LMFDB - Embedded newform 201.3.l.a.43.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(43,201)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("201.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.l (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			43.16
Character	$\chi$	$=$	201.43
Dual form			201.3.l.a.187.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43499 + 0.655336i) q^{2} +(0.936417 + 1.45709i) q^{3} +(-0.989723 - 1.14220i) q^{4} +(-0.383091 - 0.0550801i) q^{5} +(0.388860 + 2.70458i) q^{6} +(12.2137 + 5.57779i) q^{7} +(-2.44950 - 8.34222i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})$	\(q+(1.43499 + 0.655336i) q^{2} +(0.936417 + 1.45709i) q^{3} +(-0.989723 - 1.14220i) q^{4} +(-0.383091 - 0.0550801i) q^{5} +(0.388860 + 2.70458i) q^{6} +(12.2137 + 5.57779i) q^{7} +(-2.44950 - 8.34222i) q^{8} +(-1.24625 + 2.72890i) q^{9} +(-0.513634 - 0.330092i) q^{10} +(9.83550 + 1.41413i) q^{11} +(0.737501 - 2.51170i) q^{12} +(-4.02184 + 13.6971i) q^{13} +(13.8711 + 16.0081i) q^{14} +(-0.278476 - 0.609777i) q^{15} +(1.09162 - 7.59235i) q^{16} +(1.10760 - 1.27824i) q^{17} +(-3.57669 + 3.09922i) q^{18} +(2.10015 + 4.59869i) q^{19} +(0.316241 + 0.492081i) q^{20} +(3.30972 + 23.0196i) q^{21} +(13.1871 + 8.47482i) q^{22} +(11.1701 - 7.17856i) q^{23} +(9.86165 - 11.3809i) q^{24} +(-23.8436 - 7.00111i) q^{25} +(-14.7475 + 17.0195i) q^{26} +(-5.14326 + 0.739490i) q^{27} +(-5.71718 - 19.4709i) q^{28} +26.3808 q^{29} -1.05752i q^{30} +(-10.8320 - 36.8905i) q^{31} +(-12.2602 + 19.0773i) q^{32} +(7.14961 + 15.6555i) q^{33} +(2.42707 - 1.10841i) q^{34} +(-4.37171 - 2.80953i) q^{35} +(4.35039 - 1.27739i) q^{36} -53.9322 q^{37} +7.97535i q^{38} +(-23.7241 + 6.96603i) q^{39} +(0.478889 + 3.33074i) q^{40} +(-59.7340 - 51.7598i) q^{41} +(-10.3362 + 35.2017i) q^{42} +(-7.18122 - 6.22256i) q^{43} +(-8.11920 - 12.6337i) q^{44} +(0.627733 - 0.976771i) q^{45} +(20.7332 - 2.98099i) q^{46} +(72.1472 - 46.3662i) q^{47} +(12.0850 - 5.51902i) q^{48} +(85.9734 + 99.2186i) q^{49} +(-29.6272 - 25.6721i) q^{50} +(2.89969 + 0.416913i) q^{51} +(19.6254 - 8.96262i) q^{52} +(-19.5225 + 16.9163i) q^{53} +(-7.86513 - 2.30941i) q^{54} +(-3.69000 - 1.08348i) q^{55} +(16.6138 - 115.552i) q^{56} +(-4.73410 + 7.36640i) q^{57} +(37.8561 + 17.2883i) q^{58} +(42.6572 - 12.5253i) q^{59} +(-0.420874 + 0.921586i) q^{60} +(-14.1737 + 2.03787i) q^{61} +(8.63188 - 60.0360i) q^{62} +(-30.4424 + 26.3785i) q^{63} +(-55.9063 + 35.9288i) q^{64} +(2.29517 - 5.02572i) q^{65} +27.1508i q^{66} +(-65.1389 + 15.6821i) q^{67} -2.55623 q^{68} +(20.9197 + 9.55369i) q^{69} +(-4.43216 - 6.89657i) q^{70} +(-66.6827 - 76.9559i) q^{71} +(25.8177 + 3.71203i) q^{72} +(-1.86732 - 12.9875i) q^{73} +(-77.3919 - 35.3437i) q^{74} +(-12.1263 - 41.2983i) q^{75} +(3.17406 - 6.95022i) q^{76} +(112.240 + 72.1320i) q^{77} +(-38.6089 - 5.55112i) q^{78} +(-12.8940 + 43.9128i) q^{79} +(-0.836375 + 2.84843i) q^{80} +(-5.89375 - 6.80175i) q^{81} +(-51.7973 - 113.420i) q^{82} +(-9.80211 + 68.1752i) q^{83} +(23.0173 - 26.5634i) q^{84} +(-0.494717 + 0.428675i) q^{85} +(-6.22708 - 13.6354i) q^{86} +(24.7034 + 38.4393i) q^{87} +(-12.2950 - 85.5138i) q^{88} +(-110.344 - 70.9137i) q^{89} +(1.54090 - 0.990277i) q^{90} +(-125.521 + 144.859i) q^{91} +(-19.2546 - 5.65367i) q^{92} +(43.6097 - 50.3282i) q^{93} +(133.916 - 19.2542i) q^{94} +(-0.551251 - 1.87739i) q^{95} -39.2780 q^{96} +103.906i q^{97} +(58.3491 + 198.719i) q^{98} +(-16.1165 + 25.0777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) $ 220 * q + 52 * q^4 + 66 * q^8 + 66 * q^9	$ 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9} - 162 q^{10} - 72 q^{14} + 54 q^{15} - 116 q^{16} + 14 q^{17} - 84 q^{19} - 48 q^{21} + 78 q^{22} + 82 q^{23} - 36 q^{24} + 62 q^{25} + 100 q^{26} - 154 q^{28} + 52 q^{29} - 88 q^{31} + 770 q^{32} - 36 q^{33} + 180 q^{35} + 42 q^{36} - 304 q^{37} + 72 q^{39} - 1066 q^{40} + 330 q^{41} + 770 q^{43} - 242 q^{46} - 616 q^{47} - 146 q^{49} + 858 q^{50} + 264 q^{52} - 286 q^{53} - 62 q^{55} - 1484 q^{56} - 660 q^{57} - 352 q^{58} - 634 q^{59} - 504 q^{60} - 352 q^{61} + 124 q^{62} - 132 q^{63} - 1226 q^{64} + 196 q^{65} + 156 q^{67} - 192 q^{68} + 66 q^{69} + 1144 q^{70} + 280 q^{71} + 264 q^{72} + 552 q^{73} + 352 q^{74} + 396 q^{75} + 400 q^{76} - 176 q^{77} + 528 q^{78} + 682 q^{79} + 1848 q^{80} - 198 q^{81} + 728 q^{82} + 246 q^{83} - 1320 q^{84} - 1120 q^{86} + 1120 q^{88} + 448 q^{89} + 486 q^{90} - 128 q^{91} + 604 q^{92} + 72 q^{93} + 704 q^{94} - 462 q^{95} + 144 q^{96} - 176 q^{98}+O(q^{100}) $ 220 * q + 52 * q^4 + 66 * q^8 + 66 * q^9 - 162 * q^10 - 72 * q^14 + 54 * q^15 - 116 * q^16 + 14 * q^17 - 84 * q^19 - 48 * q^21 + 78 * q^22 + 82 * q^23 - 36 * q^24 + 62 * q^25 + 100 * q^26 - 154 * q^28 + 52 * q^29 - 88 * q^31 + 770 * q^32 - 36 * q^33 + 180 * q^35 + 42 * q^36 - 304 * q^37 + 72 * q^39 - 1066 * q^40 + 330 * q^41 + 770 * q^43 - 242 * q^46 - 616 * q^47 - 146 * q^49 + 858 * q^50 + 264 * q^52 - 286 * q^53 - 62 * q^55 - 1484 * q^56 - 660 * q^57 - 352 * q^58 - 634 * q^59 - 504 * q^60 - 352 * q^61 + 124 * q^62 - 132 * q^63 - 1226 * q^64 + 196 * q^65 + 156 * q^67 - 192 * q^68 + 66 * q^69 + 1144 * q^70 + 280 * q^71 + 264 * q^72 + 552 * q^73 + 352 * q^74 + 396 * q^75 + 400 * q^76 - 176 * q^77 + 528 * q^78 + 682 * q^79 + 1848 * q^80 - 198 * q^81 + 728 * q^82 + 246 * q^83 - 1320 * q^84 - 1120 * q^86 + 1120 * q^88 + 448 * q^89 + 486 * q^90 - 128 * q^91 + 604 * q^92 + 72 * q^93 + 704 * q^94 - 462 * q^95 + 144 * q^96 - 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	1.43499	+	0.655336i	0.717493	+	0.327668i	0.740490	−	0.672067i	$-0.234594\pi$
$2$	1.43499	+	0.655336i	0.717493	+	0.327668i	−0.0229969	+	0.999736i	$0.507321\pi$
$3$	0.936417	+	1.45709i	0.312139	+	0.485698i
$3$	0.936417	+	1.45709i	0.312139	+	0.485698i
$4$	−0.989723	−	1.14220i	−0.247431	−	0.285550i
$5$	−0.383091	−	0.0550801i	−0.0766181	−	0.0110160i	0.103899	−	0.994588i	$-0.466868\pi$
$5$	−0.383091	−	0.0550801i	−0.0766181	−	0.0110160i	−0.180517	+	0.983572i	$0.557777\pi$
$6$	0.388860	+	2.70458i	0.0648099	+	0.450763i
$7$	12.2137	+	5.57779i	1.74481	+	0.796827i	0.990032	+	0.140844i	$0.0449815\pi$
$7$	12.2137	+	5.57779i	1.74481	+	0.796827i	0.754776	+	0.655983i	$0.227746\pi$
$8$	−2.44950	−	8.34222i	−0.306187	−	1.04278i
$9$	−1.24625	+	2.72890i	−0.138472	+	0.303211i
$10$	−0.513634	−	0.330092i	−0.0513634	−	0.0330092i
$11$	9.83550	+	1.41413i	0.894136	+	0.128557i	0.574040	−	0.818828i	$-0.305376\pi$
$11$	9.83550	+	1.41413i	0.894136	+	0.128557i	0.320097	+	0.947385i	$0.396285\pi$
$12$	0.737501	−	2.51170i	0.0614584	−	0.209308i
$13$	−4.02184	+	13.6971i	−0.309372	+	1.05363i	0.647246	+	0.762281i	$0.275921\pi$
$13$	−4.02184	+	13.6971i	−0.309372	+	1.05363i	−0.956618	+	0.291344i	$0.905897\pi$
$14$	13.8711	+	16.0081i	0.990792	+	1.14344i
$15$	−0.278476	−	0.609777i	−0.0185650	−	0.0406518i
$16$	1.09162	−	7.59235i	0.0682260	−	0.474522i
$17$	1.10760	−	1.27824i	0.0651530	−	0.0751906i	−0.722237	−	0.691645i	$-0.756886\pi$
$17$	1.10760	−	1.27824i	0.0651530	−	0.0751906i	0.787390	+	0.616455i	$0.211432\pi$
$18$	−3.57669	+	3.09922i	−0.198705	+	0.172179i
$19$	2.10015	+	4.59869i	0.110534	+	0.242036i	0.956813	−	0.290704i	$-0.0938895\pi$
$19$	2.10015	+	4.59869i	0.110534	+	0.242036i	−0.846279	+	0.532740i	$0.821162\pi$
$20$	0.316241	+	0.492081i	0.0158121	+	0.0246040i
$21$	3.30972	+	23.0196i	0.157605	+	1.09617i
$22$	13.1871	+	8.47482i	0.599412	+	0.385219i
$23$	11.1701	−	7.17856i	0.485655	−	0.312111i	−0.274801	−	0.961501i	$-0.588612\pi$
$23$	11.1701	−	7.17856i	0.485655	−	0.312111i	0.760456	+	0.649390i	$0.224976\pi$
$24$	9.86165	−	11.3809i	0.410902	−	0.474206i
$25$	−23.8436	−	7.00111i	−0.953744	−	0.280045i
$26$	−14.7475	+	17.0195i	−0.567212	+	0.654598i
$27$	−5.14326	+	0.739490i	−0.190491	+	0.0273885i
$28$	−5.71718	−	19.4709i	−0.204185	−	0.695390i
$29$	26.3808			0.909683			0.454842	−	0.890572i	$-0.349696\pi$
$29$	26.3808			0.909683			0.454842	+	0.890572i	$0.349696\pi$
$30$		−	1.05752i		−	0.0352505i
$31$	−10.8320	−	36.8905i	−0.349421	−	1.19002i	−0.927433	−	0.373989i	$-0.877990\pi$
$31$	−10.8320	−	36.8905i	−0.349421	−	1.19002i	0.578012	−	0.816028i	$-0.303829\pi$
$32$	−12.2602	+	19.0773i	−0.383131	+	0.596164i
$33$	7.14961	+	15.6555i	0.216655	+	0.474408i
$34$	2.42707	−	1.10841i	0.0713844	−	0.0326002i
$35$	−4.37171	−	2.80953i	−0.124906	−	0.0802722i
$36$	4.35039	−	1.27739i	0.120844	−	0.0354830i
$37$	−53.9322			−1.45763			−0.728813	−	0.684712i	$-0.759928\pi$
$37$	−53.9322			−1.45763			−0.728813	+	0.684712i	$0.759928\pi$
$38$			7.97535i			0.209878i
$39$	−23.7241	+	6.96603i	−0.608311	+	0.178616i
$40$	0.478889	+	3.33074i	0.0119722	+	0.0832686i
$41$	−59.7340	−	51.7598i	−1.45693	−	1.26243i	−0.902842	−	0.429972i	$-0.858523\pi$
$41$	−59.7340	−	51.7598i	−1.45693	−	1.26243i	−0.554084	−	0.832461i	$-0.686931\pi$
$42$	−10.3362	+	35.2017i	−0.246099	+	0.838137i
$43$	−7.18122	−	6.22256i	−0.167005	−	0.144711i	0.567349	−	0.823478i	$-0.307969\pi$
$43$	−7.18122	−	6.22256i	−0.167005	−	0.144711i	−0.734354	+	0.678767i	$0.762515\pi$
$44$	−8.11920	−	12.6337i	−0.184527	−	0.287130i
$45$	0.627733	−	0.976771i	0.0139496	−	0.0217060i
$46$	20.7332	−	2.98099i	0.450723	−	0.0648042i
$47$	72.1472	−	46.3662i	1.53505	−	0.986515i	0.546188	−	0.837663i	$-0.316079\pi$
$47$	72.1472	−	46.3662i	1.53505	−	0.986515i	0.988859	−	0.148852i	$-0.0475579\pi$
$48$	12.0850	−	5.51902i	0.251770	−	0.114980i
$49$	85.9734	+	99.2186i	1.75456	+	2.02487i
$50$	−29.6272	−	25.6721i	−0.592543	−	0.513441i
$51$	2.89969	+	0.416913i	0.0568567	+	0.00817476i
$52$	19.6254	−	8.96262i	0.377412	−	0.172358i
$53$	−19.5225	+	16.9163i	−0.368349	+	0.319176i	−0.819292	−	0.573377i	$-0.805633\pi$
$53$	−19.5225	+	16.9163i	−0.368349	+	0.319176i	0.450943	+	0.892553i	$0.351088\pi$
$54$	−7.86513	−	2.30941i	−0.145650	−	0.0427668i
$55$	−3.69000	−	1.08348i	−0.0670908	−	0.0196996i
$56$	16.6138	−	115.552i	0.296676	−	2.06342i
$57$	−4.73410	+	7.36640i	−0.0830544	+	0.129235i
$58$	37.8561	+	17.2883i	0.652691	+	0.298074i
$59$	42.6572	−	12.5253i	0.723003	−	0.212293i	0.100530	−	0.994934i	$-0.467946\pi$
$59$	42.6572	−	12.5253i	0.723003	−	0.212293i	0.622473	+	0.782641i	$0.286128\pi$
$60$	−0.420874	+	0.921586i	−0.00701457	+	0.0153598i
$61$	−14.1737	+	2.03787i	−0.232356	+	0.0334078i	−0.257509	−	0.966276i	$-0.582902\pi$
$61$	−14.1737	+	2.03787i	−0.232356	+	0.0334078i	0.0251531	+	0.999684i	$0.491993\pi$
$62$	8.63188	−	60.0360i	0.139224	−	0.968323i
$63$	−30.4424	+	26.3785i	−0.483213	+	0.418706i
$64$	−55.9063	+	35.9288i	−0.873536	+	0.561388i
$65$	2.29517	−	5.02572i	0.0353103	−	0.0773188i
$66$			27.1508i			0.411375i
$67$	−65.1389	+	15.6821i	−0.972222	+	0.234061i
$67$	−65.1389	+	15.6821i	−0.972222	+	0.234061i
$68$	−2.55623			−0.0375916
$69$	20.9197	+	9.55369i	0.303184	+	0.138459i
$70$	−4.43216	−	6.89657i	−0.0633165	−	0.0985224i
$71$	−66.6827	−	76.9559i	−0.939192	−	1.08389i	−0.996336	−	0.0855198i	$-0.972745\pi$
$71$	−66.6827	−	76.9559i	−0.939192	−	1.08389i	0.0571441	−	0.998366i	$-0.481801\pi$
$72$	25.8177	+	3.71203i	0.358580	+	0.0515560i
$73$	−1.86732	−	12.9875i	−0.0255797	−	0.177911i	0.973026	−	0.230694i	$-0.0740998\pi$
$73$	−1.86732	−	12.9875i	−0.0255797	−	0.177911i	−0.998606	+	0.0527834i	$0.983191\pi$
$74$	−77.3919	−	35.3437i	−1.04584	−	0.477618i
$75$	−12.1263	−	41.2983i	−0.161684	−	0.550644i
$76$	3.17406	−	6.95022i	0.0417639	−	0.0914503i
$77$	112.240	+	72.1320i	1.45766	+	0.936780i
$78$	−38.6089	−	5.55112i	−0.494986	−	0.0711682i
$79$	−12.8940	+	43.9128i	−0.163215	+	0.555858i	0.836751	+	0.547583i	$0.184452\pi$
$79$	−12.8940	+	43.9128i	−0.163215	+	0.555858i	−0.999966	+	0.00827465i	$0.997366\pi$
$80$	−0.836375	+	2.84843i	−0.0104547	+	0.0356054i
$81$	−5.89375	−	6.80175i	−0.0727623	−	0.0839722i
$82$	−51.7973	−	113.420i	−0.631675	−	1.38318i
$83$	−9.80211	+	68.1752i	−0.118098	+	0.821388i	0.841549	+	0.540180i	$0.181644\pi$
$83$	−9.80211	+	68.1752i	−0.118098	+	0.821388i	−0.959647	+	0.281207i	$0.909265\pi$
$84$	23.0173	−	26.5634i	0.274015	−	0.316231i
$85$	−0.494717	+	0.428675i	−0.00582020	+	0.00504323i
$86$	−6.22708	−	13.6354i	−0.0724079	−	0.158551i
$87$	24.7034	+	38.4393i	0.283948	+	0.441831i
$88$	−12.2950	−	85.5138i	−0.139716	−	0.971748i
$89$	−110.344	−	70.9137i	−1.23982	−	0.796783i	−0.254427	−	0.967092i	$-0.581887\pi$
$89$	−110.344	−	70.9137i	−1.23982	−	0.796783i	−0.985391	+	0.170309i	$0.945523\pi$
$90$	1.54090	−	0.990277i	0.0171211	−	0.0110031i
$91$	−125.521	+	144.859i	−1.37935	+	1.59186i
$92$	−19.2546	−	5.65367i	−0.209289	−	0.0614529i
$93$	43.6097	−	50.3282i	0.468921	−	0.541164i
$94$	133.916	−	19.2542i	1.42464	−	0.204832i
$95$	−0.551251	−	1.87739i	−0.00580265	−	0.0197620i
$96$	−39.2780			−0.409146
$97$			103.906i			1.07119i	0.844474	+	0.535597i	$0.179913\pi$
$97$			103.906i			1.07119i	−0.844474	+	0.535597i	$0.820087\pi$
$98$	58.3491	+	198.719i	0.595399	+	2.02774i
$99$	−16.1165	+	25.0777i	−0.162793	+	0.253310i
$100$	15.6019	+	34.1634i	0.156019	+	0.341634i
$101$	−5.64101	+	2.57616i	−0.0558516	+	0.0255066i	−0.443145	−	0.896450i	$-0.646137\pi$
$101$	−5.64101	+	2.57616i	−0.0558516	+	0.0255066i	0.387293	+	0.921957i	$0.373410\pi$
$102$	3.88780	+	2.49854i	0.0381157	+	0.0244955i
$103$	70.6654	−	20.7492i	0.686072	−	0.201449i	0.0799242	−	0.996801i	$-0.474532\pi$
$103$	70.6654	−	20.7492i	0.686072	−	0.201449i	0.606148	+	0.795352i	$0.292714\pi$
$104$	124.116			1.19342
$105$		−	9.00088i		−	0.0857227i
$106$	−39.1004	+	11.4809i	−0.368871	+	0.108310i
$107$	−0.745777	−	5.18699i	−0.00696988	−	0.0484766i	0.986040	−	0.166510i	$-0.0532499\pi$
$107$	−0.745777	−	5.18699i	−0.00696988	−	0.0484766i	−0.993010	+	0.118034i	$0.962341\pi$
$108$	5.93505	+	5.14275i	0.0549542	+	0.0476181i
$109$	20.3400	−	69.2716i	0.186605	−	0.635519i	−0.812046	−	0.583594i	$-0.801646\pi$
$109$	20.3400	−	69.2716i	0.186605	−	0.635519i	0.998651	−	0.0519255i	$-0.0165358\pi$
$110$	−4.58505	−	3.97297i	−0.0416823	−	0.0361179i
$111$	−50.5030	−	78.5843i	−0.454982	−	0.707966i
$112$	55.6811	−	86.6416i	0.497153	−	0.773585i
$113$	139.945	−	20.1211i	1.23846	−	0.178063i	0.508201	−	0.861239i	$-0.330311\pi$
$113$	139.945	−	20.1211i	1.23846	−	0.178063i	0.730254	+	0.683176i	$0.239402\pi$
$114$	−11.6208	+	7.46826i	−0.101937	+	0.0655111i
$115$	−4.67454	+	2.13479i	−0.0406482	+	0.0185634i
$116$	−26.1097	−	30.1322i	−0.225084	−	0.259760i
$117$	−32.3659	−	28.0452i	−0.276631	−	0.239702i
$118$	69.4207	+	9.98119i	0.588311	+	0.0845864i
$119$	20.6576	−	9.43401i	0.173593	−	0.0792774i
$120$	−4.40477	+	3.81675i	−0.0367064	+	0.0318063i
$121$	−21.3614	−	6.27227i	−0.176540	−	0.0518369i
$122$	−21.6746	−	6.36423i	−0.177661	−	0.0521658i
$123$	19.4829	−	135.507i	0.158398	−	1.10168i
$124$	−31.4157	+	48.8838i	−0.253353	+	0.394224i
$125$	17.5500	+	8.01482i	0.140400	+	0.0641185i
$126$	−60.9712	+	17.9028i	−0.483899	+	0.142085i
$127$	−68.8987	+	150.867i	−0.542509	+	1.18793i	0.417684	+	0.908593i	$0.362842\pi$
$127$	−68.8987	+	150.867i	−0.542509	+	1.18793i	−0.960193	+	0.279337i	$0.909885\pi$
$128$	−13.9849	+	2.01072i	−0.109257	+	0.0157087i
$129$	2.34224	−	16.2906i	0.0181569	−	0.126284i
$130$	6.58707	−	5.70773i	0.0506698	−	0.0439056i
$131$	−75.8960	+	48.7754i	−0.579359	+	0.372331i	−0.797257	−	0.603640i	$-0.793716\pi$
$131$	−75.8960	+	48.7754i	−0.579359	+	0.372331i	0.217898	+	0.975972i	$0.430080\pi$
$132$	10.8056	−	23.6609i	0.0818603	−	0.179249i
$133$			67.8809i			0.510383i
$134$	−103.750	−	20.1842i	−0.774257	−	0.150629i
$135$	2.01107			0.0148968
$136$	−13.3764	−	6.10881i	−0.0983561	−	0.0449177i
$137$	63.3191	+	98.5265i	0.462183	+	0.719171i	0.991622	−	0.129177i	$-0.0412336\pi$
$137$	63.3191	+	98.5265i	0.462183	+	0.719171i	−0.529438	+	0.848348i	$0.677597\pi$
$138$	23.7586	+	27.4188i	0.172163	+	0.198687i
$139$	141.303	+	20.3164i	1.01657	+	0.146161i	0.630404	−	0.776267i	$-0.282889\pi$
$139$	141.303	+	20.3164i	1.01657	+	0.146161i	0.386168	+	0.922428i	$0.373798\pi$
$140$	1.11774	+	7.77403i	0.00798383	+	0.0555288i
$141$	135.120	+	61.7072i	0.958297	+	0.437639i
$142$	−45.2567	−	154.130i	−0.318709	−	1.08542i
$143$	−58.9264	+	129.031i	−0.412072	+	0.902313i
$144$	19.3583	+	12.4408i	0.134433	+	0.0863947i
$145$	−10.1062	−	1.45306i	−0.0696982	−	0.0100211i
$146$	5.83160	−	19.8606i	0.0399425	−	0.136032i
$147$	−64.0638	+	218.181i	−0.435808	+	1.48423i
$148$	53.3779	+	61.6014i	0.360662	+	0.416226i
$149$	−53.2519	−	116.605i	−0.357395	−	0.782587i	−0.999868	−	0.0162778i	$-0.994818\pi$
$149$	−53.2519	−	116.605i	−0.357395	−	0.782587i	0.642472	−	0.766309i	$-0.277909\pi$
$150$	9.66324	−	67.2093i	0.0644216	−	0.448062i
$151$	−82.7514	+	95.5002i	−0.548023	+	0.632452i	−0.960421	−	0.278552i	$-0.910146\pi$
$151$	−82.7514	+	95.5002i	−0.548023	+	0.632452i	0.412399	+	0.911004i	$0.364691\pi$
$152$	33.2189	−	28.7844i	0.218546	−	0.189371i
$153$	2.10784	+	4.61553i	0.0137767	+	0.0301669i
$154$	113.792	+	177.063i	0.738906	+	1.14976i
$155$	2.11772	+	14.7290i	0.0136627	+	0.0950261i
$156$	31.4369	+	20.2033i	0.201519	+	0.129508i
$157$	131.318	−	84.3927i	0.836418	−	0.537533i	−0.0508931	−	0.998704i	$-0.516207\pi$
$157$	131.318	−	84.3927i	0.836418	−	0.537533i	0.887311	+	0.461171i	$0.152570\pi$
$158$	−47.2803	+	54.5644i	−0.299242	+	0.345344i
$159$	−42.9299	−	12.6053i	−0.269999	−	0.0792789i
$160$	5.74755	−	6.63302i	0.0359222	−	0.0414564i
$161$	176.468	−	25.3722i	1.09607	−	0.157591i
$162$	−4.00001	−	13.6228i	−0.0246914	−	0.0840913i
$163$	296.162			1.81694			0.908471	−	0.417948i	$-0.137251\pi$
$163$	296.162			1.81694			0.908471	+	0.417948i	$0.137251\pi$
$164$			119.456i			0.728391i
$165$	−1.87664	−	6.39126i	−0.0113736	−	0.0387349i
$166$	−58.7436	+	91.4068i	−0.353877	+	0.550643i
$167$	40.4930	+	88.6672i	0.242473	+	0.530941i	0.991268	−	0.131860i	$-0.0420948\pi$
$167$	40.4930	+	88.6672i	0.242473	+	0.530941i	−0.748796	+	0.662801i	$0.769368\pi$
$168$	183.927	−	83.9968i	1.09481	−	0.499981i
$169$	−29.2645	−	18.8071i	−0.173162	−	0.111285i
$170$	−0.990838	+	0.290936i	−0.00582846	+	0.00171139i
$171$	−15.1666			−0.0886938
$172$			14.3610i			0.0834943i
$173$	39.0692	−	11.4717i	0.225833	−	0.0663107i	−0.166858	−	0.985981i	$-0.553362\pi$
$173$	39.0692	−	11.4717i	0.225833	−	0.0663107i	0.392692	+	0.919670i	$0.371544\pi$
$174$	10.2584	+	71.3490i	0.0589565	+	0.410051i
$175$	−252.167	−	218.504i	−1.44095	−	1.24859i
$176$	21.4732	−	73.1309i	0.122007	−	0.415516i
$177$	58.1954	+	50.4266i	0.328788	+	0.284896i
$178$	−111.870	−	174.072i	−0.628481	−	0.977935i
$179$	38.0525	−	59.2108i	0.212584	−	0.330787i	−0.718543	−	0.695483i	$-0.755191\pi$
$179$	38.0525	−	59.2108i	0.212584	−	0.330787i	0.931127	+	0.364696i	$0.118827\pi$
$180$	−1.73695	+	0.249736i	−0.00964973	+	0.00138742i
$181$	262.923	−	168.970i	1.45261	−	0.933538i	0.453508	−	0.891252i	$-0.350172\pi$
$181$	262.923	−	168.970i	1.45261	−	0.933538i	0.999106	−	0.0422855i	$-0.0134639\pi$
$182$	−275.052	+	125.612i	−1.51128	+	0.690177i
$183$	−16.2419	−	18.7441i	−0.0887535	−	0.102427i
$184$	−87.2462	−	75.5992i	−0.474164	−	0.410865i
$185$	20.6609	+	2.97059i	0.111681	+	0.0160572i
$186$	95.5612	−	43.6413i	0.513770	−	0.234631i
$187$	12.7014	−	11.0058i	0.0679220	−	0.0588547i
$188$	−124.365	−	36.5170i	−0.661518	−	0.194239i
$189$	−66.9427	−	19.6562i	−0.354194	−	0.104001i
$190$	0.439283	−	3.05528i	0.00231202	−	0.0160804i
$191$	−135.010	+	210.080i	−0.706860	+	1.09990i	0.283175	+	0.959068i	$0.408612\pi$
$191$	−135.010	+	210.080i	−0.706860	+	1.09990i	−0.990034	+	0.140827i	$0.955024\pi$
$192$	−104.703	−	47.8164i	−0.545330	−	0.249044i
$193$	−271.453	+	79.7057i	−1.40649	+	0.412983i	−0.894908	−	0.446252i	$-0.852759\pi$
$193$	−271.453	+	79.7057i	−1.40649	+	0.412983i	−0.511582	+	0.859234i	$0.670940\pi$
$194$	−68.0933	+	149.103i	−0.350996	+	0.768575i
$195$	9.47218	−	1.36189i	0.0485753	−	0.00698407i
$196$	28.2378	−	196.398i	0.144070	−	1.00203i
$197$	45.3557	−	39.3009i	0.230232	−	0.199497i	−0.532103	−	0.846679i	$-0.678598\pi$
$197$	45.3557	−	39.3009i	0.230232	−	0.199497i	0.762335	+	0.647182i	$0.224053\pi$
$198$	−39.5612	+	25.4245i	−0.199804	+	0.128406i
$199$	−51.3368	+	112.412i	−0.257974	+	0.564884i	−0.993658	−	0.112440i	$-0.964133\pi$
$199$	−51.3368	+	112.412i	−0.257974	+	0.564884i	0.735685	+	0.677324i	$0.236861\pi$
$200$			216.058i			1.08029i
$201$	−83.8475	−	80.2284i	−0.417152	−	0.399146i
$202$	−9.78303			−0.0484308
$203$	322.206	+	147.147i	1.58722	+	0.724860i
$204$	−2.39370	−	3.72466i	−0.0117338	−	0.0182581i
$205$	20.0326	+	23.1188i	0.0977199	+	0.112775i
$206$	115.002	+	16.5347i	0.558260	+	0.0802657i
$207$	5.66892	+	39.4282i	0.0273861	+	0.190474i
$208$	99.6032	+	45.4872i	0.478861	+	0.218689i
$209$	14.1529	+	48.2003i	0.0677171	+	0.230623i
$210$	5.89860	−	12.9161i	0.0280886	−	0.0615054i
$211$	−261.118	−	167.811i	−1.23753	−	0.795311i	−0.252482	−	0.967602i	$-0.581247\pi$
$211$	−261.118	−	167.811i	−1.23753	−	0.795311i	−0.985046	+	0.172291i	$0.944883\pi$
$212$	38.6437	+	5.55613i	0.182282	+	0.0262081i
$213$	49.6892	−	169.226i	0.233282	−	0.794487i
$214$	2.32904	−	7.93200i	0.0108834	−	0.0370654i
$215$	2.40832	+	2.77935i	0.0112015	+	0.0129272i
$216$	18.7674	+	41.0949i	0.0868861	+	0.190254i
$217$	73.4689	−	510.987i	0.338566	−	2.35478i
$218$	74.5838	−	86.0743i	0.342127	−	0.394836i
$219$	17.1754	−	14.8826i	0.0784266	−	0.0679570i
$220$	2.41452	+	5.28706i	0.0109751	+	0.0240321i
$221$	13.0536	+	20.3118i	0.0590662	+	0.0919088i
$222$	−20.9720	−	145.864i	−0.0944687	−	0.657044i
$223$	−98.3830	−	63.2269i	−0.441179	−	0.283529i	0.301134	−	0.953582i	$-0.402635\pi$
$223$	−98.3830	−	63.2269i	−0.441179	−	0.283529i	−0.742313	+	0.670053i	$0.766271\pi$
$224$	−256.151	+	164.618i	−1.14353	+	0.734902i
$225$	48.8203	−	56.3416i	0.216979	−	0.250407i
$226$	214.006	+	62.8378i	0.946928	+	0.278043i
$227$	166.896	−	192.608i	0.735224	−	0.848494i	−0.257825	−	0.966192i	$-0.583006\pi$
$227$	166.896	−	192.608i	0.735224	−	0.848494i	0.993050	+	0.117697i	$0.0375513\pi$
$228$	13.0994	−	1.88340i	0.0574534	−	0.00826055i
$229$	28.9662	+	98.6497i	0.126490	+	0.430785i	0.998249	−	0.0591497i	$-0.0188389\pi$
$229$	28.9662	+	98.6497i	0.126490	+	0.430785i	−0.871759	+	0.489934i	$0.837021\pi$
$230$	−8.10690			−0.0352474
$231$			231.089i			1.00039i
$232$	−64.6197	−	220.075i	−0.278533	−	0.948597i
$233$	−134.179	+	208.786i	−0.575874	+	0.896077i	−0.999954	−	0.00954752i	$-0.996961\pi$
$233$	−134.179	+	208.786i	−0.575874	+	0.896077i	0.424081	+	0.905624i	$0.360597\pi$
$234$	−28.0655	−	61.4550i	−0.119938	−	0.262628i
$235$	−30.1928	+	13.7886i	−0.128480	+	0.0586748i
$236$	−56.5252	−	36.3265i	−0.239514	−	0.153926i
$237$	−76.0592	+	22.3330i	−0.320925	+	0.0942320i
$238$	35.8258			0.150529
$239$		−	79.7609i		−	0.333728i	−0.985980	−	0.166864i	$-0.946636\pi$
$239$		−	79.7609i		−	0.333728i	0.985980	−	0.166864i	$-0.0533640\pi$
$240$	−4.93363	+	1.44864i	−0.0205568	+	0.00603602i
$241$	−35.6602	−	248.022i	−0.147968	−	1.02914i	−0.919540	−	0.392997i	$-0.871438\pi$
$241$	−35.6602	−	248.022i	−0.147968	−	1.02914i	0.771572	−	0.636142i	$-0.219471\pi$
$242$	−26.5429	−	22.9995i	−0.109681	−	0.0950393i
$243$	4.39178	−	14.9570i	0.0180732	−	0.0615515i
$244$	16.3557	+	14.1723i	0.0670316	+	0.0580833i
$245$	−27.4706	−	42.7451i	−0.112125	−	0.174470i
$246$	116.760	−	181.682i	0.474635	−	0.738546i
$247$	−71.4353	+	10.2708i	−0.289212	+	0.0415824i
$248$	−281.216	+	180.727i	−1.13394	+	0.728736i
$249$	−108.517	+	49.5578i	−0.435809	+	0.199027i
$250$	19.9316	+	23.0023i	0.0797264	+	0.0920092i
$251$	85.6338	+	74.2021i	0.341171	+	0.295626i	0.808546	−	0.588433i	$-0.200255\pi$
$251$	85.6338	+	74.2021i	0.341171	+	0.295626i	−0.467375	+	0.884059i	$0.654800\pi$
$252$	60.2591	+	8.66395i	0.239123	+	0.0343808i
$253$	120.015	−	54.8088i	0.474366	−	0.216636i
$254$	−197.737	+	171.340i	−0.778494	+	0.674569i
$255$	−1.08788	−	0.319431i	−0.00426620	−	0.00125267i
$256$	233.670	+	68.6118i	0.912775	+	0.268015i
$257$	41.1922	−	286.498i	0.160281	−	1.11478i	−0.737822	−	0.674995i	$-0.764146\pi$
$257$	41.1922	−	286.498i	0.160281	−	1.11478i	0.898103	−	0.439785i	$-0.144945\pi$
$258$	14.0369	−	21.8419i	0.0544066	−	0.0846584i
$259$	−658.709	−	300.822i	−2.54328	−	1.16148i
$260$	−8.01197	+	2.35253i	−0.0308153	+	0.00904818i
$261$	−32.8770	+	71.9905i	−0.125965	+	0.275826i
$262$	−140.874	+	20.2546i	−0.537687	+	0.0773077i
$263$	40.5683	−	282.159i	0.154252	−	1.07285i	−0.754737	−	0.656027i	$-0.772236\pi$
$263$	40.5683	−	282.159i	0.154252	−	1.07285i	0.908989	−	0.416820i	$-0.136855\pi$
$264$	113.088	−	97.9916i	0.428365	−	0.371180i
$265$	8.41063	−	5.40518i	0.0317382	−	0.0203969i
$266$	−44.4848	+	97.4082i	−0.167236	+	0.366196i
$267$		−	227.186i		−	0.850884i
$268$	82.3816	+	58.8807i	0.307394	+	0.219704i
$269$	−302.317			−1.12386			−0.561928	−	0.827186i	$-0.689940\pi$
$269$	−302.317			−1.12386			−0.561928	+	0.827186i	$0.689940\pi$
$270$	2.88585	+	1.31792i	0.0106883	+	0.00488120i
$271$	202.892	+	315.707i	0.748680	+	1.16497i	0.981316	+	0.192405i	$0.0616288\pi$
$271$	202.892	+	315.707i	0.748680	+	1.16497i	−0.232635	+	0.972564i	$0.574735\pi$
$272$	−8.49577	−	9.80465i	−0.0312345	−	0.0360465i
$273$	−328.613	−	47.2475i	−1.20371	−	0.173068i
$274$	26.2941	+	182.879i	0.0959638	+	0.667443i
$275$	−224.613	−	102.577i	−0.816775	−	0.373009i
$276$	−9.79244	−	33.3500i	−0.0354799	−	0.120833i
$277$	−45.7546	+	100.189i	−0.165179	+	0.361692i	−0.974063	−	0.226276i	$-0.927345\pi$
$277$	−45.7546	+	100.189i	−0.165179	+	0.361692i	0.808884	+	0.587968i	$0.200072\pi$
$278$	189.454	+	121.755i	0.681491	+	0.437968i
$279$	114.170	+	16.4151i	0.409211	+	0.0588356i
$280$	−12.7292	+	43.3517i	−0.0454614	+	0.154827i
$281$	76.7620	−	261.427i	0.273174	−	0.930347i	−0.702603	−	0.711582i	$-0.747979\pi$
$281$	76.7620	−	261.427i	0.273174	−	0.930347i	0.975778	−	0.218765i	$-0.0702027\pi$
$282$	153.456	+	177.098i	0.544171	+	0.628006i
$283$	−77.3875	−	169.455i	−0.273454	−	0.598781i	0.722223	−	0.691660i	$-0.243120\pi$
$283$	−77.3875	−	169.455i	−0.273454	−	0.598781i	−0.995677	+	0.0928791i	$0.970393\pi$
$284$	−21.9018	+	152.330i	−0.0771189	+	0.536373i
$285$	2.21933	−	2.56124i	0.00778713	−	0.00898682i
$286$	−169.117	+	146.541i	−0.591318	+	0.512380i
$287$	−440.865	−	965.359i	−1.53611	−	3.36362i
$288$	−36.7806	−	57.2318i	−0.127710	−	0.198721i
$289$	40.7219	+	283.227i	0.140906	+	0.980024i
$290$	−13.5501	−	8.70810i	−0.0467244	−	0.0300279i
$291$	−151.401	+	97.2993i	−0.520277	+	0.334362i
$292$	−12.9862	+	14.9869i	−0.0444734	+	0.0513250i
$293$	194.990	+	57.2544i	0.665497	+	0.195407i	0.596997	−	0.802244i	$-0.296361\pi$
$293$	194.990	+	57.2544i	0.665497	+	0.195407i	0.0684999	+	0.997651i	$0.478179\pi$
$294$	−234.913	+	271.104i	−0.799023	+	0.922122i
$295$	−17.0315	+	2.44875i	−0.0577337	+	0.00830086i
$296$	132.107	+	449.914i	0.446307	+	1.51998i
$297$	−51.6323			−0.173846
$298$		−	202.225i		−	0.678608i
$299$	53.4015	+	181.869i	0.178600	+	0.608257i
$300$	−35.1693	+	54.7246i	−0.117231	+	0.182415i
$301$	−53.0008	−	116.056i	−0.176082	−	0.385566i
$302$	−181.332	+	82.8115i	−0.600437	+	0.274210i
$303$	−9.03606	−	5.80712i	−0.0298220	−	0.0191654i
$304$	37.2074	−	10.9251i	0.122393	−	0.0359378i
$305$	5.54206			0.0181707
$306$			8.00457i			0.0261587i
$307$	193.420	−	56.7932i	0.630032	−	0.184994i	0.0489006	−	0.998804i	$-0.484428\pi$
$307$	193.420	−	56.7932i	0.630032	−	0.184994i	0.581132	+	0.813809i	$0.302610\pi$
$308$	−28.6969	−	199.591i	−0.0931716	−	0.648023i
$309$	96.4059	+	83.5362i	0.311993	+	0.270344i
$310$	−6.61358	+	22.5238i	−0.0213341	+	0.0726574i
$311$	−71.3523	−	61.8271i	−0.229429	−	0.198801i	0.532558	−	0.846393i	$-0.321231\pi$
$311$	−71.3523	−	61.8271i	−0.229429	−	0.198801i	−0.761987	+	0.647592i	$0.775776\pi$
$312$	116.224	+	180.849i	0.372514	+	0.579643i
$313$	−84.4479	+	131.404i	−0.269802	+	0.419820i	−0.949545	−	0.313630i	$-0.898455\pi$
$313$	−84.4479	+	131.404i	−0.269802	+	0.419820i	0.679744	+	0.733450i	$0.262091\pi$
$314$	243.745	−	35.0452i	0.776257	−	0.111609i
$315$	13.1151	−	8.42858i	0.0416353	−	0.0267574i
$316$	62.9187	−	28.7340i	0.199110	−	0.0909304i
$317$	125.377	+	144.692i	0.395510	+	0.456443i	0.918222	−	0.396066i	$-0.129625\pi$
$317$	125.377	+	144.692i	0.395510	+	0.456443i	−0.522712	+	0.852510i	$0.675080\pi$
$318$	−53.3430	−	46.2220i	−0.167745	−	0.145352i
$319$	259.468	+	37.3059i	0.813381	+	0.116946i
$320$	23.3961	−	10.6847i	0.0731130	−	0.0333896i
$321$	6.85958	−	5.94386i	0.0213694	−	0.0185167i
$322$	269.856	+	79.2369i	0.838062	+	0.246077i
$323$	8.20435	+	2.40902i	0.0254005	+	0.00745825i
$324$	−1.93579	+	13.4637i	−0.00597465	+	0.0415546i
$325$	191.790	−	298.432i	0.590124	−	0.918251i
$326$	424.988	+	194.085i	1.30364	+	0.595354i
$327$	119.982	−	35.2299i	0.366917	−	0.107737i
$328$	−285.473	+	625.099i	−0.870345	+	1.90579i
$329$	1139.80	−	163.879i	3.46444	−	0.498112i
$330$	1.49547	−	10.4012i	0.00453172	−	0.0315188i
$331$	42.3606	−	36.7056i	0.127978	−	0.110893i	−0.588520	−	0.808482i	$-0.700289\pi$
$331$	42.3606	−	36.7056i	0.127978	−	0.110893i	0.716498	+	0.697589i	$0.245744\pi$
$332$	87.5712	−	56.2786i	0.263769	−	0.169514i
$333$	67.2127	−	147.175i	0.201840	−	0.441968i
$334$			153.773i			0.460397i
$335$	25.8179	−	2.41982i	0.0770682	−	0.00722333i
$336$	178.386			0.530910
$337$	−224.445	−	102.500i	−0.666008	−	0.304155i	0.0535735	−	0.998564i	$-0.482939\pi$
$337$	−224.445	−	102.500i	−0.666008	−	0.304155i	−0.719581	+	0.694408i	$0.755666\pi$
$338$	−29.6691	−	46.1660i	−0.0877784	−	0.136586i
$339$	160.366	+	185.072i	0.473055	+	0.545935i
$340$	0.979266	+	0.140797i	0.00288019	+	0.000414109i
$341$	−54.3705	−	378.155i	−0.159444	−	1.10896i
$342$	−21.7639	−	9.93925i	−0.0636372	−	0.0290621i
$343$	311.270	+	1060.09i	0.907493	+	3.09064i
$344$	−34.3196	+	75.1495i	−0.0997663	+	0.218458i
$345$	−7.48791	−	4.81219i	−0.0217041	−	0.0139484i
$346$	63.5816	+	9.14165i	0.183762	+	0.0264209i
$347$	−176.855	+	602.313i	−0.509669	+	1.73577i	0.154312	+	0.988022i	$0.450684\pi$
$347$	−176.855	+	602.313i	−0.509669	+	1.73577i	−0.663980	+	0.747750i	$0.731134\pi$
$348$	19.4559	−	66.2606i	0.0559077	−	0.190404i
$349$	−69.1871	−	79.8461i	−0.198244	−	0.228786i	0.647920	−	0.761708i	$-0.275639\pi$
$349$	−69.1871	−	79.8461i	−0.198244	−	0.228786i	−0.846164	+	0.532923i	$0.821094\pi$
$350$	−218.662	−	478.804i	−0.624750	−	1.36801i
$351$	10.5565	−	73.4221i	0.0300755	−	0.209180i
$352$	−147.563	+	170.297i	−0.419213	+	0.483798i
$353$	106.372	−	92.1722i	0.301338	−	0.261111i	−0.491046	−	0.871134i	$-0.663385\pi$
$353$	106.372	−	92.1722i	0.301338	−	0.261111i	0.792384	+	0.610023i	$0.208840\pi$
$354$	50.4632	+	110.499i	0.142552	+	0.312144i
$355$	21.3068	+	33.1540i	0.0600190	+	0.0933914i
$356$	28.2121	+	196.220i	0.0792476	+	0.551179i
$357$	33.0904	+	21.2659i	0.0926902	+	0.0595684i
$358$	93.4078	−	60.0295i	0.260916	−	0.167680i
$359$	−86.0949	+	99.3588i	−0.239819	+	0.276766i	−0.862882	−	0.505406i	$-0.831343\pi$
$359$	−86.0949	+	99.3588i	−0.239819	+	0.276766i	0.623063	+	0.782172i	$0.285888\pi$
$360$	−9.68607	−	2.84409i	−0.0269057	−	0.00790024i
$361$	219.667	−	253.510i	0.608497	−	0.702243i
$362$	488.023	−	70.1672i	1.34813	−	0.193832i
$363$	−10.8639	−	36.9990i	−0.0299281	−	0.101926i
$364$	289.689			0.795850
$365$			5.07824i			0.0139130i
$366$	−11.0232	−	37.5415i	−0.0301180	−	0.102572i
$367$	120.560	−	187.595i	0.328502	−	0.511159i	−0.637240	−	0.770666i	$-0.719924\pi$
$367$	120.560	−	187.595i	0.328502	−	0.511159i	0.965741	+	0.259507i	$0.0835602\pi$
$368$	−42.3087	−	92.6432i	−0.114969	−	0.251748i
$369$	215.690	−	98.5024i	0.584526	−	0.266944i
$370$	27.7014	+	17.8026i	0.0748686	+	0.0481151i
$371$	−332.796	+	97.7178i	−0.897025	+	0.263390i
$372$	−100.647			−0.270555
$373$			15.7239i			0.0421552i	0.999778	+	0.0210776i	$0.00670971\pi$
$373$			15.7239i			0.0421552i	−0.999778	+	0.0210776i	$0.993290\pi$
$374$	25.4389	−	7.46953i	0.0680184	−	0.0199720i
$375$	4.75579	+	33.0772i	0.0126821	+	0.0882059i
$376$	−563.522	−	488.294i	−1.49873	−	1.29865i
$377$	−106.099	+	361.342i	−0.281431	+	0.958466i
$378$	−83.1805	−	72.0763i	−0.220054	−	0.190678i
$379$	211.427	+	328.986i	0.557854	+	0.868038i	0.999576	−	0.0291139i	$-0.00926854\pi$
$379$	211.427	+	328.986i	0.557854	+	0.868038i	−0.441722	+	0.897152i	$0.645632\pi$
$380$	−1.59877	+	2.48774i	−0.00420729	+	0.00654667i
$381$	−284.345	+	40.8827i	−0.746314	+	0.107304i
$382$	−331.411	+	212.985i	−0.867567	+	0.557552i
$383$	−534.966	+	244.311i	−1.39678	+	0.637887i	−0.964555	−	0.263881i	$-0.914998\pi$
$383$	−534.966	+	244.311i	−1.39678	+	0.637887i	−0.432222	+	0.901767i	$0.642270\pi$
$384$	−16.0255	−	18.4944i	−0.0417330	−	0.0481624i
$385$	−39.0249	−	33.8153i	−0.101363	−	0.0878319i
$386$	−441.765	−	63.5162i	−1.14447	−	0.164550i
$387$	25.9303	−	11.8420i	0.0670033	−	0.0305994i
$388$	118.681	−	102.838i	0.305880	−	0.265047i
$389$	437.182	+	128.368i	1.12386	+	0.329996i	0.790292	−	0.612730i	$-0.209929\pi$
$389$	437.182	+	128.368i	1.12386	+	0.329996i	0.333570	+	0.942725i	$0.391747\pi$
$390$	14.4849	+	4.25316i	0.0371409	+	0.0109055i
$391$	3.19605	−	22.2290i	0.00817403	−	0.0568517i
$392$	617.112	−	960.245i	1.57427	−	2.44960i
$393$	−142.141	−	64.9135i	−0.361681	−	0.165174i
$394$	90.8401	−	26.6731i	0.230559	−	0.0676981i
$395$	7.35827	−	16.1124i	0.0186285	−	0.0407908i
$396$	44.5946	−	6.41174i	0.112613	−	0.0161913i
$397$	−103.967	+	723.105i	−0.261881	+	1.82142i	0.256812	+	0.966461i	$0.417328\pi$
$397$	−103.967	+	723.105i	−0.261881	+	1.82142i	−0.518693	+	0.854961i	$0.673581\pi$
$398$	−147.335	+	127.667i	−0.370189	+	0.320770i
$399$	−98.9089	+	63.5649i	−0.247892	+	0.159311i
$400$	−79.1830	+	173.386i	−0.197957	+	0.433466i
$401$		−	6.54602i		−	0.0163242i	−0.999967	−	0.00816212i	$-0.997402\pi$
$401$		−	6.54602i		−	0.0163242i	0.999967	−	0.00816212i	$-0.00259811\pi$
$402$	−67.7434	−	170.075i	−0.168516	−	0.423072i
$403$	548.860			1.36193
$404$	8.52554	+	3.89348i	0.0211028	+	0.00963734i
$405$	1.88320	+	2.93031i	0.00464987	+	0.00723534i
$406$	365.931	+	422.307i	0.901307	+	1.04016i
$407$	−530.450	−	76.2672i	−1.30332	−	0.187389i
$408$	−3.62481	−	25.2111i	−0.00888434	−	0.0617919i
$409$	275.508	+	125.820i	0.673614	+	0.307629i	0.722696	−	0.691166i	$-0.242903\pi$
$409$	275.508	+	125.820i	0.673614	+	0.307629i	−0.0490827	+	0.998795i	$0.515630\pi$
$410$	13.5959	+	46.3033i	0.0331607	+	0.112935i
$411$	−84.2692	+	184.524i	−0.205035	+	0.448963i
$412$	−93.6390	−	60.1781i	−0.227279	−	0.146063i
$413$	590.863	+	84.9533i	1.43066	+	0.205698i
$414$	−17.7039	+	60.2939i	−0.0427630	+	0.145637i
$415$	7.51019	−	25.5774i	0.0180968	−	0.0616322i
$416$	−211.995	−	244.655i	−0.509604	−	0.588114i
$417$	102.716	+	224.917i	0.246322	+	0.539369i
$418$	−11.2782	+	78.4416i	−0.0269813	+	0.187659i
$419$	494.871	−	571.111i	1.18108	−	1.36303i	0.263901	−	0.964550i	$-0.414991\pi$
$419$	494.871	−	571.111i	1.18108	−	1.36303i	0.917175	−	0.398484i	$-0.130464\pi$
$420$	−10.2808	+	8.90838i	−0.0244781	+	0.0212104i
$421$	116.467	+	255.027i	0.276644	+	0.605765i	0.996047	−	0.0888273i	$-0.0283119\pi$
$421$	116.467	+	255.027i	0.276644	+	0.605765i	−0.719403	+	0.694593i	$0.755585\pi$
$422$	−264.729	−	411.926i	−0.627320	−	0.976129i
$423$	36.6154	+	254.666i	0.0865613	+	0.602047i
$424$	188.940	+	121.424i	0.445613	+	0.286378i
$425$	−35.3583	+	22.7234i	−0.0831960	+	0.0534668i
$426$	182.203	−	210.273i	0.427707	−	0.493600i
$427$	−184.480	−	54.1681i	−0.432037	−	0.126857i
$428$	−5.18648	+	5.98552i	−0.0121179	+	0.0139848i
$429$	−243.190	+	34.9654i	−0.566875	+	0.0815044i
$430$	1.63450	+	5.56658i	0.00380115	+	0.0129455i
$431$	−585.533			−1.35854			−0.679272	−	0.733886i	$-0.737705\pi$
$431$	−585.533			−1.35854			−0.679272	+	0.733886i	$0.737705\pi$
$432$			39.8567i			0.0922609i
$433$	−43.4036	−	147.819i	−0.100239	−	0.341383i	0.894068	−	0.447930i	$-0.147839\pi$
$433$	−43.4036	−	147.819i	−0.100239	−	0.341383i	−0.994308	+	0.106547i	$0.966021\pi$
$434$	440.295	−	685.113i	1.01450	−	1.57860i
$435$	−7.34642	−	16.0864i	−0.0168883	−	0.0369802i
$436$	−99.2531	+	45.3274i	−0.227645	+	0.103962i
$437$	56.4707	+	36.2915i	0.129224	+	0.0830470i
$438$	34.3996	−	10.1006i	0.0785379	−	0.0230608i
$439$	−1.74188			−0.00396784			−0.00198392	−	0.999998i	$-0.500632\pi$
$439$	−1.74188			−0.00396784			−0.00198392	+	0.999998i	$0.500632\pi$
$440$			33.4367i			0.0759926i
$441$	−377.901	+	110.962i	−0.856919	+	0.251614i
$442$	5.42069	+	37.7017i	0.0122640	+	0.0852980i
$443$	367.358	+	318.318i	0.829252	+	0.718551i	0.962133	−	0.272581i	$-0.0878774\pi$
$443$	367.358	+	318.318i	0.829252	+	0.718551i	−0.132881	+	0.991132i	$0.542423\pi$
$444$	−39.7750	+	135.461i	−0.0895834	+	0.305093i
$445$	38.3657	+	33.2441i	0.0862151	+	0.0747058i
$446$	−99.7433	−	155.204i	−0.223640	−	0.347990i
$447$	120.039	−	186.784i	0.268544	−	0.417862i
$448$	−883.224	+	126.988i	−1.97148	+	0.283456i
$449$	33.4285	−	21.4832i	0.0744509	−	0.0478467i	−0.502886	−	0.864353i	$-0.667728\pi$
$449$	33.4285	−	21.4832i	0.0744509	−	0.0478467i	0.577337	+	0.816506i	$0.304092\pi$
$450$	106.979	−	48.8557i	0.237731	−	0.108568i
$451$	−514.318	−	593.555i	−1.14039	−	1.31609i
$452$	−161.490	−	139.932i	−0.357278	−	0.309583i
$453$	−216.643	−	31.1485i	−0.478240	−	0.0687605i
$454$	365.716	−	167.017i	0.805543	−	0.367879i
$455$	56.0648	−	48.5804i	0.123219	−	0.106770i
$456$	73.0483	+	21.4489i	0.160194	+	0.0470371i
$457$	−348.033	−	102.192i	−0.761560	−	0.223614i	−0.122183	−	0.992508i	$-0.538989\pi$
$457$	−348.033	−	102.192i	−0.761560	−	0.223614i	−0.639377	+	0.768894i	$0.720808\pi$
$458$	−23.0827	+	160.544i	−0.0503989	+	0.350532i
$459$	−4.75144	+	7.39339i	−0.0103517	+	0.0161076i
$460$	7.06486	+	3.22641i	0.0153584	+	0.00701394i
$461$	−662.810	+	194.618i	−1.43777	+	0.422166i	−0.905476	−	0.424397i	$-0.860486\pi$
$461$	−662.810	+	194.618i	−1.43777	+	0.422166i	−0.532289	+	0.846563i	$0.678668\pi$
$462$	−151.441	+	331.610i	−0.327795	+	0.717771i
$463$	−140.338	+	20.1776i	−0.303106	+	0.0435800i	−0.292190	−	0.956360i	$-0.594384\pi$
$463$	−140.338	+	20.1776i	−0.303106	+	0.0435800i	−0.0109161	+	0.999940i	$0.503475\pi$
$464$	28.7977	−	200.292i	0.0620640	−	0.431665i
$465$	−19.4785	+	16.8782i	−0.0418893	+	0.0362973i
$466$	−329.369	+	211.673i	−0.706801	+	0.454233i
$467$	−122.238	+	267.664i	−0.261752	+	0.573156i	−0.994185	−	0.107682i	$-0.965657\pi$
$467$	−122.238	+	267.664i	−0.261752	+	0.573156i	0.732434	+	0.680838i	$0.238384\pi$
$468$			64.7253i			0.138302i
$469$	−883.055	−	171.795i	−1.88285	−	0.366300i
$470$	−52.3624			−0.111409
$471$	245.936	+	112.315i	0.522158	+	0.238461i
$472$	−208.977	−	325.175i	−0.442748	−	0.688930i
$473$	−61.8313	−	71.3572i	−0.130722	−	0.150861i
$474$	−123.779	−	17.7968i	−0.261138	−	0.0375460i
$475$	−17.8792	−	124.353i	−0.0376404	−	0.261795i
$476$	−31.2209	−	14.2581i	−0.0655901	−	0.0299540i
$477$	−21.8331	−	74.3567i	−0.0457717	−	0.155884i
$478$	52.2702	−	114.456i	0.109352	−	0.239447i
$479$	−308.949	−	198.549i	−0.644987	−	0.414508i	0.176844	−	0.984239i	$-0.443411\pi$
$479$	−308.949	−	198.549i	−0.644987	−	0.414508i	−0.821831	+	0.569731i	$0.807047\pi$
$480$	15.0470	+	2.16344i	0.0313480	+	0.00450716i
$481$	216.907	−	738.716i	0.450950	−	1.53579i
$482$	111.366	−	379.278i	0.231050	−	0.786884i
$483$	202.217	+	233.371i	0.418669	+	0.483170i
$484$	13.9777	+	30.6068i	0.0288795	+	0.0632372i
$485$	5.72315	−	39.8054i	0.0118003	−	0.0820729i
$486$	16.1040	−	18.5850i	0.0331358	−	0.0382408i
$487$	203.418	−	176.262i	0.417696	−	0.361935i	−0.420512	−	0.907287i	$-0.638149\pi$
$487$	203.418	−	176.262i	0.417696	−	0.361935i	0.838207	+	0.545352i	$0.183604\pi$
$488$	51.7189	+	113.249i	0.105981	+	0.232067i
$489$	277.331	+	431.535i	0.567139	+	0.882485i
$490$	−11.4075	−	79.3412i	−0.0232807	−	0.161921i
$491$	110.329	+	70.9045i	0.224704	+	0.144408i	0.648149	−	0.761513i	$-0.275543\pi$
$491$	110.329	+	70.9045i	0.224704	+	0.144408i	−0.423446	+	0.905921i	$0.639180\pi$
$492$	−174.059	+	111.861i	−0.353778	+	0.227359i
$493$	29.2194	−	33.7210i	0.0592686	−	0.0683996i
$494$	−109.240	−	32.0756i	−0.221133	−	0.0649304i
$495$	7.55534	−	8.71933i	0.0152633	−	0.0176148i
$496$	−291.910	+	41.9704i	−0.588529	+	0.0846177i
$497$	−385.195	−	1311.85i	−0.775041	−	2.63955i
$498$	−188.197			−0.377905
$499$			851.088i			1.70559i	0.522248	+	0.852794i	$0.325094\pi$
$499$			851.088i			1.70559i	−0.522248	+	0.852794i	$0.674906\pi$
$500$	−8.21511	−	27.9781i	−0.0164302	−	0.0559562i
$501$	−91.2781	+	142.032i	−0.182192	+	0.283496i
$502$	74.2560	+	162.598i	0.147920	+	0.323900i
$503$	−561.070	+	256.232i	−1.11545	+	0.509408i	−0.885894	−	0.463889i	$-0.846454\pi$
$503$	−561.070	+	256.232i	−1.11545	+	0.509408i	−0.229553	+	0.973296i	$0.573727\pi$
$504$	294.624	+	189.343i	0.584571	+	0.375681i
$505$	2.30291	−	0.676197i	0.00456023	−	0.00133900i
$506$	208.137			0.411339
$507$		−	60.2524i		−	0.118841i
$508$	240.511	−	70.6205i	0.473447	−	0.139017i
$509$	76.0056	+	528.630i	0.149323	+	1.03857i	0.917331	+	0.398126i	$0.130339\pi$
$509$	76.0056	+	528.630i	0.149323	+	1.03857i	−0.768008	+	0.640441i	$0.778752\pi$
$510$	−1.35176	−	1.17131i	−0.00265051	−	0.00229668i
$511$	49.6347	−	169.040i	0.0971326	−	0.330803i
$512$	333.061	+	288.599i	0.650510	+	0.563670i
$513$	−14.2023	−	22.0992i	−0.0276848	−	0.0430784i
$514$	246.863	−	384.126i	0.480278	−	0.747328i
$515$	−28.2141	+	4.05658i	−0.0547847	+	0.00787685i
$516$	−20.9253	+	13.4479i	−0.0405530	+	0.0260618i
$517$	775.172	−	354.009i	1.49937	−	0.684737i
$518$	−748.098	−	863.352i	−1.44421	−	1.66670i
$519$	53.3005	+	46.1851i	0.102698	+	0.0889886i
$520$	−47.5477	−	6.83632i	−0.0914378	−	0.0131468i
$521$	730.932	−	333.805i	1.40294	−	0.640701i	0.436999	−	0.899462i	$-0.356041\pi$
$521$	730.932	−	333.805i	1.40294	−	0.640701i	0.965941	+	0.258761i	$0.0833142\pi$
$522$	−94.3559	+	81.7599i	−0.180759	+	0.156628i
$523$	−137.532	−	40.3830i	−0.262967	−	0.0772141i	0.147591	−	0.989048i	$-0.452848\pi$
$523$	−137.532	−	40.3830i	−0.262967	−	0.0772141i	−0.410558	+	0.911834i	$0.634666\pi$
$524$	130.827	+	38.4144i	0.249671	+	0.0733099i
$525$	82.2471	−	572.041i	0.156661	−	1.08960i
$526$	243.124	−	378.308i	0.462213	−	0.719217i
$527$	−59.1526	−	27.0141i	−0.112244	−	0.0512601i
$528$	126.666	−	37.1926i	0.239898	−	0.0704406i
$529$	−146.516	+	320.825i	−0.276968	+	0.606475i
$530$	15.6113	−	2.24457i	0.0294554	−	0.00423504i
$531$	−18.9811	+	132.017i	−0.0357460	+	0.248619i
$532$	77.5337	−	67.1834i	0.145740	−	0.126284i
$533$	949.201	−	610.014i	1.78087	−	1.14449i
$534$	148.883	−	326.009i	0.278808	−	0.610503i
$535$			2.02817i			0.00379096i
$536$	290.381	+	504.989i	0.541756	+	0.942145i
$537$	121.909			0.227018
$538$	−433.821	−	198.119i	−0.806359	−	0.368252i
$539$	705.283	+	1097.44i	1.30850	+	2.03607i
$540$	−1.99040	−	2.29704i	−0.00368592	−	0.00425378i
$541$	−560.466	−	80.5829i	−1.03598	−	0.148952i	−0.396719	−	0.917940i	$-0.629851\pi$
$541$	−560.466	−	80.5829i	−1.03598	−	0.148952i	−0.639263	+	0.768988i	$0.720760\pi$
$542$	84.2537	+	585.997i	0.155450	+	1.08118i
$543$	492.411	+	224.877i	0.906835	+	0.414138i
$544$	10.8059	+	36.8015i	0.0198638	+	0.0676498i
$545$	−11.6075	+	25.4170i	−0.0212982	+	0.0466366i
$546$	−440.593	−	283.152i	−0.806946	−	0.518593i
$547$	523.785	+	75.3090i	0.957560	+	0.137676i	0.603338	−	0.797485i	$-0.293837\pi$
$547$	523.785	+	75.3090i	0.957560	+	0.137676i	0.354221	+	0.935162i	$0.384746\pi$
$548$	49.8687	−	169.837i	0.0910012	−	0.309922i
$549$	12.1028	−	41.2183i	0.0220451	−	0.0750789i
$550$	−255.094	−	294.394i	−0.463808	−	0.535262i
$551$	55.4037	+	121.317i	0.100551	+	0.220176i
$552$	28.4564	−	197.918i	0.0515514	−	0.358548i
$553$	−402.419	+	464.416i	−0.727701	+	0.839811i
$554$	−131.315	+	113.785i	−0.237030	+	0.205388i
$555$	15.0188	+	32.8866i	0.0270609	+	0.0592551i
$556$	−116.646	−	181.505i	−0.209795	−	0.326447i
$557$	21.4800	+	149.397i	0.0385638	+	0.268217i	0.999976	−	0.00689406i	$-0.00219447\pi$
$557$	21.4800	+	149.397i	0.0385638	+	0.268217i	−0.961412	+	0.275111i	$0.911285\pi$
$558$	153.075	+	98.3751i	0.274327	+	0.176300i
$559$	114.113	−	73.3360i	0.204138	−	0.131191i
$560$	−26.1031	+	30.1246i	−0.0466128	+	0.0537940i
$561$	27.9304	+	8.20109i	0.0497867	+	0.0146187i
$562$	281.475	−	324.840i	0.500846	−	0.578007i
$563$	−612.948	+	88.1286i	−1.08872	+	0.156534i	−0.663219	−	0.748425i	$-0.730810\pi$
$563$	−612.948	+	88.1286i	−1.08872	+	0.156534i	−0.425499	+	0.904959i	$0.639901\pi$
$564$	−63.2492	−	215.407i	−0.112144	−	0.381927i
$565$	−54.7200			−0.0968496
$566$		−	293.880i		−	0.519223i
$567$	−34.0455	−	115.948i	−0.0600449	−	0.204494i
$568$	−478.644	+	744.785i	−0.842683	+	1.31124i
$569$	391.435	+	857.123i	0.687935	+	1.50637i	0.854011	+	0.520254i	$0.174163\pi$
$569$	391.435	+	857.123i	0.687935	+	1.50637i	−0.166076	+	0.986113i	$0.553110\pi$
$570$	4.86319	−	2.22094i	0.00853191	−	0.00389639i
$571$	542.816	+	348.847i	0.950641	+	0.610940i	0.921393	−	0.388632i	$-0.127052\pi$
$571$	542.816	+	348.847i	0.950641	+	0.610940i	0.0292483	+	0.999572i	$0.490689\pi$
$572$	205.700	−	60.3989i	0.359615	−	0.105593i
$573$	−432.532			−0.754855
$574$		−	1674.19i		−	2.91671i
$575$	−316.592	+	92.9599i	−0.550595	+	0.161669i
$576$	−28.3730	−	197.339i	−0.0492587	−	0.342602i
$577$	569.472	+	493.451i	0.986954	+	0.855200i	0.989461	−	0.144797i	$-0.0462528\pi$
$577$	569.472	+	493.451i	0.986954	+	0.855200i	−0.00250777	+	0.999997i	$0.500798\pi$
$578$	−127.173	+	433.113i	−0.220023	+	0.749331i
$579$	−370.331	−	320.894i	−0.639605	−	0.554221i
$580$	8.34269	+	12.9815i	0.0143840	+	0.0223819i
$581$	−499.986	+	777.994i	−0.860562	+	1.33906i
$582$	−281.021	+	40.4048i	−0.482855	+	0.0694240i
$583$	−215.935	+	138.773i	−0.370386	+	0.238033i
$584$	−103.771	+	47.3905i	−0.177689	+	0.0811481i
$585$	10.8543	+	12.5266i	0.0185544	+	0.0214129i
$586$	242.288	+	209.944i	0.413460	+	0.358265i
$587$	−457.564	−	65.7878i	−0.779496	−	0.112075i	−0.258930	−	0.965896i	$-0.583370\pi$
$587$	−457.564	−	65.7878i	−0.779496	−	0.112075i	−0.520566	+	0.853822i	$0.674279\pi$
$588$	312.613	−	142.765i	0.531654	−	0.242798i
$589$	146.899	−	127.289i	0.249404	−	0.216110i
$590$	−26.0447	−	7.64740i	−0.0441435	−	0.0129617i
$591$	99.7370	+	29.2854i	0.168760	+	0.0495523i
$592$	−58.8732	+	409.472i	−0.0994480	+	0.691676i
$593$	581.557	−	904.920i	0.980703	−	1.52600i	0.136040	−	0.990703i	$-0.456562\pi$
$593$	581.557	−	904.920i	0.980703	−	1.52600i	0.844662	−	0.535300i	$-0.179801\pi$
$594$	−74.0916	−	33.8365i	−0.124733	−	0.0569638i
$595$	−8.43336	+	2.47626i	−0.0141737	+	0.00416178i
$596$	−80.4823	+	176.232i	−0.135037	+	0.295691i
$597$	−211.867	+	30.4619i	−0.354887	+	0.0510250i
$598$	−42.5548	+	295.975i	−0.0711619	+	0.494942i
$599$	−617.680	+	535.223i	−1.03119	+	0.893527i	−0.994388	−	0.105795i	$-0.966261\pi$
$599$	−617.680	+	535.223i	−1.03119	+	0.893527i	−0.0367977	+	0.999323i	$0.511716\pi$
$600$	−314.816	+	202.320i	−0.524694	+	0.337200i
$601$	372.260	−	815.135i	0.619400	−	1.35630i	−0.296554	−	0.955016i	$-0.595838\pi$
$601$	372.260	−	815.135i	0.619400	−	1.35630i	0.915955	−	0.401282i	$-0.131435\pi$
$602$		−	201.271i		−	0.334338i
$603$	38.3841	−	197.301i	0.0636552	−	0.327199i
$604$	190.982			0.316195
$605$	7.83787	+	3.57943i	0.0129552	+	0.00591642i
$606$	−9.16100	−	14.2548i	−0.0151172	−	0.0235228i
$607$	−233.534	−	269.512i	−0.384734	−	0.444007i	0.530040	−	0.847973i	$-0.322177\pi$
$607$	−233.534	−	269.512i	−0.384734	−	0.444007i	−0.914774	+	0.403966i	$0.867631\pi$
$608$	−113.479	−	16.3158i	−0.186642	−	0.0268351i
$609$	87.3130	+	607.275i	0.143371	+	0.997168i
$610$	7.95278	+	3.63191i	0.0130374	+	0.00595396i
$611$	344.919	+	1174.69i	0.564516	+	1.92257i
$612$	3.18569	−	6.97568i	0.00520537	−	0.0113982i
$613$	−745.742	−	479.259i	−1.21655	−	0.781826i	−0.234803	−	0.972043i	$-0.575444\pi$
$613$	−745.742	−	479.259i	−1.21655	−	0.781826i	−0.981742	+	0.190217i	$0.939081\pi$
$614$	314.774	+	45.2576i	0.512661	+	0.0737095i
$615$	−14.9274	+	50.8382i	−0.0242723	+	0.0826638i
$616$	326.811	−	1113.02i	0.530537	−	1.80684i
$617$	349.137	+	402.926i	0.565863	+	0.653040i	0.964504	−	0.264066i	$-0.0850638\pi$
$617$	349.137	+	402.926i	0.565863	+	0.653040i	−0.398642	+	0.917107i	$0.630518\pi$
$618$	83.5968	+	183.052i	0.135270	+	0.296200i
$619$	23.5751	−	163.969i	0.0380858	−	0.264893i	−0.961877	−	0.273481i	$-0.911825\pi$
$619$	23.5751	−	163.969i	0.0380858	−	0.264893i	0.999963	+	0.00858861i	$0.00273387\pi$
$620$	14.7276	−	16.9965i	0.0237542	−	0.0274138i
$621$	−52.1421	+	45.1814i	−0.0839647	+	0.0727558i
$622$	−61.8720	−	135.481i	−0.0994727	−	0.217815i
$623$	−952.159	−	1481.59i	−1.52835	−	2.37815i
$624$	26.9910	+	187.726i	0.0432547	+	0.300843i
$625$	516.351	+	331.839i	0.826162	+	0.530942i
$626$	−207.295	+	133.220i	−0.331142	+	0.212812i
$627$	−56.9793	+	65.7576i	−0.0908761	+	0.104877i
$628$	−226.362	−	66.4658i	−0.360449	−	0.105837i
$629$	−59.7354	+	68.9383i	−0.0949688	+	0.109600i
$630$	24.3436	−	3.50008i	0.0386406	−	0.00555568i
$631$	−140.418	−	478.221i	−0.222533	−	0.757879i	−0.992761	−	0.120109i	$-0.961675\pi$
$631$	−140.418	−	478.221i	−0.222533	−	0.757879i	0.770227	−	0.637769i	$-0.220143\pi$
$632$	397.914			0.629611
$633$		−	537.615i		−	0.849312i
$634$	85.0917	+	289.796i	0.134214	+	0.457091i
$635$	34.7042	−	54.0008i	0.0546523	−	0.0850406i
$636$	28.0908	+	61.5104i	0.0441680	+	0.0967144i
$637$	−1704.78	+	778.548i	−2.67627	+	1.22221i
$638$	347.886	+	223.573i	0.545275	+	0.350427i
$639$	293.108	−	86.0641i	0.458697	−	0.134686i
$640$	5.46822			0.00854409
$641$			1037.90i			1.61919i	0.586986	+	0.809597i	$0.300315\pi$
$641$			1037.90i			1.61919i	−0.586986	+	0.809597i	$0.699685\pi$
$642$	13.7386	−	4.03402i	0.0213997	−	0.00628353i
$643$	109.874	+	764.188i	0.170877	+	1.18847i	0.877038	+	0.480421i	$0.159516\pi$
$643$	109.874	+	764.188i	0.170877	+	1.18847i	−0.706161	+	0.708051i	$0.749575\pi$
$644$	−203.634	−	176.450i	−0.316202	−	0.273991i
$645$	−1.79458	+	6.11177i	−0.00278229	+	0.00947562i
$646$	10.1944	+	8.83351i	0.0157808	+	0.0136742i
$647$	−226.436	−	352.341i	−0.349978	−	0.544577i	0.620980	−	0.783827i	$-0.286735\pi$
$647$	−226.436	−	352.341i	−0.349978	−	0.544577i	−0.970958	+	0.239250i	$0.923098\pi$
$648$	−42.3050	+	65.8278i	−0.0652854	+	0.101586i
$649$	437.267	−	62.8695i	0.673755	−	0.0968714i
$650$	470.790	−	302.558i	0.724292	−	0.465474i
$651$	813.354	−	371.446i	1.24939	−	0.570578i
$652$	−293.118	−	338.276i	−0.449567	−	0.518828i
$653$	631.099	+	546.851i	0.966461	+	0.837444i	0.986733	−	0.162351i	$-0.0519077\pi$
$653$	631.099	+	546.851i	0.966461	+	0.837444i	−0.0202717	+	0.999795i	$0.506453\pi$
$654$	195.260	+	28.0741i	0.298562	+	0.0429268i
$655$	31.7616	−	14.5050i	0.0484910	−	0.0221451i
$656$	−458.185	+	397.019i	−0.698453	+	0.605213i
$657$	37.7687	+	11.0899i	0.0574866	+	0.0168796i
$658$	1743.00	+	511.790i	2.64893	+	0.777796i
$659$	55.8850	−	388.689i	0.0848027	−	0.589816i	−0.902467	−	0.430759i	$-0.858246\pi$
$659$	55.8850	−	388.689i	0.0848027	−	0.589816i	0.987270	−	0.159056i	$-0.0508452\pi$
$660$	−5.44275	+	8.46908i	−0.00824659	+	0.0128319i
$661$	573.719	+	262.009i	0.867957	+	0.396383i	0.799067	−	0.601242i	$-0.205327\pi$
$661$	573.719	+	262.009i	0.867957	+	0.396383i	0.0688896	+	0.997624i	$0.478054\pi$
$662$	84.8413	−	24.9117i	0.128159	−	0.0376309i
$663$	−17.3726	+	38.0407i	−0.0262030	+	0.0573767i
$664$	592.743	−	85.2235i	0.892685	−	0.128349i
$665$	3.73889	−	26.0045i	0.00562239	−	0.0391046i
$666$	192.899	−	167.148i	0.289638	−	0.250972i
$667$	294.675	−	189.376i	0.441792	−	0.283922i
$668$	61.1990	−	134.007i	0.0916153	−	0.200609i
$669$		−	202.560i		−	0.302780i
$670$	38.6341	+	13.4470i	0.0576628	+	0.0200701i
$671$	−142.287			−0.212053
$672$	−479.728	−	219.084i	−0.713881	−	0.326019i
$673$	256.894	+	399.735i	0.381715	+	0.593960i	0.977947	−	0.208852i	$-0.0669728\pi$
$673$	256.894	+	399.735i	0.381715	+	0.593960i	−0.596233	+	0.802812i	$0.703336\pi$
$674$	−254.903	−	294.173i	−0.378194	−	0.436459i
$675$	127.811	+	18.3765i	0.189350	+	0.0272244i
$676$	7.48219	+	52.0397i	0.0110683	+	0.0769819i
$677$	−44.7710	−	20.4462i	−0.0661315	−	0.0302012i	0.382075	−	0.924131i	$-0.375210\pi$
$677$	−44.7710	−	20.4462i	−0.0661315	−	0.0302012i	−0.448206	+	0.893930i	$0.647937\pi$
$678$	108.838	+	370.669i	0.160528	+	0.546709i
$679$	−579.565	+	1269.07i	−0.853557	+	1.86903i
$680$	4.78791	+	3.07700i	0.00704104	+	0.00452500i
$681$	436.932	+	62.8214i	0.641604	+	0.0922488i
$682$	169.798	−	578.278i	0.248970	−	0.847915i
$683$	174.209	−	593.303i	0.255065	−	0.868672i	−0.728025	−	0.685550i	$-0.759562\pi$
$683$	174.209	−	593.303i	0.255065	−	0.868672i	0.983090	−	0.183121i	$-0.0586201\pi$
$684$	15.0108	+	17.3234i	0.0219456	+	0.0253265i
$685$	−18.8301	−	41.2322i	−0.0274892	−	0.0601930i
$686$	−248.046	+	1725.20i	−0.361584	+	2.51487i
$687$	−116.617	+	134.584i	−0.169749	+	0.195901i
$688$	−55.0830	+	47.7297i	−0.0800625	+	0.0693746i
$689$	−153.189	−	335.437i	−0.222335	−	0.486846i
$690$	−7.59145	−	11.8125i	−0.0110021	−	0.0171196i
$691$	−109.023	−	758.270i	−0.157775	−	1.09735i	−0.902721	−	0.430226i	$-0.858434\pi$
$691$	−109.023	−	758.270i	−0.157775	−	1.09735i	0.744946	−	0.667125i	$-0.232475\pi$
$692$	−51.7707	−	33.2710i	−0.0748132	−	0.0480795i
$693$	−336.719	+	216.396i	−0.485886	+	0.312260i
$694$	−648.502	+	748.411i	−0.934441	+	1.07840i
$695$	−53.0130	−	15.5660i	−0.0762777	−	0.0223971i
$696$	260.158	−	300.239i	0.373791	−	0.431377i
$697$	−132.323	+	19.0252i	−0.189846	+	0.0272958i
$698$	−46.9564	−	159.919i	−0.0672728	−	0.229110i
$699$	−429.868			−0.614975
$700$			504.283i			0.720405i
$701$	180.948	+	616.254i	0.258129	+	0.879107i	0.981954	+	0.189123i	$0.0605643\pi$
$701$	180.948	+	616.254i	0.258129	+	0.879107i	−0.723825	+	0.689984i	$0.757617\pi$
$702$	63.2646	−	98.4416i	0.0901205	−	0.140230i
$703$	−113.266	−	248.017i	−0.161118	−	0.352798i
$704$	−600.675	+	274.319i	−0.853231	+	0.389658i
$705$	−48.3643	−	31.0818i	−0.0686018	−	0.0440877i
$706$	213.047	−	62.5562i	0.301766	−	0.0886065i
$707$	−83.2667			−0.117775
$708$		−	116.379i		−	0.164378i
$709$	−754.914	+	221.663i	−1.06476	+	0.312642i	−0.766766	−	0.641926i	$-0.778135\pi$
$709$	−754.914	+	221.663i	−1.06476	+	0.312642i	−0.297993	+	0.954568i	$0.596317\pi$
$710$	8.84791	+	61.5386i	0.0124618	+	0.0866740i
$711$	−103.764	−	89.9124i	−0.145941	−	0.126459i
$712$	−321.291	+	1094.22i	−0.451251	+	1.53682i
$713$	−385.816	−	334.311i	−0.541116	−	0.468879i
$714$	33.5479	+	52.2016i	0.0469859	+	0.0731115i
$715$	29.6812	−	46.1848i	0.0415121	−	0.0645941i
$716$	−105.292	+	15.1387i	−0.147056	+	0.0211435i
$717$	116.219	−	74.6895i	0.162091	−	0.104169i
$718$	−188.658	+	86.1574i	−0.262755	+	0.119996i
$719$	−353.055	−	407.448i	−0.491037	−	0.566686i	0.455106	−	0.890437i	$-0.349601\pi$
$719$	−353.055	−	407.448i	−0.491037	−	0.566686i	−0.946142	+	0.323751i	$0.895056\pi$
$720$	−6.73075	−	5.83222i	−0.00934826	−	0.00810031i
$721$	978.818	+	140.733i	1.35758	+	0.195191i
$722$	481.354	−	219.827i	0.666695	−	0.304469i
$723$	327.999	−	284.213i	0.453664	−	0.393102i
$724$	−453.219	−	133.077i	−0.625993	−	0.183808i
$725$	−629.014	−	184.695i	−0.867605	−	0.254752i
$726$	8.65726	−	60.2126i	0.0119246	−	0.0829374i
$727$	703.580	−	1094.79i	0.967785	−	1.50590i	0.108698	−	0.994075i	$-0.465332\pi$
$727$	703.580	−	1094.79i	0.967785	−	1.50590i	0.859088	−	0.511829i	$-0.171032\pi$
$728$	1515.91	+	692.293i	2.08229	+	0.950952i
$729$	25.9063	−	7.60678i	0.0355368	−	0.0104345i
$730$	−3.32796	+	7.28721i	−0.00455884	+	0.00998248i
$731$	−15.9079	+	2.28720i	−0.0217618	+	0.00312887i
$732$	−5.33461	+	37.1030i	−0.00728772	+	0.0506872i
$733$	−194.162	+	168.243i	−0.264887	+	0.229526i	−0.777170	−	0.629291i	$-0.783345\pi$
$733$	−194.162	+	168.243i	−0.264887	+	0.229526i	0.512283	+	0.858817i	$0.328800\pi$
$734$	295.940	−	190.189i	0.403188	−	0.259113i
$735$	36.5597	−	80.0546i	0.0497411	−	0.108918i
$736$			301.105i			0.409110i
$737$	−662.850	+	62.1266i	−0.899389	+	0.0842966i
$738$	374.065			0.506863
$739$	1249.71	+	570.723i	1.69108	+	0.772291i	0.998711	+	0.0507487i	$0.0161607\pi$
$739$	1249.71	+	570.723i	1.69108	+	0.772291i	0.692370	+	0.721542i	$0.256567\pi$
$740$	−17.0556	−	26.5390i	−0.0230481	−	0.0358635i
$741$	−81.8588	−	94.4701i	−0.110471	−	0.127490i
$742$	−541.596	−	77.8698i	−0.729914	−	0.104946i
$743$	−113.302	−	788.030i	−0.152492	−	1.06061i	−0.912024	−	0.410136i	$-0.865481\pi$
$743$	−113.302	−	788.030i	−0.152492	−	1.06061i	0.759532	−	0.650469i	$-0.225428\pi$
$744$	−526.671	−	240.523i	−0.707891	−	0.323283i
$745$	13.9777	+	47.6036i	0.0187620	+	0.0638974i
$746$	−10.3044	+	22.5636i	−0.0138129	+	0.0302461i
$747$	−173.827	−	111.712i	−0.232700	−	0.149547i
$748$	−25.1418	−	3.61484i	−0.0336120	−	0.00483267i
$749$	19.8233	−	67.5119i	0.0264663	−	0.0901361i
$750$	−14.8522	+	50.5820i	−0.0198029	+	0.0674427i
$751$	193.087	+	222.834i	0.257106	+	0.296717i	0.869598	−	0.493761i	$-0.164378\pi$
$751$	193.087	+	222.834i	0.257106	+	0.296717i	−0.612492	+	0.790477i	$0.709833\pi$
$752$	−273.272	−	598.381i	−0.363393	−	0.795720i
$753$	−27.9305	+	194.261i	−0.0370922	+	0.257982i
$754$	−389.051	+	448.989i	−0.515983	+	0.595477i
$755$	36.9614	−	32.0273i	0.0489556	−	0.0424202i
$756$	43.8035	+	95.9163i	0.0579411	+	0.126873i
$757$	−575.316	−	895.209i	−0.759995	−	1.18257i	−0.978401	−	0.206717i	$-0.933722\pi$
$757$	−575.316	−	895.209i	−0.759995	−	1.18257i	0.218406	−	0.975858i	$-0.429914\pi$
$758$	87.7977	+	610.647i	0.115828	+	0.805602i
$759$	192.245	+	123.549i	0.253288	+	0.162778i
$760$	−14.3113	+	9.19732i	−0.0188307	+	0.0121017i
$761$	−785.451	+	906.459i	−1.03213	+	1.19114i	−0.0508209	+	0.998708i	$0.516184\pi$
$761$	−785.451	+	906.459i	−1.03213	+	1.19114i	−0.981310	+	0.192435i	$0.938362\pi$
$762$	−434.824	−	127.676i	−0.570635	−	0.167554i
$763$	634.808	−	732.607i	0.831989	−	0.960167i
$764$	373.576	−	53.7122i	0.488974	−	0.0703039i
$765$	−0.553270	−	1.88427i	−0.000723229	−	0.00246309i
$766$	−927.774			−1.21119
$767$			634.656i			0.827452i
$768$	118.839	+	404.729i	0.154739	+	0.526991i
$769$	73.4339	−	114.265i	0.0954928	−	0.148590i	−0.790220	−	0.612823i	$-0.790034\pi$
$769$	73.4339	−	114.265i	0.0954928	−	0.148590i	0.885713	+	0.464234i	$0.153670\pi$
$770$	−33.8398	−	74.0989i	−0.0439478	−	0.0962323i
$771$	456.028	−	208.261i	0.591476	−	0.270118i
$772$	359.703	+	231.167i	0.465936	+	0.299439i
$773$	304.084	−	89.2871i	0.393381	−	0.115507i	−0.0790587	−	0.996870i	$-0.525191\pi$
$773$	304.084	−	89.2871i	0.393381	−	0.115507i	0.472440	+	0.881363i	$0.343373\pi$
$774$	44.9701			0.0581008
$775$			955.440i			1.23283i
$776$	866.806	−	254.517i	1.11702	−	0.327986i
$777$	−178.500	−	1241.50i	−0.229730	−	1.59781i
$778$	543.226	+	470.708i	0.698234	+	0.605023i
$779$	112.577	−	383.401i	0.144514	−	0.492171i
$780$	−10.9304	−	9.47124i	−0.0140133	−	0.0121426i
$781$	−547.031	−	851.198i	−0.700424	−	1.08988i
$782$	19.1538	−	29.8038i	0.0244933	−	0.0381123i
$783$	−135.683	+	19.5083i	−0.173287	+	0.0249149i
$784$	847.152	−	544.432i	1.08055	−	0.694428i
$785$	−54.9549	+	25.0971i	−0.0700063	+	0.0319708i
$786$	−161.430	−	186.300i	−0.205381	−	0.237023i
$787$	−575.265	−	498.470i	−0.730959	−	0.633380i	0.207713	−	0.978190i	$-0.433398\pi$
$787$	−575.265	−	498.470i	−0.730959	−	0.633380i	−0.938672	+	0.344810i	$0.887943\pi$
$788$	−89.7791	−	12.9083i	−0.113933	−	0.0163811i
$789$	449.121	−	205.107i	0.569228	−	0.259958i
$790$	21.1180	−	18.2989i	0.0267317	−	0.0231631i
$791$	1821.48	+	534.834i	2.30275	+	0.676149i
$792$	248.681	+	73.0193i	0.313991	+	0.0921961i
$793$	29.0914	−	202.335i	0.0366853	−	0.255152i
$794$	−623.067	+	969.512i	−0.784720	+	1.22105i
$795$	15.7517	+	7.19357i	0.0198135	+	0.00904851i
$796$	179.206	−	52.6197i	0.225134	−	0.0661052i
$797$	−396.298	+	867.772i	−0.497238	+	1.08880i	0.480120	+	0.877203i	$0.340593\pi$
$797$	−396.298	+	867.772i	−0.497238	+	1.08880i	−0.977357	+	0.211596i	$0.932134\pi$
$798$	−183.589	+	26.3962i	−0.230062	+	0.0330779i
$799$	20.6432	−	143.577i	0.0258363	−	0.179696i
$800$	425.889	−	369.035i	0.532362	−	0.461294i
$801$	331.031	−	212.741i	0.413273	−	0.265594i
$802$	4.28984	−	9.39345i	0.00534893	−	0.0117125i
$803$		−	130.379i		−	0.162365i
$804$	−8.65123	+	175.175i	−0.0107602	+	0.217879i
$805$	−69.0006			−0.0857150
$806$	787.606	+	359.688i	0.977178	+	0.446262i
$807$	−283.095	−	440.504i	−0.350799	−	0.545854i
$808$	35.3086	+	40.7483i	0.0436987	+	0.0504310i
$809$	344.911	+	49.5907i	0.426343	+	0.0612988i	0.352147	−	0.935945i	$-0.385452\pi$
$809$	344.911	+	49.5907i	0.426343	+	0.0612988i	0.0741960	+	0.997244i	$0.476361\pi$
$810$	0.782022	+	5.43909i	0.000965460	+	0.00671492i
$811$	900.432	+	411.214i	1.11027	+	0.507045i	0.884220	−	0.467070i	$-0.154690\pi$
$811$	900.432	+	411.214i	1.11027	+	0.507045i	0.226053	+	0.974115i	$0.427418\pi$
$812$	−150.824	−	513.659i	−0.185744	−	0.632585i
$813$	−270.022	+	591.266i	−0.332131	+	0.727265i
$814$	−711.208	−	457.065i	−0.873719	−	0.561505i
$815$	−113.457	−	16.3126i	−0.139211	−	0.0200155i
$816$	6.33070	−	21.5604i	0.00775821	−	0.0264220i
$817$	13.5340	−	46.0925i	0.0165655	−	0.0564167i
$818$	312.896	+	361.101i	0.382513	+	0.441443i
$819$	−238.875	−	523.064i	−0.291667	−	0.638662i
$820$	6.57965	−	45.7625i	0.00802397	−	0.0558079i
$821$	−935.373	+	1079.48i	−1.13931	+	1.31483i	−0.196881	+	0.980427i	$0.563081\pi$
$821$	−935.373	+	1079.48i	−1.13931	+	1.31483i	−0.942429	+	0.334406i	$0.891464\pi$
$822$	−241.850	+	209.564i	−0.294222	+	0.254945i
$823$	−167.878	−	367.601i	−0.203983	−	0.446660i	0.779799	−	0.626030i	$-0.215321\pi$
$823$	−167.878	−	367.601i	−0.203983	−	0.446660i	−0.983782	+	0.179370i	$0.942594\pi$
$824$	−346.189	−	538.681i	−0.420133	−	0.653739i
$825$	−60.8668	−	423.338i	−0.0737779	−	0.513137i
$826$	792.208	+	509.121i	0.959089	+	0.616369i
$827$	447.760	−	287.758i	0.541426	−	0.347954i	−0.241170	−	0.970483i	$-0.577531\pi$
$827$	447.760	−	287.758i	0.541426	−	0.347954i	0.782597	+	0.622529i	$0.213895\pi$
$828$	39.4243	−	45.4980i	0.0476138	−	0.0549493i
$829$	29.0254	+	8.52262i	0.0350125	+	0.0102806i	0.299192	−	0.954193i	$-0.403283\pi$
$829$	29.0254	+	8.52262i	0.0350125	+	0.0102806i	−0.264179	+	0.964474i	$0.585101\pi$
$830$	27.5388	−	31.7815i	0.0331793	−	0.0382909i
$831$	−188.830	+	27.1496i	−0.227232	+	0.0326710i
$832$	−267.275	−	910.257i	−0.321245	−	1.09406i
$833$	222.049			0.266566
$834$			390.066i			0.467706i
$835$	−10.6287	−	36.1979i	−0.0127289	−	0.0433508i
$836$	41.0470	−	63.8704i	0.0490993	−	0.0763999i
$837$	82.9922	+	181.728i	0.0991544	+	0.217118i
$838$	1084.40	−	495.230i	1.29404	−	0.590967i
$839$	−262.635	−	168.785i	−0.313033	−	0.201174i	0.374685	−	0.927152i	$-0.377751\pi$
$839$	−262.635	−	168.785i	−0.313033	−	0.201174i	−0.687718	+	0.725978i	$0.741387\pi$
$840$	−75.0873	+	22.0476i	−0.0893897	+	0.0262472i
$841$	−145.053			−0.172477
$842$			442.286i			0.525280i
$843$	452.806	−	132.956i	0.537136	−	0.157717i
$844$	66.7614	+	464.336i	0.0791012	+	0.550161i
$845$	10.1750	+	8.81672i	0.0120415	+	0.0104340i
$846$	−114.349	+	389.437i	−0.135164	+	0.460328i
$847$	−225.915	−	195.757i	−0.266724	−	0.231118i
$848$	107.124	+	166.688i	0.126325	+	0.196566i
$849$	174.445	−	271.441i	0.205471	−	0.319719i
$850$	−65.6302	+	9.43619i	−0.0772119	+	0.0111014i
$851$	−602.426	+	387.155i	−0.707903	+	0.454942i
$852$	−242.468	+	110.732i	−0.284587	+	0.129967i
$853$	−190.879	−	220.286i	−0.223774	−	0.258249i	0.632750	−	0.774356i	$-0.281926\pi$
$853$	−190.879	−	220.286i	−0.223774	−	0.258249i	−0.856524	+	0.516107i	$0.827381\pi$
$854$	−229.227	−	198.627i	−0.268416	−	0.232584i
$855$	5.81019	+	0.835380i	0.00679555	+	0.000977053i
$856$	−41.4443	+	18.9270i	−0.0484162	+	0.0221109i
$857$	−829.166	+	718.477i	−0.967522	+	0.838362i	−0.986881	−	0.161450i	$-0.948383\pi$
$857$	−829.166	+	718.477i	−0.967522	+	0.838362i	0.0193591	+	0.999813i	$0.493837\pi$
$858$	−371.888	−	109.196i	−0.433436	−	0.127268i
$859$	368.268	+	108.133i	0.428718	+	0.125883i	0.488971	−	0.872300i	$-0.337373\pi$
$859$	368.268	+	108.133i	0.428718	+	0.125883i	−0.0602529	+	0.998183i	$0.519191\pi$
$860$	0.791006	−	5.50157i	0.000919774	−	0.00639717i
$861$	993.785	−	1546.36i	1.15422	−	1.79601i
$862$	−840.232	−	383.721i	−0.974747	−	0.445152i
$863$	−748.048	+	219.647i	−0.866799	+	0.254515i	−0.684753	−	0.728775i	$-0.740090\pi$
$863$	−748.048	+	219.647i	−0.866799	+	0.254515i	−0.182046	+	0.983290i	$0.558272\pi$
$864$	48.9500	−	107.186i	0.0566551	−	0.124057i
$865$	−15.5989	+	2.24278i	−0.0180334	+	0.00259281i
$866$	34.5876	−	240.562i	0.0399395	−	0.277785i
$867$	−374.555	+	324.554i	−0.432013	+	0.374342i
$868$	−656.364	+	421.820i	−0.756180	+	0.485967i
$869$	−188.917	+	413.670i	−0.217396	+	0.476030i
$870$		−	27.8981i		−	0.0320668i
$871$	47.1781	−	955.287i	0.0541654	−	1.09677i
$872$	−627.702			−0.719842
$873$	−283.548	−	129.492i	−0.324798	−	0.148330i
$874$	57.2516	+	89.0852i	0.0655052	+	0.101928i
$875$	169.645	+	195.780i	0.193880	+	0.223749i
$876$	−33.9978	−	4.88815i	−0.0388103	−	0.00558008i
$877$	−0.863212	−	6.00377i	−0.000984278	−	0.00684581i	0.989323	−	0.145737i	$-0.0465553\pi$
$877$	−0.863212	−	6.00377i	−0.000984278	−	0.00684581i	−0.990308	+	0.138891i	$0.955646\pi$
$878$	−2.49958	−	1.14152i	−0.00284690	−	0.00130014i
$879$	99.1675	+	337.733i	0.112819	+	0.384225i
$880$	−12.2542	+	26.8330i	−0.0139253	+	0.0304920i
$881$	110.789	+	71.2001i	0.125754	+	0.0808173i	0.602006	−	0.798492i	$-0.294368\pi$
$881$	110.789	+	71.2001i	0.125754	+	0.0808173i	−0.476251	+	0.879309i	$0.658005\pi$
$882$	−615.000	−	88.4237i	−0.697279	−	0.100254i
$883$	132.934	−	452.731i	0.150548	−	0.512719i	−0.849338	−	0.527850i	$-0.822998\pi$
$883$	132.934	−	452.731i	0.150548	−	0.512719i	0.999886	+	0.0151308i	$0.00481648\pi$
$884$	10.2807	−	35.0130i	0.0116298	−	0.0396074i
$885$	−19.5166	−	22.5234i	−0.0220527	−	0.0254501i
$886$	318.549	+	697.525i	0.359536	+	0.787274i
$887$	145.223	−	1010.05i	0.163724	−	1.13872i	−0.727813	−	0.685776i	$-0.759463\pi$
$887$	145.223	−	1010.05i	0.163724	−	1.13872i	0.891536	−	0.452949i	$-0.149628\pi$
$888$	−531.860	+	613.799i	−0.598942	+	0.691216i
$889$	−1683.01	+	1458.34i	−1.89315	+	1.64042i
$890$	33.2682	+	72.8473i	0.0373800	+	0.0818509i
$891$	−48.3494	−	75.2331i	−0.0542642	−	0.0844367i
$892$	25.1541	+	174.950i	0.0281996	+	0.196133i
$893$	364.744	+	234.406i	0.408447	+	0.262493i
$894$	294.661	−	189.367i	0.329598	−	0.211820i
$895$	−17.8389	+	20.5872i	−0.0199317	+	0.0230024i
$896$	−182.021	−	53.4463i	−0.203149	−	0.0596499i
$897$	−214.994	+	248.116i	−0.239681	+	0.276607i
$898$	62.0481	−	8.92117i	0.0690959	−	0.00993449i
$899$	−285.758	−	973.202i	−0.317862	−	1.08254i
$900$	−112.672			−0.125191
$901$			43.6910i			0.0484916i
$902$	−349.061	−	1188.79i	−0.386986	−	1.31795i
$903$	119.473	−	185.903i	0.132307	−	0.205873i
$904$	−510.651	−	1118.17i	−0.564879	−	1.23691i
$905$	−110.030	+	50.2491i	−0.121580	+	0.0555239i
$906$	−290.466	−	186.671i	−0.320603	−	0.206039i
$907$	146.492	−	43.0139i	0.161513	−	0.0474244i	−0.199977	−	0.979801i	$-0.564087\pi$
$907$	146.492	−	43.0139i	0.161513	−	0.0474244i	0.361489	+	0.932376i	$0.382268\pi$
$908$	−385.178			−0.424205
$909$		−	18.6043i		−	0.0204667i
$910$	112.289	−	32.9709i	0.123394	−	0.0362318i
$911$	−229.644	−	1597.21i	−0.252079	−	1.75325i	−0.585685	−	0.810539i	$-0.699175\pi$
$911$	−229.644	−	1597.21i	−0.252079	−	1.75325i	0.333606	−	0.942713i	$-0.391735\pi$
$912$	50.7605	+	43.9842i	0.0556585	+	0.0482283i
$913$	−192.817	+	656.675i	−0.211191	+	0.719250i
$914$	−432.452	−	374.722i	−0.473142	−	0.409980i
$915$	5.18968	+	8.07531i	0.00567179	+	0.00882547i
$916$	84.0094	−	130.721i	0.0917133	−	0.142709i
$917$	−1199.03	+	172.394i	−1.30755	+	0.187998i
$918$	−11.6634	+	7.49561i	−0.0127052	+	0.00816516i
$919$	62.9627	−	28.7541i	0.0685122	−	0.0312885i	−0.380864	−	0.924631i	$-0.624373\pi$
$919$	62.9627	−	28.7541i	0.0685122	−	0.0312885i	0.449376	+	0.893342i	$0.351646\pi$
$920$	29.2592	+	33.7669i	0.0318034	+	0.0367031i
$921$	263.875	+	228.649i	0.286509	+	0.248262i
$922$	−1078.66	−	155.088i	−1.16992	−	0.168209i
$923$	1322.26	−	603.857i	1.43257	−	0.654233i
$924$	263.951	−	228.715i	0.285661	−	0.247527i
$925$	1285.94	+	377.585i	1.39020	+	0.408200i
$926$	−214.606	−	63.0140i	−0.231756	−	0.0680497i
$927$	−31.4439	+	218.697i	−0.0339201	+	0.235919i
$928$	−323.434	+	503.273i	−0.348528	+	0.542321i
$929$	205.129	+	93.6795i	0.220807	+	0.100839i	0.522747	−	0.852488i	$-0.324907\pi$
$929$	205.129	+	93.6795i	0.220807	+	0.100839i	−0.301941	+	0.953327i	$0.597634\pi$
$930$	−39.0124	+	11.4551i	−0.0419488	+	0.0123173i
$931$	−275.718	+	603.739i	−0.296153	+	0.648484i
$932$	371.275	−	53.3813i	0.398364	−	0.0572761i
$933$	23.2724	−	161.863i	0.0249436	−	0.173487i
$934$	−350.820	+	303.987i	−0.375610	+	0.325468i
$935$	−5.47199	+	3.51664i	−0.00585240	+	0.00376111i
$936$	−154.679	+	338.700i	−0.165255	+	0.361859i
$937$		−	1187.98i		−	1.26786i	−0.773391	−	0.633929i	$-0.781441\pi$
$937$		−	1187.98i		−	1.26786i	0.773391	−	0.633929i	$-0.218559\pi$
$938$	−1154.59	−	825.221i	−1.23090	−	0.879767i
$939$	−270.546			−0.288121
$940$	45.6318	+	20.8394i	0.0485445	+	0.0221695i
$941$	−496.402	−	772.416i	−0.527526	−	0.820846i	0.470581	−	0.882357i	$-0.344044\pi$
$941$	−496.402	−	772.416i	−0.527526	−	0.820846i	−0.998106	+	0.0615110i	$0.980408\pi$
$942$	279.311	+	322.342i	0.296508	+	0.342189i
$943$	−1038.79	−	149.356i	−1.10158	−	0.158384i
$944$	−48.5311	−	337.541i	−0.0514101	−	0.357565i
$945$	24.5625	+	11.2173i	0.0259920	+	0.0118702i
$946$	−41.9642	−	142.917i	−0.0443596	−	0.151075i
$947$	482.383	−	1056.27i	0.509381	−	1.11539i	−0.463925	−	0.885874i	$-0.653559\pi$
$947$	482.383	−	1056.27i	0.509381	−	1.11539i	0.973306	−	0.229513i	$-0.0737134\pi$
$948$	100.786	+	64.7714i	0.106315	+	0.0683243i
$949$	185.402	+	26.6567i	0.195365	+	0.0280893i
$950$	55.8364	−	190.161i	0.0587751	−	0.200170i
$951$	−93.4256	+	318.178i	−0.0982393	+	0.334572i
$952$	−129.301	−	149.222i	−0.135821	−	0.156746i
$953$	−700.555	−	1534.00i	−0.735105	−	1.60965i	−0.791443	−	0.611243i	$-0.790670\pi$
$953$	−700.555	−	1534.00i	−0.735105	−	1.60965i	0.0563382	−	0.998412i	$-0.482057\pi$
$954$	17.3984	−	121.009i	0.0182374	−	0.126844i
$955$	63.2923	−	73.0433i	0.0662747	−	0.0764851i
$956$	−91.1030	+	78.9412i	−0.0952960	+	0.0825745i
$957$	188.613	+	413.004i	0.197087	+	0.431561i
$958$	−313.221	−	487.381i	−0.326953	−	0.508748i
$959$	223.798	+	1556.55i	0.233366	+	1.62310i
$960$	37.4771	+	24.0851i	0.0390387	+	0.0250886i
$961$	−435.134	+	279.644i	−0.452793	+	0.290993i
$962$	795.366	−	917.901i	0.826784	−	0.954159i
$963$	15.0842	+	4.42912i	0.0156637	+	0.00459929i
$964$	−247.998	+	286.205i	−0.257259	+	0.296893i
$965$	108.381	−	15.5828i	0.112312	−	0.0161480i
$966$	137.242	+	467.404i	0.142073	+	0.483855i
$967$	1239.59			1.28189			0.640947	−	0.767585i	$-0.278542\pi$
$967$	1239.59			1.28189			0.640947	+	0.767585i	$0.278542\pi$
$968$			193.565i			0.199964i
$969$	4.17254	+	14.2104i	0.00430602	+	0.0146650i
$970$	34.2985	−	53.3695i	0.0353593	−	0.0550201i
$971$	430.587	+	942.855i	0.443447	+	0.971014i	0.990953	+	0.134212i	$0.0428503\pi$
$971$	430.587	+	942.855i	0.443447	+	0.971014i	−0.547505	+	0.836802i	$0.684422\pi$
$972$	−21.4306	+	9.78701i	−0.0220479	+	0.0100689i
$973$	1612.51	+	1036.30i	1.65726	+	1.06505i
$974$	407.413	−	119.627i	0.418288	−	0.122821i
$975$	614.439			0.630194
$976$			109.836i			0.112537i
$977$	1491.20	−	437.855i	1.52630	−	0.448162i	0.592385	−	0.805655i	$-0.298187\pi$
$977$	1491.20	−	437.855i	1.52630	−	0.448162i	0.933916	+	0.357493i	$0.116368\pi$
$978$	115.165	+	800.992i	0.117756	+	0.819010i
$979$	−985.005	−	853.512i	−1.00613	−	0.871820i
$980$	−21.6352	+	73.6828i	−0.0220768	+	0.0751866i
$981$	163.686	+	141.835i	0.166857	+	0.144582i
$982$	111.855	+	174.050i	0.113905	+	0.177240i
$983$	523.805	−	815.056i	0.532863	−	0.829152i	−0.465575	−	0.885008i	$-0.654153\pi$
$983$	523.805	−	815.056i	0.532863	−	0.829152i	0.998439	+	0.0558565i	$0.0177889\pi$
$984$	−1178.15	+	169.392i	−1.19731	+	0.172147i
$985$	−19.5400	+	12.5576i	−0.0198376	+	0.0127488i
$986$	64.0281	−	29.2406i	0.0649372	−	0.0296558i
$987$	1306.12	+	1507.34i	1.32332	+	1.52719i
$988$	82.4326	+	71.4282i	0.0834338	+	0.0722958i
$989$	−124.884	−	17.9556i	−0.126273	−	0.0181553i
$990$	16.5559	−	7.56083i	0.0167231	−	0.00763720i
$991$	−857.631	+	743.142i	−0.865420	+	0.749891i	−0.969607	−	0.244667i	$-0.921321\pi$
$991$	−857.631	+	743.142i	−0.865420	+	0.749891i	0.104187	+	0.994558i	$0.466776\pi$
$992$	836.573	+	245.640i	0.843320	+	0.247621i
$993$	93.1507	+	27.3515i	0.0938074	+	0.0275443i
$994$	306.956	−	2134.92i	0.308809	−	2.14781i
$995$	25.8583	−	40.2363i	0.0259882	−	0.0404385i
$996$	164.006	+	74.8992i	0.164665	+	0.0752000i
$997$	203.176	−	59.6578i	0.203787	−	0.0598373i	−0.178246	−	0.983986i	$-0.557042\pi$
$997$	203.176	−	59.6578i	0.203787	−	0.0598373i	0.382033	+	0.924149i	$0.375224\pi$
$998$	−557.749	+	1221.30i	−0.558867	+	1.22375i
$999$	277.387	−	39.8823i	0.277665	−	0.0399222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.16	✓	220
67.53	odd	22	inner	201.3.l.a.187.16	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.16	✓	220	1.1	even	1	trivial
201.3.l.a.187.16	yes	220	67.53	odd	22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.l (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43499 + 0.655336i) q^{2} +(0.936417 + 1.45709i) q^{3} +(-0.989723 - 1.14220i) q^{4} +(-0.383091 - 0.0550801i) q^{5} +(0.388860 + 2.70458i) q^{6} +(12.2137 + 5.57779i) q^{7} +(-2.44950 - 8.34222i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)	\(q+(1.43499 + 0.655336i) q^{2} +(0.936417 + 1.45709i) q^{3} +(-0.989723 - 1.14220i) q^{4} +(-0.383091 - 0.0550801i) q^{5} +(0.388860 + 2.70458i) q^{6} +(12.2137 + 5.57779i) q^{7} +(-2.44950 - 8.34222i) q^{8} +(-1.24625 + 2.72890i) q^{9} +(-0.513634 - 0.330092i) q^{10} +(9.83550 + 1.41413i) q^{11} +(0.737501 - 2.51170i) q^{12} +(-4.02184 + 13.6971i) q^{13} +(13.8711 + 16.0081i) q^{14} +(-0.278476 - 0.609777i) q^{15} +(1.09162 - 7.59235i) q^{16} +(1.10760 - 1.27824i) q^{17} +(-3.57669 + 3.09922i) q^{18} +(2.10015 + 4.59869i) q^{19} +(0.316241 + 0.492081i) q^{20} +(3.30972 + 23.0196i) q^{21} +(13.1871 + 8.47482i) q^{22} +(11.1701 - 7.17856i) q^{23} +(9.86165 - 11.3809i) q^{24} +(-23.8436 - 7.00111i) q^{25} +(-14.7475 + 17.0195i) q^{26} +(-5.14326 + 0.739490i) q^{27} +(-5.71718 - 19.4709i) q^{28} +26.3808 q^{29} -1.05752i q^{30} +(-10.8320 - 36.8905i) q^{31} +(-12.2602 + 19.0773i) q^{32} +(7.14961 + 15.6555i) q^{33} +(2.42707 - 1.10841i) q^{34} +(-4.37171 - 2.80953i) q^{35} +(4.35039 - 1.27739i) q^{36} -53.9322 q^{37} +7.97535i q^{38} +(-23.7241 + 6.96603i) q^{39} +(0.478889 + 3.33074i) q^{40} +(-59.7340 - 51.7598i) q^{41} +(-10.3362 + 35.2017i) q^{42} +(-7.18122 - 6.22256i) q^{43} +(-8.11920 - 12.6337i) q^{44} +(0.627733 - 0.976771i) q^{45} +(20.7332 - 2.98099i) q^{46} +(72.1472 - 46.3662i) q^{47} +(12.0850 - 5.51902i) q^{48} +(85.9734 + 99.2186i) q^{49} +(-29.6272 - 25.6721i) q^{50} +(2.89969 + 0.416913i) q^{51} +(19.6254 - 8.96262i) q^{52} +(-19.5225 + 16.9163i) q^{53} +(-7.86513 - 2.30941i) q^{54} +(-3.69000 - 1.08348i) q^{55} +(16.6138 - 115.552i) q^{56} +(-4.73410 + 7.36640i) q^{57} +(37.8561 + 17.2883i) q^{58} +(42.6572 - 12.5253i) q^{59} +(-0.420874 + 0.921586i) q^{60} +(-14.1737 + 2.03787i) q^{61} +(8.63188 - 60.0360i) q^{62} +(-30.4424 + 26.3785i) q^{63} +(-55.9063 + 35.9288i) q^{64} +(2.29517 - 5.02572i) q^{65} +27.1508i q^{66} +(-65.1389 + 15.6821i) q^{67} -2.55623 q^{68} +(20.9197 + 9.55369i) q^{69} +(-4.43216 - 6.89657i) q^{70} +(-66.6827 - 76.9559i) q^{71} +(25.8177 + 3.71203i) q^{72} +(-1.86732 - 12.9875i) q^{73} +(-77.3919 - 35.3437i) q^{74} +(-12.1263 - 41.2983i) q^{75} +(3.17406 - 6.95022i) q^{76} +(112.240 + 72.1320i) q^{77} +(-38.6089 - 5.55112i) q^{78} +(-12.8940 + 43.9128i) q^{79} +(-0.836375 + 2.84843i) q^{80} +(-5.89375 - 6.80175i) q^{81} +(-51.7973 - 113.420i) q^{82} +(-9.80211 + 68.1752i) q^{83} +(23.0173 - 26.5634i) q^{84} +(-0.494717 + 0.428675i) q^{85} +(-6.22708 - 13.6354i) q^{86} +(24.7034 + 38.4393i) q^{87} +(-12.2950 - 85.5138i) q^{88} +(-110.344 - 70.9137i) q^{89} +(1.54090 - 0.990277i) q^{90} +(-125.521 + 144.859i) q^{91} +(-19.2546 - 5.65367i) q^{92} +(43.6097 - 50.3282i) q^{93} +(133.916 - 19.2542i) q^{94} +(-0.551251 - 1.87739i) q^{95} -39.2780 q^{96} +103.906i q^{97} +(58.3491 + 198.719i) q^{98} +(-16.1165 + 25.0777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \) 220 * q + 52 * q^4 + 66 * q^8 + 66 * q^9	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9} - 162 q^{10} - 72 q^{14} + 54 q^{15} - 116 q^{16} + 14 q^{17} - 84 q^{19} - 48 q^{21} + 78 q^{22} + 82 q^{23} - 36 q^{24} + 62 q^{25} + 100 q^{26} - 154 q^{28} + 52 q^{29} - 88 q^{31} + 770 q^{32} - 36 q^{33} + 180 q^{35} + 42 q^{36} - 304 q^{37} + 72 q^{39} - 1066 q^{40} + 330 q^{41} + 770 q^{43} - 242 q^{46} - 616 q^{47} - 146 q^{49} + 858 q^{50} + 264 q^{52} - 286 q^{53} - 62 q^{55} - 1484 q^{56} - 660 q^{57} - 352 q^{58} - 634 q^{59} - 504 q^{60} - 352 q^{61} + 124 q^{62} - 132 q^{63} - 1226 q^{64} + 196 q^{65} + 156 q^{67} - 192 q^{68} + 66 q^{69} + 1144 q^{70} + 280 q^{71} + 264 q^{72} + 552 q^{73} + 352 q^{74} + 396 q^{75} + 400 q^{76} - 176 q^{77} + 528 q^{78} + 682 q^{79} + 1848 q^{80} - 198 q^{81} + 728 q^{82} + 246 q^{83} - 1320 q^{84} - 1120 q^{86} + 1120 q^{88} + 448 q^{89} + 486 q^{90} - 128 q^{91} + 604 q^{92} + 72 q^{93} + 704 q^{94} - 462 q^{95} + 144 q^{96} - 176 q^{98}+O(q^{100}) \) 220 * q + 52 * q^4 + 66 * q^8 + 66 * q^9 - 162 * q^10 - 72 * q^14 + 54 * q^15 - 116 * q^16 + 14 * q^17 - 84 * q^19 - 48 * q^21 + 78 * q^22 + 82 * q^23 - 36 * q^24 + 62 * q^25 + 100 * q^26 - 154 * q^28 + 52 * q^29 - 88 * q^31 + 770 * q^32 - 36 * q^33 + 180 * q^35 + 42 * q^36 - 304 * q^37 + 72 * q^39 - 1066 * q^40 + 330 * q^41 + 770 * q^43 - 242 * q^46 - 616 * q^47 - 146 * q^49 + 858 * q^50 + 264 * q^52 - 286 * q^53 - 62 * q^55 - 1484 * q^56 - 660 * q^57 - 352 * q^58 - 634 * q^59 - 504 * q^60 - 352 * q^61 + 124 * q^62 - 132 * q^63 - 1226 * q^64 + 196 * q^65 + 156 * q^67 - 192 * q^68 + 66 * q^69 + 1144 * q^70 + 280 * q^71 + 264 * q^72 + 552 * q^73 + 352 * q^74 + 396 * q^75 + 400 * q^76 - 176 * q^77 + 528 * q^78 + 682 * q^79 + 1848 * q^80 - 198 * q^81 + 728 * q^82 + 246 * q^83 - 1320 * q^84 - 1120 * q^86 + 1120 * q^88 + 448 * q^89 + 486 * q^90 - 128 * q^91 + 604 * q^92 + 72 * q^93 + 704 * q^94 - 462 * q^95 + 144 * q^96 - 176 * q^98

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