LMFDB - Embedded newform 45.3.k.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(7,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("45.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.k (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:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	45.13
Dual form			45.3.k.a.7.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84813 + 0.495206i) q^{2} +(2.82294 + 1.01538i) q^{3} +(-0.293735 - 0.169588i) q^{4} +(-4.92689 - 0.851907i) q^{5} +(4.71435 + 3.27449i) q^{6} +(-3.01652 - 0.808273i) q^{7} +(-5.87059 - 5.87059i) q^{8} +(6.93801 + 5.73271i) q^{9} +O(q^{10})$	\(q+(1.84813 + 0.495206i) q^{2} +(2.82294 + 1.01538i) q^{3} +(-0.293735 - 0.169588i) q^{4} +(-4.92689 - 0.851907i) q^{5} +(4.71435 + 3.27449i) q^{6} +(-3.01652 - 0.808273i) q^{7} +(-5.87059 - 5.87059i) q^{8} +(6.93801 + 5.73271i) q^{9} +(-8.68368 - 4.01426i) q^{10} +(3.31892 + 5.74855i) q^{11} +(-0.657001 - 0.776989i) q^{12} +(17.0268 - 4.56232i) q^{13} +(-5.17466 - 2.98759i) q^{14} +(-13.0433 - 7.40754i) q^{15} +(-7.26413 - 12.5818i) q^{16} +(-19.7493 + 19.7493i) q^{17} +(9.98350 + 14.0306i) q^{18} -16.1463i q^{19} +(1.30273 + 1.08578i) q^{20} +(-7.69475 - 5.34462i) q^{21} +(3.28710 + 12.2676i) q^{22} +(-5.05098 + 1.35341i) q^{23} +(-10.6115 - 22.5332i) q^{24} +(23.5485 + 8.39451i) q^{25} +33.7271 q^{26} +(13.7647 + 23.2278i) q^{27} +(0.748983 + 0.748983i) q^{28} +(3.51558 - 2.02972i) q^{29} +(-20.4375 - 20.1493i) q^{30} +(2.76468 - 4.78857i) q^{31} +(1.40066 + 5.22734i) q^{32} +(3.53219 + 19.5978i) q^{33} +(-46.2792 + 26.7193i) q^{34} +(14.1735 + 6.55207i) q^{35} +(-1.06574 - 2.86050i) q^{36} +(19.9941 - 19.9941i) q^{37} +(7.99576 - 29.8406i) q^{38} +(52.6983 + 4.40949i) q^{39} +(23.9226 + 33.9249i) q^{40} +(22.6986 - 39.3151i) q^{41} +(-11.5742 - 13.6880i) q^{42} +(-20.8248 + 77.7192i) q^{43} -2.25140i q^{44} +(-29.2991 - 34.1550i) q^{45} -10.0051 q^{46} +(-13.6796 - 3.66543i) q^{47} +(-7.73089 - 42.8937i) q^{48} +(-33.9892 - 19.6237i) q^{49} +(39.3638 + 27.1755i) q^{50} +(-75.8041 + 35.6981i) q^{51} +(-5.77509 - 1.54743i) q^{52} +(-49.3170 - 49.3170i) q^{53} +(13.9365 + 49.7445i) q^{54} +(-11.4548 - 31.1499i) q^{55} +(12.9637 + 22.4538i) q^{56} +(16.3946 - 45.5802i) q^{57} +(7.50240 - 2.01026i) q^{58} +(4.60398 + 2.65811i) q^{59} +(2.57505 + 4.38784i) q^{60} +(-24.9404 - 43.1981i) q^{61} +(7.48083 - 7.48083i) q^{62} +(-16.2950 - 22.9006i) q^{63} +68.4675i q^{64} +(-87.7760 + 7.97280i) q^{65} +(-3.17698 + 37.9685i) q^{66} +(7.28994 + 27.2064i) q^{67} +(9.15029 - 2.45181i) q^{68} +(-15.6328 - 1.30807i) q^{69} +(22.9498 + 19.1279i) q^{70} +55.3458 q^{71} +(-7.07584 - 74.3846i) q^{72} +(-21.2670 - 21.2670i) q^{73} +(46.8529 - 27.0505i) q^{74} +(57.9525 + 47.6079i) q^{75} +(-2.73822 + 4.74274i) q^{76} +(-5.36520 - 20.0232i) q^{77} +(95.2098 + 34.2458i) q^{78} +(101.867 - 58.8128i) q^{79} +(25.0710 + 68.1777i) q^{80} +(15.2721 + 79.5472i) q^{81} +(61.4190 - 61.4190i) q^{82} +(-23.4922 + 87.6742i) q^{83} +(1.35383 + 2.87484i) q^{84} +(114.127 - 80.4780i) q^{85} +(-76.9740 + 133.323i) q^{86} +(11.9852 - 2.16015i) q^{87} +(14.2633 - 53.2314i) q^{88} -34.2372i q^{89} +(-37.2349 - 77.6320i) q^{90} -55.0493 q^{91} +(1.71317 + 0.459043i) q^{92} +(12.6668 - 10.7107i) q^{93} +(-23.4666 - 13.5484i) q^{94} +(-13.7552 + 79.5513i) q^{95} +(-1.35374 + 16.1787i) q^{96} +(-17.0629 - 4.57199i) q^{97} +(-53.0988 - 53.0988i) q^{98} +(-9.92800 + 58.9099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8}+O(q^{10}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23} - 8 q^{25} - 112 q^{26} - 198 q^{27} - 88 q^{28} + 162 q^{30} - 4 q^{31} - 14 q^{32} + 96 q^{33} + 352 q^{35} + 264 q^{36} - 92 q^{37} + 330 q^{38} + 30 q^{40} - 28 q^{41} + 498 q^{42} - 2 q^{43} - 72 q^{45} - 136 q^{46} + 64 q^{47} - 510 q^{48} - 458 q^{50} - 396 q^{51} - 74 q^{52} - 608 q^{53} + 224 q^{55} - 192 q^{56} - 114 q^{57} + 30 q^{58} - 798 q^{60} + 92 q^{61} - 100 q^{62} + 24 q^{63} - 326 q^{65} + 588 q^{66} - 80 q^{67} + 626 q^{68} - 102 q^{70} + 248 q^{71} - 162 q^{72} - 8 q^{73} + 810 q^{75} - 96 q^{76} + 338 q^{77} + 1062 q^{78} + 1444 q^{80} + 204 q^{81} + 104 q^{82} + 370 q^{83} - 98 q^{85} - 328 q^{86} + 534 q^{87} - 210 q^{88} + 462 q^{90} + 152 q^{91} + 388 q^{92} - 1062 q^{93} - 360 q^{95} - 876 q^{96} + 292 q^{97} - 1876 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.84813	+	0.495206i	0.924066	+	0.247603i	0.689323	−	0.724454i	$-0.257908\pi$
$2$	1.84813	+	0.495206i	0.924066	+	0.247603i	0.234744	+	0.972057i	$0.424575\pi$
$3$	2.82294	+	1.01538i	0.940981	+	0.338459i
$3$	2.82294	+	1.01538i	0.940981	+	0.338459i
$4$	−0.293735	−	0.169588i	−0.0734337	−	0.0423970i
$5$	−4.92689	−	0.851907i	−0.985378	−	0.170381i
$5$	−4.92689	−	0.851907i	−0.985378	−	0.170381i
$6$	4.71435	+	3.27449i	0.785725	+	0.545749i
$7$	−3.01652	−	0.808273i	−0.430931	−	0.115468i	0.0368322	−	0.999321i	$-0.488273\pi$
$7$	−3.01652	−	0.808273i	−0.430931	−	0.115468i	−0.467763	+	0.883854i	$0.654940\pi$
$8$	−5.87059	−	5.87059i	−0.733824	−	0.733824i
$9$	6.93801	+	5.73271i	0.770890	+	0.636968i
$10$	−8.68368	−	4.01426i	−0.868368	−	0.401426i
$11$	3.31892	+	5.74855i	0.301720	+	0.522595i	0.976526	−	0.215401i	$-0.0691058\pi$
$11$	3.31892	+	5.74855i	0.301720	+	0.522595i	−0.674805	+	0.737996i	$0.735772\pi$
$12$	−0.657001	−	0.776989i	−0.0547501	−	0.0647491i
$13$	17.0268	−	4.56232i	1.30976	−	0.350948i	0.464625	−	0.885507i	$-0.346189\pi$
$13$	17.0268	−	4.56232i	1.30976	−	0.350948i	0.845131	+	0.534559i	$0.179522\pi$
$14$	−5.17466	−	2.98759i	−0.369619	−	0.213399i
$15$	−13.0433	−	7.40754i	−0.869555	−	0.493836i
$16$	−7.26413	−	12.5818i	−0.454008	−	0.786365i
$17$	−19.7493	+	19.7493i	−1.16172	+	1.16172i	−0.177623	+	0.984099i	$0.556841\pi$
$17$	−19.7493	+	19.7493i	−1.16172	+	1.16172i	−0.984099	+	0.177623i	$0.943159\pi$
$18$	9.98350	+	14.0306i	0.554639	+	0.779475i
$19$		−	16.1463i		−	0.849808i	−0.905238	−	0.424904i	$-0.860308\pi$
$19$		−	16.1463i		−	0.849808i	0.905238	−	0.424904i	$-0.139692\pi$
$20$	1.30273	+	1.08578i	0.0651363	+	0.0542888i
$21$	−7.69475	−	5.34462i	−0.366417	−	0.254505i
$22$	3.28710	+	12.2676i	0.149414	+	0.557619i
$23$	−5.05098	+	1.35341i	−0.219608	+	0.0588437i	−0.366945	−	0.930243i	$-0.619596\pi$
$23$	−5.05098	+	1.35341i	−0.219608	+	0.0588437i	0.147337	+	0.989086i	$0.452930\pi$
$24$	−10.6115	−	22.5332i	−0.442145	−	0.938884i
$25$	23.5485	+	8.39451i	0.941940	+	0.335780i
$26$	33.7271			1.29720
$27$	13.7647	+	23.2278i	0.509805	+	0.860290i
$28$	0.748983	+	0.748983i	0.0267494	+	0.0267494i
$29$	3.51558	−	2.02972i	0.121227	−	0.0699905i	−0.438160	−	0.898897i	$-0.644370\pi$
$29$	3.51558	−	2.02972i	0.121227	−	0.0699905i	0.559387	+	0.828906i	$0.311036\pi$
$30$	−20.4375	−	20.1493i	−0.681251	−	0.671642i
$31$	2.76468	−	4.78857i	0.0891833	−	0.154470i	−0.817983	−	0.575243i	$-0.804908\pi$
$31$	2.76468	−	4.78857i	0.0891833	−	0.154470i	0.907166	+	0.420773i	$0.138241\pi$
$32$	1.40066	+	5.22734i	0.0437707	+	0.163355i
$33$	3.53219	+	19.5978i	0.107036	+	0.593872i
$34$	−46.2792	+	26.7193i	−1.36115	+	0.785863i
$35$	14.1735	+	6.55207i	0.404956	+	0.187202i
$36$	−1.06574	−	2.86050i	−0.0296038	−	0.0794583i
$37$	19.9941	−	19.9941i	0.540380	−	0.540380i	−0.383260	−	0.923640i	$-0.625199\pi$
$37$	19.9941	−	19.9941i	0.540380	−	0.540380i	0.923640	+	0.383260i	$0.125199\pi$
$38$	7.99576	−	29.8406i	0.210415	−	0.785279i
$39$	52.6983	+	4.40949i	1.35124	+	0.113064i
$40$	23.9226	+	33.9249i	0.598064	+	0.848124i
$41$	22.6986	−	39.3151i	0.553624	−	0.958904i	−0.444385	−	0.895836i	$-0.646578\pi$
$41$	22.6986	−	39.3151i	0.553624	−	0.958904i	0.998009	−	0.0630688i	$-0.0200887\pi$
$42$	−11.5742	−	13.6880i	−0.275577	−	0.325906i
$43$	−20.8248	+	77.7192i	−0.484298	+	1.80742i	0.0989041	+	0.995097i	$0.468466\pi$
$43$	−20.8248	+	77.7192i	−0.484298	+	1.80742i	−0.583202	+	0.812327i	$0.698200\pi$
$44$		−	2.25140i		−	0.0511681i
$45$	−29.2991	−	34.1550i	−0.651091	−	0.759000i
$46$	−10.0051			−0.217502
$47$	−13.6796	−	3.66543i	−0.291055	−	0.0779880i	0.110337	−	0.993894i	$-0.464807\pi$
$47$	−13.6796	−	3.66543i	−0.291055	−	0.0779880i	−0.401392	+	0.915906i	$0.631474\pi$
$48$	−7.73089	−	42.8937i	−0.161060	−	0.893618i
$49$	−33.9892	−	19.6237i	−0.693657	−	0.400483i
$50$	39.3638	+	27.1755i	0.787275	+	0.543510i
$51$	−75.8041	+	35.6981i	−1.48635	+	0.699962i
$52$	−5.77509	−	1.54743i	−0.111059	−	0.0297583i
$53$	−49.3170	−	49.3170i	−0.930509	−	0.930509i	0.0672288	−	0.997738i	$-0.478584\pi$
$53$	−49.3170	−	49.3170i	−0.930509	−	0.930509i	−0.997738	+	0.0672288i	$0.978584\pi$
$54$	13.9365	+	49.7445i	0.258084	+	0.921194i
$55$	−11.4548	−	31.1499i	−0.208268	−	0.566361i
$56$	12.9637	+	22.4538i	0.231494	+	0.400960i
$57$	16.3946	−	45.5802i	0.287625	−	0.799653i
$58$	7.50240	−	2.01026i	0.129352	−	0.0346597i
$59$	4.60398	+	2.65811i	0.0780335	+	0.0450527i	0.538509	−	0.842620i	$-0.318988\pi$
$59$	4.60398	+	2.65811i	0.0780335	+	0.0450527i	−0.460476	+	0.887672i	$0.652321\pi$
$60$	2.57505	+	4.38784i	0.0429175	+	0.0731307i
$61$	−24.9404	−	43.1981i	−0.408860	−	0.708166i	0.585902	−	0.810382i	$-0.300740\pi$
$61$	−24.9404	−	43.1981i	−0.408860	−	0.708166i	−0.994762	+	0.102216i	$0.967407\pi$
$62$	7.48083	−	7.48083i	0.120659	−	0.120659i
$63$	−16.2950	−	22.9006i	−0.258651	−	0.363502i
$64$			68.4675i			1.06980i
$65$	−87.7760	+	7.97280i	−1.35040	+	0.122659i
$66$	−3.17698	+	37.9685i	−0.0481361	+	0.575280i
$67$	7.28994	+	27.2064i	0.108805	+	0.406066i	0.998749	−	0.0500038i	$-0.0159233\pi$
$67$	7.28994	+	27.2064i	0.108805	+	0.406066i	−0.889944	+	0.456070i	$0.849257\pi$
$68$	9.15029	−	2.45181i	0.134563	−	0.0360561i
$69$	−15.6328	−	1.30807i	−0.226563	−	0.0189575i
$70$	22.9498	+	19.1279i	0.327855	+	0.273255i
$71$	55.3458			0.779519			0.389759	−	0.920917i	$-0.372558\pi$
$71$	55.3458			0.779519			0.389759	+	0.920917i	$0.372558\pi$
$72$	−7.07584	−	74.3846i	−0.0982756	−	1.03312i
$73$	−21.2670	−	21.2670i	−0.291329	−	0.291329i	0.546276	−	0.837605i	$-0.316045\pi$
$73$	−21.2670	−	21.2670i	−0.291329	−	0.291329i	−0.837605	+	0.546276i	$0.816045\pi$
$74$	46.8529	−	27.0505i	0.633147	−	0.365547i
$75$	57.9525	+	47.6079i	0.772700	+	0.634771i
$76$	−2.73822	+	4.74274i	−0.0360293	+	0.0624045i
$77$	−5.36520	−	20.0232i	−0.0696779	−	0.260041i
$78$	95.2098	+	34.2458i	1.22064	+	0.439049i
$79$	101.867	−	58.8128i	1.28945	−	0.744465i	0.310896	−	0.950444i	$-0.399371\pi$
$79$	101.867	−	58.8128i	1.28945	−	0.744465i	0.978556	+	0.205979i	$0.0660377\pi$
$80$	25.0710	+	68.1777i	0.313388	+	0.852221i
$81$	15.2721	+	79.5472i	0.188544	+	0.982065i
$82$	61.4190	−	61.4190i	0.749013	−	0.749013i
$83$	−23.4922	+	87.6742i	−0.283039	+	1.05632i	0.667222	+	0.744859i	$0.267483\pi$
$83$	−23.4922	+	87.6742i	−0.283039	+	1.05632i	−0.950261	+	0.311456i	$0.899183\pi$
$84$	1.35383	+	2.87484i	0.0161171	+	0.0342242i
$85$	114.127	−	80.4780i	1.34267	−	0.946800i
$86$	−76.9740	+	133.323i	−0.895047	+	1.55027i
$87$	11.9852	−	2.16015i	0.137761	−	0.0248293i
$88$	14.2633	−	53.2314i	0.162083	−	0.604902i
$89$		−	34.2372i		−	0.384687i	−0.981328	−	0.192344i	$-0.938391\pi$
$89$		−	34.2372i		−	0.384687i	0.981328	−	0.192344i	$-0.0616088\pi$
$90$	−37.2349	−	77.6320i	−0.413721	−	0.862578i
$91$	−55.0493			−0.604938
$92$	1.71317	+	0.459043i	0.0186214	+	0.00498959i
$93$	12.6668	−	10.7107i	0.136202	−	0.115168i
$94$	−23.4666	−	13.5484i	−0.249644	−	0.144132i
$95$	−13.7552	+	79.5513i	−0.144791	+	0.837382i
$96$	−1.35374	+	16.1787i	−0.0141015	+	0.168528i
$97$	−17.0629	−	4.57199i	−0.175906	−	0.0471339i	0.169791	−	0.985480i	$-0.445691\pi$
$97$	−17.0629	−	4.57199i	−0.175906	−	0.0471339i	−0.345697	+	0.938346i	$0.612357\pi$
$98$	−53.0988	−	53.0988i	−0.541824	−	0.541824i
$99$	−9.92800	+	58.9099i	−0.100283	+	0.595050i
$100$	−5.49341	−	6.45930i	−0.0549341	−	0.0645930i
$101$	−26.8252	−	46.4626i	−0.265596	−	0.460025i	0.702124	−	0.712055i	$-0.252235\pi$
$101$	−26.8252	−	46.4626i	−0.265596	−	0.460025i	−0.967720	+	0.252030i	$0.918902\pi$
$102$	−157.774	+	28.4362i	−1.54680	+	0.278786i
$103$	−133.385	+	35.7403i	−1.29500	+	0.346993i	−0.839556	−	0.543274i	$-0.817185\pi$
$103$	−133.385	+	35.7403i	−1.29500	+	0.346993i	−0.455440	+	0.890267i	$0.650518\pi$
$104$	−126.741	−	73.1740i	−1.21866	−	0.703596i
$105$	33.3581	+	32.8875i	0.317696	+	0.313215i
$106$	−66.7223	−	115.566i	−0.629455	−	1.09025i
$107$	−15.5982	+	15.5982i	−0.145777	+	0.145777i	−0.776229	−	0.630451i	$-0.782870\pi$
$107$	−15.5982	+	15.5982i	−0.145777	+	0.145777i	0.630451	+	0.776229i	$0.282870\pi$
$108$	−0.104029	−	9.15715i	−0.000963227	−	0.0847885i
$109$			132.500i			1.21560i	0.794092	+	0.607798i	$0.207947\pi$
$109$			132.500i			1.21560i	−0.794092	+	0.607798i	$0.792053\pi$
$110$	−5.74431	−	63.2416i	−0.0522210	−	0.574923i
$111$	76.7436	−	36.1406i	0.691384	−	0.325591i
$112$	11.7428	+	43.8247i	0.104846	+	0.391292i
$113$	70.0870	−	18.7798i	0.620239	−	0.166192i	0.0650025	−	0.997885i	$-0.479294\pi$
$113$	70.0870	−	18.7798i	0.620239	−	0.166192i	0.555236	+	0.831693i	$0.312628\pi$
$114$	52.8711	−	76.1196i	0.463781	−	0.667716i
$115$	26.0386	−	2.36512i	0.226423	−	0.0205662i
$116$	−1.37687			−0.0118695
$117$	144.287	+	65.9564i	1.23322	+	0.563730i
$118$	7.19245	+	7.19245i	0.0609530	+	0.0609530i
$119$	75.5368	−	43.6112i	0.634763	−	0.366481i
$120$	33.0854	+	120.059i	0.275711	+	1.00049i
$121$	38.4695	−	66.6311i	0.317930	−	0.550670i
$122$	−24.7013	−	92.1865i	−0.202470	−	0.755627i
$123$	103.996	−	87.9366i	0.845500	−	0.714932i
$124$	−1.62417	+	0.937714i	−0.0130981	+	0.00756221i
$125$	−108.870	−	61.4200i	−0.870957	−	0.491360i
$126$	−18.7749	−	50.3928i	−0.149007	−	0.399943i
$127$	−122.969	+	122.969i	−0.968263	+	0.968263i	−0.999512	−	0.0312482i	$-0.990052\pi$
$127$	−122.969	+	122.969i	−0.968263	+	0.968263i	0.0312482	+	0.999512i	$0.490052\pi$
$128$	−28.3028	+	105.628i	−0.221116	+	0.825216i
$129$	−137.702	+	198.252i	−1.06745	+	1.53684i
$130$	−166.170	−	28.7324i	−1.27823	−	0.221018i
$131$	61.3445	−	106.252i	0.468278	−	0.811082i	−0.531064	−	0.847332i	$-0.678208\pi$
$131$	61.3445	−	106.252i	0.468278	−	0.811082i	0.999343	+	0.0362495i	$0.0115411\pi$
$132$	2.28602	−	6.35557i	0.0173183	−	0.0481482i
$133$	−13.0507	+	48.7057i	−0.0981253	+	0.366208i
$134$			53.8911i			0.402173i
$135$	−48.0295	−	126.167i	−0.355774	−	0.934572i
$136$	231.880			1.70500
$137$	221.466	+	59.3417i	1.61654	+	0.433151i	0.949983	−	0.312302i	$-0.101100\pi$
$137$	221.466	+	59.3417i	1.61654	+	0.433151i	0.666558	+	0.745453i	$0.267767\pi$
$138$	−28.2438	−	10.1590i	−0.204665	−	0.0736156i
$139$	−73.4301	−	42.3949i	−0.528274	−	0.304999i	0.212039	−	0.977261i	$-0.431990\pi$
$139$	−73.4301	−	42.3949i	−0.528274	−	0.304999i	−0.740313	+	0.672262i	$0.765323\pi$
$140$	−3.05209	−	4.32822i	−0.0218007	−	0.0309159i
$141$	−34.8949	−	24.2373i	−0.247482	−	0.171896i
$142$	102.286	+	27.4076i	0.720327	+	0.193011i
$143$	82.7375	+	82.7375i	0.578584	+	0.578584i
$144$	21.7294	−	128.936i	0.150899	−	0.895390i
$145$	−19.0500	+	7.00527i	−0.131380	+	0.0483122i
$146$	−28.7727	−	49.8359i	−0.197074	−	0.341342i
$147$	−76.0241	−	89.9083i	−0.517171	−	0.611621i
$148$	−9.26370	+	2.48220i	−0.0625926	+	0.0167716i
$149$	12.5553	+	7.24882i	0.0842639	+	0.0486498i	0.541540	−	0.840675i	$-0.317842\pi$
$149$	12.5553	+	7.24882i	0.0842639	+	0.0486498i	−0.457276	+	0.889325i	$0.651175\pi$
$150$	83.5282	+	116.684i	0.556855	+	0.777894i
$151$	103.595	+	179.432i	0.686060	+	1.18829i	0.973103	+	0.230372i	$0.0739944\pi$
$151$	103.595	+	179.432i	0.686060	+	1.18829i	−0.287043	+	0.957918i	$0.592672\pi$
$152$	−94.7886	+	94.7886i	−0.623609	+	0.623609i
$153$	−250.238	+	23.8039i	−1.63554	+	0.155581i
$154$		−	39.6624i		−	0.257548i
$155$	−17.7007	+	21.2375i	−0.114198	+	0.137016i
$156$	−14.7315	−	10.2322i	−0.0944328	−	0.0655911i
$157$	4.35418	+	16.2500i	0.0277336	+	0.103503i	0.978405	−	0.206696i	$-0.0662710\pi$
$157$	4.35418	+	16.2500i	0.0277336	+	0.103503i	−0.950672	+	0.310199i	$0.899604\pi$
$158$	217.388	−	58.2488i	1.37587	−	0.368664i
$159$	−89.1436	−	189.294i	−0.560652	−	1.19053i
$160$	−2.44770	−	26.9478i	−0.0152981	−	0.168424i
$161$	16.3303			0.101430
$162$	−11.1674	+	154.577i	−0.0689348	+	0.954177i
$163$	105.806	+	105.806i	0.649119	+	0.649119i	0.952780	−	0.303661i	$-0.0982090\pi$
$163$	105.806	+	105.806i	0.649119	+	0.649119i	−0.303661	+	0.952780i	$0.598209\pi$
$164$	−13.3347	+	7.69881i	−0.0813093	+	0.0469439i
$165$	−0.707206	−	99.5652i	−0.00428610	−	0.603426i
$166$	−86.8335	+	150.400i	−0.523093	+	0.906024i
$167$	4.31257	+	16.0947i	0.0258238	+	0.0963756i	0.977635	−	0.210309i	$-0.0674470\pi$
$167$	4.31257	+	16.0947i	0.0258238	+	0.0963756i	−0.951811	+	0.306685i	$0.900780\pi$
$168$	13.7967	+	76.5488i	0.0821231	+	0.455647i
$169$	122.740	−	70.8638i	0.726271	−	0.419313i
$170$	250.775	−	92.2176i	1.47515	−	0.542457i
$171$	92.5623	−	112.024i	0.541300	−	0.655109i
$172$	19.2972	−	19.2972i	0.112193	−	0.112193i
$173$	10.2835	−	38.3785i	0.0594422	−	0.221841i	−0.929815	−	0.368027i	$-0.880033\pi$
$173$	10.2835	−	38.3785i	0.0594422	−	0.221841i	0.989257	+	0.146186i	$0.0466999\pi$
$174$	23.2200	+	1.94292i	0.133448	+	0.0111662i
$175$	−64.2494	−	44.3558i	−0.367140	−	0.253462i
$176$	48.2182	−	83.5163i	0.273967	−	0.474525i
$177$	10.2978	+	12.1785i	0.0581796	+	0.0688049i
$178$	16.9544	−	63.2749i	0.0952497	−	0.355477i
$179$			267.079i			1.49206i	0.665913	+	0.746030i	$0.268042\pi$
$179$			267.079i			1.49206i	−0.665913	+	0.746030i	$0.731958\pi$
$180$	2.81390	+	15.0013i	0.0156328	+	0.0833404i
$181$	−73.1699			−0.404254			−0.202127	−	0.979359i	$-0.564785\pi$
$181$	−73.1699			−0.404254			−0.202127	+	0.979359i	$0.564785\pi$
$182$	−101.738	−	27.2607i	−0.559003	−	0.149784i
$183$	−26.5430	−	147.270i	−0.145044	−	0.804753i
$184$	37.5975	+	21.7069i	0.204334	+	0.117972i
$185$	−115.542	+	81.4755i	−0.624549	+	0.440408i
$186$	28.7138	−	13.5221i	0.154375	−	0.0726994i
$187$	−179.076	−	47.9833i	−0.957625	−	0.256595i
$188$	3.39656	+	3.39656i	0.0180668	+	0.0180668i
$189$	−22.7472	−	81.1928i	−0.120355	−	0.429592i
$190$	−64.8157	+	140.210i	−0.341135	+	0.737946i
$191$	−17.8137	−	30.8543i	−0.0932656	−	0.161541i	0.815618	−	0.578591i	$-0.196397\pi$
$191$	−17.8137	−	30.8543i	−0.0932656	−	0.161541i	−0.908883	+	0.417050i	$0.863064\pi$
$192$	−69.5204	+	193.280i	−0.362085	+	1.00667i
$193$	279.932	−	75.0075i	1.45042	−	0.388640i	0.554252	−	0.832349i	$-0.313004\pi$
$193$	279.932	−	75.0075i	1.45042	−	0.388640i	0.896171	+	0.443709i	$0.146338\pi$
$194$	−29.2704	−	16.8993i	−0.150878	−	0.0871097i
$195$	−255.882	−	66.6191i	−1.31222	−	0.341636i
$196$	6.65587	+	11.5283i	0.0339585	+	0.0588179i
$197$	11.0087	−	11.0087i	0.0558817	−	0.0558817i	−0.678614	−	0.734495i	$-0.737419\pi$
$197$	11.0087	−	11.0087i	0.0558817	−	0.0558817i	0.734495	+	0.678614i	$0.237419\pi$
$198$	−47.5208	+	103.957i	−0.240004	+	0.525035i
$199$		−	163.374i		−	0.820973i	−0.911867	−	0.410487i	$-0.865359\pi$
$199$		−	163.374i		−	0.820973i	0.911867	−	0.410487i	$-0.134641\pi$
$200$	−88.9629	−	187.524i	−0.444815	−	0.937622i
$201$	−7.04573	+	84.2043i	−0.0350534	+	0.418927i
$202$	−26.5680	−	99.1530i	−0.131525	−	0.490856i
$203$	−12.2454	+	3.28114i	−0.0603221	+	0.0161633i
$204$	28.3203	+	2.36968i	0.138825	+	0.0116161i
$205$	−145.326	+	174.364i	−0.708908	+	0.850556i
$206$	−264.211			−1.28258
$207$	−42.8025	−	19.5659i	−0.206775	−	0.0945210i
$208$	−181.088	−	181.088i	−0.870613	−	0.870613i
$209$	92.8180	−	53.5885i	0.444105	−	0.256404i
$210$	45.3641	+	77.2997i	0.216019	+	0.368094i
$211$	−89.5818	+	155.160i	−0.424558	+	0.735357i	−0.996379	−	0.0850220i	$-0.972904\pi$
$211$	−89.5818	+	155.160i	−0.424558	+	0.735357i	0.571821	+	0.820379i	$0.306237\pi$
$212$	6.12255	+	22.8497i	0.0288800	+	0.107781i
$213$	156.238	+	56.1970i	0.733512	+	0.263836i
$214$	−36.5518	+	21.1032i	−0.170803	+	0.0986129i
$215$	168.811	−	365.173i	0.785168	−	1.69848i
$216$	55.5538	−	217.168i	0.257194	−	1.00541i
$217$	−12.2102	+	12.2102i	−0.0562682	+	0.0562682i
$218$	−65.6148	+	244.878i	−0.300985	+	1.12329i
$219$	−38.4415	−	81.6297i	−0.175532	−	0.372738i
$220$	−1.91798	+	11.0924i	−0.00871810	+	0.0504199i
$221$	−246.165	+	426.370i	−1.11387	+	1.92928i
$222$	159.729	−	28.7887i	0.719502	−	0.129679i
$223$	62.3187	−	232.577i	0.279456	−	1.04294i	−0.673340	−	0.739333i	$-0.735141\pi$
$223$	62.3187	−	232.577i	0.279456	−	1.04294i	0.952796	−	0.303611i	$-0.0981924\pi$
$224$		−	16.9005i		−	0.0754486i
$225$	115.257	+	193.238i	0.512252	+	0.858835i
$226$	138.830			0.614292
$227$	−74.1598	−	19.8711i	−0.326695	−	0.0875377i	0.0917437	−	0.995783i	$-0.470756\pi$
$227$	−74.1598	−	19.8711i	−0.326695	−	0.0875377i	−0.418439	+	0.908245i	$0.637423\pi$
$228$	−12.5455	+	10.6082i	−0.0550243	+	0.0465270i
$229$	27.2203	+	15.7156i	0.118866	+	0.0686272i	0.558254	−	0.829670i	$-0.311471\pi$
$229$	27.2203	+	15.7156i	0.118866	+	0.0686272i	−0.439388	+	0.898297i	$0.644805\pi$
$230$	49.2940	+	8.52341i	0.214322	+	0.0370583i
$231$	5.18546	−	61.9720i	0.0224479	−	0.268277i
$232$	−32.5542	−	8.72288i	−0.140320	−	0.0375986i
$233$	−264.496	−	264.496i	−1.13518	−	1.13518i	−0.989303	−	0.145874i	$-0.953401\pi$
$233$	−264.496	−	264.496i	−1.13518	−	1.13518i	−0.145874	−	0.989303i	$-0.546599\pi$
$234$	233.999	+	193.348i	0.999997	+	0.826273i
$235$	64.2752	+	29.7129i	0.273512	+	0.126438i
$236$	−0.901566	−	1.56156i	−0.00382019	−	0.00661677i
$237$	347.281	−	62.5919i	1.46532	−	0.264101i
$238$	161.199	−	43.1930i	0.677305	−	0.181483i
$239$	87.9779	+	50.7940i	0.368108	+	0.212527i	0.672632	−	0.739977i	$-0.265164\pi$
$239$	87.9779	+	50.7940i	0.368108	+	0.212527i	−0.304523	+	0.952505i	$0.598497\pi$
$240$	1.54786	+	217.918i	0.00644942	+	0.907993i
$241$	78.9022	+	136.663i	0.327395	+	0.567065i	0.981994	−	0.188911i	$-0.0604959\pi$
$241$	78.9022	+	136.663i	0.327395	+	0.567065i	−0.654599	+	0.755976i	$0.727163\pi$
$242$	104.093	−	104.093i	0.430136	−	0.430136i
$243$	−37.6584	+	240.064i	−0.154973	+	0.987919i
$244$			16.9184i			0.0693377i
$245$	150.743	+	125.639i	0.615279	+	0.512813i
$246$	235.746	−	111.019i	0.958317	−	0.451296i
$247$	−73.6649	−	274.921i	−0.298238	−	1.11304i
$248$	−44.3421	+	11.8814i	−0.178799	+	0.0479090i
$249$	−155.340	+	223.646i	−0.623854	+	0.898175i
$250$	−170.790	−	167.425i	−0.683160	−	0.669700i
$251$	225.813			0.899654			0.449827	−	0.893116i	$-0.351486\pi$
$251$	225.813			0.899654			0.449827	+	0.893116i	$0.351486\pi$
$252$	0.902752	+	9.49015i	0.00358235	+	0.0376593i
$253$	−24.5439	−	24.5439i	−0.0970116	−	0.0970116i
$254$	−288.159	+	166.369i	−1.13448	+	0.654995i
$255$	403.890	−	111.303i	1.58388	−	0.436481i
$256$	32.3201	−	55.9801i	0.126251	−	0.218672i
$257$	−100.527	−	375.172i	−0.391156	−	1.45981i	−0.828230	−	0.560389i	$-0.810652\pi$
$257$	−100.527	−	375.172i	−0.391156	−	1.45981i	0.437073	−	0.899426i	$-0.356015\pi$
$258$	−352.666	+	298.205i	−1.36692	+	1.15583i
$259$	−76.4731	+	44.1518i	−0.295263	+	0.170470i
$260$	27.1350	+	12.5439i	0.104365	+	0.0482456i
$261$	36.0270	+	6.07157i	0.138034	+	0.0232627i
$262$	165.989	−	165.989i	0.633547	−	0.633547i
$263$	−16.6068	+	61.9775i	−0.0631438	+	0.235656i	−0.990284	−	0.139058i	$-0.955592\pi$
$263$	−16.6068	+	61.9775i	−0.0631438	+	0.235656i	0.927140	+	0.374714i	$0.122259\pi$
$264$	94.3145	−	135.787i	0.357252	−	0.514343i
$265$	200.966	+	284.993i	0.758362	+	1.07544i
$266$	−48.2387	+	83.5519i	−0.181349	+	0.314105i
$267$	34.7637	−	96.6496i	0.130201	−	0.361984i
$268$	2.47257	−	9.22776i	0.00922601	−	0.0344319i
$269$			258.723i			0.961795i	0.876777	+	0.480898i	$0.159689\pi$
$269$			258.723i			0.961795i	−0.876777	+	0.480898i	$0.840311\pi$
$270$	−26.2861	−	256.958i	−0.0973559	−	0.951697i
$271$	−420.290			−1.55088			−0.775442	−	0.631418i	$-0.782473\pi$
$271$	−420.290			−1.55088			−0.775442	+	0.631418i	$0.782473\pi$
$272$	391.943	+	105.021i	1.44097	+	0.386106i
$273$	−155.401	−	55.8959i	−0.569235	−	0.204747i
$274$	379.912	+	219.343i	1.38654	+	0.800520i
$275$	29.8995	+	163.230i	0.108726	+	0.593565i
$276$	4.37008	+	3.03537i	0.0158336	+	0.0109977i
$277$	−38.6770	−	10.3635i	−0.139628	−	0.0374133i	0.188328	−	0.982106i	$-0.439693\pi$
$277$	−38.6770	−	10.3635i	−0.139628	−	0.0374133i	−0.327956	+	0.944693i	$0.606360\pi$
$278$	−114.714	−	114.714i	−0.412642	−	0.412642i
$279$	46.6329	−	17.3741i	0.167143	−	0.0622726i
$280$	−44.7422	−	121.671i	−0.159793	−	0.434540i
$281$	−237.241	−	410.913i	−0.844273	−	1.46232i	−0.886251	−	0.463205i	$-0.846699\pi$
$281$	−237.241	−	410.913i	−0.844273	−	1.46232i	0.0419779	−	0.999119i	$-0.486634\pi$
$282$	−52.4880	−	62.0739i	−0.186128	−	0.220120i
$283$	−25.0948	+	6.72412i	−0.0886741	+	0.0237602i	−0.302883	−	0.953028i	$-0.597949\pi$
$283$	−25.0948	+	6.72412i	−0.0886741	+	0.0237602i	0.214209	+	0.976788i	$0.431283\pi$
$284$	−16.2570	−	9.38598i	−0.0572430	−	0.0330492i
$285$	−119.605	+	210.602i	−0.419666	+	0.738954i
$286$	111.938	+	193.882i	0.391391	+	0.677909i
$287$	−100.248	+	100.248i	−0.349296	+	0.349296i
$288$	−20.2490	+	44.2970i	−0.0703091	+	0.153809i
$289$		−	491.068i		−	1.69920i
$290$	−38.6760	+	3.51299i	−0.133366	+	0.0121138i
$291$	−43.5252	−	30.2317i	−0.149571	−	0.103889i
$292$	2.64024	+	9.85350i	0.00904191	+	0.0337449i
$293$	56.1100	−	15.0346i	0.191502	−	0.0513127i	−0.161793	−	0.986825i	$-0.551728\pi$
$293$	56.1100	−	15.0346i	0.191502	−	0.0513127i	0.353295	+	0.935512i	$0.385061\pi$
$294$	−95.9795	−	203.810i	−0.326461	−	0.693232i
$295$	−20.4188	−	17.0184i	−0.0692164	−	0.0576894i
$296$	−234.754			−0.793087
$297$	−87.8420	+	156.219i	−0.295764	+	0.525989i
$298$	19.6142	+	19.6142i	0.0658196	+	0.0658196i
$299$	−79.8275	+	46.0884i	−0.266982	+	0.154142i
$300$	−8.94895	−	23.8121i	−0.0298298	−	0.0793738i
$301$	125.637	−	217.609i	0.417398	−	0.722954i
$302$	102.602	+	382.915i	0.339741	+	1.26793i
$303$	−28.5488	−	158.399i	−0.0942206	−	0.522768i
$304$	−203.151	+	117.289i	−0.668259	+	0.385820i
$305$	86.0781	+	234.079i	0.282223	+	0.767473i
$306$	−474.260	−	79.9264i	−1.54987	−	0.261197i
$307$	−143.570	+	143.570i	−0.467655	+	0.467655i	−0.901154	−	0.433499i	$-0.857279\pi$
$307$	−143.570	+	143.570i	−0.467655	+	0.467655i	0.433499	+	0.901154i	$0.357279\pi$
$308$	−1.81974	+	6.79138i	−0.00590826	+	0.0220499i
$309$	−412.827	−	34.5430i	−1.33601	−	0.111790i
$310$	−43.2302	+	30.4843i	−0.139452	+	0.0983363i
$311$	158.142	−	273.911i	0.508497	−	0.880742i	−0.491455	−	0.870903i	$-0.663535\pi$
$311$	158.142	−	273.911i	0.508497	−	0.880742i	0.999952	−	0.00983893i	$-0.00313188\pi$
$312$	−283.483	−	335.256i	−0.908601	−	1.07454i
$313$	16.4557	−	61.4135i	0.0525741	−	0.196209i	−0.934644	−	0.355585i	$-0.884282\pi$
$313$	16.4557	−	61.4135i	0.0525741	−	0.196209i	0.987218	+	0.159376i	$0.0509482\pi$
$314$			32.1884i			0.102511i
$315$	60.7747	+	126.711i	0.192935	+	0.402256i
$316$	−39.8957			−0.126252
$317$	−175.985	−	47.1551i	−0.555159	−	0.148754i	−0.0296774	−	0.999560i	$-0.509448\pi$
$317$	−175.985	−	47.1551i	−0.555159	−	0.148754i	−0.525481	+	0.850805i	$0.676115\pi$
$318$	−71.0096	−	393.986i	−0.223301	−	1.23895i
$319$	23.3359	+	13.4730i	0.0731533	+	0.0422351i
$320$	58.3279	−	337.332i	0.182275	−	1.05416i
$321$	−59.8707	+	28.1947i	−0.186513	+	0.0878339i
$322$	30.1805	+	8.08685i	0.0937284	+	0.0251144i
$323$	318.879	+	318.879i	0.987240	+	0.987240i
$324$	9.00431	−	25.9558i	0.0277911	−	0.0801103i
$325$	439.255	+	35.4959i	1.35155	+	0.109218i
$326$	143.148	+	247.940i	0.439106	+	0.760553i
$327$	−134.538	+	374.040i	−0.411430	+	1.14385i
$328$	−364.057	+	97.5487i	−1.10993	+	0.297405i
$329$	38.3020	+	22.1137i	0.116420	+	0.0672149i
$330$	47.9983	−	184.360i	0.145449	−	0.558667i
$331$	66.5330	+	115.238i	0.201006	+	0.348152i	0.948853	−	0.315719i	$-0.102246\pi$
$331$	66.5330	+	115.238i	0.201006	+	0.348152i	−0.747847	+	0.663871i	$0.768912\pi$
$332$	21.7690	−	21.7690i	0.0655692	−	0.0655692i
$333$	253.339	−	24.0989i	0.760779	−	0.0723691i
$334$			31.8808i			0.0954515i
$335$	−12.7394	−	140.253i	−0.0380280	−	0.418667i
$336$	−11.3494	+	135.638i	−0.0337780	+	0.403685i
$337$	82.5706	+	308.158i	0.245017	+	0.914414i	0.973375	+	0.229218i	$0.0736169\pi$
$337$	82.5706	+	308.158i	0.245017	+	0.914414i	−0.728359	+	0.685196i	$0.759716\pi$
$338$	261.932	−	70.1844i	0.774946	−	0.207646i
$339$	216.920	+	18.1506i	0.639882	+	0.0535417i
$340$	−47.1712	+	4.28462i	−0.138739	+	0.0126018i
$341$	36.7031			0.107634
$342$	226.542	−	161.197i	0.662404	−	0.471336i
$343$	194.872	+	194.872i	0.568139	+	0.568139i
$344$	578.512	−	334.004i	1.68172	−	0.970941i
$345$	75.9070	+	19.7624i	0.220020	+	0.0572824i
$346$	38.0105	−	65.8362i	0.109857	−	0.190278i
$347$	−116.181	−	433.595i	−0.334817	−	1.24955i	−0.904067	−	0.427390i	$-0.859433\pi$
$347$	−116.181	−	433.595i	−0.334817	−	1.24955i	0.569250	−	0.822164i	$-0.307233\pi$
$348$	−3.88681	−	1.39804i	−0.0111690	−	0.00401736i
$349$	−264.288	+	152.587i	−0.757272	+	0.437211i	−0.828315	−	0.560262i	$-0.810700\pi$
$349$	−264.288	+	152.587i	−0.757272	+	0.437211i	0.0710435	+	0.997473i	$0.477367\pi$
$350$	−96.7762	−	113.792i	−0.276503	−	0.325120i
$351$	340.343	+	332.697i	0.969638	+	0.947854i
$352$	−25.4009	+	25.4009i	−0.0721617	+	0.0721617i
$353$	2.27410	−	8.48704i	0.00644220	−	0.0240426i	−0.962630	−	0.270820i	$-0.912705\pi$
$353$	2.27410	−	8.48704i	0.00644220	−	0.0240426i	0.969072	+	0.246778i	$0.0793717\pi$
$354$	13.0008	+	27.6070i	0.0367255	+	0.0779857i
$355$	−272.683	−	47.1495i	−0.768121	−	0.132816i
$356$	−5.80621	+	10.0567i	−0.0163096	+	0.0282490i
$357$	257.518	−	46.4135i	0.721339	−	0.130010i
$358$	−132.259	+	493.597i	−0.369438	+	1.37876i
$359$		−	280.501i		−	0.781339i	−0.920531	−	0.390670i	$-0.872243\pi$
$359$		−	280.501i		−	0.781339i	0.920531	−	0.390670i	$-0.127757\pi$
$360$	−28.5069	+	372.513i	−0.0791858	+	1.03476i
$361$	100.296			0.277827
$362$	−135.228	−	36.2341i	−0.373557	−	0.100094i
$363$	176.253	−	149.035i	0.485545	−	0.410564i
$364$	16.1699	+	9.33570i	0.0444228	+	0.0256475i
$365$	86.6628	+	122.898i	0.237432	+	0.336707i
$366$	23.8738	−	285.319i	0.0652290	−	0.779559i
$367$	277.315	+	74.3063i	0.755626	+	0.202469i	0.616012	−	0.787737i	$-0.288747\pi$
$367$	277.315	+	74.3063i	0.755626	+	0.202469i	0.139614	+	0.990206i	$0.455414\pi$
$368$	53.7193	+	53.7193i	0.145976	+	0.145976i
$369$	382.865	−	142.644i	1.03757	−	0.386570i
$370$	−253.883	+	93.3606i	−0.686172	+	0.252326i
$371$	108.904	+	188.627i	0.293541	+	0.508429i
$372$	−5.53707	+	0.997967i	−0.0148846	+	0.00268271i
$373$	−217.402	+	58.2527i	−0.582848	+	0.156174i	−0.538182	−	0.842828i	$-0.680889\pi$
$373$	−217.402	+	58.2527i	−0.582848	+	0.156174i	−0.0446653	+	0.999002i	$0.514222\pi$
$374$	−307.195	−	177.359i	−0.821376	−	0.474222i
$375$	−244.968	−	283.929i	−0.653248	−	0.757144i
$376$	58.7890	+	101.826i	0.156354	+	0.270813i
$377$	50.5990	−	50.5990i	0.134215	−	0.134215i
$378$	−1.83265	−	161.320i	−0.00484827	−	0.426771i
$379$			68.5964i			0.180993i	0.995897	+	0.0904966i	$0.0288454\pi$
$379$			68.5964i			0.180993i	−0.995897	+	0.0904966i	$0.971155\pi$
$380$	17.5313	−	21.0343i	0.0461350	−	0.0553533i
$381$	−471.996	+	222.275i	−1.23884	+	0.583400i
$382$	−17.6429	−	65.8443i	−0.0461857	−	0.172367i
$383$	−119.300	+	31.9663i	−0.311488	+	0.0834630i	−0.411177	−	0.911556i	$-0.634882\pi$
$383$	−119.300	+	31.9663i	−0.311488	+	0.0834630i	0.0996886	+	0.995019i	$0.468215\pi$
$384$	−187.149	+	269.443i	−0.487368	+	0.701674i
$385$	9.37584	+	103.223i	0.0243528	+	0.268111i
$386$	554.495			1.43652
$387$	−590.025	+	419.835i	−1.52461	+	1.08484i
$388$	4.23661	+	4.23661i	0.0109191	+	0.0109191i
$389$	140.653	−	81.2059i	0.361575	−	0.208755i	−0.308196	−	0.951323i	$-0.599725\pi$
$389$	140.653	−	81.2059i	0.361575	−	0.208755i	0.669771	+	0.742567i	$0.266392\pi$
$390$	−439.914	−	249.835i	−1.12798	−	0.640603i
$391$	73.0244	−	126.482i	0.186763	−	0.323483i
$392$	84.3340	+	314.739i	0.215138	+	0.802905i
$393$	281.058	−	237.655i	0.715159	−	0.604720i
$394$	25.7971	−	14.8940i	0.0654748	−	0.0378019i
$395$	−551.989	+	202.983i	−1.39744	+	0.513881i
$396$	12.9066	−	15.6202i	0.0325924	−	0.0394450i
$397$	61.0977	−	61.0977i	0.153899	−	0.153899i	−0.625958	−	0.779857i	$-0.715292\pi$
$397$	61.0977	−	61.0977i	0.153899	−	0.153899i	0.779857	+	0.625958i	$0.215292\pi$
$398$	80.9036	−	301.936i	0.203275	−	0.758634i
$399$	−86.2960	+	124.242i	−0.216281	+	0.311384i
$400$	−65.4411	−	357.262i	−0.163603	−	0.893156i
$401$	54.1568	−	93.8023i	0.135054	−	0.233921i	−0.790564	−	0.612380i	$-0.790212\pi$
$401$	54.1568	−	93.8023i	0.135054	−	0.233921i	0.925618	+	0.378459i	$0.123546\pi$
$402$	−54.7199	+	152.132i	−0.136119	+	0.378437i
$403$	25.2268	−	94.1476i	0.0625974	−	0.233617i
$404$			18.1969i			0.0450418i
$405$	−7.47696	−	404.931i	−0.0184616	−	0.999830i
$406$	−24.2559			−0.0597437
$407$	181.296	+	48.5780i	0.445444	+	0.119356i
$408$	654.583	+	235.446i	1.60437	+	0.577073i
$409$	−8.83799	−	5.10262i	−0.0216088	−	0.0124758i	0.489157	−	0.872196i	$-0.337305\pi$
$409$	−8.83799	−	5.10262i	−0.0216088	−	0.0124758i	−0.510765	+	0.859720i	$0.670638\pi$
$410$	−354.928	+	250.282i	−0.865679	+	0.610443i
$411$	564.932	+	392.390i	1.37453	+	0.954720i
$412$	45.2408	+	12.1222i	0.109808	+	0.0294229i
$413$	−11.7395	−	11.7395i	−0.0284249	−	0.0284249i
$414$	−69.4155	−	57.3563i	−0.167670	−	0.138542i
$415$	190.434	−	411.948i	0.458877	−	0.992645i
$416$	47.6977	+	82.6148i	0.114658	+	0.198593i
$417$	−164.242	−	194.238i	−0.393866	−	0.465798i
$418$	198.077	−	53.0747i	0.473869	−	0.126973i
$419$	−172.082	−	99.3518i	−0.410698	−	0.237117i	0.280392	−	0.959886i	$-0.409536\pi$
$419$	−172.082	−	99.3518i	−0.410698	−	0.237117i	−0.691090	+	0.722769i	$0.742869\pi$
$420$	−4.22110	−	15.3173i	−0.0100502	−	0.0364699i
$421$	−417.463	−	723.067i	−0.991598	−	1.71750i	−0.607826	−	0.794070i	$-0.707958\pi$
$421$	−417.463	−	723.067i	−0.991598	−	1.71750i	−0.383772	−	0.923428i	$-0.625375\pi$
$422$	−242.395	+	242.395i	−0.574397	+	0.574397i
$423$	−73.8963	−	103.852i	−0.174696	−	0.245513i
$424$			579.039i			1.36566i
$425$	−630.851	+	299.281i	−1.48436	+	0.704189i
$426$	260.920	+	181.230i	0.612488	+	0.425421i
$427$	40.3174	+	150.467i	0.0944201	+	0.352381i
$428$	7.22698	−	1.93646i	0.0168855	−	0.00452445i
$429$	149.553	+	317.573i	0.348609	+	0.740264i
$430$	492.821	−	591.293i	1.14610	−	1.37510i
$431$	−300.059			−0.696194			−0.348097	−	0.937459i	$-0.613172\pi$
$431$	−300.059			−0.696194			−0.348097	+	0.937459i	$0.613172\pi$
$432$	192.260	−	341.916i	0.445046	−	0.791472i
$433$	−222.651	−	222.651i	−0.514205	−	0.514205i	0.401607	−	0.915812i	$-0.368452\pi$
$433$	−222.651	−	222.651i	−0.514205	−	0.514205i	−0.915812	+	0.401607i	$0.868452\pi$
$434$	−28.6126	+	16.5195i	−0.0659277	+	0.0380634i
$435$	−60.8902	+	0.432499i	−0.139977	+	0.000994251i
$436$	22.4704	−	38.9199i	0.0515376	−	0.0892657i
$437$	21.8526	+	81.5549i	0.0500059	+	0.186624i
$438$	−30.6216	−	169.899i	−0.0699123	−	0.387897i
$439$	376.432	−	217.333i	0.857476	−	0.495064i	−0.00569024	−	0.999984i	$-0.501811\pi$
$439$	376.432	−	217.333i	0.857476	−	0.495064i	0.863166	+	0.504920i	$0.168478\pi$
$440$	−115.622	+	250.114i	−0.262777	+	0.568441i
$441$	−123.321	−	330.999i	−0.279639	−	0.750565i
$442$	−666.086	+	666.086i	−1.50698	+	1.50698i
$443$	2.52796	−	9.43446i	0.00570644	−	0.0212967i	−0.963014	−	0.269452i	$-0.913158\pi$
$443$	2.52796	−	9.43446i	0.00570644	−	0.0212967i	0.968720	+	0.248155i	$0.0798242\pi$
$444$	−28.6713	−	2.39905i	−0.0645750	−	0.00540326i
$445$	−29.1669	+	168.683i	−0.0655436	+	0.379063i
$446$	230.347	−	398.972i	0.516472	−	0.894556i
$447$	28.0827	+	33.2114i	0.0628247	+	0.0742984i
$448$	55.3404	−	206.533i	0.123528	−	0.461012i
$449$		−	529.226i		−	1.17868i	−0.807886	−	0.589339i	$-0.799388\pi$
$449$		−	529.226i		−	1.17868i	0.807886	−	0.589339i	$-0.200612\pi$
$450$	117.317	+	414.205i	0.260704	+	0.920456i
$451$	301.339			0.668158
$452$	−23.7718	−	6.36964i	−0.0525925	−	0.0140921i
$453$	110.252	+	611.714i	0.243381	+	1.35036i
$454$	−127.217	−	73.4488i	−0.280214	−	0.161781i
$455$	271.222	+	46.8969i	0.596092	+	0.103070i
$456$	−363.829	+	171.336i	−0.797871	+	0.375738i
$457$	315.433	+	84.5200i	0.690225	+	0.184945i	0.586848	−	0.809697i	$-0.300368\pi$
$457$	315.433	+	84.5200i	0.690225	+	0.184945i	0.103377	+	0.994642i	$0.467035\pi$
$458$	42.5242	+	42.5242i	0.0928476	+	0.0928476i
$459$	−730.576	−	186.889i	−1.59167	−	0.407165i
$460$	−8.04954	−	3.72111i	−0.0174990	−	0.00808938i
$461$	123.842	+	214.501i	0.268638	+	0.465294i	0.968510	−	0.248973i	$-0.0800932\pi$
$461$	123.842	+	214.501i	0.268638	+	0.465294i	−0.699872	+	0.714268i	$0.746760\pi$
$462$	40.2723	−	111.965i	0.0871695	−	0.242348i
$463$	−389.085	+	104.255i	−0.840356	+	0.225173i	−0.653226	−	0.757163i	$-0.726585\pi$
$463$	−389.085	+	104.255i	−0.840356	+	0.225173i	−0.187129	+	0.982335i	$0.559918\pi$
$464$	−51.0753	−	29.4883i	−0.110076	−	0.0635525i
$465$	−71.5322	+	41.9794i	−0.153833	+	0.0902783i
$466$	−357.844	−	619.804i	−0.767906	−	1.33005i
$467$	−74.7515	+	74.7515i	−0.160067	+	0.160067i	−0.782597	−	0.622529i	$-0.786105\pi$
$467$	−74.7515	+	74.7515i	−0.160067	+	0.160067i	0.622529	+	0.782597i	$0.286105\pi$
$468$	−31.1967	−	43.8430i	−0.0666595	−	0.0936816i
$469$		−	87.9609i		−	0.187550i
$470$	104.075	+	86.7429i	0.221437	+	0.184559i
$471$	−4.20832	+	50.2940i	−0.00893486	+	0.106781i
$472$	−11.4234	−	42.6327i	−0.0242021	−	0.0903236i
$473$	−515.889	+	138.232i	−1.09067	+	0.292245i
$474$	672.818	+	56.2975i	1.41945	+	0.118771i
$475$	135.541	−	380.222i	0.285349	−	0.800468i
$476$	−29.5837			−0.0621507
$477$	−59.4419	−	624.882i	−0.124616	−	1.31002i
$478$	137.441	+	137.441i	0.287534	+	0.287534i
$479$	−607.427	+	350.698i	−1.26811	+	0.732146i	−0.974631	−	0.223818i	$-0.928148\pi$
$479$	−607.427	+	350.698i	−1.26811	+	0.732146i	−0.293483	+	0.955964i	$0.594814\pi$
$480$	20.4525	−	78.5574i	0.0426093	−	0.163661i
$481$	249.216	−	431.655i	0.518121	−	0.897411i
$482$	78.1457	+	291.644i	0.162128	+	0.605070i
$483$	46.0995	+	16.5814i	0.0954440	+	0.0343301i
$484$	−22.5997	+	13.0479i	−0.0466935	+	0.0269585i
$485$	80.1720	+	37.0617i	0.165303	+	0.0764158i
$486$	−188.479	+	425.022i	−0.387817	+	0.874531i
$487$	274.700	−	274.700i	0.564065	−	0.564065i	−0.366395	−	0.930460i	$-0.619408\pi$
$487$	274.700	−	274.700i	0.564065	−	0.564065i	0.930460	+	0.366395i	$0.119408\pi$
$488$	−107.183	+	400.014i	−0.219638	+	0.819700i
$489$	191.252	+	406.119i	0.391108	+	0.830509i
$490$	216.377	+	306.847i	0.441585	+	0.626218i
$491$	−277.356	+	480.395i	−0.564881	+	0.978402i	0.432180	+	0.901787i	$0.357745\pi$
$491$	−277.356	+	480.395i	−0.564881	+	0.978402i	−0.997061	+	0.0766148i	$0.975589\pi$
$492$	−45.4604	+	8.19350i	−0.0923991	+	0.0166535i
$493$	−29.3447	+	109.516i	−0.0595226	+	0.222142i
$494$		−	544.570i		−	1.10237i
$495$	99.1000	−	281.785i	0.200202	−	0.569263i
$496$	−80.3321			−0.161960
$497$	−166.952	−	44.7346i	−0.335919	−	0.0900092i
$498$	−397.839	+	336.402i	−0.798873	+	0.675506i
$499$	−367.132	−	211.964i	−0.735736	−	0.424778i	0.0847806	−	0.996400i	$-0.472981\pi$
$499$	−367.132	−	211.964i	−0.735736	−	0.424778i	−0.820517	+	0.571622i	$0.806314\pi$
$500$	21.5627	+	36.5041i	0.0431254	+	0.0730083i
$501$	−4.16810	+	49.8134i	−0.00831956	+	0.0994279i
$502$	417.333	+	111.824i	0.831340	+	0.222757i
$503$	−307.613	−	307.613i	−0.611557	−	0.611557i	0.331795	−	0.943352i	$-0.392346\pi$
$503$	−307.613	−	307.613i	−0.611557	−	0.611557i	−0.943352	+	0.331795i	$0.892346\pi$
$504$	−38.7787	+	230.102i	−0.0769419	+	0.456551i
$505$	92.5829	+	251.768i	0.183332	+	0.498551i
$506$	−33.2062	−	57.5148i	−0.0656248	−	0.113666i
$507$	418.441	−	75.4173i	0.825327	−	0.148752i
$508$	56.9745	−	15.2663i	0.112155	−	0.0300517i
$509$	697.404	+	402.646i	1.37014	+	0.791053i	0.990946	−	0.134262i	$-0.0428664\pi$
$509$	697.404	+	402.646i	1.37014	+	0.791053i	0.379199	+	0.925315i	$0.376200\pi$
$510$	801.560	−	5.69343i	1.57169	−	0.0111636i
$511$	46.9628	+	81.3419i	0.0919037	+	0.159182i
$512$	396.753	−	396.753i	0.774908	−	0.774908i
$513$	375.044	−	222.250i	0.731081	−	0.433237i
$514$		−	743.150i		−	1.44582i
$515$	687.619	−	62.4572i	1.33518	−	0.121276i
$516$	74.0689	−	34.8810i	0.143544	−	0.0675988i
$517$	−24.3306	−	90.8030i	−0.0470611	−	0.175635i
$518$	−163.197	+	43.7284i	−0.315051	+	0.0844178i
$519$	67.9984	−	97.8987i	0.131018	−	0.188630i
$520$	562.102	+	468.492i	1.08097	+	0.900946i
$521$	752.815			1.44494			0.722471	−	0.691401i	$-0.243006\pi$
$521$	752.815			1.44494			0.722471	+	0.691401i	$0.243006\pi$
$522$	63.5760	+	29.0618i	0.121793	+	0.0556740i
$523$	637.569	+	637.569i	1.21906	+	1.21906i	0.967961	+	0.251100i	$0.0807924\pi$
$523$	637.569	+	637.569i	1.21906	+	1.21906i	0.251100	+	0.967961i	$0.419208\pi$
$524$	−36.0380	+	20.8066i	−0.0687748	+	0.0397072i
$525$	−136.335	−	190.451i	−0.259685	−	0.362764i
$526$	−61.3832	+	106.319i	−0.116698	+	0.202127i
$527$	39.9703	+	149.171i	0.0758450	+	0.283058i
$528$	220.918	−	186.802i	0.418405	−	0.353792i
$529$	−434.447	+	250.828i	−0.821260	+	0.474155i
$530$	230.282	+	626.224i	0.434493	+	1.18155i
$531$	16.7043	+	44.8353i	0.0314582	+	0.0844355i
$532$	12.0933	−	12.0933i	0.0227318	−	0.0227318i
$533$	207.117	−	772.969i	0.388586	−	1.45022i
$534$	112.109	−	161.406i	0.209943	−	0.302259i
$535$	90.1386	−	63.5622i	0.168483	−	0.118808i
$536$	116.922	−	202.514i	0.218137	−	0.377825i
$537$	−271.186	+	753.948i	−0.505002	+	1.40400i
$538$	−128.121	+	478.154i	−0.238143	+	0.888763i
$539$		−	260.518i		−	0.483335i
$540$	−7.28851	+	45.2049i	−0.0134972	+	0.0837128i
$541$	−771.736			−1.42650			−0.713250	−	0.700910i	$-0.752778\pi$
$541$	−771.736			−1.42650			−0.713250	+	0.700910i	$0.752778\pi$
$542$	−776.751	−	208.130i	−1.43312	−	0.384004i
$543$	−206.554	−	74.2951i	−0.380395	−	0.136823i
$544$	−130.898	−	75.5742i	−0.240622	−	0.138923i
$545$	112.878	−	652.813i	0.207115	−	1.19782i
$546$	−259.522	−	180.259i	−0.475315	−	0.330144i
$547$	−158.434	−	42.4522i	−0.289642	−	0.0776092i	0.111073	−	0.993812i	$-0.464571\pi$
$547$	−158.434	−	42.4522i	−0.289642	−	0.0776092i	−0.400714	+	0.916203i	$0.631238\pi$
$548$	−54.9887	−	54.9887i	−0.100344	−	0.100344i
$549$	74.6052	−	442.686i	0.135893	−	0.806349i
$550$	−25.5743	+	316.478i	−0.0464988	+	0.575414i
$551$	−32.7726	−	56.7638i	−0.0594784	−	0.103020i
$552$	84.0949	+	99.4532i	0.152346	+	0.180169i
$553$	−354.819	+	95.0736i	−0.641626	+	0.171923i
$554$	−66.3482	−	38.3061i	−0.119762	−	0.0691447i
$555$	−408.896	+	112.682i	−0.736749	+	0.203031i
$556$	14.3793	+	24.9057i	0.0258621	+	0.0447945i
$557$	−63.7862	+	63.7862i	−0.114517	+	0.114517i	−0.762043	−	0.647526i	$-0.775804\pi$
$557$	−63.7862	+	63.7862i	−0.114517	+	0.114517i	0.647526	+	0.762043i	$0.275804\pi$
$558$	94.7876	−	9.01667i	0.169870	−	0.0161589i
$559$			1418.32i			2.53725i
$560$	−20.5209	−	225.923i	−0.0366445	−	0.403435i
$561$	−456.800	−	317.284i	−0.814260	−	0.565568i
$562$	−234.966	−	876.905i	−0.418089	−	1.56033i
$563$	−659.684	+	176.762i	−1.17173	+	0.313964i	−0.791641	−	0.610986i	$-0.790773\pi$
$563$	−659.684	+	176.762i	−1.17173	+	0.313964i	−0.380089	+	0.924950i	$0.624107\pi$
$564$	6.13950	+	13.0371i	0.0108856	+	0.0231154i
$565$	−361.310	+	32.8182i	−0.639486	+	0.0580853i
$566$	−49.7083			−0.0878238
$567$	18.2275	−	252.300i	0.0321472	−	0.444973i
$568$	−324.913	−	324.913i	−0.572029	−	0.572029i
$569$	−11.9524	+	6.90074i	−0.0210060	+	0.0121278i	−0.510466	−	0.859898i	$-0.670527\pi$
$569$	−11.9524	+	6.90074i	−0.0210060	+	0.0121278i	0.489460	+	0.872026i	$0.337194\pi$
$570$	−325.337	+	329.992i	−0.570766	+	0.578933i
$571$	−454.365	+	786.984i	−0.795736	+	1.37826i	0.126634	+	0.991949i	$0.459583\pi$
$571$	−454.365	+	786.984i	−0.795736	+	1.37826i	−0.922371	+	0.386306i	$0.873751\pi$
$572$	−10.2716	−	38.3342i	−0.0179574	−	0.0670178i
$573$	−18.9584	−	105.188i	−0.0330862	−	0.183573i
$574$	−234.915	+	135.628i	−0.409259	+	0.236286i
$575$	−130.304	−	10.5298i	−0.226616	−	0.0183127i
$576$	−392.504	+	475.028i	−0.681431	+	0.824702i
$577$	585.604	−	585.604i	1.01491	−	1.01491i	0.0150252	−	0.999887i	$-0.495217\pi$
$577$	585.604	−	585.604i	1.01491	−	1.01491i	0.999887	−	0.0150252i	$-0.00478284\pi$
$578$	243.179	−	907.558i	0.420726	−	1.57017i
$579$	866.392	+	72.4948i	1.49636	+	0.125207i
$580$	6.78367	+	1.17296i	0.0116960	+	0.00202235i
$581$	141.729	−	245.482i	0.243940	−	0.422517i
$582$	−65.4695	−	77.4262i	−0.112491	−	0.133035i
$583$	119.822	−	447.180i	0.205526	−	0.767033i
$584$			249.700i			0.427569i
$585$	−654.697	−	447.879i	−1.11914	−	0.765605i
$586$	111.144			0.189665
$587$	384.041	+	102.904i	0.654244	+	0.175304i	0.570647	−	0.821195i	$-0.306692\pi$
$587$	384.041	+	102.904i	0.654244	+	0.175304i	0.0835973	+	0.996500i	$0.473359\pi$
$588$	7.08355	+	39.3020i	0.0120469	+	0.0668401i
$589$	−77.3179	−	44.6395i	−0.131270	−	0.0757887i
$590$	−29.3091	−	41.5637i	−0.0496765	−	0.0704470i
$591$	42.2549	−	19.8989i	0.0714973	−	0.0336699i
$592$	−396.802	−	106.323i	−0.670273	−	0.179599i
$593$	211.922	+	211.922i	0.357372	+	0.357372i	0.862843	−	0.505471i	$-0.168681\pi$
$593$	211.922	+	211.922i	0.357372	+	0.357372i	−0.505471	+	0.862843i	$0.668681\pi$
$594$	−239.704	+	245.213i	−0.403542	+	0.412816i
$595$	−409.314	+	150.517i	−0.687923	+	0.252970i
$596$	−2.45862	−	4.25846i	−0.00412521	−	0.00714507i
$597$	165.886	−	461.194i	0.277866	−	0.772520i
$598$	−170.355	+	45.6465i	−0.284875	+	0.0763319i
$599$	889.994	+	513.838i	1.48580	+	0.857827i	0.999869	−	0.0161711i	$-0.00514763\pi$
$599$	889.994	+	513.838i	1.48580	+	0.857827i	0.485930	+	0.873998i	$0.338481\pi$
$600$	−60.7291	−	619.701i	−0.101215	−	1.03284i
$601$	233.016	+	403.595i	0.387713	+	0.671539i	0.992142	−	0.125120i	$-0.0399317\pi$
$601$	233.016	+	403.595i	0.387713	+	0.671539i	−0.604428	+	0.796660i	$0.706598\pi$
$602$	339.955	−	339.955i	0.564709	−	0.564709i
$603$	−105.389	+	230.550i	−0.174774	+	0.382338i
$604$		−	70.2738i		−	0.116347i
$605$	−246.298	+	295.512i	−0.407105	+	0.488449i
$606$	25.6779	−	306.880i	0.0423728	−	0.506402i
$607$	162.287	+	605.663i	0.267359	+	0.997798i	0.960790	+	0.277275i	$0.0894314\pi$
$607$	162.287	+	605.663i	0.267359	+	0.997798i	−0.693431	+	0.720523i	$0.743902\pi$
$608$	84.4025	−	22.6156i	0.138820	−	0.0371967i
$609$	−37.8996	−	3.17123i	−0.0622326	−	0.00520727i
$610$	43.1663	+	475.236i	0.0707644	+	0.779076i
$611$	−249.643			−0.408581
$612$	77.5403	+	35.4452i	0.126700	+	0.0579170i
$613$	−176.801	−	176.801i	−0.288419	−	0.288419i	0.548036	−	0.836455i	$-0.315376\pi$
$613$	−176.801	−	176.801i	−0.288419	−	0.288419i	−0.836455	+	0.548036i	$0.815376\pi$
$614$	−336.434	+	194.240i	−0.547938	+	0.316352i
$615$	−587.293	+	344.659i	−0.954948	+	0.560421i
$616$	−86.0510	+	149.045i	−0.139693	+	0.241956i
$617$	−66.1511	−	246.879i	−0.107214	−	0.400128i	0.891373	−	0.453271i	$-0.149743\pi$
$617$	−66.1511	−	246.879i	−0.107214	−	0.400128i	−0.998587	+	0.0531425i	$0.983076\pi$
$618$	−745.853	−	268.274i	−1.20688	−	0.434101i
$619$	635.172	−	366.717i	1.02613	−	0.592434i	0.110254	−	0.993903i	$-0.464834\pi$
$619$	635.172	−	366.717i	1.02613	−	0.592434i	0.915873	+	0.401469i	$0.131500\pi$
$620$	8.80094	−	3.23637i	0.0141951	−	0.00521996i
$621$	−100.962	−	98.6940i	−0.162580	−	0.158927i
$622$	427.910	−	427.910i	0.687959	−	0.687959i
$623$	−27.6730	+	103.277i	−0.0444189	+	0.165774i
$624$	−327.327	−	695.072i	−0.524563	−	1.11390i
$625$	484.065	+	395.356i	0.774503	+	0.632570i
$626$	60.8247	−	105.351i	0.0971640	−	0.168293i
$627$	316.433	−	57.0319i	0.504677	−	0.0909600i
$628$	1.47683	−	5.51161i	0.00235164	−	0.00877646i
$629$			789.736i			1.25554i
$630$	49.5718	+	264.274i	0.0786854	+	0.419483i
$631$	476.284			0.754808			0.377404	−	0.926049i	$-0.376817\pi$
$631$	476.284			0.754808			0.377404	+	0.926049i	$0.376817\pi$
$632$	−943.283	−	252.752i	−1.49254	−	0.399924i
$633$	−410.431	+	347.049i	−0.648390	+	0.548261i
$634$	−301.893	−	174.298i	−0.476171	−	0.274918i
$635$	710.616	−	501.099i	1.11908	−	0.789132i
$636$	−5.91745	+	70.7200i	−0.00930416	+	0.111195i
$637$	−668.257	−	179.059i	−1.04907	−	0.281097i
$638$	36.4560	+	36.4560i	0.0571410	+	0.0571410i
$639$	383.990	+	317.282i	0.600924	+	0.496528i
$640$	229.430	−	496.304i	0.358484	−	0.775476i
$641$	558.647	+	967.605i	0.871524	+	1.50952i	0.860420	+	0.509586i	$0.170201\pi$
$641$	558.647	+	967.605i	0.871524	+	1.50952i	0.0111041	+	0.999938i	$0.496465\pi$
$642$	−124.611	+	22.4592i	−0.194098	+	0.0349831i
$643$	1122.39	−	300.742i	1.74555	−	0.467717i	0.761879	−	0.647719i	$-0.224277\pi$
$643$	1122.39	−	300.742i	1.74555	−	0.467717i	0.983666	+	0.180002i	$0.0576104\pi$
$644$	−4.79677	−	2.76942i	−0.00744841	−	0.00430034i
$645$	847.333	−	859.457i	1.31370	−	1.33249i
$646$	431.420	+	747.241i	0.667832	+	1.15672i
$647$	−172.070	+	172.070i	−0.265951	+	0.265951i	−0.827466	−	0.561516i	$-0.810218\pi$
$647$	−172.070	+	172.070i	−0.265951	+	0.265951i	0.561516	+	0.827466i	$0.310218\pi$
$648$	377.333	−	556.645i	0.582304	−	0.859020i
$649$			35.2882i			0.0543733i
$650$	794.224	+	283.123i	1.22188	+	0.435573i
$651$	−46.8666	+	22.0707i	−0.0719918	+	0.0339028i
$652$	−13.1355	−	49.0225i	−0.0201465	−	0.0751879i
$653$	706.599	−	189.333i	1.08208	−	0.289943i	0.326633	−	0.945151i	$-0.394086\pi$
$653$	706.599	−	189.333i	1.08208	−	0.289943i	0.755448	+	0.655208i	$0.227419\pi$
$654$	−433.870	+	624.652i	−0.663410	+	0.955125i
$655$	−392.754	+	471.231i	−0.599625	+	0.719437i
$656$	−659.541			−1.00540
$657$	−25.6332	−	269.469i	−0.0390156	−	0.410150i
$658$	59.8364	+	59.8364i	0.0909368	+	0.0909368i
$659$	288.199	−	166.392i	0.437328	−	0.252491i	−0.265136	−	0.964211i	$-0.585417\pi$
$659$	288.199	−	166.392i	0.437328	−	0.252491i	0.702463	+	0.711720i	$0.252083\pi$
$660$	−16.6773	+	29.3657i	−0.0252687	+	0.0444935i
$661$	89.6994	−	155.364i	0.135703	−	0.235044i	−0.790163	−	0.612897i	$-0.790004\pi$
$661$	89.6994	−	155.364i	0.135703	−	0.235044i	0.925866	+	0.377853i	$0.123337\pi$
$662$	65.8950	+	245.924i	0.0995393	+	0.371486i
$663$	−1127.84	+	953.668i	−1.70111	+	1.43841i
$664$	652.612	−	376.786i	0.982850	−	0.567449i
$665$	105.792	−	228.850i	0.159086	−	0.344135i
$666$	480.139	+	80.9171i	0.720929	+	0.121497i
$667$	−15.0101	+	15.0101i	−0.0225039	+	0.0225039i
$668$	1.46272	−	5.45894i	0.00218970	−	0.00817207i
$669$	412.075	−	593.273i	0.615957	−	0.886806i
$670$	45.9102	−	265.516i	0.0685227	−	0.396292i
$671$	165.551	−	286.743i	0.246723	−	0.427336i
$672$	17.1604	−	47.7091i	0.0255363	−	0.0709957i
$673$	−119.799	+	447.097i	−0.178008	+	0.664334i	0.818012	+	0.575201i	$0.195076\pi$
$673$	−119.799	+	447.097i	−0.178008	+	0.664334i	−0.996020	+	0.0891327i	$0.971590\pi$
$674$			610.406i			0.905646i
$675$	129.153	+	662.529i	0.191338	+	0.981524i
$676$	−48.0706			−0.0711104
$677$	783.429	+	209.919i	1.15721	+	0.310073i	0.785850	−	0.618417i	$-0.212226\pi$
$677$	783.429	+	209.919i	1.15721	+	0.310073i	0.371357	+	0.928490i	$0.378892\pi$
$678$	391.909	+	140.965i	0.578037	+	0.207913i
$679$	47.7751	+	27.5829i	0.0703609	+	0.0406229i
$680$	−1142.45	−	197.540i	−1.68007	−	0.290500i
$681$	−189.172	−	131.395i	−0.277786	−	0.192944i
$682$	67.8322	+	18.1756i	0.0994607	+	0.0266504i
$683$	312.857	+	312.857i	0.458064	+	0.458064i	0.898019	−	0.439956i	$-0.145006\pi$
$683$	312.857	+	312.857i	0.458064	+	0.458064i	−0.439956	+	0.898019i	$0.645006\pi$
$684$	−46.1866	+	17.2078i	−0.0675243	+	0.0251576i
$685$	−1040.59	−	481.038i	−1.51910	−	0.702246i
$686$	263.647	+	456.650i	0.384325	+	0.665671i
$687$	60.8840	+	72.0032i	0.0886230	+	0.104808i
$688$	1129.13	−	302.548i	1.64117	−	0.439750i
$689$	−1064.71	−	614.712i	−1.54530	−	0.892179i
$690$	130.500	+	74.1132i	0.189130	+	0.107410i
$691$	−391.710	−	678.461i	−0.566874	−	0.981854i	−0.996873	−	0.0790250i	$-0.974819\pi$
$691$	−391.710	−	678.461i	−0.566874	−	0.981854i	0.429999	−	0.902830i	$-0.358514\pi$
$692$	−9.52915	+	9.52915i	−0.0137705	+	0.0137705i
$693$	77.5633	−	169.678i	0.111924	−	0.244846i
$694$		−	858.875i		−	1.23757i
$695$	325.666	+	271.431i	0.468584	+	0.390548i
$696$	−83.0417	−	57.6790i	−0.119313	−	0.0828722i
$697$	328.164	+	1224.72i	0.470823	+	1.75714i
$698$	−564.001	+	151.124i	−0.808024	+	0.216509i
$699$	−478.094	−	1015.22i	−0.683969	−	1.45239i
$700$	11.3501	+	23.9248i	0.0162144	+	0.0341782i
$701$	−502.118			−0.716289			−0.358144	−	0.933666i	$-0.616590\pi$
$701$	−502.118			−0.716289			−0.358144	+	0.933666i	$0.616590\pi$
$702$	464.245	+	783.408i	0.661318	+	1.11597i
$703$	−322.831	−	322.831i	−0.459219	−	0.459219i
$704$	−393.588	+	227.238i	−0.559074	+	0.322782i
$705$	151.275	+	149.142i	0.214575	+	0.211548i
$706$	8.40567	−	14.5590i	0.0119060	−	0.0206219i
$707$	43.3641	+	161.837i	0.0613354	+	0.228907i
$708$	−0.959497	−	5.32362i	−0.00135522	−	0.00751924i
$709$	−494.504	+	285.502i	−0.697468	+	0.402683i	−0.806403	−	0.591366i	$-0.798589\pi$
$709$	−494.504	+	285.502i	−0.697468	+	0.402683i	0.108936	+	0.994049i	$0.465256\pi$
$710$	−480.606	−	222.173i	−0.676909	−	0.312919i
$711$	1043.91	+	175.928i	1.46823	+	0.247438i
$712$	−200.992	+	200.992i	−0.282293	+	0.282293i
$713$	−7.48348	+	27.9287i	−0.0104958	+	0.0391707i
$714$	498.912	+	41.7461i	0.698756	+	0.0584679i
$715$	−337.154	−	478.123i	−0.471544	−	0.668704i
$716$	45.2933	−	78.4503i	0.0632588	−	0.109567i
$717$	196.781	+	232.719i	0.274451	+	0.324574i
$718$	138.906	−	518.403i	0.193462	−	0.722009i
$719$		−	1063.07i		−	1.47854i	−0.673410	−	0.739269i	$-0.735171\pi$
$719$		−	1063.07i		−	1.47854i	0.673410	−	0.739269i	$-0.264829\pi$
$720$	−216.900	+	616.743i	−0.301250	+	0.856587i
$721$	431.245			0.598120
$722$	185.359	+	49.6669i	0.256731	+	0.0687907i
$723$	83.9722	+	465.906i	0.116144	+	0.644407i
$724$	21.4925	+	12.4087i	0.0296858	+	0.0171391i
$725$	99.8253	−	18.2854i	0.137690	−	0.0252212i
$726$	399.542	−	188.155i	0.550333	−	0.259166i
$727$	−1143.56	−	306.415i	−1.57298	−	0.421479i	−0.636238	−	0.771493i	$-0.719510\pi$
$727$	−1143.56	−	306.415i	−1.57298	−	0.421479i	−0.936744	+	0.350014i	$0.886177\pi$
$728$	323.172	+	323.172i	0.443917	+	0.443917i
$729$	−350.063	+	639.450i	−0.480197	+	0.877161i
$730$	99.3047	+	270.048i	0.136034	+	0.369928i
$731$	−1123.62	−	1946.17i	−1.53710	−	2.66234i
$732$	−17.1786	+	47.7597i	−0.0234680	+	0.0652454i
$733$	−764.676	+	204.894i	−1.04321	+	0.279529i	−0.739445	−	0.673217i	$-0.764912\pi$
$733$	−764.676	+	204.894i	−1.04321	+	0.279529i	−0.303770	+	0.952745i	$0.598245\pi$
$734$	475.718	+	274.656i	0.648117	+	0.374190i
$735$	297.969	+	507.734i	0.405400	+	0.690795i
$736$	−14.1494	−	24.5075i	−0.0192248	−	0.0332983i
$737$	−132.203	+	132.203i	−0.179379	+	0.179379i
$738$	778.224	−	74.0286i	1.05450	−	0.100310i
$739$		−	286.434i		−	0.387597i	−0.981041	−	0.193798i	$-0.937919\pi$
$739$		−	286.434i		−	0.387597i	0.981041	−	0.193798i	$-0.0620808\pi$
$740$	47.7559	−	4.33772i	0.0645349	−	0.00586179i
$741$	71.1971	−	850.884i	0.0960825	−	1.14829i
$742$	107.860	+	402.538i	0.145363	+	0.542504i
$743$	−1235.17	+	330.963i	−1.66241	+	0.445442i	−0.963049	−	0.269326i	$-0.913199\pi$
$743$	−1235.17	+	330.963i	−1.66241	+	0.445442i	−0.699362	+	0.714768i	$0.746532\pi$
$744$	−137.239	−	11.4834i	−0.184461	−	0.0154347i
$745$	−55.6834	−	46.4101i	−0.0747428	−	0.0622954i
$746$	−430.635			−0.577259
$747$	−665.600	+	473.610i	−0.891031	+	0.634017i
$748$	44.4635	+	44.4635i	0.0594431	+	0.0594431i
$749$	59.6597	−	34.4445i	0.0796524	−	0.0459874i
$750$	−312.131	−	646.048i	−0.416174	−	0.861397i
$751$	135.404	−	234.527i	0.180299	−	0.312286i	−0.761684	−	0.647949i	$-0.775627\pi$
$751$	135.404	−	234.527i	0.180299	−	0.312286i	0.941982	+	0.335663i	$0.108960\pi$
$752$	53.2524	+	198.741i	0.0708143	+	0.264283i
$753$	637.458	+	229.286i	0.846558	+	0.304497i
$754$	118.571	−	68.4567i	0.157255	−	0.0907914i
$755$	−357.542	−	972.294i	−0.473566	−	1.28781i
$756$	−7.08768	+	27.7068i	−0.00937524	+	0.0366492i
$757$	−384.680	+	384.680i	−0.508163	+	0.508163i	−0.913962	−	0.405799i	$-0.866993\pi$
$757$	−384.680	+	384.680i	−0.508163	+	0.508163i	0.405799	+	0.913962i	$0.366993\pi$
$758$	−33.9693	+	126.775i	−0.0448144	+	0.167250i
$759$	−44.3648	−	94.2075i	−0.0584516	−	0.124121i
$760$	547.764	−	386.262i	0.720742	−	0.508239i
$761$	−448.501	+	776.827i	−0.589357	+	1.02080i	0.404959	+	0.914335i	$0.367286\pi$
$761$	−448.501	+	776.827i	−0.589357	+	1.02080i	−0.994317	+	0.106462i	$0.966048\pi$
$762$	−982.384	+	177.059i	−1.28922	+	0.232361i
$763$	107.096	−	399.688i	0.140362	−	0.523838i
$764$			12.0840i			0.0158167i
$765$	1253.17	+	95.9001i	1.63813	+	0.125360i
$766$	−236.312			−0.308501
$767$	90.5183	+	24.2543i	0.118016	+	0.0316223i
$768$	148.079	−	125.212i	0.192811	−	0.163036i
$769$	427.597	+	246.873i	0.556042	+	0.321031i	0.751555	−	0.659670i	$-0.229304\pi$
$769$	427.597	+	246.873i	0.556042	+	0.321031i	−0.195513	+	0.980701i	$0.562637\pi$
$770$	−33.7887	+	195.412i	−0.0438814	+	0.253782i
$771$	97.1595	−	1161.16i	0.126018	−	1.50605i
$772$	−94.9460	−	25.4407i	−0.122987	−	0.0329543i
$773$	753.113	+	753.113i	0.974273	+	0.974273i	0.999677	−	0.0254041i	$-0.00808725\pi$
$773$	753.113	+	753.113i	0.974273	+	0.974273i	−0.0254041	+	0.999677i	$0.508087\pi$
$774$	−1298.35	+	483.727i	−1.67745	+	0.624970i
$775$	105.302	−	89.5556i	0.135873	−	0.115556i
$776$	73.3289	+	127.009i	0.0944960	+	0.163672i
$777$	−260.710	+	46.9888i	−0.335534	+	0.0604746i
$778$	300.158	−	80.4272i	0.385808	−	0.103377i
$779$	−634.795	−	366.499i	−0.814884	−	0.470474i
$780$	63.8637	+	62.9628i	0.0818765	+	0.0807216i
$781$	183.689	+	318.158i	0.235197	+	0.407373i
$782$	197.593	−	197.593i	0.252677	−	0.252677i
$783$	95.5372	+	53.7207i	0.122014	+	0.0686088i
$784$			570.195i			0.727290i
$785$	−7.60906	−	83.7714i	−0.00969308	−	0.106715i
$786$	637.120	−	300.036i	0.810585	−	0.381726i
$787$	−400.905	−	1496.20i	−0.509409	−	1.90114i	−0.426257	−	0.904602i	$-0.640168\pi$
$787$	−400.905	−	1496.20i	−0.509409	−	1.90114i	−0.0831516	−	0.996537i	$-0.526499\pi$
$788$	−5.10057	+	1.36669i	−0.00647281	+	0.00173438i
$789$	−109.811	+	158.097i	−0.139177	+	0.200376i
$790$	−1120.67	+	101.792i	−1.41857	+	0.128850i
$791$	−226.598			−0.286470
$792$	404.119	−	287.553i	0.510251	−	0.363072i
$793$	−621.741	−	621.741i	−0.784036	−	0.784036i
$794$	143.173	−	82.6608i	0.180318	−	0.104107i
$795$	277.940	+	1008.57i	0.349610	+	1.26865i
$796$	−27.7062	+	47.9885i	−0.0348068	+	0.0602871i
$797$	269.915	+	1007.34i	0.338663	+	1.26391i	0.899843	+	0.436215i	$0.143681\pi$
$797$	269.915	+	1007.34i	0.338663	+	1.26391i	−0.561179	+	0.827694i	$0.689652\pi$
$798$	−221.012	+	186.882i	−0.276957	+	0.234188i
$799$	342.552	−	197.772i	0.428725	−	0.247525i
$800$	−10.8975	+	134.854i	−0.0136218	+	0.168568i
$801$	196.272	−	237.538i	0.245033	−	0.296552i
$802$	146.540	−	146.540i	0.182719	−	0.182719i
$803$	51.6708	−	192.838i	0.0643472	−	0.240147i
$804$	16.3496	−	23.5388i	0.0203353	−	0.0292772i
$805$	−80.4575	−	13.9119i	−0.0999473	−	0.0172818i
$806$	93.2449	−	161.505i	0.115688	−	0.200378i
$807$	−262.702	+	730.360i	−0.325529	+	0.905031i
$808$	−115.283	+	430.242i	−0.142677	+	0.532478i
$809$		−	467.191i		−	0.577492i	−0.957406	−	0.288746i	$-0.906762\pi$
$809$		−	467.191i		−	0.577492i	0.957406	−	0.288746i	$-0.0932383\pi$
$810$	186.706	−	752.069i	0.230501	−	0.928480i
$811$	645.976			0.796518			0.398259	−	0.917273i	$-0.369615\pi$
$811$	645.976			0.796518			0.398259	+	0.917273i	$0.369615\pi$
$812$	4.15334	+	1.11288i	0.00511495	+	0.00137055i
$813$	−1186.45	−	426.753i	−1.45935	−	0.524912i
$814$	311.002	+	179.557i	0.382067	+	0.220586i
$815$	−431.160	−	611.434i	−0.529030	−	0.750226i
$816$	999.798	+	694.439i	1.22524	+	0.851028i
$817$	1254.88	+	336.245i	1.53596	+	0.411560i
$818$	−13.8069	−	13.8069i	−0.0168789	−	0.0168789i
$819$	−381.933	−	315.582i	−0.466341	−	0.385326i
$820$	72.2574	−	26.5712i	0.0881188	−	0.0324039i
$821$	463.438	+	802.699i	0.564480	+	0.977709i	0.997098	+	0.0761312i	$0.0242568\pi$
$821$	463.438	+	802.699i	0.564480	+	0.977709i	−0.432617	+	0.901578i	$0.642410\pi$
$822$	849.756	+	1004.95i	1.03377	+	1.22256i
$823$	506.278	−	135.657i	0.615162	−	0.164832i	0.0622344	−	0.998062i	$-0.480177\pi$
$823$	506.278	−	135.657i	0.615162	−	0.164832i	0.552927	+	0.833229i	$0.313511\pi$
$824$	992.862	+	573.229i	1.20493	+	0.695667i
$825$	−81.3360	+	491.149i	−0.0985891	+	0.595333i
$826$	−15.8827	−	27.5096i	−0.0192284	−	0.0333046i
$827$	524.578	−	524.578i	0.634314	−	0.634314i	−0.314833	−	0.949147i	$-0.601948\pi$
$827$	524.578	−	524.578i	0.634314	−	0.634314i	0.949147	+	0.314833i	$0.101948\pi$
$828$	9.25444	+	13.0060i	0.0111769	+	0.0157077i
$829$		−	800.305i		−	0.965386i	−0.875790	−	0.482693i	$-0.839659\pi$
$829$		−	800.305i		−	0.965386i	0.875790	−	0.482693i	$-0.160341\pi$
$830$	555.946	−	667.030i	0.669814	−	0.803651i
$831$	−98.6601	−	68.5273i	−0.118725	−	0.0824636i
$832$	312.371	+	1165.78i	0.375446	+	1.40118i
$833$	1058.81	−	283.708i	1.27109	−	0.340586i
$834$	−207.354	−	440.311i	−0.248626	−	0.527951i
$835$	−7.53634	−	82.9709i	−0.00902556	−	0.0993663i
$836$	−36.3518			−0.0434831
$837$	149.283	−	1.69591i	0.178355	−	0.00202618i
$838$	−268.832	−	268.832i	−0.320801	−	0.320801i
$839$	−1135.49	+	655.573i	−1.35338	+	0.781374i	−0.988721	−	0.149767i	$-0.952148\pi$
$839$	−1135.49	+	655.573i	−1.35338	+	0.781374i	−0.364658	+	0.931141i	$0.618814\pi$
$840$	−2.76234	−	388.901i	−0.00328850	−	0.462977i
$841$	−412.260	+	714.056i	−0.490203	+	0.849056i
$842$	−413.460	−	1543.05i	−0.491045	−	1.83260i
$843$	−252.485	−	1400.87i	−0.299508	−	1.66177i
$844$	52.6266	−	30.3840i	0.0623538	−	0.0360000i
$845$	−665.095	+	244.576i	−0.787095	+	0.289439i
$846$	−85.1421	−	228.526i	−0.100641	−	0.270125i
$847$	−169.900	+	169.900i	−0.200590	+	0.200590i
$848$	−262.253	+	978.743i	−0.309261	+	1.15418i
$849$	−77.6686	−	6.49887i	−0.0914825	−	0.00765473i
$850$	−1314.10	+	240.709i	−1.54600	+	0.283187i
$851$	−73.9295	+	128.050i	−0.0868737	+	0.150470i
$852$	−36.3623	−	43.0031i	−0.0426787	−	0.0504731i
$853$	−255.055	+	951.879i	−0.299010	+	1.11592i	0.638971	+	0.769231i	$0.279360\pi$
$853$	−255.055	+	951.879i	−0.299010	+	1.11592i	−0.937980	+	0.346688i	$0.887306\pi$
$854$			298.048i			0.349002i
$855$	−551.478	+	473.073i	−0.645004	+	0.553302i
$856$	183.141			0.213949
$857$	−1138.22	−	304.985i	−1.32815	−	0.355875i	−0.476122	−	0.879379i	$-0.657958\pi$
$857$	−1138.22	−	304.985i	−1.32815	−	0.355875i	−0.852023	+	0.523504i	$0.824625\pi$
$858$	119.130	+	660.977i	0.138847	+	0.770369i
$859$	937.566	+	541.304i	1.09146	+	0.630156i	0.933965	−	0.357363i	$-0.116324\pi$
$859$	937.566	+	541.304i	1.09146	+	0.630156i	0.157497	+	0.987519i	$0.449658\pi$
$860$	−111.515	+	78.6358i	−0.129668	+	0.0914370i
$861$	−384.784	+	181.205i	−0.446903	+	0.210458i
$862$	−554.550	−	148.591i	−0.643329	−	0.172380i
$863$	854.886	+	854.886i	0.990598	+	0.990598i	0.999956	−	0.00935826i	$-0.00297887\pi$
$863$	854.886	+	854.886i	0.990598	+	0.990598i	−0.00935826	+	0.999956i	$0.502979\pi$
$864$	−102.140	+	104.487i	−0.118218	+	0.120935i
$865$	−83.3606	+	180.326i	−0.0963706	+	0.208470i
$866$	−301.230	−	521.746i	−0.347841	−	0.602479i
$867$	498.619	−	1386.26i	0.575109	−	1.59891i
$868$	5.65726	−	1.51586i	0.00651758	−	0.00174638i
$869$	676.176	+	390.390i	0.778108	+	0.449241i
$870$	−112.747	−	29.3538i	−0.129595	−	0.0337400i
$871$	248.249	+	429.980i	0.285016	+	0.493663i
$872$	777.853	−	777.853i	0.892033	−	0.892033i
$873$	−92.1726	−	129.537i	−0.105581	−	0.148381i
$874$			161.546i			0.184835i
$875$	278.763	+	273.271i	0.318586	+	0.312309i
$876$	−2.55179	+	30.4967i	−0.00291300	+	0.0348136i
$877$	−98.1561	−	366.323i	−0.111923	−	0.417701i	0.887116	−	0.461547i	$-0.152705\pi$
$877$	−98.1561	−	366.323i	−0.111923	−	0.417701i	−0.999038	+	0.0438464i	$0.986039\pi$
$878$	803.321	−	215.249i	0.914944	−	0.245159i
$879$	173.661	+	14.5310i	0.197567	+	0.0165313i
$880$	−308.714	+	370.399i	−0.350811	+	0.420907i
$881$	570.971			0.648094			0.324047	−	0.946041i	$-0.394956\pi$
$881$	570.971			0.648094			0.324047	+	0.946041i	$0.394956\pi$
$882$	−64.0001	−	672.800i	−0.0725625	−	0.762812i
$883$	−119.737	−	119.737i	−0.135603	−	0.135603i	0.636047	−	0.771650i	$-0.280568\pi$
$883$	−119.737	−	119.737i	−0.135603	−	0.135603i	−0.771650	+	0.636047i	$0.780568\pi$
$884$	144.614	−	83.4932i	0.163591	−	0.0944493i
$885$	−40.3611	−	68.7747i	−0.0456058	−	0.0777116i
$886$	9.34399	−	16.1843i	0.0105463	−	0.0182667i
$887$	251.576	+	938.896i	0.283626	+	1.05851i	0.949837	+	0.312744i	$0.101248\pi$
$887$	251.576	+	938.896i	0.283626	+	1.05851i	−0.666211	+	0.745763i	$0.732085\pi$
$888$	−662.697	−	238.364i	−0.746280	−	0.268428i
$889$	470.332	−	271.547i	0.529058	−	0.305452i
$890$	−137.437	+	297.305i	−0.154424	+	0.334050i
$891$	−406.594	+	351.803i	−0.456335	+	0.394841i
$892$	−57.7473	+	57.7473i	−0.0647392	+	0.0647392i
$893$	−59.1834	+	220.875i	−0.0662748	+	0.247341i
$894$	35.4540	+	75.2858i	0.0396577	+	0.0842123i
$895$	227.526	−	1315.87i	0.254219	−	1.47024i
$896$	170.752	−	295.751i	0.190571	−	0.330079i
$897$	−272.146	+	49.0499i	−0.303395	+	0.0546821i
$898$	262.076	−	978.080i	0.291844	−	1.08918i
$899$		−	22.4462i		−	0.0249679i
$900$	−1.08406	−	76.3068i	−0.00120451	−	0.0847854i
$901$	1947.95			2.16198
$902$	556.915	+	149.225i	0.617423	+	0.165438i
$903$	575.621	−	486.730i	0.637454	−	0.539014i
$904$	−521.700	−	301.204i	−0.577102	−	0.333190i
$905$	360.500	+	62.3339i	0.398343	+	0.0688773i
$906$	−99.1646	+	1185.13i	−0.109453	+	1.30809i
$907$	852.678	+	228.474i	0.940108	+	0.251901i	0.696160	−	0.717887i	$-0.254891\pi$
$907$	852.678	+	228.474i	0.940108	+	0.251901i	0.243948	+	0.969788i	$0.421557\pi$
$908$	18.4134	+	18.4134i	0.0202791	+	0.0202791i
$909$	80.2430	−	476.139i	0.0882761	−	0.523805i
$910$	478.031	+	220.982i	0.525308	+	0.242838i
$911$	−374.442	−	648.552i	−0.411023	−	0.711912i	0.583979	−	0.811769i	$-0.301495\pi$
$911$	−374.442	−	648.552i	−0.411023	−	0.711912i	−0.995002	+	0.0998564i	$0.968162\pi$
$912$	−692.576	+	124.826i	−0.759403	+	0.136870i
$913$	−581.968	+	155.938i	−0.637424	+	0.170797i
$914$	541.107	+	312.409i	0.592021	+	0.341804i
$915$	5.31438	+	748.195i	0.00580807	+	0.817699i
$916$	−5.33036	−	9.23246i	−0.00581917	−	0.0100791i
$917$	−270.927	+	270.927i	−0.295449	+	0.295449i
$918$	−1257.65	−	707.181i	−1.36999	−	0.770350i
$919$			1476.26i			1.60638i	0.595724	+	0.803189i	$0.296865\pi$
$919$			1476.26i			1.60638i	−0.595724	+	0.803189i	$0.703135\pi$
$920$	−166.747	−	138.977i	−0.181246	−	0.151062i
$921$	−551.069	+	259.512i	−0.598337	+	0.281772i
$922$	122.655	+	457.753i	0.133031	+	0.496479i
$923$	942.364	−	252.506i	1.02098	−	0.273571i
$924$	−12.0329	+	17.3239i	−0.0130226	+	0.0187489i
$925$	638.671	−	302.990i	0.690455	−	0.327557i
$926$	−770.708			−0.832298
$927$	−1130.31	−	516.688i	−1.21932	−	0.557377i
$928$	15.5342	+	15.5342i	0.0167395	+	0.0167395i
$929$	104.797	−	60.5047i	0.112807	−	0.0651289i	−0.442535	−	0.896751i	$-0.645921\pi$
$929$	104.797	−	60.5047i	0.112807	−	0.0651289i	0.555342	+	0.831622i	$0.312587\pi$
$930$	−152.989	+	42.1603i	−0.164505	+	0.0453337i
$931$	−316.850	+	548.801i	−0.340333	+	0.589475i
$932$	32.8364	+	122.547i	0.0352322	+	0.131488i
$933$	724.550	−	612.660i	0.776581	−	0.656656i
$934$	−175.168	+	101.133i	−0.187546	+	0.108280i
$935$	841.410	+	388.964i	0.899904	+	0.416005i
$936$	−459.846	−	1234.25i	−0.491288	−	1.31865i
$937$	−21.6794	+	21.6794i	−0.0231370	+	0.0231370i	−0.718581	−	0.695444i	$-0.755208\pi$
$937$	−21.6794	+	21.6794i	−0.0231370	+	0.0231370i	0.695444	+	0.718581i	$0.255208\pi$
$938$	43.5588	−	162.563i	0.0464379	−	0.173309i
$939$	108.811	−	156.658i	0.115880	−	0.166835i
$940$	−13.8409	−	19.6280i	−0.0147244	−	0.0208809i
$941$	−376.717	+	652.494i	−0.400337	+	0.693404i	−0.993766	−	0.111482i	$-0.964440\pi$
$941$	−376.717	+	652.494i	−0.400337	+	0.693404i	0.593429	+	0.804886i	$0.297774\pi$
$942$	−32.6834	+	90.8661i	−0.0346958	+	0.0964608i
$943$	−61.4408	+	229.300i	−0.0651546	+	0.243160i
$944$		−	77.2354i		−	0.0818171i
$945$	42.9041	+	419.407i	0.0454012	+	0.443816i
$946$	−1021.88			−1.08022
$947$	276.473	+	74.0806i	0.291946	+	0.0782266i	0.401819	−	0.915719i	$-0.368378\pi$
$947$	276.473	+	74.0806i	0.291946	+	0.0782266i	−0.109874	+	0.993946i	$0.535045\pi$
$948$	−112.623	−	40.5093i	−0.118801	−	0.0427313i
$949$	−459.137	−	265.083i	−0.483812	−	0.279329i
$950$	438.785	−	635.581i	0.461879	−	0.669033i
$951$	−448.916	−	311.808i	−0.472046	−	0.327874i
$952$	−699.469	−	187.422i	−0.734736	−	0.196872i
$953$	−124.868	−	124.868i	−0.131026	−	0.131026i	0.638552	−	0.769578i	$-0.279534\pi$
$953$	−124.868	−	124.868i	−0.131026	−	0.131026i	−0.769578	+	0.638552i	$0.779534\pi$
$954$	199.588	−	1184.30i	0.209212	−	1.24141i
$955$	61.4813	+	167.191i	0.0643783	+	0.175069i
$956$	−17.2281	−	29.8400i	−0.0180210	−	0.0312133i
$957$	52.1958	+	61.7283i	0.0545410	+	0.0645019i
$958$	−1296.27	+	347.335i	−1.35310	+	0.362563i
$959$	−620.092	−	358.010i	−0.646603	−	0.373316i
$960$	507.176	−	893.043i	0.528308	−	0.930254i
$961$	465.213	+	805.773i	0.484093	+	0.838473i
$962$	674.342	−	674.342i	0.700980	−	0.700980i
$963$	−197.640	+	18.8005i	−0.205234	+	0.0195229i
$964$		−	53.5234i		−	0.0555222i
$965$	−1443.09	+	131.078i	−1.49543	+	0.135832i
$966$	76.9867	+	53.4734i	0.0796964	+	0.0553555i
$967$	−328.646	−	1226.52i	−0.339861	−	1.26838i	−0.898502	−	0.438970i	$-0.855344\pi$
$967$	−328.646	−	1226.52i	−0.339861	−	1.26838i	0.558641	−	0.829410i	$-0.311323\pi$
$968$	−617.002	+	165.325i	−0.637399	+	0.170791i
$969$	576.394	+	1223.96i	0.594833	+	1.26312i
$970$	129.815	+	108.197i	0.133830	+	0.111543i
$971$	−1494.20			−1.53883			−0.769413	−	0.638752i	$-0.779451\pi$
$971$	−1494.20			−1.53883			−0.769413	+	0.638752i	$0.779451\pi$
$972$	51.7736	−	64.1288i	0.0532650	−	0.0659762i
$973$	187.237	+	187.237i	0.192432	+	0.192432i
$974$	643.714	−	371.649i	0.660898	−	0.381569i
$975$	1203.95	+	546.213i	1.23482	+	0.560218i
$976$	−362.341	+	627.593i	−0.371251	+	0.643026i
$977$	−438.550	−	1636.69i	−0.448874	−	1.67522i	−0.705501	−	0.708709i	$-0.749278\pi$
$977$	−438.550	−	1636.69i	−0.448874	−	1.67522i	0.256628	−	0.966510i	$-0.417389\pi$
$978$	152.347	+	845.271i	0.155774	+	0.864286i
$979$	196.814	−	113.631i	0.201036	−	0.116068i
$980$	−22.9717	−	62.4689i	−0.0234405	−	0.0637438i
$981$	−759.584	+	919.287i	−0.774296	+	0.937091i
$982$	−750.486	+	750.486i	−0.764243	+	0.764243i
$983$	399.405	−	1490.60i	0.406312	−	1.51638i	−0.395311	−	0.918547i	$-0.629363\pi$
$983$	399.405	−	1490.60i	0.406312	−	1.51638i	0.801623	−	0.597829i	$-0.203970\pi$
$984$	−1126.76	−	94.2809i	−1.14508	−	0.0958139i
$985$	−63.6170	+	44.8602i	−0.0645858	+	0.0455434i
$986$	−108.466	+	187.868i	−0.110006	+	0.190536i
$987$	85.6707	+	101.317i	0.0867991	+	0.102651i
$988$	−24.9853	+	93.2466i	−0.0252888	+	0.0943791i
$989$		−	420.743i		−	0.425422i
$990$	322.691	−	471.701i	0.325951	−	0.476466i
$991$	−1790.72			−1.80698			−0.903491	−	0.428607i	$-0.859004\pi$
$991$	−1790.72			−1.80698			−0.903491	+	0.428607i	$0.859004\pi$
$992$	28.9039	+	7.74478i	0.0291370	+	0.00780724i
$993$	70.8081	+	392.868i	0.0713073	+	0.395637i
$994$	−286.396	−	165.351i	−0.288125	−	0.166349i
$995$	−139.179	+	804.924i	−0.139879	+	0.808969i
$996$	83.5563	−	39.3488i	0.0838918	−	0.0395068i
$997$	−1440.38	−	385.948i	−1.44471	−	0.387110i	−0.550532	−	0.834814i	$-0.685575\pi$
$997$	−1440.38	−	385.948i	−1.44471	−	0.387110i	−0.894181	+	0.447705i	$0.852242\pi$
$998$	−573.544	−	573.544i	−0.574693	−	0.574693i
$999$	739.632	+	189.205i	0.740372	+	0.189395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.13.8	yes	40
3.2	odd	2		135.3.l.a.118.3		40
5.2	odd	4	inner	45.3.k.a.22.3	yes	40
5.3	odd	4		225.3.o.b.157.8		40
5.4	even	2		225.3.o.b.193.3		40
9.2	odd	6		135.3.l.a.73.8		40
9.4	even	3		405.3.g.h.163.3		20
9.5	odd	6		405.3.g.g.163.8		20
9.7	even	3	inner	45.3.k.a.43.3	yes	40
15.2	even	4		135.3.l.a.37.8		40
45.2	even	12		135.3.l.a.127.3		40
45.7	odd	12	inner	45.3.k.a.7.8	✓	40
45.22	odd	12		405.3.g.h.82.3		20
45.32	even	12		405.3.g.g.82.8		20
45.34	even	6		225.3.o.b.43.8		40
45.43	odd	12		225.3.o.b.7.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.8	✓	40	45.7	odd	12	inner
45.3.k.a.13.8	yes	40	1.1	even	1	trivial
45.3.k.a.22.3	yes	40	5.2	odd	4	inner
45.3.k.a.43.3	yes	40	9.7	even	3	inner
135.3.l.a.37.8		40	15.2	even	4
135.3.l.a.73.8		40	9.2	odd	6
135.3.l.a.118.3		40	3.2	odd	2
135.3.l.a.127.3		40	45.2	even	12
225.3.o.b.7.3		40	45.43	odd	12
225.3.o.b.43.8		40	45.34	even	6
225.3.o.b.157.8		40	5.3	odd	4
225.3.o.b.193.3		40	5.4	even	2
405.3.g.g.82.8		20	45.32	even	12
405.3.g.g.163.8		20	9.5	odd	6
405.3.g.h.82.3		20	45.22	odd	12
405.3.g.h.163.3		20	9.4	even	3

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84813 + 0.495206i) q^{2} +(2.82294 + 1.01538i) q^{3} +(-0.293735 - 0.169588i) q^{4} +(-4.92689 - 0.851907i) q^{5} +(4.71435 + 3.27449i) q^{6} +(-3.01652 - 0.808273i) q^{7} +(-5.87059 - 5.87059i) q^{8} +(6.93801 + 5.73271i) q^{9} +O(q^{10})\)	\(q+(1.84813 + 0.495206i) q^{2} +(2.82294 + 1.01538i) q^{3} +(-0.293735 - 0.169588i) q^{4} +(-4.92689 - 0.851907i) q^{5} +(4.71435 + 3.27449i) q^{6} +(-3.01652 - 0.808273i) q^{7} +(-5.87059 - 5.87059i) q^{8} +(6.93801 + 5.73271i) q^{9} +(-8.68368 - 4.01426i) q^{10} +(3.31892 + 5.74855i) q^{11} +(-0.657001 - 0.776989i) q^{12} +(17.0268 - 4.56232i) q^{13} +(-5.17466 - 2.98759i) q^{14} +(-13.0433 - 7.40754i) q^{15} +(-7.26413 - 12.5818i) q^{16} +(-19.7493 + 19.7493i) q^{17} +(9.98350 + 14.0306i) q^{18} -16.1463i q^{19} +(1.30273 + 1.08578i) q^{20} +(-7.69475 - 5.34462i) q^{21} +(3.28710 + 12.2676i) q^{22} +(-5.05098 + 1.35341i) q^{23} +(-10.6115 - 22.5332i) q^{24} +(23.5485 + 8.39451i) q^{25} +33.7271 q^{26} +(13.7647 + 23.2278i) q^{27} +(0.748983 + 0.748983i) q^{28} +(3.51558 - 2.02972i) q^{29} +(-20.4375 - 20.1493i) q^{30} +(2.76468 - 4.78857i) q^{31} +(1.40066 + 5.22734i) q^{32} +(3.53219 + 19.5978i) q^{33} +(-46.2792 + 26.7193i) q^{34} +(14.1735 + 6.55207i) q^{35} +(-1.06574 - 2.86050i) q^{36} +(19.9941 - 19.9941i) q^{37} +(7.99576 - 29.8406i) q^{38} +(52.6983 + 4.40949i) q^{39} +(23.9226 + 33.9249i) q^{40} +(22.6986 - 39.3151i) q^{41} +(-11.5742 - 13.6880i) q^{42} +(-20.8248 + 77.7192i) q^{43} -2.25140i q^{44} +(-29.2991 - 34.1550i) q^{45} -10.0051 q^{46} +(-13.6796 - 3.66543i) q^{47} +(-7.73089 - 42.8937i) q^{48} +(-33.9892 - 19.6237i) q^{49} +(39.3638 + 27.1755i) q^{50} +(-75.8041 + 35.6981i) q^{51} +(-5.77509 - 1.54743i) q^{52} +(-49.3170 - 49.3170i) q^{53} +(13.9365 + 49.7445i) q^{54} +(-11.4548 - 31.1499i) q^{55} +(12.9637 + 22.4538i) q^{56} +(16.3946 - 45.5802i) q^{57} +(7.50240 - 2.01026i) q^{58} +(4.60398 + 2.65811i) q^{59} +(2.57505 + 4.38784i) q^{60} +(-24.9404 - 43.1981i) q^{61} +(7.48083 - 7.48083i) q^{62} +(-16.2950 - 22.9006i) q^{63} +68.4675i q^{64} +(-87.7760 + 7.97280i) q^{65} +(-3.17698 + 37.9685i) q^{66} +(7.28994 + 27.2064i) q^{67} +(9.15029 - 2.45181i) q^{68} +(-15.6328 - 1.30807i) q^{69} +(22.9498 + 19.1279i) q^{70} +55.3458 q^{71} +(-7.07584 - 74.3846i) q^{72} +(-21.2670 - 21.2670i) q^{73} +(46.8529 - 27.0505i) q^{74} +(57.9525 + 47.6079i) q^{75} +(-2.73822 + 4.74274i) q^{76} +(-5.36520 - 20.0232i) q^{77} +(95.2098 + 34.2458i) q^{78} +(101.867 - 58.8128i) q^{79} +(25.0710 + 68.1777i) q^{80} +(15.2721 + 79.5472i) q^{81} +(61.4190 - 61.4190i) q^{82} +(-23.4922 + 87.6742i) q^{83} +(1.35383 + 2.87484i) q^{84} +(114.127 - 80.4780i) q^{85} +(-76.9740 + 133.323i) q^{86} +(11.9852 - 2.16015i) q^{87} +(14.2633 - 53.2314i) q^{88} -34.2372i q^{89} +(-37.2349 - 77.6320i) q^{90} -55.0493 q^{91} +(1.71317 + 0.459043i) q^{92} +(12.6668 - 10.7107i) q^{93} +(-23.4666 - 13.5484i) q^{94} +(-13.7552 + 79.5513i) q^{95} +(-1.35374 + 16.1787i) q^{96} +(-17.0629 - 4.57199i) q^{97} +(-53.0988 - 53.0988i) q^{98} +(-9.92800 + 58.9099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8}+O(q^{10}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23} - 8 q^{25} - 112 q^{26} - 198 q^{27} - 88 q^{28} + 162 q^{30} - 4 q^{31} - 14 q^{32} + 96 q^{33} + 352 q^{35} + 264 q^{36} - 92 q^{37} + 330 q^{38} + 30 q^{40} - 28 q^{41} + 498 q^{42} - 2 q^{43} - 72 q^{45} - 136 q^{46} + 64 q^{47} - 510 q^{48} - 458 q^{50} - 396 q^{51} - 74 q^{52} - 608 q^{53} + 224 q^{55} - 192 q^{56} - 114 q^{57} + 30 q^{58} - 798 q^{60} + 92 q^{61} - 100 q^{62} + 24 q^{63} - 326 q^{65} + 588 q^{66} - 80 q^{67} + 626 q^{68} - 102 q^{70} + 248 q^{71} - 162 q^{72} - 8 q^{73} + 810 q^{75} - 96 q^{76} + 338 q^{77} + 1062 q^{78} + 1444 q^{80} + 204 q^{81} + 104 q^{82} + 370 q^{83} - 98 q^{85} - 328 q^{86} + 534 q^{87} - 210 q^{88} + 462 q^{90} + 152 q^{91} + 388 q^{92} - 1062 q^{93} - 360 q^{95} - 876 q^{96} + 292 q^{97} - 1876 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

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