LMFDB - Embedded newform 210.3.v.b.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(37,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("210.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.v (of order $12$, degree $4$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	210.193
Dual form			210.3.v.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(3.95091 + 3.06436i) q^{5} -2.44949 q^{6} +(3.71395 - 5.93351i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(3.95091 + 3.06436i) q^{5} -2.44949 q^{6} +(3.71395 - 5.93351i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(4.27541 + 5.63213i) q^{10} +(-3.58312 + 6.20615i) q^{11} +(-3.34607 - 0.896575i) q^{12} +(7.28383 + 7.28383i) q^{13} +(7.24516 - 6.74593i) q^{14} +(-7.98372 - 3.35564i) q^{15} +(2.00000 + 3.46410i) q^{16} +(4.87353 + 18.1882i) q^{17} +(4.09808 - 1.09808i) q^{18} +(7.65544 - 4.41987i) q^{19} +(3.77881 + 9.25854i) q^{20} +(-3.55363 + 11.5919i) q^{21} +(-7.16624 + 7.16624i) q^{22} +(-0.107714 + 0.401994i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(6.21935 + 24.2140i) q^{25} +(7.28383 + 12.6160i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(12.3663 - 6.56320i) q^{28} -27.7751i q^{29} +(-9.67771 - 7.50613i) q^{30} +(12.5266 - 21.6967i) q^{31} +(1.46410 + 5.46410i) q^{32} +(3.21254 - 11.9894i) q^{33} +26.6294i q^{34} +(32.8559 - 12.0619i) q^{35} +6.00000 q^{36} +(-51.5702 - 13.8182i) q^{37} +(12.0753 - 3.23557i) q^{38} +(-15.4513 - 8.92083i) q^{39} +(1.77309 + 14.0305i) q^{40} +46.7769 q^{41} +(-9.09728 + 14.5341i) q^{42} +(-37.3270 - 37.3270i) q^{43} +(-12.4123 + 7.16624i) q^{44} +(14.8613 + 2.03509i) q^{45} +(-0.294280 + 0.509708i) q^{46} +(-31.0816 - 8.32828i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(-21.4132 - 44.0735i) q^{49} +(-0.367156 + 35.3534i) q^{50} +(-16.3071 - 28.2448i) q^{51} +(5.33213 + 19.8998i) q^{52} +(-68.8397 + 18.4455i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-33.1745 + 13.5399i) q^{55} +(19.2949 - 4.43914i) q^{56} +(-10.8264 + 10.8264i) q^{57} +(10.1664 - 37.9414i) q^{58} +(-35.2552 - 20.3546i) q^{59} +(-10.4726 - 13.7958i) q^{60} +(3.30356 + 5.72193i) q^{61} +(25.0531 - 25.0531i) q^{62} +(0.748846 - 20.9866i) q^{63} +8.00000i q^{64} +(6.45744 + 51.0980i) q^{65} +(8.77682 - 15.2019i) q^{66} +(-34.4848 - 128.699i) q^{67} +(-9.74705 + 36.3765i) q^{68} -0.720836i q^{69} +(49.2970 - 4.45075i) q^{70} +129.870 q^{71} +(8.19615 + 2.19615i) q^{72} +(-7.85719 + 2.10533i) q^{73} +(-65.3884 - 37.7520i) q^{74} +(-21.2600 - 37.7228i) q^{75} +17.6795 q^{76} +(23.5168 + 44.3098i) q^{77} +(-17.8417 - 17.8417i) q^{78} +(-59.9499 + 34.6121i) q^{79} +(-2.71345 + 19.8151i) q^{80} +(4.50000 - 7.79423i) q^{81} +(63.8984 + 17.1215i) q^{82} +(57.0471 + 57.0471i) q^{83} +(-17.7470 + 16.5241i) q^{84} +(-36.4805 + 86.7944i) q^{85} +(-37.3270 - 64.6523i) q^{86} +(12.4512 + 46.4686i) q^{87} +(-19.5785 + 5.24605i) q^{88} +(114.055 - 65.8494i) q^{89} +(19.5560 + 8.21960i) q^{90} +(70.2705 - 16.1670i) q^{91} +(-0.588560 + 0.588560i) q^{92} +(-11.2310 + 41.9147i) q^{93} +(-39.4099 - 22.7533i) q^{94} +(43.7901 + 5.99655i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(-46.0520 + 46.0520i) q^{97} +(-13.1189 - 68.0433i) q^{98} +21.4987i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	3.95091	+	3.06436i	0.790182	+	0.612873i
$5$	3.95091	+	3.06436i	0.790182	+	0.612873i
$6$	−2.44949			−0.408248
$7$	3.71395	−	5.93351i	0.530564	−	0.847645i
$7$	3.71395	−	5.93351i	0.530564	−	0.847645i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	4.27541	+	5.63213i	0.427541	+	0.563213i
$11$	−3.58312	+	6.20615i	−0.325738	+	0.564195i	−0.981662	−	0.190632i	$-0.938946\pi$
$11$	−3.58312	+	6.20615i	−0.325738	+	0.564195i	0.655923	+	0.754828i	$0.272280\pi$
$12$	−3.34607	−	0.896575i	−0.278839	−	0.0747146i
$13$	7.28383	+	7.28383i	0.560295	+	0.560295i	0.929391	−	0.369097i	$-0.120333\pi$
$13$	7.28383	+	7.28383i	0.560295	+	0.560295i	−0.369097	+	0.929391i	$0.620333\pi$
$14$	7.24516	−	6.74593i	0.517512	−	0.481852i
$15$	−7.98372	−	3.35564i	−0.532248	−	0.223709i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	4.87353	+	18.1882i	0.286678	+	1.06990i	0.947604	+	0.319446i	$0.103497\pi$
$17$	4.87353	+	18.1882i	0.286678	+	1.06990i	−0.660926	+	0.750451i	$0.729836\pi$
$18$	4.09808	−	1.09808i	0.227671	−	0.0610042i
$19$	7.65544	−	4.41987i	0.402918	−	0.232625i	−0.284824	−	0.958580i	$-0.591935\pi$
$19$	7.65544	−	4.41987i	0.402918	−	0.232625i	0.687742	+	0.725955i	$0.258602\pi$
$20$	3.77881	+	9.25854i	0.188941	+	0.462927i
$21$	−3.55363	+	11.5919i	−0.169221	+	0.551994i
$22$	−7.16624	+	7.16624i	−0.325738	+	0.325738i
$23$	−0.107714	+	0.401994i	−0.00468322	+	0.0174780i	−0.968228	−	0.250069i	$-0.919547\pi$
$23$	−0.107714	+	0.401994i	−0.00468322	+	0.0174780i	0.963545	+	0.267547i	$0.0862132\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$	6.21935	+	24.2140i	0.248774	+	0.968562i
$26$	7.28383	+	12.6160i	0.280147	+	0.485229i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	12.3663	−	6.56320i	0.441652	−	0.234400i
$29$		−	27.7751i		−	0.957761i	−0.877880	−	0.478880i	$-0.841043\pi$
$29$		−	27.7751i		−	0.957761i	0.877880	−	0.478880i	$-0.158957\pi$
$30$	−9.67771	−	7.50613i	−0.322590	−	0.250204i
$31$	12.5266	−	21.6967i	0.404083	−	0.699892i	−0.590131	−	0.807307i	$-0.700924\pi$
$31$	12.5266	−	21.6967i	0.404083	−	0.699892i	0.994214	+	0.107415i	$0.0342574\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	3.21254	−	11.9894i	0.0973497	−	0.363314i
$34$			26.6294i			0.783219i
$35$	32.8559	−	12.0619i	0.938740	−	0.344625i
$36$	6.00000			0.166667
$37$	−51.5702	−	13.8182i	−1.39379	−	0.373464i	−0.517678	−	0.855575i	$-0.673204\pi$
$37$	−51.5702	−	13.8182i	−1.39379	−	0.373464i	−0.876110	+	0.482111i	$0.839870\pi$
$38$	12.0753	−	3.23557i	0.317771	−	0.0851466i
$39$	−15.4513	−	8.92083i	−0.396188	−	0.228739i
$40$	1.77309	+	14.0305i	0.0443273	+	0.350764i
$41$	46.7769			1.14090			0.570450	−	0.821333i	$-0.306769\pi$
$41$	46.7769			1.14090			0.570450	+	0.821333i	$0.306769\pi$
$42$	−9.09728	+	14.5341i	−0.216602	+	0.346050i
$43$	−37.3270	−	37.3270i	−0.868070	−	0.868070i	0.124189	−	0.992259i	$-0.460367\pi$
$43$	−37.3270	−	37.3270i	−0.868070	−	0.868070i	−0.992259	+	0.124189i	$0.960367\pi$
$44$	−12.4123	+	7.16624i	−0.282098	+	0.162869i
$45$	14.8613	+	2.03509i	0.330251	+	0.0452242i
$46$	−0.294280	+	0.509708i	−0.00639739	+	0.0110806i
$47$	−31.0816	−	8.32828i	−0.661310	−	0.177198i	−0.0874729	−	0.996167i	$-0.527879\pi$
$47$	−31.0816	−	8.32828i	−0.661310	−	0.177198i	−0.573837	+	0.818969i	$0.694546\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$	−21.4132	−	44.0735i	−0.437004	−	0.899460i
$50$	−0.367156	+	35.3534i	−0.00734313	+	0.707069i
$51$	−16.3071	−	28.2448i	−0.319748	−	0.553819i
$52$	5.33213	+	19.8998i	0.102541	+	0.382688i
$53$	−68.8397	+	18.4455i	−1.29886	+	0.348029i	−0.841020	−	0.541004i	$-0.818044\pi$
$53$	−68.8397	+	18.4455i	−1.29886	+	0.348029i	−0.457842	+	0.889033i	$0.651378\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$	−33.1745	+	13.5399i	−0.603172	+	0.246181i
$56$	19.2949	−	4.43914i	0.344552	−	0.0792703i
$57$	−10.8264	+	10.8264i	−0.189937	+	0.189937i
$58$	10.1664	−	37.9414i	0.175282	−	0.654163i
$59$	−35.2552	−	20.3546i	−0.597546	−	0.344993i	0.170530	−	0.985353i	$-0.445452\pi$
$59$	−35.2552	−	20.3546i	−0.597546	−	0.344993i	−0.768075	+	0.640359i	$0.778785\pi$
$60$	−10.4726	−	13.7958i	−0.174543	−	0.229931i
$61$	3.30356	+	5.72193i	0.0541567	+	0.0938021i	0.891833	−	0.452365i	$-0.149420\pi$
$61$	3.30356	+	5.72193i	0.0541567	+	0.0938021i	−0.837676	+	0.546167i	$0.816086\pi$
$62$	25.0531	−	25.0531i	0.404083	−	0.404083i
$63$	0.748846	−	20.9866i	0.0118864	−	0.333121i
$64$			8.00000i			0.125000i
$65$	6.45744	+	51.0980i	0.0993453	+	0.786124i
$66$	8.77682	−	15.2019i	0.132982	−	0.230332i
$67$	−34.4848	−	128.699i	−0.514699	−	1.92088i	−0.360133	−	0.932901i	$-0.617269\pi$
$67$	−34.4848	−	128.699i	−0.514699	−	1.92088i	−0.154566	−	0.987982i	$-0.549398\pi$
$68$	−9.74705	+	36.3765i	−0.143339	+	0.534948i
$69$		−	0.720836i		−	0.0104469i
$70$	49.2970	−	4.45075i	0.704242	−	0.0635821i
$71$	129.870			1.82915			0.914576	−	0.404414i	$-0.132525\pi$
$71$	129.870			1.82915			0.914576	+	0.404414i	$0.132525\pi$
$72$	8.19615	+	2.19615i	0.113835	+	0.0305021i
$73$	−7.85719	+	2.10533i	−0.107633	+	0.0288401i	−0.312233	−	0.950005i	$-0.601077\pi$
$73$	−7.85719	+	2.10533i	−0.107633	+	0.0288401i	0.204601	+	0.978846i	$0.434410\pi$
$74$	−65.3884	−	37.7520i	−0.883626	−	0.510162i
$75$	−21.2600	−	37.7228i	−0.283467	−	0.502971i
$76$	17.6795			0.232625
$77$	23.5168	+	44.3098i	0.305412	+	0.575452i
$78$	−17.8417	−	17.8417i	−0.228739	−	0.228739i
$79$	−59.9499	+	34.6121i	−0.758860	+	0.438128i	−0.828886	−	0.559417i	$-0.811025\pi$
$79$	−59.9499	+	34.6121i	−0.758860	+	0.438128i	0.0700264	+	0.997545i	$0.477692\pi$
$80$	−2.71345	+	19.8151i	−0.0339181	+	0.247688i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	63.8984	+	17.1215i	0.779249	+	0.208799i
$83$	57.0471	+	57.0471i	0.687314	+	0.687314i	0.961638	−	0.274323i	$-0.0884538\pi$
$83$	57.0471	+	57.0471i	0.687314	+	0.687314i	−0.274323	+	0.961638i	$0.588454\pi$
$84$	−17.7470	+	16.5241i	−0.211273	+	0.196715i
$85$	−36.4805	+	86.7944i	−0.429183	+	1.02111i
$86$	−37.3270	−	64.6523i	−0.434035	−	0.751771i
$87$	12.4512	+	46.4686i	0.143117	+	0.534122i
$88$	−19.5785	+	5.24605i	−0.222483	+	0.0596143i
$89$	114.055	−	65.8494i	1.28151	−	0.739881i	0.304387	−	0.952548i	$-0.401548\pi$
$89$	114.055	−	65.8494i	1.28151	−	0.739881i	0.977125	+	0.212667i	$0.0682151\pi$
$90$	19.5560	+	8.21960i	0.217289	+	0.0913288i
$91$	70.2705	−	16.1670i	0.772203	−	0.177659i
$92$	−0.588560	+	0.588560i	−0.00639739	+	0.00639739i
$93$	−11.2310	+	41.9147i	−0.120764	+	0.450696i
$94$	−39.4099	−	22.7533i	−0.419254	−	0.242056i
$95$	43.7901	+	5.99655i	0.460948	+	0.0631216i
$96$	−4.89898	−	8.48528i	−0.0510310	−	0.0883883i
$97$	−46.0520	+	46.0520i	−0.474763	+	0.474763i	−0.903452	−	0.428689i	$-0.858976\pi$
$97$	−46.0520	+	46.0520i	−0.474763	+	0.474763i	0.428689	+	0.903452i	$0.358976\pi$
$98$	−13.1189	−	68.0433i	−0.133867	−	0.694320i
$99$			21.4987i			0.217159i
$100$	−13.4418	+	48.1593i	−0.134418	+	0.481593i
$101$	−34.0993	+	59.0617i	−0.337617	+	0.584769i	−0.983984	−	0.178257i	$-0.942954\pi$
$101$	−34.0993	+	59.0617i	−0.337617	+	0.584769i	0.646367	+	0.763027i	$0.276287\pi$
$102$	−11.9377	−	44.5519i	−0.117036	−	0.436784i
$103$	35.9466	−	134.155i	0.348996	−	1.30247i	−0.538877	−	0.842384i	$-0.681151\pi$
$103$	35.9466	−	134.155i	0.348996	−	1.30247i	0.887874	−	0.460087i	$-0.152182\pi$
$104$			29.1353i			0.280147i
$105$	−49.5618	+	34.9088i	−0.472017	+	0.332465i
$106$	−100.788			−0.950833
$107$	−41.1642	−	11.0299i	−0.384712	−	0.103083i	0.0612792	−	0.998121i	$-0.480482\pi$
$107$	−41.1642	−	11.0299i	−0.384712	−	0.103083i	−0.445991	+	0.895037i	$0.647149\pi$
$108$	−10.0382	+	2.68973i	−0.0929463	+	0.0249049i
$109$	−149.701	−	86.4300i	−1.37341	−	0.792936i	−0.382050	−	0.924141i	$-0.624782\pi$
$109$	−149.701	−	86.4300i	−1.37341	−	0.792936i	−0.991355	+	0.131205i	$0.958115\pi$
$110$	−50.2731	+	6.35320i	−0.457029	+	0.0577563i
$111$	92.4731			0.833091
$112$	27.9822	+	0.998461i	0.249841	+	0.00891483i
$113$	−2.87483	−	2.87483i	−0.0254409	−	0.0254409i	0.694272	−	0.719713i	$-0.255727\pi$
$113$	−2.87483	−	2.87483i	−0.0254409	−	0.0254409i	−0.719713	+	0.694272i	$0.755727\pi$
$114$	−18.7519	+	10.8264i	−0.164491	+	0.0949687i
$115$	−1.65742	+	1.25817i	−0.0144124	+	0.0109406i
$116$	27.7751	−	48.1078i	0.239440	−	0.414723i
$117$	29.8497	+	7.99820i	0.255126	+	0.0683607i
$118$	−40.7092	−	40.7092i	−0.344993	−	0.344993i
$119$	126.020	+	38.6331i	1.05899	+	0.324648i
$120$	−9.25616	−	22.6787i	−0.0771347	−	0.188989i
$121$	34.8225	+	60.3143i	0.287789	+	0.498465i
$122$	2.41837	+	9.02549i	0.0198227	+	0.0739794i
$123$	−78.2592	+	20.9695i	−0.636254	+	0.170484i
$124$	43.3933	−	25.0531i	0.349946	−	0.202041i
$125$	−49.6285	+	114.726i	−0.397028	+	0.917806i
$126$	8.70459	−	28.3942i	0.0690840	−	0.225351i
$127$	−17.1629	+	17.1629i	−0.135141	+	0.135141i	−0.771441	−	0.636300i	$-0.780464\pi$
$127$	−17.1629	+	17.1629i	−0.135141	+	0.135141i	0.636300	+	0.771441i	$0.280464\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	79.1826	+	45.7161i	0.613818	+	0.354388i
$130$	−9.88215	+	72.1648i	−0.0760165	+	0.555114i
$131$	−63.5362	−	110.048i	−0.485010	−	0.840061i	0.514842	−	0.857285i	$-0.327851\pi$
$131$	−63.5362	−	110.048i	−0.485010	−	0.840061i	−0.999852	+	0.0172239i	$0.994517\pi$
$132$	17.5536	−	17.5536i	0.132982	−	0.132982i
$133$	2.20653	−	61.8389i	0.0165905	−	0.464954i
$134$		−	188.429i		−	1.40618i
$135$	−25.7758	+	3.25737i	−0.190932	+	0.0241287i
$136$	−26.6294	+	46.1236i	−0.195805	+	0.339144i
$137$	24.3746	+	90.9671i	0.177917	+	0.663994i	0.996036	+	0.0889460i	$0.0283498\pi$
$137$	24.3746	+	90.9671i	0.177917	+	0.663994i	−0.818120	+	0.575048i	$0.804983\pi$
$138$	0.263844	−	0.984680i	0.00191191	−	0.00713536i
$139$			91.9640i			0.661612i	0.943699	+	0.330806i	$0.107321\pi$
$139$			91.9640i			0.661612i	−0.943699	+	0.330806i	$0.892679\pi$
$140$	68.9700	+	11.9641i	0.492643	+	0.0854579i
$141$	55.7340			0.395276
$142$	177.405	+	47.5356i	1.24933	+	0.334758i
$143$	−71.3034	+	19.1057i	−0.498625	+	0.133606i
$144$	10.3923	+	6.00000i	0.0721688	+	0.0416667i
$145$	85.1129	−	109.737i	0.586986	−	0.756805i
$146$	−11.5037			−0.0787926
$147$	55.5826	+	64.1372i	0.378113	+	0.436307i
$148$	−75.5040	−	75.5040i	−0.510162	−	0.510162i
$149$	45.8944	−	26.4971i	0.308016	−	0.177833i	−0.338022	−	0.941138i	$-0.609758\pi$
$149$	45.8944	−	26.4971i	0.308016	−	0.177833i	0.646038	+	0.763305i	$0.276425\pi$
$150$	−15.2342	−	59.3120i	−0.101562	−	0.395414i
$151$	−12.0722	+	20.9097i	−0.0799483	+	0.138475i	−0.903227	−	0.429162i	$-0.858809\pi$
$151$	−12.0722	+	20.9097i	−0.0799483	+	0.138475i	0.823279	+	0.567637i	$0.192142\pi$
$152$	24.1506	+	6.47114i	0.158886	+	0.0425733i
$153$	39.9442	+	39.9442i	0.261073	+	0.261073i
$154$	15.9060	+	69.1361i	0.103285	+	0.448935i
$155$	115.978	−	47.3355i	0.748244	−	0.305391i
$156$	−17.8417	−	30.9027i	−0.114370	−	0.198094i
$157$	45.2960	+	169.047i	0.288510	+	1.07673i	0.946236	+	0.323476i	$0.104852\pi$
$157$	45.2960	+	169.047i	0.288510	+	1.07673i	−0.657727	+	0.753257i	$0.728482\pi$
$158$	−94.5620	+	25.3378i	−0.598494	+	0.160366i
$159$	106.902	−	61.7200i	0.672340	−	0.388176i
$160$	−10.9595	+	26.0747i	−0.0684966	+	0.162967i
$161$	1.98519	+	2.13211i	0.0123304	+	0.0132429i
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−64.5303	+	240.830i	−0.395891	+	1.47749i	0.424366	+	0.905491i	$0.360497\pi$
$163$	−64.5303	+	240.830i	−0.395891	+	1.47749i	−0.820257	+	0.571995i	$0.806170\pi$
$164$	81.0199	+	46.7769i	0.494024	+	0.285225i
$165$	49.4322	−	37.5245i	0.299589	−	0.227421i
$166$	57.0471	+	98.8085i	0.343657	+	0.595232i
$167$	−186.515	+	186.515i	−1.11686	+	1.11686i	−0.124657	+	0.992200i	$0.539783\pi$
$167$	−186.515	+	186.515i	−1.11686	+	1.11686i	−0.992200	+	0.124657i	$0.960217\pi$
$168$	−30.2910	+	16.0765i	−0.180304	+	0.0956934i
$169$		−	62.8917i		−	0.372140i
$170$	−81.6023	+	105.210i	−0.480013	+	0.618885i
$171$	13.2596	−	22.9663i	0.0775416	−	0.134306i
$172$	−27.3253	−	101.979i	−0.158868	−	0.592903i
$173$	−36.3047	+	135.491i	−0.209854	+	0.783185i	0.778061	+	0.628189i	$0.216203\pi$
$173$	−36.3047	+	135.491i	−0.209854	+	0.783185i	−0.987915	+	0.154997i	$0.950463\pi$
$174$			68.0347i			0.391004i
$175$	166.773	+	53.0270i	0.952987	+	0.303012i
$176$	−28.6650			−0.162869
$177$	68.1078	+	18.2494i	0.384790	+	0.103104i
$178$	179.904	−	48.2051i	1.01070	−	0.270815i
$179$	191.781	+	110.725i	1.07140	+	0.618573i	0.928564	−	0.371173i	$-0.121044\pi$
$179$	191.781	+	110.725i	1.07140	+	0.618573i	0.142836	+	0.989746i	$0.454378\pi$
$180$	23.7055	+	18.3862i	0.131697	+	0.102145i
$181$	149.607			0.826556			0.413278	−	0.910605i	$-0.364384\pi$
$181$	149.607			0.826556			0.413278	+	0.910605i	$0.364384\pi$
$182$	101.909	+	3.63631i	0.559938	+	0.0199797i
$183$	−8.09203	−	8.09203i	−0.0442187	−	0.0442187i
$184$	−1.01942	+	0.588560i	−0.00554030	+	0.00319870i
$185$	−161.405	−	212.624i	−0.872460	−	1.14932i
$186$	−30.6837	+	53.1457i	−0.164966	+	0.285730i
$187$	−130.341	−	34.9249i	−0.697013	−	0.186764i
$188$	−45.5066	−	45.5066i	−0.242056	−	0.242056i
$189$	8.15521	+	35.4470i	0.0431493	+	0.187550i
$190$	57.6234	+	24.2197i	0.303281	+	0.127472i
$191$	−142.890	−	247.493i	−0.748116	−	1.29578i	−0.948725	−	0.316104i	$-0.897625\pi$
$191$	−142.890	−	247.493i	−0.748116	−	1.29578i	0.200608	−	0.979672i	$-0.435708\pi$
$192$	−3.58630	−	13.3843i	−0.0186787	−	0.0697097i
$193$	228.339	−	61.1833i	1.18310	−	0.317012i	0.386947	−	0.922102i	$-0.373529\pi$
$193$	228.339	−	61.1833i	1.18310	−	0.317012i	0.796157	+	0.605090i	$0.206863\pi$
$194$	−79.7644	+	46.0520i	−0.411157	+	0.237382i
$195$	−33.7101	−	82.5939i	−0.172873	−	0.423558i
$196$	6.98478	−	97.7508i	0.0356366	−	0.498728i
$197$	−72.1108	+	72.1108i	−0.366045	+	0.366045i	−0.866032	−	0.499988i	$-0.833338\pi$
$197$	−72.1108	+	72.1108i	−0.366045	+	0.366045i	0.499988	+	0.866032i	$0.333338\pi$
$198$	−7.86908	+	29.3678i	−0.0397428	+	0.148322i
$199$	−248.372	−	143.398i	−1.24810	−	0.720592i	−0.277371	−	0.960763i	$-0.589463\pi$
$199$	−248.372	−	143.398i	−1.24810	−	0.720592i	−0.970731	+	0.240171i	$0.922797\pi$
$200$	−35.9894	+	60.8668i	−0.179947	+	0.304334i
$201$	115.389	+	199.859i	0.574072	+	0.994322i
$202$	−68.1986	+	68.1986i	−0.337617	+	0.337617i
$203$	−164.804	−	103.155i	−0.811841	−	0.508153i
$204$		−	65.2286i		−	0.319748i
$205$	184.811	+	143.341i	0.901518	+	0.699226i
$206$	98.2080	−	170.101i	0.476738	−	0.825734i
$207$	0.323142	+	1.20598i	0.00156107	+	0.00582600i
$208$	−10.6643	+	39.7996i	−0.0512705	+	0.191344i
$209$			63.3478i			0.303099i
$210$	−80.4802	+	29.5455i	−0.383239	+	0.140693i
$211$	293.048			1.38885			0.694427	−	0.719563i	$-0.255658\pi$
$211$	293.048			1.38885			0.694427	+	0.719563i	$0.255658\pi$
$212$	−137.679	−	36.8911i	−0.649431	−	0.174015i
$213$	−217.276	+	58.2190i	−1.02008	+	0.273329i
$214$	−52.1941	−	30.1343i	−0.243897	−	0.140814i
$215$	−33.0921	−	261.859i	−0.153917	−	1.21795i
$216$	−14.6969			−0.0680414
$217$	−82.2144	−	154.907i	−0.378868	−	0.713856i
$218$	−172.860	−	172.860i	−0.792936	−	0.792936i
$219$	12.2015	−	7.04456i	0.0557148	−	0.0321670i
$220$	−70.9998	−	9.72262i	−0.322726	−	0.0441937i
$221$	−96.9822	+	167.978i	−0.438833	+	0.760082i
$222$	126.321	+	33.8475i	0.569012	+	0.152466i
$223$	166.941	+	166.941i	0.748615	+	0.748615i	0.974219	−	0.225604i	$-0.0724356\pi$
$223$	166.941	+	166.941i	0.748615	+	0.748615i	−0.225604	+	0.974219i	$0.572436\pi$
$224$	37.8589	+	11.6061i	0.169013	+	0.0518130i
$225$	52.4794	+	53.5809i	0.233242	+	0.238137i
$226$	−2.87483	−	4.97934i	−0.0127205	−	0.0220325i
$227$	−78.8916	−	294.427i	−0.347540	−	1.29704i	−0.889617	−	0.456708i	$-0.849028\pi$
$227$	−78.8916	−	294.427i	−0.347540	−	1.29704i	0.542076	−	0.840329i	$-0.317638\pi$
$228$	−29.5784	+	7.92550i	−0.129730	+	0.0347610i
$229$	194.928	−	112.542i	0.851213	−	0.491448i	−0.00984691	−	0.999952i	$-0.503134\pi$
$229$	194.928	−	112.542i	0.851213	−	0.491448i	0.861060	+	0.508503i	$0.169801\pi$
$230$	−2.72460	+	1.11203i	−0.0118461	+	0.00483491i
$231$	−59.2078	−	63.5895i	−0.256311	−	0.275279i
$232$	55.5501	−	55.5501i	0.239440	−	0.239440i
$233$	−26.2312	+	97.8963i	−0.112580	+	0.420156i	−0.999095	−	0.0425458i	$-0.986453\pi$
$233$	−26.2312	+	97.8963i	−0.112580	+	0.420156i	0.886514	+	0.462702i	$0.153120\pi$
$234$	37.8479	+	21.8515i	0.161743	+	0.0933824i
$235$	−97.2796	−	128.150i	−0.413956	−	0.545317i
$236$	−40.7092	−	70.5104i	−0.172497	−	0.298773i
$237$	84.7820	−	84.7820i	0.357730	−	0.357730i
$238$	158.006	+	98.9003i	0.663892	+	0.415548i
$239$		−	191.422i		−	0.800927i	−0.916313	−	0.400464i	$-0.868849\pi$
$239$		−	191.422i		−	0.800927i	0.916313	−	0.400464i	$-0.131151\pi$
$240$	−4.34317	−	34.3677i	−0.0180965	−	0.143199i
$241$	−134.250	+	232.528i	−0.557054	+	0.964846i	0.440687	+	0.897661i	$0.354735\pi$
$241$	−134.250	+	232.528i	−0.557054	+	0.964846i	−0.997741	+	0.0671848i	$0.978598\pi$
$242$	25.4918	+	95.1368i	0.105338	+	0.393127i
$243$	−4.03459	+	15.0573i	−0.0166032	+	0.0619642i
$244$			13.2142i			0.0541567i
$245$	50.4557	−	239.748i	0.205942	−	0.978564i
$246$	−114.579			−0.465770
$247$	87.9545	+	23.5673i	0.356091	+	0.0954144i
$248$	68.4465	−	18.3402i	0.275994	−	0.0739523i
$249$	−121.015	−	69.8681i	−0.486005	−	0.280595i
$250$	−109.786	+	138.553i	−0.439145	+	0.554212i
$251$	−314.645			−1.25357			−0.626784	−	0.779193i	$-0.715629\pi$
$251$	−314.645			−1.25357			−0.626784	+	0.779193i	$0.715629\pi$
$252$	22.2837	−	35.6011i	0.0884273	−	0.141274i
$253$	−2.10888	−	2.10888i	−0.00833550	−	0.00833550i
$254$	−29.7271	+	17.1629i	−0.117036	+	0.0675706i
$255$	22.1243	−	161.564i	0.0867619	−	0.633583i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−360.739	−	96.6597i	−1.40365	−	0.376108i	−0.523998	−	0.851720i	$-0.675560\pi$
$257$	−360.739	−	96.6597i	−1.40365	−	0.376108i	−0.879655	+	0.475612i	$0.842227\pi$
$258$	91.4321	+	91.4321i	0.354388	+	0.354388i
$259$	−273.519	+	254.672i	−1.05606	+	0.983291i
$260$	−39.9134	+	94.9618i	−0.153513	+	0.365238i
$261$	−41.6626	−	72.1617i	−0.159627	−	0.276482i
$262$	−46.5118	−	173.584i	−0.177526	−	0.662535i
$263$	−24.9311	+	6.68028i	−0.0947952	+	0.0254003i	−0.305905	−	0.952062i	$-0.598959\pi$
$263$	−24.9311	+	6.68028i	−0.0947952	+	0.0254003i	0.211110	+	0.977462i	$0.432292\pi$
$264$	30.4038	−	17.5536i	0.115166	−	0.0664911i
$265$	−328.503	−	138.073i	−1.23963	−	0.521031i
$266$	25.6488	−	83.6658i	0.0964240	−	0.314533i
$267$	−161.297	+	161.297i	−0.604110	+	0.604110i
$268$	68.9697	−	257.398i	0.257350	−	0.960442i
$269$	−189.173	−	109.219i	−0.703246	−	0.406020i	0.105309	−	0.994440i	$-0.466417\pi$
$269$	−189.173	−	109.219i	−0.703246	−	0.406020i	−0.808555	+	0.588420i	$0.799750\pi$
$270$	−36.4026	−	4.98492i	−0.134825	−	0.0184627i
$271$	14.9730	+	25.9340i	0.0552510	+	0.0956975i	0.892328	−	0.451387i	$-0.149071\pi$
$271$	14.9730	+	25.9340i	0.0552510	+	0.0956975i	−0.837077	+	0.547085i	$0.815737\pi$
$272$	−53.2589	+	53.2589i	−0.195805	+	0.195805i
$273$	−110.317	+	58.5492i	−0.404093	+	0.214466i
$274$			133.185i			0.486077i
$275$	−172.561	−	48.1636i	−0.627493	−	0.175140i
$276$	0.720836	−	1.24852i	0.00261172	−	0.00452364i
$277$	−137.756	−	514.112i	−0.497314	−	1.85600i	−0.516665	−	0.856188i	$-0.672827\pi$
$277$	−137.756	−	514.112i	−0.497314	−	1.85600i	0.0193511	−	0.999813i	$-0.493840\pi$
$278$	−33.6612	+	125.625i	−0.121083	+	0.451889i
$279$		−	75.1594i		−	0.269389i
$280$	89.8356	+	41.5880i	0.320841	+	0.148529i
$281$	69.2961			0.246605			0.123303	−	0.992369i	$-0.460651\pi$
$281$	69.2961			0.246605			0.123303	+	0.992369i	$0.460651\pi$
$282$	76.1340	+	20.4000i	0.269979	+	0.0723406i
$283$	338.641	−	90.7385i	1.19661	−	0.320631i	0.395115	−	0.918632i	$-0.370705\pi$
$283$	338.641	−	90.7385i	1.19661	−	0.320631i	0.801495	+	0.598001i	$0.204038\pi$
$284$	224.941	+	129.870i	0.792046	+	0.457288i
$285$	−75.9504	+	9.59812i	−0.266493	+	0.0336776i
$286$	−104.395			−0.365019
$287$	173.727	−	277.551i	0.605320	−	0.967078i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	−56.7798	+	32.7818i	−0.196470	+	0.113432i
$290$	156.433	−	118.750i	0.539424	−	0.409482i
$291$	56.4020	−	97.6911i	0.193821	−	0.335708i
$292$	−15.7144	−	4.21066i	−0.0538164	−	0.0144201i
$293$	371.421	+	371.421i	1.26765	+	1.26765i	0.947299	+	0.320351i	$0.103801\pi$
$293$	371.421	+	371.421i	1.26765	+	1.26765i	0.320351	+	0.947299i	$0.396199\pi$
$294$	52.4514	+	107.958i	0.178406	+	0.367203i
$295$	−76.9162	−	188.454i	−0.260733	−	0.638827i
$296$	−75.5040	−	130.777i	−0.255081	−	0.441813i
$297$	−9.63762	−	35.9681i	−0.0324499	−	0.121105i
$298$	72.3915	−	19.3972i	0.242924	−	0.0650914i
$299$	−3.71263	+	2.14349i	−0.0124168	+	0.00716885i
$300$	0.899346	−	86.5979i	0.00299782	−	0.288660i
$301$	−360.111	+	82.8498i	−1.19638	+	0.275249i
$302$	−24.1444	+	24.1444i	−0.0799483	+	0.0799483i
$303$	30.5726	−	114.098i	0.100900	−	0.376563i
$304$	30.6218	+	17.6795i	0.100730	+	0.0581562i
$305$	−4.48202	+	32.7301i	−0.0146951	+	0.107312i
$306$	39.9442	+	69.1853i	0.130536	+	0.226096i
$307$	−76.4698	+	76.4698i	−0.249087	+	0.249087i	−0.820596	−	0.571509i	$-0.806358\pi$
$307$	−76.4698	+	76.4698i	−0.249087	+	0.249087i	0.571509	+	0.820596i	$0.306358\pi$
$308$	−3.57761	+	100.264i	−0.0116156	+	0.325531i
$309$			240.559i			0.778509i
$310$	175.755	−	22.2107i	0.566950	−	0.0716476i
$311$	−104.711	+	181.364i	−0.336690	+	0.583164i	−0.983808	−	0.179226i	$-0.942641\pi$
$311$	−104.711	+	181.364i	−0.336690	+	0.583164i	0.647118	+	0.762390i	$0.275974\pi$
$312$	−13.0610	−	48.7443i	−0.0418622	−	0.156232i
$313$	76.3577	−	284.971i	0.243954	−	0.910450i	−0.729952	−	0.683499i	$-0.760457\pi$
$313$	76.3577	−	284.971i	0.243954	−	0.910450i	0.973906	−	0.226952i	$-0.0728759\pi$
$314$			247.502i			0.788223i
$315$	67.2693	−	80.6216i	0.213553	−	0.255942i
$316$	−138.448			−0.438128
$317$	602.418	+	161.418i	1.90037	+	0.509204i	0.996719	+	0.0809415i	$0.0257927\pi$
$317$	602.418	+	161.418i	1.90037	+	0.509204i	0.903655	+	0.428262i	$0.140874\pi$
$318$	168.622	−	45.1822i	0.530258	−	0.142082i
$319$	172.376	+	99.5215i	0.540364	+	0.311979i
$320$	−24.5149	+	31.6073i	−0.0766091	+	0.0987727i
$321$	73.8135			0.229949
$322$	1.93142	+	3.63914i	0.00599820	+	0.0113017i
$323$	117.699	+	117.699i	0.364392	+	0.364392i
$324$	15.5885	−	9.00000i	0.0481125	−	0.0277778i
$325$	−131.070	+	221.672i	−0.403293	+	0.682067i
$326$	−176.300	+	305.361i	−0.540797	+	0.936689i
$327$	289.201	+	77.4911i	0.884405	+	0.236976i
$328$	93.5538	+	93.5538i	0.285225	+	0.285225i
$329$	−164.851	+	153.492i	−0.501068	+	0.466542i
$330$	81.2606	−	33.1659i	0.246244	−	0.100503i
$331$	79.4501	+	137.612i	0.240031	+	0.415745i	0.960723	−	0.277510i	$-0.0895092\pi$
$331$	79.4501	+	137.612i	0.240031	+	0.415745i	−0.720692	+	0.693255i	$0.756176\pi$
$332$	41.7614	+	155.856i	0.125787	+	0.469445i
$333$	−154.711	+	41.4546i	−0.464596	+	0.124488i
$334$	−323.054	+	186.515i	−0.967226	+	0.558428i
$335$	258.135	−	614.153i	0.770551	−	1.83329i
$336$	−47.2627	+	10.8736i	−0.140663	+	0.0323620i
$337$	−39.4387	+	39.4387i	−0.117029	+	0.117029i	−0.763196	−	0.646167i	$-0.776371\pi$
$337$	−39.4387	+	39.4387i	−0.117029	+	0.117029i	0.646167	+	0.763196i	$0.276371\pi$
$338$	23.0199	−	85.9116i	0.0681064	−	0.254176i
$339$	6.09843	+	3.52093i	0.0179895	+	0.0103862i
$340$	−149.981	+	113.852i	−0.441119	+	0.334858i
$341$	89.7685	+	155.484i	0.263251	+	0.455963i
$342$	26.5192	−	26.5192i	0.0775416	−	0.0775416i
$343$	−341.038	−	36.6312i	−0.994281	−	0.106797i
$344$		−	149.308i		−	0.434035i
$345$	2.20890	−	2.84796i	0.00640262	−	0.00825495i
$346$	−99.1863	+	171.796i	−0.286666	+	0.496520i
$347$	75.8074	+	282.917i	0.218465	+	0.815323i	0.984918	+	0.173023i	$0.0553533\pi$
$347$	75.8074	+	282.917i	0.218465	+	0.815323i	−0.766453	+	0.642301i	$0.777980\pi$
$348$	−24.9024	+	92.9372i	−0.0715587	+	0.267061i
$349$		−	475.392i		−	1.36216i	−0.732211	−	0.681078i	$-0.761511\pi$
$349$		−	475.392i		−	1.36216i	0.732211	−	0.681078i	$-0.238489\pi$
$350$	208.407	+	133.479i	0.595447	+	0.381369i
$351$	−53.5250			−0.152493
$352$	−39.1571	−	10.4921i	−0.111242	−	0.0298071i
$353$	556.098	−	149.006i	1.57535	−	0.422114i	0.637867	−	0.770147i	$-0.279817\pi$
$353$	556.098	−	149.006i	1.57535	−	0.422114i	0.937482	+	0.348033i	$0.113150\pi$
$354$	86.3573	+	49.8584i	0.243947	+	0.140843i
$355$	513.104	+	397.968i	1.44536	+	1.12104i
$356$	263.398			0.739881
$357$	−228.155	−	8.14102i	−0.639089	−	0.0228040i
$358$	221.449	+	221.449i	0.618573	+	0.618573i
$359$	−38.5401	+	22.2511i	−0.107354	+	0.0619808i	−0.552716	−	0.833370i	$-0.686408\pi$
$359$	−38.5401	+	22.2511i	−0.107354	+	0.0619808i	0.445362	+	0.895351i	$0.353075\pi$
$360$	25.6524	+	33.7928i	0.0712568	+	0.0938689i
$361$	−141.429	+	244.963i	−0.391771	+	0.678568i
$362$	204.366	+	54.7598i	0.564548	+	0.151270i
$363$	−85.2973	−	85.2973i	−0.234979	−	0.234979i
$364$	137.879	+	42.2685i	0.378788	+	0.116122i
$365$	−37.4945	−	15.7593i	−0.102725	−	0.0431762i
$366$	−8.09203	−	14.0158i	−0.0221094	−	0.0382945i
$367$	96.2112	+	359.065i	0.262156	+	0.978379i	0.963968	+	0.266017i	$0.0857078\pi$
$367$	96.2112	+	359.065i	0.262156	+	0.978379i	−0.701812	+	0.712362i	$0.747625\pi$
$368$	−1.60798	+	0.430856i	−0.00436950	+	0.00117080i
$369$	121.530	−	70.1653i	0.329349	−	0.190150i
$370$	−142.658	−	349.528i	−0.385561	−	0.944671i
$371$	−146.220	+	476.967i	−0.394124	+	1.28563i
$372$	−61.3674	+	61.3674i	−0.164966	+	0.164966i
$373$	164.380	−	613.473i	0.440696	−	1.64470i	−0.286361	−	0.958122i	$-0.592446\pi$
$373$	164.380	−	613.473i	0.440696	−	1.64470i	0.727057	−	0.686577i	$-0.240888\pi$
$374$	−165.266	−	95.4165i	−0.441889	−	0.255124i
$375$	31.5999	−	214.188i	0.0842665	−	0.571168i
$376$	−45.5066	−	78.8197i	−0.121028	−	0.209627i
$377$	202.309	−	202.309i	0.536628	−	0.536628i
$378$	−1.83429	+	51.4066i	−0.00485262	+	0.135996i
$379$			203.740i			0.537573i	0.963200	+	0.268787i	$0.0866226\pi$
$379$			203.740i			0.537573i	−0.963200	+	0.268787i	$0.913377\pi$
$380$	69.8500	+	54.1764i	0.183816	+	0.142569i
$381$	21.0202	−	36.4081i	0.0551711	−	0.0955592i
$382$	−104.603	−	390.383i	−0.273830	−	1.02195i
$383$	36.0986	−	134.722i	0.0942522	−	0.351754i	−0.902653	−	0.430370i	$-0.858383\pi$
$383$	36.0986	−	134.722i	0.0942522	−	0.351754i	0.996905	+	0.0786154i	$0.0250499\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−42.8688	+	247.128i	−0.111348	+	0.641891i
$386$	334.312			0.866093
$387$	−152.969	−	40.9879i	−0.395269	−	0.105912i
$388$	−125.816	+	33.7124i	−0.324269	+	0.0868877i
$389$	477.792	+	275.853i	1.22826	+	0.709134i	0.966665	−	0.256044i	$-0.0824193\pi$
$389$	477.792	+	275.853i	1.22826	+	0.709134i	0.261592	+	0.965179i	$0.415753\pi$
$390$	−15.8174	−	125.164i	−0.0405575	−	0.320934i
$391$	−7.83651			−0.0200422
$392$	45.3207	−	130.973i	0.115614	−	0.334116i
$393$	155.631	+	155.631i	0.396009	+	0.396009i
$394$	−124.900	+	72.1108i	−0.317004	+	0.183022i
$395$	−342.921	−	46.9591i	−0.868154	−	0.118884i
$396$	−21.4987	+	37.2369i	−0.0542897	+	0.0940326i
$397$	−435.093	−	116.583i	−1.09595	−	0.293660i	−0.334837	−	0.942276i	$-0.608681\pi$
$397$	−435.093	−	116.583i	−1.09595	−	0.293660i	−0.761115	+	0.648617i	$0.775348\pi$
$398$	−286.796	−	286.796i	−0.720592	−	0.720592i
$399$	24.0300	+	104.448i	0.0602256	+	0.261773i
$400$	−71.4412	+	69.9726i	−0.178603	+	0.174931i
$401$	−228.287	−	395.405i	−0.569295	−	0.986048i	−0.996636	−	0.0819577i	$-0.973883\pi$
$401$	−228.287	−	395.405i	−0.569295	−	0.986048i	0.427340	−	0.904091i	$-0.359451\pi$
$402$	84.4703	+	315.247i	0.210125	+	0.784197i
$403$	249.276	−	66.7933i	0.618551	−	0.165740i
$404$	−118.123	+	68.1986i	−0.292385	+	0.168808i
$405$	41.6634	−	17.0046i	0.102873	−	0.0419868i
$406$	−187.369	−	201.235i	−0.461499	−	0.495652i
$407$	270.540	−	270.540i	0.664717	−	0.664717i
$408$	23.8753	−	89.1039i	0.0585179	−	0.218392i
$409$	502.237	+	289.967i	1.22796	+	0.708965i	0.966604	−	0.256276i	$-0.0824955\pi$
$409$	502.237	+	289.967i	1.22796	+	0.708965i	0.261361	+	0.965241i	$0.415829\pi$
$410$	199.990	+	263.454i	0.487781	+	0.642570i
$411$	−81.5589	−	141.264i	−0.198440	−	0.343708i
$412$	196.416	−	196.416i	0.476738	−	0.476738i
$413$	−251.710	+	133.591i	−0.609468	+	0.323466i
$414$			1.76568i			0.00426493i
$415$	50.5748	+	400.201i	0.121867	+	0.964340i
$416$	−29.1353	+	50.4638i	−0.0700368	+	0.121307i
$417$	−41.2263	−	153.859i	−0.0988641	−	0.368966i
$418$	−23.1869	+	86.5347i	−0.0554710	+	0.207021i
$419$			466.412i			1.11315i	0.830796	+	0.556577i	$0.187886\pi$
$419$			466.412i			1.11315i	−0.830796	+	0.556577i	$0.812114\pi$
$420$	−120.752	+	10.9021i	−0.287506	+	0.0259573i
$421$	−8.56578			−0.0203463			−0.0101731	−	0.999948i	$-0.503238\pi$
$421$	−8.56578			−0.0203463			−0.0101731	+	0.999948i	$0.503238\pi$
$422$	400.311	+	107.263i	0.948605	+	0.254178i
$423$	−93.2447	+	24.9849i	−0.220437	+	0.0590658i
$424$	−174.570	−	100.788i	−0.411723	−	0.237708i
$425$	−410.101	+	231.127i	−0.964943	+	0.543828i
$426$	−318.115			−0.746748
$427$	46.2204	+	1.64924i	0.108244	+	0.00386238i
$428$	−60.2685	−	60.2685i	−0.140814	−	0.140814i
$429$	110.728	−	63.9289i	0.258107	−	0.149018i
$430$	50.6425	−	369.819i	0.117773	−	0.860044i
$431$	−70.0856	+	121.392i	−0.162612	+	0.281652i	−0.935805	−	0.352519i	$-0.885325\pi$
$431$	−70.0856	+	121.392i	−0.162612	+	0.281652i	0.773193	+	0.634171i	$0.218658\pi$
$432$	−20.0764	−	5.37945i	−0.0464731	−	0.0124524i
$433$	20.7110	+	20.7110i	0.0478314	+	0.0478314i	0.730618	−	0.682787i	$-0.239232\pi$
$433$	20.7110	+	20.7110i	0.0478314	+	0.0478314i	−0.682787	+	0.730618i	$0.739232\pi$
$434$	−55.6071	−	241.699i	−0.128127	−	0.556911i
$435$	−93.2030	+	221.748i	−0.214260	+	0.509766i
$436$	−172.860	−	299.402i	−0.396468	−	0.686703i
$437$	0.952164	+	3.55352i	0.00217887	+	0.00813164i
$438$	19.2461	−	5.15698i	0.0439409	−	0.0117739i
$439$	262.272	−	151.423i	0.597430	−	0.344926i	−0.170600	−	0.985340i	$-0.554571\pi$
$439$	262.272	−	151.423i	0.597430	−	0.344926i	0.768030	+	0.640414i	$0.221237\pi$
$440$	−93.4288	−	39.2691i	−0.212338	−	0.0892479i
$441$	−121.743	−	82.3866i	−0.276062	−	0.186818i
$442$	−193.964	+	193.964i	−0.438833	+	0.438833i
$443$	−149.400	+	557.570i	−0.337247	+	1.25862i	0.564166	+	0.825661i	$0.309198\pi$
$443$	−149.400	+	557.570i	−0.337247	+	1.25862i	−0.901413	+	0.432961i	$0.857469\pi$
$444$	160.168	+	92.4731i	0.360739	+	0.208273i
$445$	652.406	+	89.3395i	1.46608	+	0.200763i
$446$	166.941	+	289.151i	0.374307	+	0.648320i
$447$	−64.9044	+	64.9044i	−0.145200	+	0.145200i
$448$	47.4681	+	29.7116i	0.105956	+	0.0663205i
$449$			31.4156i			0.0699679i	0.999388	+	0.0349840i	$0.0111380\pi$
$449$			31.4156i			0.0699679i	−0.999388	+	0.0349840i	$0.988862\pi$
$450$	52.0762	+	92.4016i	0.115725	+	0.205337i
$451$	−167.607	+	290.304i	−0.371635	+	0.643690i
$452$	−2.10452	−	7.85417i	−0.00465601	−	0.0173765i
$453$	10.8236	−	40.3943i	0.0238932	−	0.0891707i
$454$		−	431.072i		−	0.949497i
$455$	327.174	+	151.460i	0.719063	+	0.332879i
$456$	−43.3057			−0.0949687
$457$	274.333	+	73.5073i	0.600291	+	0.160848i	0.546152	−	0.837686i	$-0.316092\pi$
$457$	274.333	+	73.5073i	0.600291	+	0.160848i	0.0541389	+	0.998533i	$0.482759\pi$
$458$	307.469	−	82.3862i	0.671331	−	0.179882i
$459$	−84.7344	−	48.9214i	−0.184606	−	0.106583i
$460$	−4.12891	+	0.521785i	−0.00897589	+	0.00113432i
$461$	−8.38183			−0.0181818			−0.00909092	−	0.999959i	$-0.502894\pi$
$461$	−8.38183			−0.0181818			−0.00909092	+	0.999959i	$0.502894\pi$
$462$	−57.6040	−	108.536i	−0.124684	−	0.234927i
$463$	−59.5826	−	59.5826i	−0.128688	−	0.128688i	0.639829	−	0.768517i	$-0.279005\pi$
$463$	−59.5826	−	59.5826i	−0.128688	−	0.128688i	−0.768517	+	0.639829i	$0.779005\pi$
$464$	96.2157	−	55.5501i	0.207361	−	0.119720i
$465$	−172.815	+	131.185i	−0.371644	+	0.282119i
$466$	−71.6651	+	124.128i	−0.153788	+	0.266368i
$467$	−473.750	−	126.941i	−1.01445	−	0.271822i	−0.286964	−	0.957941i	$-0.592646\pi$
$467$	−473.750	−	126.941i	−1.01445	−	0.271822i	−0.727489	+	0.686119i	$0.759313\pi$
$468$	43.7030	+	43.7030i	0.0933824	+	0.0933824i
$469$	−891.713	−	273.366i	−1.90131	−	0.582869i
$470$	−85.9804	−	210.662i	−0.182937	−	0.448218i
$471$	−151.563	−	262.516i	−0.321791	−	0.557358i
$472$	−29.8012	−	111.220i	−0.0631381	−	0.235635i
$473$	365.404	−	97.9098i	0.772525	−	0.206997i
$474$	146.847	−	84.7820i	0.309803	−	0.178865i
$475$	154.635	+	157.880i	0.325547	+	0.332380i
$476$	179.640	+	192.935i	0.377396	+	0.405325i
$477$	−151.182	+	151.182i	−0.316944	+	0.316944i
$478$	70.0652	−	261.487i	0.146580	−	0.547044i
$479$	395.262	+	228.205i	0.825183	+	0.476419i	0.852200	−	0.523216i	$-0.175268\pi$
$479$	395.262	+	228.205i	0.825183	+	0.476419i	−0.0270178	+	0.999635i	$0.508601\pi$
$480$	6.64657	−	48.5368i	0.0138470	−	0.101118i
$481$	−274.979	−	476.278i	−0.571682	−	0.990182i
$482$	−268.500	+	268.500i	−0.557054	+	0.557054i
$483$	−4.27709	−	2.67715i	−0.00885526	−	0.00554275i
$484$			139.290i			0.287789i
$485$	−323.067	+	40.8272i	−0.666118	+	0.0841798i
$486$	−11.0227	+	19.0919i	−0.0226805	+	0.0392837i
$487$	−0.190899	−	0.712445i	−0.000391990	−	0.00146293i	0.965730	−	0.259550i	$-0.0835744\pi$
$487$	−0.190899	−	0.712445i	−0.000391990	−	0.00146293i	−0.966122	+	0.258088i	$0.916908\pi$
$488$	−4.83674	+	18.0510i	−0.00991136	+	0.0369897i
$489$		−	431.845i		−	0.883119i
$490$	156.678	−	309.034i	0.319750	−	0.630682i
$491$	335.358			0.683010			0.341505	−	0.939880i	$-0.389063\pi$
$491$	335.358			0.683010			0.341505	+	0.939880i	$0.389063\pi$
$492$	−156.518	−	41.9390i	−0.318127	−	0.0852419i
$493$	505.180	−	135.363i	1.02471	−	0.274569i
$494$	111.522	+	64.3872i	0.225753	+	0.130338i
$495$	−65.8799	+	84.9395i	−0.133091	+	0.171595i
$496$	100.213			0.202041
$497$	482.329	−	770.584i	0.970482	−	1.55047i
$498$	−139.736	−	139.736i	−0.280595	−	0.280595i
$499$	−530.603	+	306.344i	−1.06333	+	0.613915i	−0.926352	−	0.376658i	$-0.877073\pi$
$499$	−530.603	+	306.344i	−1.06333	+	0.613915i	−0.136980	+	0.990574i	$0.543740\pi$
$500$	−200.685	+	149.082i	−0.401370	+	0.298165i
$501$	228.433	−	395.658i	0.455955	−	0.789737i
$502$	−429.814	−	115.168i	−0.856202	−	0.229419i
$503$	−377.103	−	377.103i	−0.749707	−	0.749707i	0.224717	−	0.974424i	$-0.427854\pi$
$503$	−377.103	−	377.103i	−0.749707	−	0.749707i	−0.974424	+	0.224717i	$0.927854\pi$
$504$	43.4710	−	40.4756i	0.0862519	−	0.0803087i
$505$	−315.710	+	128.855i	−0.625168	+	0.255158i
$506$	−2.10888	−	3.65269i	−0.00416775	−	0.00721876i
$507$	28.1936	+	105.220i	0.0556086	+	0.207534i
$508$	−46.8900	+	12.5641i	−0.0923031	+	0.0247325i
$509$	−683.042	+	394.355i	−1.34193	+	0.774764i	−0.987091	−	0.160163i	$-0.948798\pi$
$509$	−683.042	+	394.355i	−1.34193	+	0.774764i	−0.354840	+	0.934927i	$0.615465\pi$
$510$	89.3587	−	212.602i	0.175213	−	0.416866i
$511$	−16.6892	+	54.4398i	−0.0326599	+	0.106536i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−11.8882	+	44.3675i	−0.0231740	+	0.0864864i
$514$	−457.398	−	264.079i	−0.889880	−	0.513773i
$515$	553.120	−	419.879i	1.07402	−	0.815299i
$516$	91.4321	+	158.365i	0.177194	+	0.306909i
$517$	163.056	−	163.056i	0.315388	−	0.315388i
$518$	−466.851	+	247.774i	−0.901257	+	0.478328i
$519$		−	242.956i		−	0.468123i
$520$	−89.2812	+	115.111i	−0.171695	+	0.221367i
$521$	−5.25649	+	9.10450i	−0.0100892	+	0.0174750i	−0.871026	−	0.491237i	$-0.836545\pi$
$521$	−5.25649	+	9.10450i	−0.0100892	+	0.0174750i	0.860937	+	0.508712i	$0.169878\pi$
$522$	−30.4991	−	113.824i	−0.0584275	−	0.218054i
$523$	−180.122	+	672.226i	−0.344402	+	1.28533i	0.548906	+	0.835884i	$0.315044\pi$
$523$	−180.122	+	672.226i	−0.344402	+	1.28533i	−0.893309	+	0.449444i	$0.851622\pi$
$524$		−	254.145i		−	0.485010i
$525$	−302.788	−	13.9538i	−0.576738	−	0.0265786i
$526$	−36.5017			−0.0693949
$527$	455.673	+	122.097i	0.864654	+	0.231683i
$528$	47.9574	−	12.8502i	0.0908285	−	0.0243374i
$529$	457.977	+	264.413i	0.865742	+	0.499836i
$530$	−398.205	−	308.852i	−0.751331	−	0.582740i
$531$	−122.128			−0.229995
$532$	65.6607	−	104.902i	0.123422	−	0.197183i
$533$	340.715	+	340.715i	0.639240	+	0.639240i
$534$	−279.375	+	161.297i	−0.523175	+	0.302055i
$535$	−128.836	−	169.720i	−0.240815	−	0.317234i
$536$	188.429	−	326.368i	0.351546	−	0.608896i
$537$	−370.492	−	99.2729i	−0.689928	−	0.184866i
$538$	−218.439	−	218.439i	−0.406020	−	0.406020i
$539$	350.253	+	25.0273i	0.649820	+	0.0464329i
$540$	−47.9023	−	20.1338i	−0.0887079	−	0.0372848i
$541$	−370.192	−	641.191i	−0.684273	−	1.18520i	−0.973665	−	0.227985i	$-0.926786\pi$
$541$	−370.192	−	641.191i	−0.684273	−	1.18520i	0.289392	−	0.957211i	$-0.406547\pi$
$542$	10.9610	+	40.9070i	0.0202233	+	0.0754742i
$543$	−250.297	+	67.0668i	−0.460951	+	0.123512i
$544$	−92.2471	+	53.2589i	−0.169572	+	0.0979024i
$545$	−326.603	−	800.216i	−0.599271	−	1.46829i
$546$	−172.127	+	39.6008i	−0.315251	+	0.0725289i
$547$	−452.053	+	452.053i	−0.826421	+	0.826421i	−0.987020	−	0.160598i	$-0.948658\pi$
$547$	−452.053	+	452.053i	−0.826421	+	0.826421i	0.160598	+	0.987020i	$0.448658\pi$
$548$	−48.7491	+	181.934i	−0.0889583	+	0.331997i
$549$	17.1658	+	9.91067i	0.0312674	+	0.0180522i
$550$	−218.093	−	128.954i	−0.396533	−	0.234462i
$551$	−122.762	−	212.630i	−0.222799	−	0.385899i
$552$	1.44167	−	1.44167i	0.00261172	−	0.00261172i
$553$	−17.2794	+	484.261i	−0.0312467	+	0.875698i
$554$		−	752.712i		−	1.35869i
$555$	365.353	+	283.371i	0.658293	+	0.510579i
$556$	−91.9640	+	159.286i	−0.165403	+	0.286486i
$557$	116.113	+	433.341i	0.208462	+	0.777991i	0.988366	+	0.152092i	$0.0486011\pi$
$557$	116.113	+	433.341i	0.208462	+	0.777991i	−0.779904	+	0.625899i	$0.784732\pi$
$558$	27.5103	−	102.670i	0.0493015	−	0.183996i
$559$		−	543.767i		−	0.972750i
$560$	107.495	+	89.6924i	0.191956	+	0.160165i
$561$	233.722			0.416616
$562$	94.6602	+	25.3641i	0.168435	+	0.0451319i
$563$	−473.720	+	126.933i	−0.841422	+	0.225458i	−0.653690	−	0.756762i	$-0.726780\pi$
$563$	−473.720	+	126.933i	−0.841422	+	0.225458i	−0.187731	+	0.982220i	$0.560113\pi$
$564$	96.5341	+	55.7340i	0.171160	+	0.0988191i
$565$	−2.54866	−	20.1677i	−0.00451091	−	0.0356950i
$566$	495.805			0.875980
$567$	−29.5344	−	55.6482i	−0.0520889	−	0.0981449i
$568$	259.740	+	259.740i	0.457288	+	0.457288i
$569$	−489.271	+	282.480i	−0.859878	+	0.496451i	−0.863971	−	0.503541i	$-0.832030\pi$
$569$	−489.271	+	282.480i	−0.859878	+	0.496451i	0.00409346	+	0.999992i	$0.498697\pi$
$570$	−107.263	−	14.6885i	−0.188181	−	0.0257693i
$571$	−54.3972	+	94.2188i	−0.0952666	+	0.165007i	−0.909720	−	0.415223i	$-0.863704\pi$
$571$	−54.3972	+	94.2188i	−0.0952666	+	0.165007i	0.814453	+	0.580229i	$0.197037\pi$
$572$	−142.607	−	38.2114i	−0.249313	−	0.0668031i
$573$	350.008	+	350.008i	0.610834	+	0.610834i
$574$	338.906	−	315.554i	0.590429	−	0.549745i
$575$	−10.4038	−	0.108047i	−0.0180936	−	0.000187907i
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−94.6298	−	353.163i	−0.164003	−	0.612068i	−0.998165	−	0.0605486i	$-0.980715\pi$
$577$	−94.6298	−	353.163i	−0.164003	−	0.612068i	0.834162	−	0.551519i	$-0.185952\pi$
$578$	−89.5616	+	23.9980i	−0.154951	+	0.0415190i
$579$	−354.591	+	204.723i	−0.612420	+	0.353581i
$580$	257.157	−	104.957i	0.443373	−	0.180960i
$581$	550.360	−	126.620i	0.947263	−	0.217934i
$582$	112.804	−	112.804i	0.193821	−	0.193821i
$583$	132.185	−	493.322i	0.226733	−	0.846178i
$584$	−19.9250	−	11.5037i	−0.0341182	−	0.0196982i
$585$	93.4240	+	123.070i	0.159699	+	0.210377i
$586$	371.421	+	643.321i	0.633825	+	1.09782i
$587$	−488.112	+	488.112i	−0.831537	+	0.831537i	−0.987727	−	0.156190i	$-0.950079\pi$
$587$	−488.112	+	488.112i	−0.831537	+	0.831537i	0.156190	+	0.987727i	$0.450079\pi$
$588$	32.1347	+	166.671i	0.0546509	+	0.283455i
$589$		−	221.463i		−	0.375999i
$590$	−36.0905	−	285.586i	−0.0611704	−	0.484044i
$591$	88.3173	−	152.970i	0.149437	−	0.258833i
$592$	−55.2727	−	206.281i	−0.0933661	−	0.348447i
$593$	−54.6805	+	204.070i	−0.0922099	+	0.344132i	−0.996582	−	0.0826135i	$-0.973673\pi$
$593$	−54.6805	+	204.070i	−0.0922099	+	0.344132i	0.904372	+	0.426745i	$0.140340\pi$
$594$		−	52.6609i		−	0.0886547i
$595$	379.509	+	538.808i	0.637830	+	0.905559i
$596$	105.988			0.177833
$597$	479.818	+	128.567i	0.803716	+	0.215355i
$598$	−5.85611	+	1.56914i	−0.00979283	+	0.00262398i
$599$	245.514	+	141.748i	0.409874	+	0.236641i	0.690735	−	0.723108i	$-0.257287\pi$
$599$	245.514	+	141.748i	0.409874	+	0.236641i	−0.280862	+	0.959748i	$0.590620\pi$
$600$	32.9255	−	117.966i	0.0548759	−	0.196610i
$601$	685.441			1.14050			0.570251	−	0.821471i	$-0.306846\pi$
$601$	685.441			1.14050			0.570251	+	0.821471i	$0.306846\pi$
$602$	−522.246	−	18.6348i	−0.867518	−	0.0309548i
$603$	−282.643	−	282.643i	−0.468728	−	0.468728i
$604$	−41.8193	+	24.1444i	−0.0692373	+	0.0399741i
$605$	−47.2445	+	345.005i	−0.0780901	+	0.570256i
$606$	83.5259	−	144.671i	0.137831	−	0.238731i
$607$	997.957	+	267.402i	1.64408	+	0.440530i	0.957947	−	0.286945i	$-0.0926396\pi$
$607$	997.957	+	267.402i	1.64408	+	0.440530i	0.686134	+	0.727475i	$0.259306\pi$
$608$	35.3590	+	35.3590i	0.0581562	+	0.0581562i
$609$	321.965	+	98.7024i	0.528679	+	0.162073i
$610$	−18.1026	+	43.0696i	−0.0296764	+	0.0706060i
$611$	−165.731	−	287.055i	−0.271246	−	0.469811i
$612$	29.2412	+	109.129i	0.0477797	+	0.178316i
$613$	−604.447	+	161.961i	−0.986048	+	0.264211i	−0.715589	−	0.698521i	$-0.753842\pi$
$613$	−604.447	+	161.961i	−0.986048	+	0.264211i	−0.270458	+	0.962732i	$0.587175\pi$
$614$	−132.450	+	76.4698i	−0.215716	+	0.124544i
$615$	−373.453	−	156.966i	−0.607241	−	0.255230i
$616$	−41.5861	+	135.653i	−0.0675099	+	0.220216i
$617$	230.449	−	230.449i	0.373498	−	0.373498i	−0.495251	−	0.868750i	$-0.664924\pi$
$617$	230.449	−	230.449i	0.373498	−	0.373498i	0.868750	+	0.495251i	$0.164924\pi$
$618$	−88.0508	+	328.610i	−0.142477	+	0.531732i
$619$	459.874	+	265.509i	0.742931	+	0.428931i	0.823134	−	0.567847i	$-0.192224\pi$
$619$	459.874	+	265.509i	0.742931	+	0.428931i	−0.0802030	+	0.996779i	$0.525557\pi$
$620$	248.215	+	33.9902i	0.400347	+	0.0548229i
$621$	−1.08125	−	1.87279i	−0.00174115	−	0.00301576i
$622$	−209.421	+	209.421i	−0.336690	+	0.336690i
$623$	32.8740	−	921.305i	0.0527673	−	1.47882i
$624$		−	71.3667i		−	0.114370i
$625$	−547.639	+	301.191i	−0.876223	+	0.481906i
$626$	208.613	−	361.329i	0.333248	−	0.577202i
$627$	−28.3980	−	105.983i	−0.0452919	−	0.169032i
$628$	−90.5920	+	338.094i	−0.144255	+	0.538366i
$629$		−	1005.31i		−	1.59827i
$630$	121.401	−	85.5088i	0.192700	−	0.135728i
$631$	545.090			0.863852			0.431926	−	0.901909i	$-0.357834\pi$
$631$	545.090			0.863852			0.431926	+	0.901909i	$0.357834\pi$
$632$	−189.124	−	50.6756i	−0.299247	−	0.0801830i
$633$	−490.279	+	131.370i	−0.774533	+	0.207535i
$634$	763.836	+	441.001i	1.20479	+	0.695585i
$635$	−120.403	+	15.2157i	−0.189610	+	0.0239617i
$636$	246.880			0.388176
$637$	165.054	−	476.994i	0.259111	−	0.748813i
$638$	199.043	+	199.043i	0.311979	+	0.311979i
$639$	337.412	−	194.805i	0.528031	−	0.304859i
$640$	−45.0570	+	34.2033i	−0.0704016	+	0.0534426i
$641$	−377.578	+	653.985i	−0.589046	+	1.02026i	0.405312	+	0.914179i	$0.367163\pi$
$641$	−377.578	+	653.985i	−0.589046	+	1.02026i	−0.994358	+	0.106079i	$0.966170\pi$
$642$	100.831	+	27.0176i	0.157058	+	0.0420835i
$643$	−222.457	−	222.457i	−0.345967	−	0.345967i	0.512638	−	0.858605i	$-0.328668\pi$
$643$	−222.457	−	222.457i	−0.345967	−	0.345967i	−0.858605	+	0.512638i	$0.828668\pi$
$644$	1.30635	+	5.67811i	0.00202849	+	0.00881694i
$645$	172.752	+	423.264i	0.267833	+	0.656223i
$646$	117.699	+	203.860i	0.182196	+	0.315573i
$647$	103.822	+	387.467i	0.160466	+	0.598867i	0.998575	+	0.0533647i	$0.0169946\pi$
$647$	103.822	+	387.467i	0.160466	+	0.598867i	−0.838109	+	0.545503i	$0.816339\pi$
$648$	24.5885	−	6.58846i	0.0379452	−	0.0101674i
$649$	252.647	−	145.866i	0.389287	−	0.224755i
$650$	−260.183	+	254.834i	−0.400281	+	0.392052i
$651$	206.990	+	222.308i	0.317957	+	0.341488i
$652$	−352.600	+	352.600i	−0.540797	+	0.540797i
$653$	233.236	−	870.447i	0.357175	−	1.33300i	−0.520549	−	0.853832i	$-0.674273\pi$
$653$	233.236	−	870.447i	0.357175	−	1.33300i	0.877725	−	0.479165i	$-0.159061\pi$
$654$	366.692	+	211.709i	0.560691	+	0.323715i
$655$	86.2012	−	629.488i	0.131605	−	0.961050i
$656$	93.5538	+	162.040i	0.142612	+	0.247012i
$657$	−17.2556	+	17.2556i	−0.0262642	+	0.0262642i
$658$	−281.373	+	149.334i	−0.427619	+	0.226952i
$659$			996.771i			1.51255i	0.654253	+	0.756275i	$0.272983\pi$
$659$			996.771i			1.51255i	−0.654253	+	0.756275i	$0.727017\pi$
$660$	123.144	−	15.5621i	0.186581	−	0.0235789i
$661$	582.202	−	1008.40i	0.880789	−	1.52557i	0.0303238	−	0.999540i	$-0.490346\pi$
$661$	582.202	−	1008.40i	0.880789	−	1.52557i	0.850465	−	0.526031i	$-0.176321\pi$
$662$	58.1615	+	217.062i	0.0878573	+	0.327888i
$663$	86.9518	−	324.509i	0.131149	−	0.489455i
$664$			228.188i			0.343657i
$665$	198.215	−	237.558i	0.298067	−	0.357230i
$666$	−226.512			−0.340108
$667$	11.1654	+	2.99176i	0.0167397	+	0.00448540i
$668$	−509.569	+	136.539i	−0.762827	+	0.204399i
$669$	−354.136	−	204.460i	−0.529351	−	0.305621i
$670$	577.414	−	744.464i	0.861812	−	1.11114i
$671$	−47.3482			−0.0705636
$672$	−68.5421	−	2.44572i	−0.101997	−	0.00363946i
$673$	−419.133	−	419.133i	−0.622783	−	0.622783i	0.323459	−	0.946242i	$-0.395154\pi$
$673$	−419.133	−	419.133i	−0.622783	−	0.622783i	−0.946242	+	0.323459i	$0.895154\pi$
$674$	−68.3098	+	39.4387i	−0.101350	+	0.0585144i
$675$	−111.819	−	66.1167i	−0.165658	−	0.0979506i
$676$	62.8917	−	108.932i	0.0930350	−	0.161141i
$677$	−704.503	−	188.771i	−1.04062	−	0.278834i	−0.302252	−	0.953228i	$-0.597739\pi$
$677$	−704.503	−	188.771i	−1.04062	−	0.278834i	−0.738372	+	0.674393i	$0.764405\pi$
$678$	7.04185	+	7.04185i	0.0103862	+	0.0103862i
$679$	102.216	+	444.285i	0.150538	+	0.654323i
$680$	−246.550	+	100.628i	−0.362573	+	0.147982i
$681$	263.976	+	457.221i	0.387631	+	0.671396i
$682$	65.7151	+	245.252i	0.0963564	+	0.359607i
$683$	−1033.71	+	276.981i	−1.51348	+	0.405535i	−0.917589	−	0.397531i	$-0.869867\pi$
$683$	−1033.71	+	276.981i	−1.51348	+	0.405535i	−0.595890	+	0.803066i	$0.703200\pi$
$684$	45.9327	−	26.5192i	0.0671530	−	0.0387708i
$685$	−182.455	+	434.095i	−0.266357	+	0.633716i
$686$	−452.459	−	174.868i	−0.659561	−	0.254909i
$687$	−275.670	+	275.670i	−0.401266	+	0.401266i
$688$	54.6505	−	203.959i	0.0794339	−	0.296451i
$689$	−635.771	−	367.062i	−0.922744	−	0.532747i
$690$	4.05984	−	3.08187i	0.00588383	−	0.00446647i
$691$	490.628	+	849.792i	0.710026	+	1.22980i	0.964847	+	0.262812i	$0.0846500\pi$
$691$	490.628	+	849.792i	0.710026	+	1.22980i	−0.254821	+	0.966988i	$0.582017\pi$
$692$	−198.373	+	198.373i	−0.286666	+	0.286666i
$693$	127.563	+	79.8452i	0.184074	+	0.115217i
$694$			414.220i			0.596858i
$695$	−281.811	+	363.341i	−0.405484	+	0.522793i
$696$	−68.0347	+	117.840i	−0.0977511	+	0.169310i
$697$	227.968	+	850.790i	0.327071	+	1.22064i
$698$	174.006	−	649.398i	0.249292	−	0.930370i
$699$		−	175.543i		−	0.251134i
$700$	235.832	+	258.618i	0.336903	+	0.369455i
$701$	−940.348			−1.34144			−0.670719	−	0.741711i	$-0.734014\pi$
$701$	−940.348			−1.34144			−0.670719	+	0.741711i	$0.734014\pi$
$702$	−73.1165	−	19.5915i	−0.104155	−	0.0279081i
$703$	−455.867	+	122.149i	−0.648460	+	0.173754i
$704$	−49.6492	−	28.6650i	−0.0705244	−	0.0407173i
$705$	220.200	+	170.789i	0.312340	+	0.242254i
$706$	814.184			1.15324
$707$	223.801	+	421.681i	0.316550	+	0.596437i
$708$	99.7168	+	99.7168i	0.140843	+	0.140843i
$709$	364.698	−	210.559i	0.514384	−	0.296980i	−0.220250	−	0.975443i	$-0.570687\pi$
$709$	364.698	−	210.559i	0.514384	−	0.296980i	0.734634	+	0.678464i	$0.237354\pi$
$710$	555.246	+	731.444i	0.782037	+	1.03020i
$711$	−103.836	+	179.850i	−0.146043	+	0.252953i
$712$	359.808	+	96.4102i	0.505348	+	0.135408i
$713$	7.37264	+	7.37264i	0.0103403	+	0.0103403i
$714$	−308.685	−	94.6313i	−0.432332	−	0.132537i
$715$	−340.260	−	143.015i	−0.475888	−	0.200020i
$716$	221.449	+	383.561i	0.309286	+	0.535700i
$717$	85.8120	+	320.255i	0.119682	+	0.446659i
$718$	−60.7912	+	16.2889i	−0.0846674	+	0.0226865i
$719$	331.576	−	191.436i	0.461163	−	0.266253i	−0.251370	−	0.967891i	$-0.580881\pi$
$719$	331.576	−	191.436i	0.461163	−	0.266253i	0.712533	+	0.701638i	$0.247548\pi$
$720$	22.6729	+	55.5512i	0.0314901	+	0.0771545i
$721$	−662.504	−	711.533i	−0.918869	−	0.986869i
$722$	−282.859	+	282.859i	−0.391771	+	0.391771i
$723$	120.365	−	449.209i	0.166480	−	0.621313i
$724$	259.126	+	149.607i	0.357909	+	0.206639i
$725$	672.547	−	172.743i	0.927650	−	0.238266i
$726$	−85.2973	−	147.739i	−0.117489	−	0.203498i
$727$	−666.033	+	666.033i	−0.916139	+	0.916139i	−0.996746	−	0.0806067i	$-0.974314\pi$
$727$	−666.033	+	666.033i	−0.916139	+	0.916139i	0.0806067	+	0.996746i	$0.474314\pi$
$728$	172.875	+	108.207i	0.237465	+	0.148636i
$729$		−	27.0000i		−	0.0370370i
$730$	−45.4502	−	35.2516i	−0.0622605	−	0.0482899i
$731$	496.999	−	860.827i	0.679889	−	1.17760i
$732$	−5.92378	−	22.1078i	−0.00809259	−	0.0302020i
$733$	8.24999	−	30.7894i	0.0112551	−	0.0420046i	−0.960070	−	0.279760i	$-0.909745\pi$
$733$	8.24999	−	30.7894i	0.0112551	−	0.0420046i	0.971325	+	0.237756i	$0.0764117\pi$
$734$			525.708i			0.716223i
$735$	23.0621	+	423.725i	0.0313771	+	0.576497i
$736$	−2.35424			−0.00319870
$737$	922.290	+	247.127i	1.25141	+	0.335314i
$738$	191.695	−	51.3646i	0.259750	−	0.0695997i
$739$	−770.669	−	444.946i	−1.04285	−	0.602092i	−0.122214	−	0.992504i	$-0.538999\pi$
$739$	−770.669	−	444.946i	−1.04285	−	0.602092i	−0.920640	+	0.390412i	$0.872333\pi$
$740$	−66.9377	−	529.681i	−0.0904563	−	0.715785i
$741$	−157.716			−0.212842
$742$	−374.322	+	598.029i	−0.504478	+	0.805969i
$743$	−380.855	−	380.855i	−0.512591	−	0.512591i	0.402729	−	0.915319i	$-0.368062\pi$
$743$	−380.855	−	380.855i	−0.512591	−	0.512591i	−0.915319	+	0.402729i	$0.868062\pi$
$744$	−106.291	+	61.3674i	−0.142865	+	0.0824831i
$745$	262.521	+	35.9493i	0.352377	+	0.0482541i
$746$	449.093	−	777.852i	0.602002	−	1.04270i
$747$	233.783	+	62.6421i	0.312963	+	0.0838582i
$748$	−190.833	−	190.833i	−0.255124	−	0.255124i
$749$	−218.328	+	203.284i	−0.291492	+	0.271407i
$750$	121.565	−	281.020i	0.162086	−	0.374693i
$751$	−62.9757	−	109.077i	−0.0838558	−	0.145242i	0.821047	−	0.570860i	$-0.193390\pi$
$751$	−62.9757	−	109.077i	−0.0838558	−	0.145242i	−0.904903	+	0.425618i	$0.860057\pi$
$752$	−33.3131	−	124.326i	−0.0442994	−	0.165328i
$753$	526.412	−	141.052i	0.699086	−	0.187320i
$754$	350.409	−	202.309i	0.464734	−	0.268314i
$755$	−111.771	+	45.6185i	−0.148041	+	0.0604219i
$756$	−21.3218	+	69.5513i	−0.0282034	+	0.0919991i
$757$	896.465	−	896.465i	1.18423	−	1.18423i	0.205597	−	0.978637i	$-0.434087\pi$
$757$	896.465	−	896.465i	1.18423	−	1.18423i	0.978637	−	0.205597i	$-0.0659135\pi$
$758$	−74.5741	+	278.314i	−0.0983827	+	0.367169i
$759$	4.47362	+	2.58284i	0.00589409	+	0.00340296i
$760$	75.5870	+	99.5732i	0.0994566	+	0.131017i
$761$	292.491	+	506.610i	0.384351	+	0.665716i	0.991679	−	0.128736i	$-0.0410918\pi$
$761$	292.491	+	506.610i	0.384351	+	0.665716i	−0.607328	+	0.794451i	$0.707759\pi$
$762$	42.0404	−	42.0404i	0.0551711	−	0.0551711i
$763$	−1068.82	+	567.258i	−1.40081	+	0.743457i
$764$		−	571.561i		−	0.748116i
$765$	35.4123	+	280.219i	0.0462906	+	0.366300i
$766$	98.6232	−	170.820i	0.128751	−	0.223003i
$767$	−108.533	−	405.052i	−0.141504	−	0.528099i
$768$	7.17260	−	26.7685i	0.00933933	−	0.0348548i
$769$		−	885.685i		−	1.15174i	−0.817543	−	0.575868i	$-0.804664\pi$
$769$		−	885.685i		−	1.15174i	0.817543	−	0.575868i	$-0.195336\pi$
$770$	−149.015	+	321.892i	−0.193526	+	0.418041i
$771$	646.859			0.838987
$772$	456.678	+	122.367i	0.591552	+	0.158506i
$773$	841.968	−	225.605i	1.08922	−	0.291856i	0.330853	−	0.943682i	$-0.392664\pi$
$773$	841.968	−	225.605i	1.08922	−	0.291856i	0.758368	+	0.651826i	$0.225997\pi$
$774$	−193.957	−	111.981i	−0.250590	−	0.144678i
$775$	603.271	+	168.380i	0.778414	+	0.217264i
$776$	−184.208			−0.237382
$777$	343.440	−	548.691i	0.442008	−	0.706165i
$778$	551.707	+	551.707i	0.709134	+	0.709134i
$779$	358.098	−	206.748i	0.459689	−	0.265402i
$780$	24.2062	−	176.767i	0.0310336	−	0.226624i
$781$	−465.339	+	805.991i	−0.595825	+	1.03200i
$782$	−10.7049	−	2.86836i	−0.0136891	−	0.00366798i
$783$	102.052	+	102.052i	0.130335	+	0.130335i
$784$	109.849	−	162.325i	0.140113	−	0.207047i
$785$	−339.061	+	806.693i	−0.431925	+	1.02763i
$786$	155.631	+	269.561i	0.198004	+	0.342954i
$787$	142.591	+	532.157i	0.181183	+	0.676184i	0.995416	+	0.0956451i	$0.0304914\pi$
$787$	142.591	+	532.157i	0.181183	+	0.676184i	−0.814233	+	0.580539i	$0.802842\pi$
$788$	−197.010	+	52.7888i	−0.250013	+	0.0669908i
$789$	38.7159	−	22.3526i	0.0490696	−	0.0283303i
$790$	−451.250	−	189.665i	−0.571203	−	0.240082i
$791$	−27.7348	+	6.38087i	−0.0350629	+	0.00806684i
$792$	−42.9975	+	42.9975i	−0.0542897	+	0.0542897i
$793$	−17.6150	+	65.7401i	−0.0222131	+	0.0829005i
$794$	−551.676	−	318.510i	−0.694806	−	0.401146i
$795$	611.493	+	83.7370i	0.769174	+	0.105330i
$796$	−286.796	−	496.745i	−0.360296	−	0.624051i
$797$	−522.605	+	522.605i	−0.655716	+	0.655716i	−0.954363	−	0.298648i	$-0.903464\pi$
$797$	−522.605	+	522.605i	−0.655716	+	0.655716i	0.298648	+	0.954363i	$0.403464\pi$
$798$	−5.40488	+	151.474i	−0.00677304	+	0.189817i
$799$		−	605.908i		−	0.758332i
$800$	−123.202	+	69.4350i	−0.154003	+	0.0867937i
$801$	197.548	−	342.164i	0.246627	−	0.427171i
$802$	−167.118	−	623.693i	−0.208377	−	0.777672i
$803$	15.0873	−	56.3065i	0.0187887	−	0.0701202i
$804$			461.554i			0.574072i
$805$	1.30977	+	14.5071i	0.00162704	+	0.0180213i
$806$	364.966			0.452811
$807$	365.455	+	97.9233i	0.452856	+	0.121342i
$808$	−186.322	+	49.9248i	−0.230597	+	0.0617882i
$809$	−717.903	−	414.482i	−0.887396	−	0.512338i	−0.0143061	−	0.999898i	$-0.504554\pi$
$809$	−717.903	−	414.482i	−0.887396	−	0.512338i	−0.873090	+	0.487559i	$0.837887\pi$
$810$	63.1374	−	7.97891i	0.0779475	−	0.00985050i
$811$	1182.48			1.45805			0.729024	−	0.684489i	$-0.239974\pi$
$811$	1182.48			1.45805			0.729024	+	0.684489i	$0.239974\pi$
$812$	−182.293	−	343.474i	−0.224499	−	0.422997i
$813$	−36.6762	−	36.6762i	−0.0451122	−	0.0451122i
$814$	468.589	−	270.540i	0.575662	−	0.332359i
$815$	−992.945	+	753.754i	−1.21834	+	0.924852i
$816$	65.2286	−	112.979i	0.0799369	−	0.138455i
$817$	−450.736	−	120.774i	−0.551696	−	0.147826i
$818$	579.934	+	579.934i	0.708965	+	0.708965i
$819$	158.318	−	147.409i	0.193306	−	0.179986i
$820$	176.761	+	433.086i	0.215562	+	0.528153i
$821$	−386.788	−	669.937i	−0.471119	−	0.816002i	0.528335	−	0.849036i	$-0.322816\pi$
$821$	−386.788	−	669.937i	−0.471119	−	0.816002i	−0.999454	+	0.0330341i	$0.989483\pi$
$822$	−59.7053	−	222.823i	−0.0726341	−	0.271074i
$823$	−669.726	+	179.453i	−0.813762	+	0.218047i	−0.641617	−	0.767025i	$-0.721736\pi$
$823$	−669.726	+	179.453i	−0.813762	+	0.218047i	−0.172145	+	0.985072i	$0.555070\pi$
$824$	340.202	−	196.416i	0.412867	−	0.238369i
$825$	310.291	+	3.22247i	0.376110	+	0.00390602i
$826$	−392.740	+	90.3568i	−0.475473	+	0.109391i
$827$	578.176	−	578.176i	0.699124	−	0.699124i	−0.265097	−	0.964222i	$-0.585404\pi$
$827$	578.176	−	578.176i	0.699124	−	0.699124i	0.964222	+	0.265097i	$0.0854041\pi$
$828$	−0.646284	+	2.41196i	−0.000780536	+	0.00291300i
$829$	−291.249	−	168.153i	−0.351326	−	0.202838i	0.313943	−	0.949442i	$-0.398350\pi$
$829$	−291.249	−	168.153i	−0.351326	−	0.202838i	−0.665269	+	0.746604i	$0.731683\pi$
$830$	−77.3972	+	565.196i	−0.0932496	+	0.680959i
$831$	460.940	+	798.372i	0.554681	+	0.960737i
$832$	−58.2706	+	58.2706i	−0.0700368	+	0.0700368i
$833$	697.262	−	604.262i	0.837050	−	0.725405i
$834$		−	225.265i		−	0.270102i
$835$	−1308.45	+	165.354i	−1.56701	+	0.198029i
$836$	−63.3478	+	109.722i	−0.0757748	+	0.131246i
$837$	33.6931	+	125.744i	0.0402545	+	0.150232i
$838$	−170.719	+	637.131i	−0.203722	+	0.760299i
$839$			815.549i			0.972049i	0.873945	+	0.486024i	$0.161553\pi$
$839$			815.549i			0.972049i	−0.873945	+	0.486024i	$0.838447\pi$
$840$	−168.941	−	29.3059i	−0.201121	−	0.0348880i
$841$	69.5456			0.0826939
$842$	−11.7011	−	3.13529i	−0.0138968	−	0.00372362i
$843$	−115.935	+	31.0646i	−0.137526	+	0.0368500i
$844$	507.575	+	293.048i	0.601392	+	0.347214i
$845$	192.723	−	248.479i	0.228074	−	0.294058i
$846$	−136.520			−0.161371
$847$	487.205	+	17.3844i	0.575212	+	0.0205247i
$848$	−201.577	−	201.577i	−0.237708	−	0.237708i
$849$	−525.880	+	303.617i	−0.619411	+	0.357617i
$850$	−644.806	+	165.618i	−0.758596	+	0.194845i
$851$	11.1097	−	19.2425i	0.0130548	−	0.0226116i
$852$	−434.553	−	116.438i	−0.510038	−	0.136664i
$853$	321.111	+	321.111i	0.376449	+	0.376449i	0.869819	−	0.493371i	$-0.164235\pi$
$853$	321.111	+	321.111i	0.376449	+	0.376449i	−0.493371	+	0.869819i	$0.664235\pi$
$854$	62.5346	+	19.1707i	0.0732255	+	0.0224482i
$855$	122.765	−	50.1056i	0.143584	−	0.0586030i
$856$	−60.2685	−	104.388i	−0.0704071	−	0.121949i
$857$	−213.279	−	795.967i	−0.248867	−	0.928782i	−0.971400	−	0.237447i	$-0.923689\pi$
$857$	−213.279	−	795.967i	−0.248867	−	0.928782i	0.722534	−	0.691335i	$-0.242977\pi$
$858$	174.657	−	46.7992i	0.203563	−	0.0545445i
$859$	−82.8602	+	47.8393i	−0.0964612	+	0.0556919i	−0.547455	−	0.836835i	$-0.684403\pi$
$859$	−82.8602	+	47.8393i	−0.0964612	+	0.0556919i	0.450993	+	0.892527i	$0.351070\pi$
$860$	204.542	−	486.645i	0.237840	−	0.565867i
$861$	−166.228	+	542.232i	−0.193064	+	0.629770i
$862$	−140.171	+	140.171i	−0.162612	+	0.162612i
$863$	311.803	−	1163.66i	0.361301	−	1.34839i	−0.511065	−	0.859542i	$-0.670749\pi$
$863$	311.803	−	1163.66i	0.361301	−	1.34839i	0.872367	−	0.488852i	$-0.162584\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$	−558.630	+	424.062i	−0.645815	+	0.490245i
$866$	20.7110	+	35.8725i	0.0239157	+	0.0414232i
$867$	80.2987	−	80.2987i	0.0926168	−	0.0926168i
$868$	12.5073	−	350.521i	0.0144093	−	0.403826i
$869$		−	496.078i		−	0.570860i
$870$	−208.483	+	268.799i	−0.239636	+	0.308964i
$871$	686.241	−	1188.60i	0.787877	−	1.36464i
$872$	−126.542	−	472.263i	−0.145117	−	0.541585i
$873$	−50.5686	+	188.725i	−0.0579251	+	0.216179i
$874$			5.20272i			0.00595277i
$875$	496.410	+	720.557i	0.567325	+	0.823494i
$876$	28.1783			0.0321670
$877$	305.649	+	81.8983i	0.348516	+	0.0933846i	0.428830	−	0.903385i	$-0.358926\pi$
$877$	305.649	+	81.8983i	0.348516	+	0.0933846i	−0.0803144	+	0.996770i	$0.525592\pi$
$878$	413.694	−	110.849i	0.471178	−	0.126252i
$879$	−787.904	−	454.897i	−0.896364	−	0.517516i
$880$	−113.253	−	87.8399i	−0.128696	−	0.0998181i
$881$	−905.723			−1.02806			−0.514031	−	0.857771i	$-0.671849\pi$
$881$	−905.723			−1.02806			−0.514031	+	0.857771i	$0.671849\pi$
$882$	−136.149	−	157.103i	−0.154364	−	0.178122i
$883$	−960.055	−	960.055i	−1.08726	−	1.08726i	−0.995809	−	0.0914558i	$-0.970848\pi$
$883$	−960.055	−	960.055i	−1.08726	−	1.08726i	−0.0914558	−	0.995809i	$-0.529152\pi$
$884$	−335.956	+	193.964i	−0.380041	+	0.219417i
$885$	213.165	+	280.809i	0.240864	+	0.317298i
$886$	−408.169	+	706.970i	−0.460688	+	0.797934i
$887$	−172.348	−	46.1805i	−0.194304	−	0.0520637i	0.160354	−	0.987060i	$-0.448736\pi$
$887$	−172.348	−	46.1805i	−0.194304	−	0.0520637i	−0.354659	+	0.934996i	$0.615403\pi$
$888$	184.946	+	184.946i	0.208273	+	0.208273i
$889$	38.0943	+	165.579i	0.0428507	+	0.186253i
$890$	858.502	+	360.837i	0.964609	+	0.405435i
$891$	32.2481	+	55.8553i	0.0361931	+	0.0626884i
$892$	122.209	+	456.092i	0.137006	+	0.511314i
$893$	−274.753	+	73.6199i	−0.307674	+	0.0824411i
$894$	−112.418	+	64.9044i	−0.125747	+	0.0726000i
$895$	418.407	+	1025.15i	0.467494	+	1.14542i
$896$	53.9675	+	57.9613i	0.0602315	+	0.0646890i
$897$	5.25045	−	5.25045i	0.00585334	−	0.00585334i
$898$	−11.4989	+	42.9145i	−0.0128050	+	0.0477890i
$899$	−602.626	−	347.926i	−0.670329	−	0.387015i
$900$	37.3161	+	145.284i	0.0414624	+	0.161427i
$901$	−670.984	−	1162.18i	−0.744710	−	1.28988i
$902$	−335.215	+	335.215i	−0.371635	+	0.371635i
$903$	565.337	−	300.044i	0.626065	−	0.332274i
$904$		−	11.4993i		−	0.0127205i
$905$	591.082	+	458.449i	0.653129	+	0.506573i
$906$	29.5707	−	51.2180i	0.0326388	−	0.0565320i
$907$	−259.870	−	969.850i	−0.286517	−	1.06929i	−0.947724	−	0.319091i	$-0.896622\pi$
$907$	−259.870	−	969.850i	−0.286517	−	1.06929i	0.661207	−	0.750203i	$-0.270044\pi$
$908$	157.783	−	588.855i	0.173770	−	0.648519i
$909$			204.596i			0.225078i
$910$	391.489	+	326.652i	0.430208	+	0.358958i
$911$	145.014			0.159181			0.0795905	−	0.996828i	$-0.474639\pi$
$911$	145.014			0.159181			0.0795905	+	0.996828i	$0.474639\pi$
$912$	−59.1567	−	15.8510i	−0.0648648	−	0.0173805i
$913$	−558.450	+	149.636i	−0.611664	+	0.163895i
$914$	347.840	+	200.826i	0.380569	+	0.219722i
$915$	−7.17395	−	56.7678i	−0.00784038	−	0.0620413i
$916$	450.166			0.491448
$917$	−888.942	−	31.7192i	−0.969402	−	0.0345902i
$918$	−97.8428	−	97.8428i	−0.106583	−	0.106583i
$919$	−881.023	+	508.659i	−0.958676	+	0.553492i	−0.895765	−	0.444527i	$-0.853372\pi$
$919$	−881.023	+	508.659i	−0.958676	+	0.553492i	−0.0629106	+	0.998019i	$0.520038\pi$
$920$	−5.83118	−	0.798514i	−0.00633824	−	0.000867950i
$921$	93.6560	−	162.217i	0.101689	−	0.176131i
$922$	−11.4498	−	3.06796i	−0.0124184	−	0.00332751i
$923$	945.949	+	945.949i	1.02486	+	1.02486i
$924$	−38.9615	−	169.348i	−0.0421661	−	0.183277i
$925$	13.8609	−	1334.66i	0.0149847	−	1.44288i
$926$	−59.5826	−	103.200i	−0.0643440	−	0.111447i
$927$	−107.840	−	402.464i	−0.116332	−	0.434157i
$928$	151.766	−	40.6655i	0.163541	−	0.0438206i
$929$	181.351	−	104.703i	0.195210	−	0.112705i	−0.399209	−	0.916860i	$-0.630715\pi$
$929$	181.351	−	104.703i	0.195210	−	0.112705i	0.594419	+	0.804155i	$0.297382\pi$
$930$	−284.086	+	115.948i	−0.305469	+	0.124675i
$931$	−358.727	−	242.759i	−0.385313	−	0.260751i
$932$	−143.330	+	143.330i	−0.153788	+	0.153788i
$933$	93.8809	−	350.368i	0.100623	−	0.375529i
$934$	−600.690	−	346.809i	−0.643137	−	0.371316i
$935$	−407.945	−	537.398i	−0.436304	−	0.574758i
$936$	43.7030	+	75.6958i	0.0466912	+	0.0808716i
$937$	−727.770	+	727.770i	−0.776702	+	0.776702i	−0.979269	−	0.202566i	$-0.935072\pi$
$937$	−727.770	+	727.770i	−0.776702	+	0.776702i	0.202566	+	0.979269i	$0.435072\pi$
$938$	−1118.04	−	699.814i	−1.19194	−	0.746071i
$939$			510.996i			0.544192i
$940$	−40.3436	−	319.241i	−0.0429188	−	0.339618i
$941$	−373.861	+	647.547i	−0.397302	+	0.688147i	−0.993392	−	0.114770i	$-0.963387\pi$
$941$	−373.861	+	647.547i	−0.397302	+	0.688147i	0.596090	+	0.802918i	$0.296720\pi$
$942$	−110.952	−	414.079i	−0.117784	−	0.439574i
$943$	−5.03852	+	18.8040i	−0.00534308	+	0.0199406i
$944$		−	162.837i		−	0.172497i
$945$	−76.4021	+	165.039i	−0.0808488	+	0.174644i
$946$	534.989			0.565527
$947$	−187.521	−	50.2461i	−0.198016	−	0.0530581i	0.158448	−	0.987367i	$-0.449351\pi$
$947$	−187.521	−	50.2461i	−0.198016	−	0.0530581i	−0.356464	+	0.934309i	$0.616018\pi$
$948$	231.629	−	62.0647i	0.244334	−	0.0654691i
$949$	−72.5653	−	41.8956i	−0.0764650	−	0.0441471i
$950$	153.447	+	272.269i	0.161523	+	0.286599i
$951$	−1080.23			−1.13589
$952$	174.774	+	329.307i	0.183587	+	0.345910i
$953$	292.564	+	292.564i	0.306993	+	0.306993i	0.843742	−	0.536749i	$-0.180348\pi$
$953$	292.564	+	292.564i	0.306993	+	0.306993i	−0.536749	+	0.843742i	$0.680348\pi$
$954$	−261.856	+	151.182i	−0.274482	+	0.158472i
$955$	193.863	−	1415.69i	0.202998	−	1.48240i
$956$	191.422	−	331.552i	0.200232	−	0.346812i
$957$	−333.005	−	89.2285i	−0.347968	−	0.0932377i
$958$	456.410	+	456.410i	0.476419	+	0.476419i
$959$	630.281	+	193.220i	0.657227	+	0.201481i
$960$	26.8451	−	63.8697i	0.0279636	−	0.0665310i
$961$	166.670	+	288.681i	0.173434	+	0.300396i
$962$	−201.299	−	751.257i	−0.209250	−	0.780932i
$963$	−123.492	+	33.0897i	−0.128237	+	0.0343611i
$964$	−465.056	+	268.500i	−0.482423	+	0.278527i
$965$	1089.64	+	457.985i	1.12916	+	0.474595i
$966$	−4.86271	−	5.22257i	−0.00503386	−	0.00540639i
$967$	648.542	−	648.542i	0.670674	−	0.670674i	−0.287197	−	0.957871i	$-0.592724\pi$
$967$	648.542	−	648.542i	0.670674	−	0.670674i	0.957871	+	0.287197i	$0.0927236\pi$
$968$	−50.9836	+	190.274i	−0.0526691	+	0.196564i
$969$	−249.677	−	144.151i	−0.257664	−	0.148763i
$970$	−456.262	−	62.4799i	−0.470373	−	0.0644123i
$971$	35.0337	+	60.6802i	0.0360800	+	0.0624924i	0.883502	−	0.468428i	$-0.155180\pi$
$971$	35.0337	+	60.6802i	0.0360800	+	0.0624924i	−0.847422	+	0.530921i	$0.821846\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	545.670	+	341.550i	0.560812	+	0.351027i
$974$		−	1.04309i		−	0.00107094i
$975$	119.912	−	429.621i	0.122987	−	0.440637i
$976$	−13.2142	+	22.8877i	−0.0135392	+	0.0234505i
$977$	−53.7837	−	200.723i	−0.0550498	−	0.205449i	0.932923	−	0.360076i	$-0.117249\pi$
$977$	−53.7837	−	200.723i	−0.0550498	−	0.205449i	−0.987973	+	0.154627i	$0.950582\pi$
$978$	158.066	−	589.911i	0.161622	−	0.603181i
$979$			943.786i			0.964031i
$980$	327.140	−	364.800i	0.333816	−	0.372245i
$981$	−518.580			−0.528624
$982$	458.107	+	122.750i	0.466504	+	0.125000i
$983$	910.404	−	243.942i	0.926149	−	0.248161i	0.235937	−	0.971768i	$-0.424184\pi$
$983$	910.404	−	243.942i	0.926149	−	0.248161i	0.690212	+	0.723607i	$0.257517\pi$
$984$	−198.457	−	114.579i	−0.201684	−	0.116443i
$985$	−505.877	+	63.9295i	−0.513581	+	0.0649030i
$986$	739.635			0.750137
$987$	206.993	−	330.698i	0.209719	−	0.335054i
$988$	128.774	+	128.774i	0.130338	+	0.130338i
$989$	19.0259	−	10.9846i	0.0192375	−	0.0111068i
$990$	−121.084	+	91.9158i	−0.122307	+	0.0928443i
$991$	333.587	−	577.790i	0.336617	−	0.583038i	−0.647177	−	0.762340i	$-0.724051\pi$
$991$	333.587	−	577.790i	0.336617	−	0.583038i	0.983794	+	0.179302i	$0.0573839\pi$
$992$	136.893	+	36.6803i	0.137997	+	0.0369762i
$993$	−194.612	−	194.612i	−0.195984	−	0.195984i
$994$	940.928	−	876.093i	0.946607	−	0.881381i
$995$	−541.873	−	1327.65i	−0.544596	−	1.33433i
$996$	−139.736	−	242.030i	−0.140297	−	0.243002i
$997$	72.8859	+	272.014i	0.0731052	+	0.272832i	0.992797	−	0.119809i	$-0.0382281\pi$
$997$	72.8859	+	272.014i	0.0731052	+	0.272832i	−0.919692	+	0.392641i	$0.871561\pi$
$998$	−836.947	+	224.259i	−0.838624	+	0.224709i
$999$	240.252	−	138.710i	0.240493	−	0.138849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.v.b.193.4	yes	32
5.2	odd	4	inner	210.3.v.b.67.7	yes	32
7.2	even	3	inner	210.3.v.b.163.7	yes	32
35.2	odd	12	inner	210.3.v.b.37.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.v.b.37.4	✓	32	35.2	odd	12	inner
210.3.v.b.67.7	yes	32	5.2	odd	4	inner
210.3.v.b.163.7	yes	32	7.2	even	3	inner
210.3.v.b.193.4	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(3.95091 + 3.06436i) q^{5} -2.44949 q^{6} +(3.71395 - 5.93351i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(1.73205 + 1.00000i) q^{4} +(3.95091 + 3.06436i) q^{5} -2.44949 q^{6} +(3.71395 - 5.93351i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(4.27541 + 5.63213i) q^{10} +(-3.58312 + 6.20615i) q^{11} +(-3.34607 - 0.896575i) q^{12} +(7.28383 + 7.28383i) q^{13} +(7.24516 - 6.74593i) q^{14} +(-7.98372 - 3.35564i) q^{15} +(2.00000 + 3.46410i) q^{16} +(4.87353 + 18.1882i) q^{17} +(4.09808 - 1.09808i) q^{18} +(7.65544 - 4.41987i) q^{19} +(3.77881 + 9.25854i) q^{20} +(-3.55363 + 11.5919i) q^{21} +(-7.16624 + 7.16624i) q^{22} +(-0.107714 + 0.401994i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(6.21935 + 24.2140i) q^{25} +(7.28383 + 12.6160i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(12.3663 - 6.56320i) q^{28} -27.7751i q^{29} +(-9.67771 - 7.50613i) q^{30} +(12.5266 - 21.6967i) q^{31} +(1.46410 + 5.46410i) q^{32} +(3.21254 - 11.9894i) q^{33} +26.6294i q^{34} +(32.8559 - 12.0619i) q^{35} +6.00000 q^{36} +(-51.5702 - 13.8182i) q^{37} +(12.0753 - 3.23557i) q^{38} +(-15.4513 - 8.92083i) q^{39} +(1.77309 + 14.0305i) q^{40} +46.7769 q^{41} +(-9.09728 + 14.5341i) q^{42} +(-37.3270 - 37.3270i) q^{43} +(-12.4123 + 7.16624i) q^{44} +(14.8613 + 2.03509i) q^{45} +(-0.294280 + 0.509708i) q^{46} +(-31.0816 - 8.32828i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(-21.4132 - 44.0735i) q^{49} +(-0.367156 + 35.3534i) q^{50} +(-16.3071 - 28.2448i) q^{51} +(5.33213 + 19.8998i) q^{52} +(-68.8397 + 18.4455i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-33.1745 + 13.5399i) q^{55} +(19.2949 - 4.43914i) q^{56} +(-10.8264 + 10.8264i) q^{57} +(10.1664 - 37.9414i) q^{58} +(-35.2552 - 20.3546i) q^{59} +(-10.4726 - 13.7958i) q^{60} +(3.30356 + 5.72193i) q^{61} +(25.0531 - 25.0531i) q^{62} +(0.748846 - 20.9866i) q^{63} +8.00000i q^{64} +(6.45744 + 51.0980i) q^{65} +(8.77682 - 15.2019i) q^{66} +(-34.4848 - 128.699i) q^{67} +(-9.74705 + 36.3765i) q^{68} -0.720836i q^{69} +(49.2970 - 4.45075i) q^{70} +129.870 q^{71} +(8.19615 + 2.19615i) q^{72} +(-7.85719 + 2.10533i) q^{73} +(-65.3884 - 37.7520i) q^{74} +(-21.2600 - 37.7228i) q^{75} +17.6795 q^{76} +(23.5168 + 44.3098i) q^{77} +(-17.8417 - 17.8417i) q^{78} +(-59.9499 + 34.6121i) q^{79} +(-2.71345 + 19.8151i) q^{80} +(4.50000 - 7.79423i) q^{81} +(63.8984 + 17.1215i) q^{82} +(57.0471 + 57.0471i) q^{83} +(-17.7470 + 16.5241i) q^{84} +(-36.4805 + 86.7944i) q^{85} +(-37.3270 - 64.6523i) q^{86} +(12.4512 + 46.4686i) q^{87} +(-19.5785 + 5.24605i) q^{88} +(114.055 - 65.8494i) q^{89} +(19.5560 + 8.21960i) q^{90} +(70.2705 - 16.1670i) q^{91} +(-0.588560 + 0.588560i) q^{92} +(-11.2310 + 41.9147i) q^{93} +(-39.4099 - 22.7533i) q^{94} +(43.7901 + 5.99655i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(-46.0520 + 46.0520i) q^{97} +(-13.1189 - 68.0433i) q^{98} +21.4987i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

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