585i
$676$	169.168	+	520.645i	0.250248	+	0.770185i
$677$	958.660	−	311.488i	1.41604	−	0.460100i	0.501699	−	0.865042i	$-0.332708\pi$
$677$	958.660	−	311.488i	1.41604	−	0.460100i	0.914342	+	0.404942i	$0.132708\pi$
$678$	789.076	−	1086.07i	1.16383	−	1.60187i
$679$	43.8489	+	60.3528i	0.0645786	+	0.0888848i
$680$	48.2727	−	148.568i	0.0709893	−	0.218483i
$681$		−	91.7530i		−	0.134733i
$682$	−167.945	−	1435.60i	−0.246254	−	2.10499i
$683$	−994.944			−1.45673			−0.728363	−	0.685191i	$-0.759719\pi$
$683$	−994.944			−1.45673			−0.728363	+	0.685191i	$0.759719\pi$
$684$	965.855	+	313.825i	1.41207	+	0.458809i
$685$	−864.932	+	628.410i	−1.26268	+	0.917387i
$686$	−889.029	−	645.918i	−1.29596	−	0.941571i
$687$	335.403	+	1032.27i	0.488215	+	1.50257i
$688$	645.868	−	209.855i	0.938761	−	0.305022i
$689$	−208.005	+	286.294i	−0.301894	+	0.415522i
$690$	147.972	+	203.666i	0.214452	+	0.295168i
$691$	154.549	−	475.653i	0.223660	−	0.688354i	−0.774765	−	0.632249i	$-0.782132\pi$
$691$	154.549	−	475.653i	0.223660	−	0.688354i	0.998425	−	0.0561050i	$-0.0178681\pi$
$692$			207.283i			0.299542i
$693$	−392.962	−	78.7179i	−0.567045	−	0.113590i
$694$	−815.305			−1.17479
$695$	−141.428	−	45.9529i	−0.203494	−	0.0661193i
$696$	215.486	−	156.560i	0.309607	−	0.224943i
$697$	901.657	+	655.092i	1.29363	+	0.939874i
$698$	−280.157	−	862.235i	−0.401371	−	1.23529i
$699$	−1358.59	+	441.431i	−1.94361	+	0.631518i
$700$	75.3490	−	103.709i	0.107641	−	0.148156i
$701$	−802.066	−	1103.95i	−1.14417	−	1.57482i	−0.757810	−	0.652475i	$-0.773731\pi$
$701$	−802.066	−	1103.95i	−1.14417	−	1.57482i	−0.386364	−	0.922346i	$-0.626269\pi$
$702$	136.764	−	420.917i	0.194821	−	0.599597i
$703$		−	157.690i		−	0.224310i
$704$	−391.349	−	851.931i	−0.555893	−	1.21013i
$705$	198.530			0.281603
$706$	−225.089	−	73.1358i	−0.318823	−	0.103592i
$707$	478.890	−	347.934i	0.677355	−	0.492127i
$708$	1116.09	+	810.888i	1.57640	+	1.14532i
$709$	−5.05897	−	15.5699i	−0.00713536	−	0.0219604i	0.947425	−	0.319977i	$-0.103675\pi$
$709$	−5.05897	−	15.5699i	−0.00713536	−	0.0219604i	−0.954561	+	0.298016i	$0.903675\pi$
$710$	921.066	−	299.272i	1.29728	−	0.421510i
$711$	−63.1416	+	86.9070i	−0.0888067	+	0.122232i
$712$	−67.4893	−	92.8911i	−0.0947884	−	0.130465i
$713$	−65.8471	+	202.656i	−0.0923521	+	0.284231i
$714$		−	1001.76i		−	1.40303i
$715$	−562.049	−	609.674i	−0.786082	−	0.852691i
$716$	−943.437			−1.31765
$717$	−396.687	−	128.892i	−0.553260	−	0.179765i
$718$	−644.778	+	468.459i	−0.898020	+	0.652449i
$719$	−287.665	−	209.001i	−0.400090	−	0.290682i	0.369488	−	0.929236i	$-0.379533\pi$
$719$	−287.665	−	209.001i	−0.400090	−	0.290682i	−0.769578	+	0.638553i	$0.779533\pi$
$720$	−116.440	−	358.365i	−0.161722	−	0.497729i
$721$	344.129	−	111.814i	0.477295	−	0.155082i
$722$	1111.81	−	1530.27i	1.53990	−	2.11949i
$723$	478.837	+	659.063i	0.662292	+	0.911567i
$724$	423.297	−	1302.77i	0.584664	−	1.79941i
$725$		−	152.515i		−	0.210365i
$726$	−327.939	−	1382.43i	−0.451706	−	1.90418i
$727$	−985.113			−1.35504			−0.677520	−	0.735505i	$-0.736945\pi$
$727$	−985.113			−1.35504			−0.677520	+	0.735505i	$0.736945\pi$
$728$	190.536	+	61.9088i	0.261725	+	0.0850396i
$729$	269.483	−	195.791i	0.369661	−	0.268575i
$730$	1416.07	+	1028.84i	1.93983	+	1.40937i
$731$	266.795	+	821.110i	0.364972	+	1.12327i
$732$	−577.875	+	187.763i	−0.789446	+	0.256507i
$733$	827.410	−	1138.83i	1.12880	−	1.55366i	0.338468	−	0.940978i	$-0.390091\pi$
$733$	827.410	−	1138.83i	1.12880	−	1.55366i	0.790330	−	0.612681i	$-0.209909\pi$
$734$	−267.799	−	368.594i	−0.364849	−	0.502171i
$735$	109.665	−	337.514i	0.149204	−	0.459203i
$736$			219.036i			0.297603i
$737$	−534.555	+	492.798i	−0.725312	+	0.668654i
$738$	−1407.57			−1.90727
$739$	−1193.24	−	387.708i	−1.61467	−	0.524638i	−0.643994	−	0.765030i	$-0.722724\pi$
$739$	−1193.24	−	387.708i	−1.61467	−	0.524638i	−0.970676	+	0.240392i	$0.922724\pi$
$740$	85.5662	−	62.1675i	0.115630	−	0.0840101i
$741$	1713.40	+	1244.86i	2.31228	+	1.67997i
$742$	103.291	+	317.896i	0.139206	+	0.428431i
$743$	564.159	−	183.306i	0.759298	−	0.246711i	0.0963208	−	0.995350i	$-0.469293\pi$
$743$	564.159	−	183.306i	0.759298	−	0.246711i	0.662977	+	0.748639i	$0.269293\pi$
$744$	−228.745	+	314.840i	−0.307452	+	0.423172i
$745$	546.374	+	752.020i	0.733388	+	1.00942i
$746$	−427.534	+	1315.82i	−0.573102	+	1.76383i
$747$		−	44.2629i		−	0.0592543i
$748$	751.468	−	345.199i	1.00464	−	0.461496i
$749$	−483.559			−0.645607
$750$	1498.46	+	486.879i	1.99794	+	0.649171i
$751$	445.774	−	323.874i	0.593574	−	0.431257i	−0.250018	−	0.968241i	$-0.580437\pi$
$751$	445.774	−	323.874i	0.593574	−	0.431257i	0.843592	+	0.536984i	$0.180437\pi$
$752$	112.747	+	81.9155i	0.149930	+	0.108930i
$753$	129.020	+	397.082i	0.171341	+	0.527334i
$754$	1442.30	−	468.632i	1.91286	−	0.621527i
$755$	−600.264	+	826.192i	−0.795051	+	1.09429i
$756$	−133.336	−	183.521i	−0.176370	−	0.242753i
$757$	151.195	−	465.330i	0.199729	−	0.614703i	−0.800160	−	0.599787i	$-0.795252\pi$
$757$	151.195	−	465.330i	0.199729	−	0.614703i	0.999889	−	0.0149159i	$-0.00474806\pi$
$758$		−	633.446i		−	0.835681i
$759$	−41.1415	+	205.380i	−0.0542049	+	0.270592i
$760$	311.944			0.410453
$761$	−162.447	−	52.7823i	−0.213465	−	0.0693591i	0.200332	−	0.979728i	$-0.435798\pi$
$761$	−162.447	−	52.7823i	−0.213465	−	0.0693591i	−0.413798	+	0.910369i	$0.635798\pi$
$762$	535.177	−	388.829i	0.702332	−	0.510274i
$763$	−514.593	−	373.874i	−0.674434	−	0.490005i
$764$	66.0557	+	203.298i	0.0864603	+	0.266097i
$765$	455.599	−	148.033i	0.595554	−	0.193507i
$766$	−325.832	+	448.469i	−0.425368	+	0.585469i
$767$	725.641	+	998.759i	0.946077	+	1.30216i
$768$	166.600	−	512.742i	0.216927	−	0.667633i
$769$		−	1015.06i		−	1.31998i	−0.751275	−	0.659989i	$-0.770561\pi$
$769$		−	1015.06i		−	1.31998i	0.751275	−	0.659989i	$-0.229439\pi$
$770$	−777.929	+	91.0068i	−1.01030	+	0.118191i
$771$	32.2262			0.0417979
$772$	−1709.90	−	555.580i	−2.21490	−	0.719664i
$773$	−959.035	+	696.780i	−1.24067	+	0.901397i	−0.997643	−	0.0686231i	$-0.978139\pi$
$773$	−959.035	+	696.780i	−1.24067	+	0.901397i	−0.243024	+	0.970020i	$0.578139\pi$
$774$	−882.141	−	640.913i	−1.13972	−	0.828053i
$775$	68.8595	+	211.928i	0.0888510	+	0.273455i
$776$	29.0601	−	9.44220i	0.0374486	−	0.0121678i
$777$	62.6590	−	86.2427i	0.0806422	−	0.110995i
$778$	1053.72	+	1450.32i	1.35439	+	1.86416i
$779$	−687.740	+	2116.64i	−0.882849	+	2.71713i
$780$			1420.50i			1.82115i
$781$	702.520	+	394.680i	0.899513	+	0.505352i
$782$	−224.667			−0.287298
$783$	−256.678	−	83.3996i	−0.327813	−	0.106513i
$784$	201.541	−	146.428i	0.257068	−	0.186771i
$785$	352.025	+	255.761i	0.448440	+	0.325811i
$786$	696.839	+	2144.65i	0.886563	+	2.72856i
$787$	−695.781	+	226.073i	−0.884093	+	0.287259i	−0.715656	−	0.698453i	$-0.753872\pi$
$787$	−695.781	+	226.073i	−0.884093	+	0.287259i	−0.168437	+	0.985712i	$0.553872\pi$
$788$	161.985	−	222.954i	0.205565	−	0.282936i
$789$	675.567	+	929.838i	0.856232	+	1.17850i
$790$	−64.8749	+	199.664i	−0.0821202	+	0.252740i
$791$		−	615.743i		−	0.778436i
$792$	−80.4017	+	143.113i	−0.101517	+	0.180698i
$793$	−543.736			−0.685670
$794$	−1472.15	−	478.331i	−1.85410	−	0.602432i
$795$	−301.356	+	218.948i	−0.379065	+	0.275407i
$796$	−196.549	−	142.801i	−0.246921	−	0.179398i
$797$	397.127	+	1222.23i	0.498278	+	1.53354i	0.811785	+	0.583956i	$0.198496\pi$
$797$	397.127	+	1222.23i	0.498278	+	1.53354i	−0.313508	+	0.949586i	$0.601504\pi$
$798$	1902.52	−	618.167i	2.38411	−	0.774645i
$799$	−104.142	+	143.339i	−0.130340	+	0.179397i
$800$	134.636	+	185.311i	0.168295	+	0.231638i
$801$	108.807	−	334.873i	0.135839	−	0.418068i
$802$		−	474.486i		−	0.591628i
$803$	169.220	+	1446.50i	0.210734	+	1.80136i
$804$	1245.48			1.54910
$805$	109.816	+	35.6814i	0.136418	+	0.0443248i
$806$	−1792.57	+	1302.38i	−2.22404	+	1.61586i
$807$	−656.701	−	477.121i	−0.813756	−	0.591229i
$808$	−74.9224	−	230.588i	−0.0927258	−	0.285381i
$809$	884.108	−	287.264i	1.09284	−	0.355085i	0.293497	−	0.955960i	$-0.405181\pi$
$809$	884.108	−	287.264i	1.09284	−	0.355085i	0.799343	+	0.600875i	$0.205181\pi$
$810$	746.944	−	1028.08i	0.922153	−	1.26923i
$811$	−426.405	−	586.897i	−0.525777	−	0.723670i	0.460702	−	0.887555i	$-0.347598\pi$
$811$	−426.405	−	586.897i	−0.525777	−	0.723670i	−0.986480	+	0.163884i	$0.947598\pi$
$812$	240.198	−	739.254i	0.295811	−	0.910412i
$813$			335.727i			0.412948i
$814$	159.011	+	31.8529i	0.195345	+	0.0391314i
$815$	575.640			0.706307
$816$	745.311	+	242.166i	0.913371	+	0.296772i
$817$	−1394.79	+	1013.38i	−1.70721	+	1.24036i
$818$	−664.373	−	482.696i	−0.812192	−	0.590092i
$819$	189.850	+	584.297i	0.231807	+	0.713427i
$820$	−1419.67	+	461.280i	−1.73131	+	0.562536i
$821$	−178.811	+	246.112i	−0.217796	+	0.299771i	−0.903909	−	0.427724i	$-0.859316\pi$
$821$	−178.811	+	246.112i	−0.217796	+	0.299771i	0.686113	+	0.727495i	$0.259316\pi$
$822$	1650.60	+	2271.85i	2.00802	+	2.76381i
$823$	−50.7688	+	156.250i	−0.0616874	+	0.189854i	−0.977151	−	0.212547i	$-0.931824\pi$
$823$	−50.7688	+	156.250i	−0.0616874	+	0.189854i	0.915463	+	0.402401i	$0.131824\pi$
$824$		−	148.206i		−	0.179862i
$825$	91.4350	+	199.046i	0.110830	+	0.241268i
$826$	1166.08			1.41171
$827$	−578.006	−	187.806i	−0.698919	−	0.227093i	−0.0620598	−	0.998072i	$-0.519767\pi$
$827$	−578.006	−	187.806i	−0.698919	−	0.227093i	−0.636860	+	0.770980i	$0.719767\pi$
$828$	124.565	−	90.5020i	0.150441	−	0.109302i
$829$	1004.83	+	730.053i	1.21210	+	0.880642i	0.995420	−	0.0956003i	$-0.0304771\pi$
$829$	1004.83	+	730.053i	1.21210	+	0.880642i	0.216680	+	0.976243i	$0.430477\pi$
$830$	−26.7313	−	82.2705i	−0.0322064	−	0.0991211i
$831$	−182.140	+	59.1808i	−0.219181	+	0.0712163i
$832$	−844.757	+	1162.71i	−1.01533	+	1.39749i
$833$	186.159	+	256.225i	0.223480	+	0.307593i
$834$	−120.701	+	371.479i	−0.144725	+	0.445419i
$835$		−	70.3712i		−	0.0842769i
$836$	1119.31	+	1214.15i	1.33888	+	1.45233i
$837$	394.322			0.471114
$838$	1101.95	+	358.046i	1.31498	+	0.427262i
$839$	665.127	−	483.243i	0.792761	−	0.575975i	−0.116020	−	0.993247i	$-0.537014\pi$
$839$	665.127	−	483.243i	0.792761	−	0.575975i	0.908782	+	0.417272i	$0.137014\pi$
$840$	170.606	+	123.953i	0.203103	+	0.147563i
$841$	−25.8909	−	79.6839i	−0.0307858	−	0.0947490i
$842$	1687.92	−	548.437i	2.00465	−	0.651350i
$843$	−140.162	+	192.917i	−0.166266	+	0.228846i
$844$	−5.58094	−	7.68150i	−0.00661248	−	0.00910130i
$845$	−159.348	+	490.423i	−0.188578	+	0.580382i
$846$		−	223.764i		−	0.264497i
$847$	−494.391	−	424.569i	−0.583697	−	0.501262i
$848$	−261.483			−0.308353
$849$	−798.363	−	259.404i	−0.940357	−	0.305541i
$850$	−190.075	+	138.097i	−0.223617	+	0.162467i
$851$	−19.3418	−	14.0526i	−0.0227283	−	0.0165130i
$852$	−426.559	−	1312.81i	−0.500656	−	1.54086i
$853$	−216.744	+	70.4244i	−0.254096	+	0.0825609i	−0.433295	−	0.901252i	$-0.642649\pi$
$853$	−216.744	+	70.4244i	−0.254096	+	0.0825609i	0.179199	+	0.983813i	$0.442649\pi$
$854$	−301.877	+	415.498i	−0.353486	+	0.486532i
$855$	562.280	+	773.913i	0.657638	+	0.905161i
$856$	−61.2045	+	188.368i	−0.0715006	+	0.220056i
$857$		−	892.528i		−	1.04146i	−0.853722	−	0.520728i	$-0.825660\pi$
$857$		−	892.528i		−	1.04146i	0.853722	−	0.520728i	$-0.174340\pi$
$858$	−1601.38	+	1476.29i	−1.86641	+	1.72062i
$859$	−873.333			−1.01669			−0.508343	−	0.861155i	$-0.669742\pi$
$859$	−873.333			−1.01669			−0.508343	+	0.861155i	$0.669742\pi$
$860$	−1099.76	−	357.335i	−1.27879	−	0.415506i
$861$	−1217.19	+	884.344i	−1.41370	+	1.02711i
$862$	−1246.12	−	905.358i	−1.44561	−	1.05030i
$863$	−248.204	−	763.893i	−0.287606	−	0.885160i	−0.985605	−	0.169062i	$-0.945926\pi$
$863$	−248.204	−	763.893i	−0.287606	−	0.885160i	0.697999	−	0.716098i	$-0.254074\pi$
$864$	385.495	−	125.255i	0.446175	−	0.144971i
$865$	−114.765	+	157.961i	−0.132677	+	0.182614i
$866$	510.337	+	702.419i	0.589304	+	0.811108i
$867$	46.7157	−	143.776i	0.0538820	−	0.165832i
$868$			1135.68i			1.30839i
$869$	−158.730	+	72.9154i	−0.182658	+	0.0839072i
$870$	1596.31			1.83484
$871$	1059.99	+	344.413i	1.21698	+	0.395422i
$872$	−210.773	+	153.136i	−0.241712	+	0.175614i
$873$	75.8063	+	55.0765i	0.0868343	+	0.0630888i
$874$	−138.637	−	426.681i	−0.158624	−	0.488193i
$875$	687.296	−	223.316i	0.785482	−	0.255218i
$876$	1466.42	−	2018.36i	1.67400	−	2.30406i
$877$	353.176	+	486.105i	0.402710	+	0.554282i	0.961421	−	0.275080i	$-0.0887042\pi$
$877$	353.176	+	486.105i	0.402710	+	0.554282i	−0.558712	+	0.829362i	$0.688704\pi$
$878$	600.627	−	1848.54i	0.684085	−	2.10540i
$879$		−	1158.05i		−	1.31747i
$880$	120.347	−	600.777i	0.136758	−	0.682701i
$881$	1274.34			1.44647			0.723236	−	0.690601i	$-0.242654\pi$
$881$	1274.34			1.44647			0.723236	+	0.690601i	$0.242654\pi$
$882$	−380.414	−	123.604i	−0.431308	−	0.140141i
$883$	−967.788	+	703.139i	−1.09602	+	0.796307i	−0.980406	−	0.196987i	$-0.936884\pi$
$883$	−967.788	+	703.139i	−1.09602	+	0.796307i	−0.115616	+	0.993294i	$0.536884\pi$
$884$	−1025.60	−	745.140i	−1.16018	−	0.842918i
$885$	401.563	+	1235.88i	0.453743	+	1.39648i
$886$	−134.067	+	43.5611i	−0.151318	+	0.0491661i
$887$	−800.608	+	1101.94i	−0.902602	+	1.24233i	0.0670287	+	0.997751i	$0.478648\pi$
$887$	−800.608	+	1101.94i	−0.902602	+	1.24233i	−0.969631	+	0.244574i	$0.921352\pi$
$888$	−25.6646	−	35.3243i	−0.0289016	−	0.0397796i
$889$	93.7609	−	288.566i	0.105468	−	0.324597i
$890$		−	688.131i		−	0.773181i
$891$	1050.17	−	122.855i	1.17864	−	0.137884i
$892$	−1521.37			−1.70557
$893$	−336.488	−	109.332i	−0.376806	−	0.122432i
$894$	1975.27	−	1435.12i	2.20948	−	1.60528i
$895$	−718.951	−	522.348i	−0.803297	−	0.583629i
$896$	115.441	+	355.290i	0.128840	+	0.396529i
$897$	305.380	−	99.2240i	0.340446	−	0.110618i
$898$	46.6942	−	64.2690i	0.0519980	−	0.0715691i
$899$	794.199	+	1093.12i	0.883425	+	1.21593i
$900$	49.7564	−	153.135i	0.0552849	−	0.170149i
$901$		−	332.431i		−	0.368958i
$902$	−1995.45	−	1121.06i	−2.21225	−	1.24286i
$903$	−1165.50			−1.29070
$904$	−239.859	−	77.9351i	−0.265331	−	0.0862114i
$905$	1043.88	−	758.421i	1.15345	−	0.838034i
$906$	2170.09	+	1576.67i	2.39525	+	1.74025i
$907$	79.1443	+	243.581i	0.0872595	+	0.268557i	0.985159	−	0.171643i	$-0.0549075\pi$
$907$	79.1443	+	243.581i	0.0872595	+	0.268557i	−0.897900	+	0.440200i	$0.854908\pi$
$908$	−104.305	+	33.8906i	−0.114873	+	0.0373245i
$909$	437.024	−	601.512i	0.480775	−	0.661729i
$910$	705.738	+	971.365i	0.775536	+	1.06743i
$911$	50.3006	−	154.809i	0.0552147	−	0.169934i	−0.919646	−	0.392748i	$-0.871524\pi$
$911$	50.3006	−	154.809i	0.0552147	−	0.169934i	0.974861	+	0.222815i	$0.0715244\pi$
$912$			1564.91i			1.71591i
$913$	35.2532	−	62.7498i	0.0386125	−	0.0687292i
$914$	442.389			0.484014
$915$	−544.330	−	176.864i	−0.594896	−	0.193294i
$916$	1049.59	−	762.571i	1.14584	−	0.832502i
$917$	836.772	+	607.950i	0.912510	+	0.662977i
$918$	128.475	+	395.405i	0.139951	+	0.430725i
$919$	−1251.43	+	406.615i	−1.36173	+	0.442454i	−0.896622	−	0.442797i	$-0.853986\pi$
$919$	−1251.43	+	406.615i	−1.36173	+	0.442454i	−0.465112	+	0.885252i	$0.653986\pi$
$920$	27.7990	−	38.2621i	0.0302163	−	0.0415892i
$921$	−538.008	−	740.504i	−0.584156	−	0.804022i
$922$	−679.246	+	2090.50i	−0.736709	+	2.26736i
$923$		−	1235.26i		−	1.33831i
$924$	129.714	+	1108.80i	0.140383	+	1.20000i
$925$	−25.0015			−0.0270286
$926$	−357.752	−	116.241i	−0.386341	−	0.125530i
$927$	367.690	−	267.142i	0.396645	−	0.288179i
$928$	1123.65	+	816.376i	1.21082	+	0.879716i
$929$	−494.557	−	1522.09i	−0.532354	−	1.63842i	−0.749297	−	0.662234i	$-0.769608\pi$
$929$	−494.557	−	1522.09i	−0.532354	−	1.63842i	0.216942	−	0.976184i	$-0.430392\pi$
$930$	−2218.16	+	720.724i	−2.38512	+	0.774972i
$931$	−371.741	+	511.658i	−0.399293	+	0.549579i
$932$	1003.64	+	1381.39i	1.07686	+	1.48217i
$933$	118.590	−	364.984i	0.127107	−	0.391194i
$934$			11.1833i			0.0119736i
$935$	763.785	+	153.001i	0.816882	+	0.163637i
$936$	251.639			0.268845
$937$	−152.455	−	49.5356i	−0.162705	−	0.0528661i	0.226532	−	0.974004i	$-0.427261\pi$
$937$	−152.455	−	49.5356i	−0.162705	−	0.0528661i	−0.389237	+	0.921138i	$0.627261\pi$
$938$	851.682	−	618.783i	0.907977	−	0.659684i
$939$	584.492	+	424.658i	0.622462	+	0.452245i
$940$	−73.3307	−	225.689i	−0.0780114	−	0.240094i
$941$	611.610	−	198.724i	0.649957	−	0.211184i	0.0345619	−	0.999403i	$-0.488996\pi$
$941$	611.610	−	198.724i	0.649957	−	0.211184i	0.615395	+	0.788219i	$0.288996\pi$
$942$	671.789	−	924.638i	0.713151	−	0.981569i
$943$	198.333	+	272.982i	0.210321	+	0.289482i
$944$	−281.886	+	867.557i	−0.298608	+	0.919022i
$945$		−	213.677i		−	0.226113i
$946$	−740.120	−	1611.18i	−0.782368	−	1.70315i
$947$	1221.62			1.28999			0.644996	−	0.764186i	$-0.276859\pi$
$947$	1221.62			1.28999			0.644996	+	0.764186i	$0.276859\pi$
$948$	284.586	+	92.4676i	0.300196	+	0.0975396i
$949$	1806.17	−	1312.26i	1.90324	−	1.38278i
$950$	−379.561	−	275.767i	−0.399538	−	0.290281i
$951$	58.6019	+	180.358i	0.0616213	+	0.189651i
$952$	−178.988	+	58.1566i	−0.188012	+	0.0610888i
$953$	567.738	−	781.424i	0.595738	−	0.819963i	−0.399572	−	0.916702i	$-0.630841\pi$
$953$	567.738	−	781.424i	0.595738	−	0.819963i	0.995310	+	0.0967391i	$0.0308413\pi$
$954$	246.777	+	339.660i	0.258677	+	0.356038i
$955$	−62.2213	+	191.497i	−0.0651532	+	0.200521i
$956$			498.561i			0.521508i
$957$	900.250	+	976.532i	0.940700	+	1.02041i
$958$	2268.81			2.36828
$959$	1224.98	+	398.019i	1.27735	+	0.415035i
$960$	−1223.88	+	889.200i	−1.27487	+	0.926250i
$961$	−819.657	−	595.516i	−0.852921	−	0.619683i
$962$	−76.8220	−	236.434i	−0.0798565	−	0.245773i
$963$	−577.650	+	187.690i	−0.599844	+	0.194901i
$964$	572.353	−	787.777i	0.593728	−	0.817196i
$965$	−995.433	−	1370.10i	−1.03154	−	1.41979i
$966$	93.7216	−	288.446i	0.0970203	−	0.298598i
$967$		−	1026.92i		−	1.06196i	−0.847384	−	0.530981i	$-0.821824\pi$
$967$		−	1026.92i		−	1.06196i	0.847384	−	0.530981i	$-0.178176\pi$
$968$	−227.964	+	138.850i	−0.235500	+	0.143440i
$969$	−1989.51			−2.05316
$970$	174.161	+	56.5885i	0.179548	+	0.0583386i
$971$	658.590	−	478.494i	0.678260	−	0.492784i	−0.194520	−	0.980899i	$-0.562315\pi$
$971$	658.590	−	478.494i	0.678260	−	0.492784i	0.872780	+	0.488114i	$0.162315\pi$
$972$	−1158.67	−	841.820i	−1.19204	−	0.866070i
$973$	55.3618	+	170.386i	0.0568980	+	0.175114i
$974$	941.285	−	305.842i	0.966412	−	0.314006i
$975$	197.370	−	271.656i	0.202430	−	0.278621i
$976$	−236.154	−	325.038i	−0.241961	−	0.333031i
$977$	−300.760	+	925.646i	−0.307841	+	0.947437i	0.670761	+	0.741674i	$0.265968\pi$
$977$	−300.760	+	925.646i	−0.307841	+	0.947437i	−0.978602	+	0.205763i	$0.934032\pi$
$978$		−	1511.99i		−	1.54600i
$979$	420.960	−	388.076i	0.429990	−	0.396401i
$980$	−424.192			−0.432849
$981$	−759.838	−	246.886i	−0.774555	−	0.251668i
$982$	−759.348	+	551.699i	−0.773267	+	0.561811i
$983$	−609.510	−	442.835i	−0.620051	−	0.450494i	0.232888	−	0.972504i	$-0.425182\pi$
$983$	−609.510	−	442.835i	−0.620051	−	0.450494i	−0.852939	+	0.522010i	$0.825182\pi$
$984$	190.430	+	586.084i	0.193527	+	0.595614i
$985$	246.884	−	80.2173i	0.250643	−	0.0814389i
$986$	−837.364	+	1152.53i	−0.849253	+	1.16890i
$987$	−140.586	−	193.500i	−0.142438	−	0.196049i
$988$	782.275	−	2407.59i	0.791776	−	2.43684i
$989$			261.389i			0.264296i
$990$	−893.973	+	410.662i	−0.903003	+	0.414810i
$991$	868.054			0.875937			0.437969	−	0.898990i	$-0.355698\pi$
$991$	868.054			0.875937			0.437969	+	0.898990i	$0.355698\pi$
$992$	−1929.96	−	627.081i	−1.94552	−	0.632139i
$993$	−422.277	+	306.802i	−0.425253	+	0.308965i
$994$	−943.928	−	685.804i	−0.949626	−	0.689944i
$995$	−70.7170	−	217.645i	−0.0710724	−	0.218738i
$996$	−117.262	+	38.1007i	−0.117733	+	0.0382537i
$997$	−183.444	+	252.489i	−0.183996	+	0.253249i	−0.891044	−	0.453917i	$-0.850026\pi$
$997$	−183.444	+	252.489i	−0.183996	+	0.253249i	0.707048	+	0.707165i	$0.250026\pi$
$998$	1148.69	+	1581.04i	1.15100	+	1.58421i
$999$	−13.6716	+	42.0767i	−0.0136852	+	0.0421188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.g.a.24.7	✓	176
11.6	odd	10	inner	253.3.g.a.116.7	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.g.a.24.7	✓	176	1.1	even	1	trivial
253.3.g.a.116.7	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+(-2.81261 - 0.913872i) q^{2} +(-3.21219 + 2.33380i) q^{3} +(3.83953 + 2.78958i) q^{4} +(1.38144 + 4.25163i) q^{5} +(11.1674 - 3.62852i) q^{6} +(3.16567 - 4.35717i) q^{7} +(-1.29663 - 1.78466i) q^{8} +(2.09044 - 6.43370i) q^{9} -13.2206i q^{10} +(8.08764 - 7.45587i) q^{11} -18.8436 q^{12} +(-16.0373 - 5.21085i) q^{13} +(-12.8857 + 9.36199i) q^{14} +(-14.3599 - 10.4331i) q^{15} +(-3.85032 - 11.8501i) q^{16} +(15.0653 - 4.89502i) q^{17} +(-11.7592 + 16.1851i) q^{18} +(18.5930 + 25.5910i) q^{19} +(-6.55621 + 20.1779i) q^{20} +21.3841i q^{21} +(-29.5611 + 13.5794i) q^{22} +4.79583 q^{23} +(8.33006 + 2.70660i) q^{24} +(4.05741 - 2.94788i) q^{25} +(40.3447 + 29.3121i) q^{26} +(-2.74248 - 8.44049i) q^{27} +(24.3094 - 7.89859i) q^{28} +(17.8747 - 24.6024i) q^{29} +(30.8543 + 42.4673i) q^{30} +(-13.7301 + 42.2568i) q^{31} +45.6721i q^{32} +(-8.57860 + 42.8246i) q^{33} -46.8463 q^{34} +(22.8983 + 7.44009i) q^{35} +(25.9737 - 18.8710i) q^{36} +(-4.03303 - 2.93017i) q^{37} +(-28.9078 - 88.9691i) q^{38} +(63.6761 - 20.6896i) q^{39} +(5.79650 - 7.97820i) q^{40} +(41.3552 + 56.9206i) q^{41} +(19.5423 - 60.1450i) q^{42} +54.5033i q^{43} +(51.8516 - 6.06591i) q^{44} +30.2416 q^{45} +(-13.4888 - 4.38277i) q^{46} +(-9.04879 + 6.57433i) q^{47} +(40.0236 + 29.0789i) q^{48} +(6.17838 + 19.0151i) q^{49} +(-14.1059 + 4.58328i) q^{50} +(-36.9688 + 50.8832i) q^{51} +(-47.0398 - 64.7447i) q^{52} +(6.48502 - 19.9588i) q^{53} +26.2461i q^{54} +(42.8722 + 24.0859i) q^{55} -11.8808 q^{56} +(-119.448 - 38.8111i) q^{57} +(-72.7580 + 52.8618i) q^{58} +(-59.2291 - 43.0324i) q^{59} +(-26.0314 - 80.1163i) q^{60} +(30.6668 - 9.96425i) q^{61} +(77.2346 - 106.304i) q^{62} +(-21.4151 - 29.4753i) q^{63} +(26.3372 - 81.0575i) q^{64} -75.3834i q^{65} +(63.2644 - 112.609i) q^{66} -66.0953 q^{67} +(71.4989 + 23.2314i) q^{68} +(-15.4051 + 11.1925i) q^{69} +(-57.6045 - 41.8521i) q^{70} +(22.6368 + 69.6688i) q^{71} +(-14.1925 + 4.61142i) q^{72} +(-77.8206 + 107.111i) q^{73} +(8.66554 + 11.9271i) q^{74} +(-6.15344 + 18.9383i) q^{75} +150.124i q^{76} +(-6.88369 - 58.8420i) q^{77} -198.004 q^{78} +(-15.1025 - 4.90710i) q^{79} +(45.0632 - 32.7403i) q^{80} +(77.7633 + 56.4983i) q^{81} +(-64.2979 - 197.889i) q^{82} +(6.22289 - 2.02194i) q^{83} +(-59.6527 + 82.1049i) q^{84} +(41.6237 + 57.2901i) q^{85} +(49.8090 - 153.296i) q^{86} +120.744i q^{87} +(-23.7929 - 4.76617i) q^{88} +52.0498 q^{89} +(-85.0577 - 27.6369i) q^{90} +(-73.4734 + 53.3816i) q^{91} +(18.4138 + 13.3784i) q^{92} +(-54.5151 - 167.780i) q^{93} +(31.4588 - 10.2216i) q^{94} +(-83.1186 + 114.403i) q^{95} +(-106.589 - 146.708i) q^{96} +(-4.28031 + 13.1734i) q^{97} -59.1283i q^{98} +(-31.0622 - 67.6195i) 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

Related objects

Downloads

Learn more