LMFDB - Embedded newform 45.3.k.a.22.3

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			22.3
Character	$\chi$	$=$	45.22
Dual form			45.3.k.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.495206 + 1.84813i) q^{2} +(1.01538 - 2.82294i) q^{3} +(0.293735 + 0.169588i) q^{4} +(3.20122 + 3.84086i) q^{5} +(4.71435 + 3.27449i) q^{6} +(0.808273 - 3.01652i) q^{7} +(-5.87059 + 5.87059i) q^{8} +(-6.93801 - 5.73271i) q^{9} +O(q^{10})$	\(q+(-0.495206 + 1.84813i) q^{2} +(1.01538 - 2.82294i) q^{3} +(0.293735 + 0.169588i) q^{4} +(3.20122 + 3.84086i) q^{5} +(4.71435 + 3.27449i) q^{6} +(0.808273 - 3.01652i) 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} +(0.776989 - 0.657001i) q^{12} +(-4.56232 - 17.0268i) q^{13} +(5.17466 + 2.98759i) q^{14} +(14.0930 - 5.13693i) q^{15} +(-7.26413 - 12.5818i) q^{16} +(-19.7493 - 19.7493i) q^{17} +(14.0306 - 9.98350i) q^{18} +16.1463i q^{19} +(0.288946 + 1.67108i) q^{20} +(-7.69475 - 5.34462i) q^{21} +(-12.2676 + 3.28710i) q^{22} +(1.35341 + 5.05098i) q^{23} +(10.6115 + 22.5332i) q^{24} +(-4.50440 + 24.5909i) q^{25} +33.7271 q^{26} +(-23.2278 + 13.7647i) q^{27} +(0.748983 - 0.748983i) q^{28} +(-3.51558 + 2.02972i) q^{29} +(2.51481 + 28.5895i) q^{30} +(2.76468 - 4.78857i) q^{31} +(-5.22734 + 1.40066i) q^{32} +(19.5978 - 3.53219i) 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} +(-29.8406 - 7.99576i) q^{38} +(-52.6983 - 4.40949i) q^{39} +(-41.3411 - 3.75507i) q^{40} +(22.6986 - 39.3151i) q^{41} +(13.6880 - 11.5742i) q^{42} +(77.7192 + 20.8248i) q^{43} +2.25140i q^{44} +(-0.191566 - 44.9996i) q^{45} -10.0051 q^{46} +(3.66543 - 13.6796i) q^{47} +(-42.8937 + 7.73089i) q^{48} +(33.9892 + 19.6237i) q^{49} +(-43.2166 - 20.5023i) q^{50} +(-75.8041 + 35.6981i) q^{51} +(1.54743 - 5.77509i) 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} +(45.5802 + 16.3946i) q^{57} +(-2.01026 - 7.50240i) q^{58} +(-4.60398 - 2.65811i) q^{59} +(5.01076 + 0.881102i) q^{60} +(-24.9404 - 43.1981i) q^{61} +(7.48083 + 7.48083i) q^{62} +(-22.9006 + 16.2950i) q^{63} -68.4675i q^{64} +(50.7927 - 72.0298i) q^{65} +(-3.17698 + 37.9685i) q^{66} +(-27.2064 + 7.28994i) q^{67} +(-2.45181 - 9.15029i) q^{68} +(15.6328 + 1.30807i) q^{69} +(5.09030 + 29.4391i) q^{70} +55.3458 q^{71} +(74.3846 - 7.07584i) q^{72} +(-21.2670 + 21.2670i) q^{73} +(-46.8529 + 27.0505i) q^{74} +(64.8449 + 37.6847i) q^{75} +(-2.73822 + 4.74274i) q^{76} +(20.0232 - 5.36520i) q^{77} +(34.2458 - 95.2098i) 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} +(87.6742 + 23.4922i) q^{83} +(-1.35383 - 2.87484i) q^{84} +(12.6324 - 139.076i) q^{85} +(-76.9740 + 133.323i) q^{86} +(2.16015 + 11.9852i) q^{87} +(-53.2314 - 14.2633i) q^{88} +34.2372i q^{89} +(83.2601 + 21.9300i) q^{90} -55.0493 q^{91} +(-0.459043 + 1.71317i) q^{92} +(-10.7107 - 12.6668i) q^{93} +(23.4666 + 13.5484i) q^{94} +(-62.0158 + 51.6880i) q^{95} +(-1.35374 + 16.1787i) q^{96} +(4.57199 - 17.0629i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.495206	+	1.84813i	−0.247603	+	0.924066i	0.724454	+	0.689323i	$0.242092\pi$
$2$	−0.495206	+	1.84813i	−0.247603	+	0.924066i	−0.972057	+	0.234744i	$0.924575\pi$
$3$	1.01538	−	2.82294i	0.338459	−	0.940981i
$3$	1.01538	−	2.82294i	0.338459	−	0.940981i
$4$	0.293735	+	0.169588i	0.0734337	+	0.0423970i
$5$	3.20122	+	3.84086i	0.640244	+	0.768172i
$5$	3.20122	+	3.84086i	0.640244	+	0.768172i
$6$	4.71435	+	3.27449i	0.785725	+	0.545749i
$7$	0.808273	−	3.01652i	0.115468	−	0.430931i	−0.883854	−	0.467763i	$-0.845060\pi$
$7$	0.808273	−	3.01652i	0.115468	−	0.430931i	0.999321	+	0.0368322i	$0.0117267\pi$
$8$	−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	$0.735772\pi$
$12$	0.776989	−	0.657001i	0.0647491	−	0.0547501i
$13$	−4.56232	−	17.0268i	−0.350948	−	1.30976i	−0.885507	−	0.464625i	$-0.846189\pi$
$13$	−4.56232	−	17.0268i	−0.350948	−	1.30976i	0.534559	−	0.845131i	$-0.320478\pi$
$14$	5.17466	+	2.98759i	0.369619	+	0.213399i
$15$	14.0930	−	5.13693i	0.939532	−	0.342462i
$16$	−7.26413	−	12.5818i	−0.454008	−	0.786365i
$17$	−19.7493	−	19.7493i	−1.16172	−	1.16172i	−0.984099	−	0.177623i	$-0.943159\pi$
$17$	−19.7493	−	19.7493i	−1.16172	−	1.16172i	−0.177623	−	0.984099i	$-0.556841\pi$
$18$	14.0306	−	9.98350i	0.779475	−	0.554639i
$19$			16.1463i			0.849808i	0.905238	+	0.424904i	$0.139692\pi$
$19$			16.1463i			0.849808i	−0.905238	+	0.424904i	$0.860308\pi$
$20$	0.288946	+	1.67108i	0.0144473	+	0.0835541i
$21$	−7.69475	−	5.34462i	−0.366417	−	0.254505i
$22$	−12.2676	+	3.28710i	−0.557619	+	0.149414i
$23$	1.35341	+	5.05098i	0.0588437	+	0.219608i	0.989086	−	0.147337i	$-0.0470703\pi$
$23$	1.35341	+	5.05098i	0.0588437	+	0.219608i	−0.930243	+	0.366945i	$0.880404\pi$
$24$	10.6115	+	22.5332i	0.442145	+	0.938884i
$25$	−4.50440	+	24.5909i	−0.180176	+	0.983634i
$26$	33.7271			1.29720
$27$	−23.2278	+	13.7647i	−0.860290	+	0.509805i
$28$	0.748983	−	0.748983i	0.0267494	−	0.0267494i
$29$	−3.51558	+	2.02972i	−0.121227	+	0.0699905i	−0.559387	−	0.828906i	$-0.688964\pi$
$29$	−3.51558	+	2.02972i	−0.121227	+	0.0699905i	0.438160	+	0.898897i	$0.355630\pi$
$30$	2.51481	+	28.5895i	0.0838271	+	0.952984i
$31$	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	$0.138241\pi$
$32$	−5.22734	+	1.40066i	−0.163355	+	0.0437707i
$33$	19.5978	−	3.53219i	0.593872	−	0.107036i
$34$	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	0.923640	−	0.383260i	$-0.125199\pi$
$37$	19.9941	+	19.9941i	0.540380	+	0.540380i	−0.383260	+	0.923640i	$0.625199\pi$
$38$	−29.8406	−	7.99576i	−0.785279	−	0.210415i
$39$	−52.6983	−	4.40949i	−1.35124	−	0.113064i
$40$	−41.3411	−	3.75507i	−1.03353	−	0.0938767i
$41$	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	$-0.0200887\pi$
$42$	13.6880	−	11.5742i	0.325906	−	0.275577i
$43$	77.7192	+	20.8248i	1.80742	+	0.484298i	0.995097	−	0.0989041i	$-0.0315337\pi$
$43$	77.7192	+	20.8248i	1.80742	+	0.484298i	0.812327	+	0.583202i	$0.198200\pi$
$44$			2.25140i			0.0511681i
$45$	−0.191566	−	44.9996i	−0.00425703	−	0.999991i
$46$	−10.0051			−0.217502
$47$	3.66543	−	13.6796i	0.0779880	−	0.291055i	−0.915906	−	0.401392i	$-0.868526\pi$
$47$	3.66543	−	13.6796i	0.0779880	−	0.291055i	0.993894	+	0.110337i	$0.0351931\pi$
$48$	−42.8937	+	7.73089i	−0.893618	+	0.161060i
$49$	33.9892	+	19.6237i	0.693657	+	0.400483i
$50$	−43.2166	−	20.5023i	−0.864332	−	0.410045i
$51$	−75.8041	+	35.6981i	−1.48635	+	0.699962i
$52$	1.54743	−	5.77509i	0.0297583	−	0.111059i
$53$	−49.3170	+	49.3170i	−0.930509	+	0.930509i	−0.997738	−	0.0672288i	$-0.978584\pi$
$53$	−49.3170	+	49.3170i	−0.930509	+	0.930509i	0.0672288	+	0.997738i	$0.478584\pi$
$54$	−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
$57$	45.5802	+	16.3946i	0.799653	+	0.287625i
$58$	−2.01026	−	7.50240i	−0.0346597	−	0.129352i
$59$	−4.60398	−	2.65811i	−0.0780335	−	0.0450527i	0.460476	−	0.887672i	$-0.347679\pi$
$59$	−4.60398	−	2.65811i	−0.0780335	−	0.0450527i	−0.538509	+	0.842620i	$0.681012\pi$
$60$	5.01076	+	0.881102i	0.0835126	+	0.0146850i
$61$	−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
$63$	−22.9006	+	16.2950i	−0.363502	+	0.258651i
$64$		−	68.4675i		−	1.06980i
$65$	50.7927	−	72.0298i	0.781425	−	1.10815i
$66$	−3.17698	+	37.9685i	−0.0481361	+	0.575280i
$67$	−27.2064	+	7.28994i	−0.406066	+	0.108805i	−0.456070	−	0.889944i	$-0.650743\pi$
$67$	−27.2064	+	7.28994i	−0.406066	+	0.108805i	0.0500038	+	0.998749i	$0.484077\pi$
$68$	−2.45181	−	9.15029i	−0.0360561	−	0.134563i
$69$	15.6328	+	1.30807i	0.226563	+	0.0189575i
$70$	5.09030	+	29.4391i	0.0727186	+	0.420558i
$71$	55.3458			0.779519			0.389759	−	0.920917i	$-0.372558\pi$
$71$	55.3458			0.779519			0.389759	+	0.920917i	$0.372558\pi$
$72$	74.3846	−	7.07584i	1.03312	−	0.0982756i
$73$	−21.2670	+	21.2670i	−0.291329	+	0.291329i	−0.837605	−	0.546276i	$-0.816045\pi$
$73$	−21.2670	+	21.2670i	−0.291329	+	0.291329i	0.546276	+	0.837605i	$0.316045\pi$
$74$	−46.8529	+	27.0505i	−0.633147	+	0.365547i
$75$	64.8449	+	37.6847i	0.864599	+	0.502462i
$76$	−2.73822	+	4.74274i	−0.0360293	+	0.0624045i
$77$	20.0232	−	5.36520i	0.260041	−	0.0696779i
$78$	34.2458	−	95.2098i	0.439049	−	1.22064i
$79$	−101.867	+	58.8128i	−1.28945	+	0.744465i	−0.978556	−	0.205979i	$-0.933962\pi$
$79$	−101.867	+	58.8128i	−1.28945	+	0.744465i	−0.310896	+	0.950444i	$0.600629\pi$
$80$	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
$83$	87.6742	+	23.4922i	1.05632	+	0.283039i	0.744859	−	0.667222i	$-0.232517\pi$
$83$	87.6742	+	23.4922i	1.05632	+	0.283039i	0.311456	+	0.950261i	$0.399183\pi$
$84$	−1.35383	−	2.87484i	−0.0161171	−	0.0342242i
$85$	12.6324	−	139.076i	0.148617	−	1.63619i
$86$	−76.9740	+	133.323i	−0.895047	+	1.55027i
$87$	2.16015	+	11.9852i	0.0248293	+	0.137761i
$88$	−53.2314	−	14.2633i	−0.604902	−	0.162083i
$89$			34.2372i			0.384687i	0.981328	+	0.192344i	$0.0616088\pi$
$89$			34.2372i			0.384687i	−0.981328	+	0.192344i	$0.938391\pi$
$90$	83.2601	+	21.9300i	0.925112	+	0.243667i
$91$	−55.0493			−0.604938
$92$	−0.459043	+	1.71317i	−0.00498959	+	0.0186214i
$93$	−10.7107	−	12.6668i	−0.115168	−	0.136202i
$94$	23.4666	+	13.5484i	0.249644	+	0.144132i
$95$	−62.0158	+	51.6880i	−0.652798	+	0.544084i
$96$	−1.35374	+	16.1787i	−0.0141015	+	0.168528i
$97$	4.57199	−	17.0629i	0.0471339	−	0.175906i	−0.938346	−	0.345697i	$-0.887643\pi$
$97$	4.57199	−	17.0629i	0.0471339	−	0.175906i	0.985480	+	0.169791i	$0.0543092\pi$
$98$	−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	$0.918902\pi$
$102$	−28.4362	−	157.774i	−0.278786	−	1.54680i
$103$	35.7403	+	133.385i	0.346993	+	1.29500i	0.890267	+	0.455440i	$0.150518\pi$
$103$	35.7403	+	133.385i	0.346993	+	1.29500i	−0.543274	+	0.839556i	$0.682815\pi$
$104$	126.741	+	73.1740i	1.21866	+	0.703596i
$105$	−4.10467	−	46.6637i	−0.0390921	−	0.444417i
$106$	−66.7223	−	115.566i	−0.629455	−	1.09025i
$107$	−15.5982	−	15.5982i	−0.145777	−	0.145777i	0.630451	−	0.776229i	$-0.282870\pi$
$107$	−15.5982	−	15.5982i	−0.145777	−	0.145777i	−0.776229	+	0.630451i	$0.782870\pi$
$108$	−9.15715	+	0.104029i	−0.0847885	+	0.000963227i
$109$		−	132.500i		−	1.21560i	−0.794092	−	0.607798i	$-0.792053\pi$
$109$		−	132.500i		−	1.21560i	0.794092	−	0.607798i	$-0.207947\pi$
$110$	−51.8966	−	36.5955i	−0.471788	−	0.332686i
$111$	76.7436	−	36.1406i	0.691384	−	0.325591i
$112$	−43.8247	+	11.7428i	−0.391292	+	0.104846i
$113$	−18.7798	−	70.0870i	−0.166192	−	0.620239i	−0.997885	−	0.0650025i	$-0.979294\pi$
$113$	−18.7798	−	70.0870i	−0.166192	−	0.620239i	0.831693	−	0.555236i	$-0.187372\pi$
$114$	−52.8711	+	76.1196i	−0.463781	+	0.667716i
$115$	−15.0676	+	21.3675i	−0.131022	+	0.185805i
$116$	−1.37687			−0.0118695
$117$	−65.9564	+	144.287i	−0.563730	+	1.23322i
$118$	7.19245	−	7.19245i	0.0609530	−	0.0609530i
$119$	−75.5368	+	43.6112i	−0.634763	+	0.366481i
$120$	−52.5772	+	112.891i	−0.438144	+	0.940757i
$121$	38.4695	−	66.6311i	0.317930	−	0.550670i
$122$	92.1865	−	24.7013i	0.755627	−	0.202470i
$123$	−87.9366	−	103.996i	−0.714932	−	0.845500i
$124$	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	0.0312482	−	0.999512i	$-0.490052\pi$
$127$	−122.969	−	122.969i	−0.968263	−	0.968263i	−0.999512	+	0.0312482i	$0.990052\pi$
$128$	105.628	+	28.3028i	0.825216	+	0.221116i
$129$	137.702	−	198.252i	1.06745	−	1.53684i
$130$	107.968	+	129.541i	0.830523	+	0.996471i
$131$	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	$0.0115411\pi$
$132$	6.35557	+	2.28602i	0.0481482	+	0.0173183i
$133$	48.7057	+	13.0507i	0.366208	+	0.0981253i
$134$		−	53.8911i		−	0.402173i
$135$	−127.226	−	45.1508i	−0.942413	−	0.334451i
$136$	231.880			1.70500
$137$	−59.3417	+	221.466i	−0.433151	+	1.61654i	0.312302	+	0.949983i	$0.398900\pi$
$137$	−59.3417	+	221.466i	−0.433151	+	1.61654i	−0.745453	+	0.666558i	$0.767767\pi$
$138$	−10.1590	+	28.2438i	−0.0736156	+	0.204665i
$139$	73.4301	+	42.3949i	0.528274	+	0.304999i	0.740313	−	0.672262i	$-0.234677\pi$
$139$	73.4301	+	42.3949i	0.528274	+	0.304999i	−0.212039	+	0.977261i	$0.568010\pi$
$140$	5.27439	+	0.479080i	0.0376742	+	0.00342200i
$141$	−34.8949	−	24.2373i	−0.247482	−	0.171896i
$142$	−27.4076	+	102.286i	−0.193011	+	0.720327i
$143$	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
$147$	89.9083	−	76.0241i	0.611621	−	0.517171i
$148$	2.48220	+	9.26370i	0.0167716	+	0.0625926i
$149$	−12.5553	−	7.24882i	−0.0842639	−	0.0486498i	0.457276	−	0.889325i	$-0.348825\pi$
$149$	−12.5553	−	7.24882i	−0.0842639	−	0.0486498i	−0.541540	+	0.840675i	$0.682158\pi$
$150$	−101.758	+	101.180i	−0.678386	+	0.674536i
$151$	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
$153$	23.8039	+	250.238i	0.155581	+	1.63554i
$154$			39.6624i			0.257548i
$155$	27.2426	−	4.71051i	0.175759	−	0.0303904i
$156$	−14.7315	−	10.2322i	−0.0944328	−	0.0655911i
$157$	−16.2500	+	4.35418i	−0.103503	+	0.0277336i	−0.310199	−	0.950672i	$-0.600396\pi$
$157$	−16.2500	+	4.35418i	−0.103503	+	0.0277336i	0.206696	+	0.978405i	$0.433729\pi$
$158$	−58.2488	−	217.388i	−0.368664	−	1.37587i
$159$	89.1436	+	189.294i	0.560652	+	1.19053i
$160$	−22.1136	−	15.5937i	−0.138210	−	0.0974604i
$161$	16.3303			0.101430
$162$	−154.577	−	11.1674i	−0.954177	−	0.0689348i
$163$	105.806	−	105.806i	0.649119	−	0.649119i	−0.303661	−	0.952780i	$-0.598209\pi$
$163$	105.806	−	105.806i	0.649119	−	0.649119i	0.952780	+	0.303661i	$0.0982090\pi$
$164$	13.3347	−	7.69881i	0.0813093	−	0.0469439i
$165$	76.3034	+	63.9650i	0.462445	+	0.387667i
$166$	−86.8335	+	150.400i	−0.523093	+	0.906024i
$167$	−16.0947	+	4.31257i	−0.0963756	+	0.0258238i	−0.306685	−	0.951811i	$-0.599220\pi$
$167$	−16.0947	+	4.31257i	−0.0963756	+	0.0258238i	0.210309	+	0.977635i	$0.432553\pi$
$168$	76.5488	−	13.7967i	0.455647	−	0.0821231i
$169$	−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
$173$	−38.3785	−	10.2835i	−0.221841	−	0.0594422i	0.146186	−	0.989257i	$-0.453300\pi$
$173$	−38.3785	−	10.2835i	−0.221841	−	0.0594422i	−0.368027	+	0.929815i	$0.619967\pi$
$174$	−23.2200	−	1.94292i	−0.133448	−	0.0111662i
$175$	70.5380	+	33.4637i	0.403074	+	0.191221i
$176$	48.2182	−	83.5163i	0.273967	−	0.474525i
$177$	−12.1785	+	10.2978i	−0.0688049	+	0.0581796i
$178$	−63.2749	−	16.9544i	−0.355477	−	0.0952497i
$179$		−	267.079i		−	1.49206i	−0.665913	−	0.746030i	$-0.731958\pi$
$179$		−	267.079i		−	1.49206i	0.665913	−	0.746030i	$-0.268042\pi$
$180$	7.57512	−	13.2504i	0.0420840	−	0.0736135i
$181$	−73.1699			−0.404254			−0.202127	−	0.979359i	$-0.564785\pi$
$181$	−73.1699			−0.404254			−0.202127	+	0.979359i	$0.564785\pi$
$182$	27.2607	−	101.738i	0.149784	−	0.559003i
$183$	−147.270	+	26.5430i	−0.804753	+	0.145044i
$184$	−37.5975	−	21.7069i	−0.204334	−	0.117972i
$185$	−12.7890	+	140.800i	−0.0691298	+	0.761080i
$186$	28.7138	−	13.5221i	0.154375	−	0.0726994i
$187$	47.9833	−	179.076i	0.256595	−	0.957625i
$188$	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	$0.863064\pi$
$192$	−193.280	−	69.5204i	−1.00667	−	0.362085i
$193$	−75.0075	−	279.932i	−0.388640	−	1.45042i	−0.832349	−	0.554252i	$-0.813004\pi$
$193$	−75.0075	−	279.932i	−0.388640	−	1.45042i	0.443709	−	0.896171i	$-0.353662\pi$
$194$	29.2704	+	16.8993i	0.150878	+	0.0871097i
$195$	−151.762	−	216.522i	−0.778269	−	1.11037i
$196$	6.65587	+	11.5283i	0.0339585	+	0.0588179i
$197$	11.0087	+	11.0087i	0.0558817	+	0.0558817i	0.734495	−	0.678614i	$-0.237419\pi$
$197$	11.0087	+	11.0087i	0.0558817	+	0.0558817i	−0.678614	+	0.734495i	$0.737419\pi$
$198$	103.957	+	47.5208i	0.525035	+	0.240004i
$199$			163.374i			0.820973i	0.911867	+	0.410487i	$0.134641\pi$
$199$			163.374i			0.820973i	−0.911867	+	0.410487i	$0.865359\pi$
$200$	−117.919	−	170.806i	−0.589597	−	0.854032i
$201$	−7.04573	+	84.2043i	−0.0350534	+	0.418927i
$202$	99.1530	−	26.5680i	0.490856	−	0.131525i
$203$	3.28114	+	12.2454i	0.0161633	+	0.0603221i
$204$	−28.3203	−	2.36968i	−0.138825	−	0.0116161i
$205$	223.667	−	38.6741i	1.09106	−	0.188654i
$206$	−264.211			−1.28258
$207$	19.5659	−	42.8025i	0.0945210	−	0.206775i
$208$	−181.088	+	181.088i	−0.870613	+	0.870613i
$209$	−92.8180	+	53.5885i	−0.444105	+	0.256404i
$210$	88.2735	+	15.5222i	0.420350	+	0.0739151i
$211$	−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	$0.306237\pi$
$212$	−22.8497	+	6.12255i	−0.107781	+	0.0288800i
$213$	56.1970	−	156.238i	0.263836	−	0.733512i
$214$	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
$218$	244.878	+	65.6148i	1.12329	+	0.300985i
$219$	38.4415	+	81.6297i	0.175532	+	0.372738i
$220$	−8.64730	+	7.20721i	−0.0393059	+	0.0327601i
$221$	−246.165	+	426.370i	−1.11387	+	1.92928i
$222$	28.7887	+	159.729i	0.129679	+	0.719502i
$223$	−232.577	−	62.3187i	−1.04294	−	0.279456i	−0.303611	−	0.952796i	$-0.598192\pi$
$223$	−232.577	−	62.3187i	−1.04294	−	0.279456i	−0.739333	+	0.673340i	$0.764859\pi$
$224$			16.9005i			0.0754486i
$225$	172.224	−	144.789i	0.765439	−	0.643508i
$226$	138.830			0.614292
$227$	19.8711	−	74.1598i	0.0875377	−	0.326695i	−0.908245	−	0.418439i	$-0.862577\pi$
$227$	19.8711	−	74.1598i	0.0875377	−	0.326695i	0.995783	+	0.0917437i	$0.0292440\pi$
$228$	10.6082	+	12.5455i	0.0465270	+	0.0550243i
$229$	−27.2203	−	15.7156i	−0.118866	−	0.0686272i	0.439388	−	0.898297i	$-0.355195\pi$
$229$	−27.2203	−	15.7156i	−0.118866	−	0.0686272i	−0.558254	+	0.829670i	$0.688529\pi$
$230$	−32.0285	−	38.4282i	−0.139254	−	0.167079i
$231$	5.18546	−	61.9720i	0.0224479	−	0.268277i
$232$	8.72288	−	32.5542i	0.0375986	−	0.140320i
$233$	−264.496	+	264.496i	−1.13518	+	1.13518i	−0.145874	+	0.989303i	$0.546599\pi$
$233$	−264.496	+	264.496i	−1.13518	+	1.13518i	−0.989303	+	0.145874i	$0.953401\pi$
$234$	−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
$237$	62.5919	+	347.281i	0.264101	+	1.46532i
$238$	−43.1930	−	161.199i	−0.181483	−	0.677305i
$239$	−87.9779	−	50.7940i	−0.368108	−	0.212527i	0.304523	−	0.952505i	$-0.401503\pi$
$239$	−87.9779	−	50.7940i	−0.368108	−	0.212527i	−0.672632	+	0.739977i	$0.734836\pi$
$240$	−167.005	−	140.000i	−0.695855	−	0.583334i
$241$	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
$243$	240.064	+	37.6584i	0.987919	+	0.154973i
$244$		−	16.9184i		−	0.0693377i
$245$	33.4351	+	193.367i	0.136470	+	0.789254i
$246$	235.746	−	111.019i	0.958317	−	0.451296i
$247$	274.921	−	73.6649i	1.11304	−	0.298238i
$248$	11.8814	+	44.3421i	0.0479090	+	0.178799i
$249$	155.340	−	223.646i	0.623854	−	0.898175i
$250$	−59.5994	−	231.621i	−0.238398	−	0.926484i
$251$	225.813			0.899654			0.449827	−	0.893116i	$-0.351486\pi$
$251$	225.813			0.899654			0.449827	+	0.893116i	$0.351486\pi$
$252$	−9.49015	+	0.902752i	−0.0376593	+	0.00358235i
$253$	−24.5439	+	24.5439i	−0.0970116	+	0.0970116i
$254$	288.159	−	166.369i	1.13448	−	0.654995i
$255$	−379.777	−	176.875i	−1.48932	−	0.693629i
$256$	32.3201	−	55.9801i	0.126251	−	0.218672i
$257$	375.172	−	100.527i	1.45981	−	0.391156i	0.560389	−	0.828230i	$-0.310652\pi$
$257$	375.172	−	100.527i	1.45981	−	0.391156i	0.899426	+	0.437073i	$0.143985\pi$
$258$	298.205	+	352.666i	1.15583	+	1.36692i
$259$	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
$263$	61.9775	+	16.6068i	0.235656	+	0.0631438i	0.374714	−	0.927140i	$-0.377741\pi$
$263$	61.9775	+	16.6068i	0.235656	+	0.0631438i	−0.139058	+	0.990284i	$0.544408\pi$
$264$	−94.3145	+	135.787i	−0.357252	+	0.514343i
$265$	−347.294	−	31.5451i	−1.31054	−	0.119038i
$266$	−48.2387	+	83.5519i	−0.181349	+	0.314105i
$267$	96.6496	+	34.7637i	0.361984	+	0.130201i
$268$	−9.22776	−	2.47257i	−0.0344319	−	0.00922601i
$269$		−	258.723i		−	0.961795i	−0.876777	−	0.480898i	$-0.840311\pi$
$269$		−	258.723i		−	0.961795i	0.876777	−	0.480898i	$-0.159689\pi$
$270$	146.448	−	212.771i	0.542399	−	0.788042i
$271$	−420.290			−1.55088			−0.775442	−	0.631418i	$-0.782473\pi$
$271$	−420.290			−1.55088			−0.775442	+	0.631418i	$0.782473\pi$
$272$	−105.021	+	391.943i	−0.386106	+	1.44097i
$273$	−55.8959	+	155.401i	−0.204747	+	0.569235i
$274$	−379.912	−	219.343i	−1.38654	−	0.800520i
$275$	−156.311	+	55.7215i	−0.568405	+	0.202623i
$276$	4.37008	+	3.03537i	0.0158336	+	0.0109977i
$277$	10.3635	−	38.6770i	0.0374133	−	0.139628i	−0.944693	−	0.327956i	$-0.893640\pi$
$277$	10.3635	−	38.6770i	0.0374133	−	0.139628i	0.982106	+	0.188328i	$0.0603068\pi$
$278$	−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	$-0.486634\pi$
$282$	62.0739	−	52.4880i	0.220120	−	0.186128i
$283$	6.72412	+	25.0948i	0.0237602	+	0.0886741i	0.976788	−	0.214209i	$-0.0687174\pi$
$283$	6.72412	+	25.0948i	0.0237602	+	0.0886741i	−0.953028	+	0.302883i	$0.902051\pi$
$284$	16.2570	+	9.38598i	0.0572430	+	0.0330492i
$285$	82.9427	+	227.550i	0.291027	+	0.798421i
$286$	111.938	+	193.882i	0.391391	+	0.677909i
$287$	−100.248	−	100.248i	−0.349296	−	0.349296i
$288$	44.2970	+	20.2490i	0.153809	+	0.0703091i
$289$			491.068i			1.69920i
$290$	22.3804	−	31.7379i	0.0771737	−	0.109441i
$291$	−43.5252	−	30.2317i	−0.149571	−	0.103889i
$292$	−9.85350	+	2.64024i	−0.0337449	+	0.00904191i
$293$	−15.0346	−	56.1100i	−0.0513127	−	0.191502i	0.935512	−	0.353295i	$-0.114939\pi$
$293$	−15.0346	−	56.1100i	−0.0513127	−	0.191502i	−0.986825	+	0.161793i	$0.948272\pi$
$294$	95.9795	+	203.810i	0.326461	+	0.693232i
$295$	−4.52892	−	26.1924i	−0.0153523	−	0.0887879i
$296$	−234.754			−0.793087
$297$	−156.219	−	87.8420i	−0.525989	−	0.295764i
$298$	19.6142	−	19.6142i	0.0658196	−	0.0658196i
$299$	79.8275	−	46.0884i	0.266982	−	0.154142i
$300$	12.6563	+	22.0662i	0.0421878	+	0.0735541i
$301$	125.637	−	217.609i	0.417398	−	0.722954i
$302$	−382.915	+	102.602i	−1.26793	+	0.339741i
$303$	−158.399	+	28.5488i	−0.522768	+	0.0942206i
$304$	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	0.433499	−	0.901154i	$-0.357279\pi$
$307$	−143.570	−	143.570i	−0.467655	−	0.467655i	−0.901154	+	0.433499i	$0.857279\pi$
$308$	6.79138	+	1.81974i	0.0220499	+	0.00590826i
$309$	412.827	+	34.5430i	1.33601	+	0.111790i
$310$	−4.78504	+	52.6806i	−0.0154356	+	0.169937i
$311$	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	$-0.00313188\pi$
$312$	335.256	−	283.483i	1.07454	−	0.908601i
$313$	−61.4135	−	16.4557i	−0.196209	−	0.0525741i	0.159376	−	0.987218i	$-0.449052\pi$
$313$	−61.4135	−	16.4557i	−0.196209	−	0.0525741i	−0.355585	+	0.934644i	$0.615718\pi$
$314$		−	32.1884i		−	0.102511i
$315$	−135.897	−	35.7941i	−0.431419	−	0.113632i
$316$	−39.8957			−0.126252
$317$	47.1551	−	175.985i	0.148754	−	0.555159i	−0.850805	−	0.525481i	$-0.823885\pi$
$317$	47.1551	−	175.985i	0.148754	−	0.555159i	0.999560	−	0.0296774i	$-0.00944799\pi$
$318$	−393.986	+	71.0096i	−1.23895	+	0.223301i
$319$	−23.3359	−	13.4730i	−0.0731533	−	0.0422351i
$320$	262.974	−	219.179i	0.821793	−	0.684935i
$321$	−59.8707	+	28.1947i	−0.186513	+	0.0878339i
$322$	−8.08685	+	30.1805i	−0.0251144	+	0.0937284i
$323$	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
$327$	−374.040	−	134.538i	−1.14385	−	0.411430i
$328$	97.5487	+	364.057i	0.297405	+	1.10993i
$329$	−38.3020	−	22.1137i	−0.116420	−	0.0672149i
$330$	−156.002	+	109.343i	−0.472733	+	0.331342i
$331$	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
$333$	−24.0989	−	253.339i	−0.0723691	−	0.760779i
$334$		−	31.8808i		−	0.0954515i
$335$	−115.093	−	81.1594i	−0.343562	−	0.242267i
$336$	−11.3494	+	135.638i	−0.0337780	+	0.403685i
$337$	−308.158	+	82.5706i	−0.914414	+	0.245017i	−0.685196	−	0.728359i	$-0.740284\pi$
$337$	−308.158	+	82.5706i	−0.914414	+	0.245017i	−0.229218	+	0.973375i	$0.573617\pi$
$338$	−70.1844	−	261.932i	−0.207646	−	0.774946i
$339$	−216.920	−	18.1506i	−0.639882	−	0.0535417i
$340$	27.2962	−	38.7091i	0.0802829	−	0.113850i
$341$	36.7031			0.107634
$342$	161.197	+	226.542i	0.471336	+	0.662404i
$343$	194.872	−	194.872i	0.568139	−	0.568139i
$344$	−578.512	+	334.004i	−1.68172	+	0.970941i
$345$	45.0201	+	64.2310i	0.130493	+	0.186177i
$346$	38.0105	−	65.8362i	0.109857	−	0.190278i
$347$	433.595	−	116.181i	1.24955	−	0.334817i	0.427390	−	0.904067i	$-0.359433\pi$
$347$	433.595	−	116.181i	1.24955	−	0.334817i	0.822164	+	0.569250i	$0.192767\pi$
$348$	−1.39804	+	3.88681i	−0.00401736	+	0.0111690i
$349$	264.288	−	152.587i	0.757272	−	0.437211i	−0.0710435	−	0.997473i	$-0.522633\pi$
$349$	264.288	−	152.587i	0.757272	−	0.437211i	0.828315	+	0.560262i	$0.189300\pi$
$350$	−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
$353$	−8.48704	−	2.27410i	−0.0240426	−	0.00644220i	0.246778	−	0.969072i	$-0.420628\pi$
$353$	−8.48704	−	2.27410i	−0.0240426	−	0.00644220i	−0.270820	+	0.962630i	$0.587295\pi$
$354$	−13.0008	−	27.6070i	−0.0367255	−	0.0779857i
$355$	177.174	+	212.576i	0.499082	+	0.598804i
$356$	−5.80621	+	10.0567i	−0.0163096	+	0.0282490i
$357$	46.4135	+	257.518i	0.130010	+	0.721339i
$358$	493.597	+	132.259i	1.37876	+	0.369438i
$359$			280.501i			0.781339i	0.920531	+	0.390670i	$0.127757\pi$
$359$			280.501i			0.781339i	−0.920531	+	0.390670i	$0.872243\pi$
$360$	265.299	+	263.050i	0.736941	+	0.730693i
$361$	100.296			0.277827
$362$	36.2341	−	135.228i	0.100094	−	0.373557i
$363$	−149.035	−	176.253i	−0.410564	−	0.485545i
$364$	−16.1699	−	9.33570i	−0.0444228	−	0.0256475i
$365$	−149.764	−	13.6033i	−0.410313	−	0.0372692i
$366$	23.8738	−	285.319i	0.0652290	−	0.779559i
$367$	−74.3063	+	277.315i	−0.202469	+	0.755626i	0.787737	+	0.616012i	$0.211253\pi$
$367$	−74.3063	+	277.315i	−0.202469	+	0.755626i	−0.990206	+	0.139614i	$0.955414\pi$
$368$	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
$372$	−0.997967	−	5.53707i	−0.00268271	−	0.0148846i
$373$	58.2527	+	217.402i	0.156174	+	0.582848i	0.999002	+	0.0446653i	$0.0142221\pi$
$373$	58.2527	+	217.402i	0.156174	+	0.582848i	−0.842828	+	0.538182i	$0.819111\pi$
$374$	307.195	+	177.359i	0.821376	+	0.474222i
$375$	62.8412	+	369.697i	0.167577	+	0.985859i
$376$	58.7890	+	101.826i	0.156354	+	0.270813i
$377$	50.5990	+	50.5990i	0.134215	+	0.134215i
$378$	−161.320	+	1.83265i	−0.426771	+	0.00484827i
$379$		−	68.5964i		−	0.180993i	−0.995897	−	0.0904966i	$-0.971155\pi$
$379$		−	68.5964i		−	0.180993i	0.995897	−	0.0904966i	$-0.0288454\pi$
$380$	−26.9819	+	4.66543i	−0.0710049	+	0.0122774i
$381$	−471.996	+	222.275i	−1.23884	+	0.583400i
$382$	65.8443	−	17.6429i	0.172367	−	0.0461857i
$383$	31.9663	+	119.300i	0.0834630	+	0.311488i	0.995019	−	0.0996886i	$-0.0317846\pi$
$383$	31.9663	+	119.300i	0.0834630	+	0.311488i	−0.911556	+	0.411177i	$0.865118\pi$
$384$	187.149	−	269.443i	0.487368	−	0.701674i
$385$	84.7055	+	59.7311i	0.220014	+	0.155146i
$386$	554.495			1.43652
$387$	−419.835	−	590.025i	−1.08484	−	1.52461i
$388$	4.23661	−	4.23661i	0.0109191	−	0.0109191i
$389$	−140.653	+	81.2059i	−0.361575	+	0.208755i	−0.669771	−	0.742567i	$-0.733608\pi$
$389$	−140.653	+	81.2059i	−0.361575	+	0.208755i	0.308196	+	0.951323i	$0.400275\pi$
$390$	475.316	−	173.254i	1.21876	−	0.444241i
$391$	73.0244	−	126.482i	0.186763	−	0.323483i
$392$	−314.739	+	84.3340i	−0.802905	+	0.215138i
$393$	−237.655	−	281.058i	−0.604720	−	0.715159i
$394$	−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	0.779857	−	0.625958i	$-0.215292\pi$
$397$	61.0977	+	61.0977i	0.153899	+	0.153899i	−0.625958	+	0.779857i	$0.715292\pi$
$398$	−301.936	−	80.9036i	−0.758634	−	0.203275i
$399$	86.2960	−	124.242i	0.216281	−	0.311384i
$400$	342.119	−	121.958i	0.855297	−	0.304894i
$401$	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	$0.123546\pi$
$402$	−152.132	−	54.7199i	−0.378437	−	0.136119i
$403$	−94.1476	−	25.2268i	−0.233617	−	0.0625974i
$404$		−	18.1969i		−	0.0450418i
$405$	−256.641	+	313.306i	−0.633680	+	0.773595i
$406$	−24.2559			−0.0597437
$407$	−48.5780	+	181.296i	−0.119356	+	0.445444i
$408$	235.446	−	654.583i	0.577073	−	1.60437i
$409$	8.83799	+	5.10262i	0.0216088	+	0.0124758i	0.510765	−	0.859720i	$-0.329362\pi$
$409$	8.83799	+	5.10262i	0.0216088	+	0.0124758i	−0.489157	+	0.872196i	$0.662695\pi$
$410$	−39.2861	+	432.518i	−0.0958198	+	1.05492i
$411$	564.932	+	392.390i	1.37453	+	0.954720i
$412$	−12.1222	+	45.2408i	−0.0294229	+	0.109808i
$413$	−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
$417$	194.238	−	164.242i	0.465798	−	0.393866i
$418$	−53.0747	−	198.077i	−0.126973	−	0.473869i
$419$	172.082	+	99.3518i	0.410698	+	0.237117i	0.691090	−	0.722769i	$-0.257131\pi$
$419$	172.082	+	99.3518i	0.410698	+	0.237117i	−0.280392	+	0.959886i	$0.590464\pi$
$420$	6.70792	−	14.4029i	0.0159712	−	0.0342925i
$421$	−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
$423$	−103.852	+	73.8963i	−0.245513	+	0.174696i
$424$		−	579.039i		−	1.36566i
$425$	574.610	−	396.693i	1.35202	−	0.933395i
$426$	260.920	+	181.230i	0.612488	+	0.425421i
$427$	−150.467	+	40.3174i	−0.352381	+	0.0944201i
$428$	−1.93646	−	7.22698i	−0.00452445	−	0.0168855i
$429$	−149.553	−	317.573i	−0.348609	−	0.740264i
$430$	−758.485	+	131.149i	−1.76392	+	0.304999i
$431$	−300.059			−0.696194			−0.348097	−	0.937459i	$-0.613172\pi$
$431$	−300.059			−0.696194			−0.348097	+	0.937459i	$0.613172\pi$
$432$	341.916	+	192.260i	0.791472	+	0.445046i
$433$	−222.651	+	222.651i	−0.514205	+	0.514205i	−0.915812	−	0.401607i	$-0.868452\pi$
$433$	−222.651	+	222.651i	−0.514205	+	0.514205i	0.401607	+	0.915812i	$0.368452\pi$
$434$	28.6126	−	16.5195i	0.0659277	−	0.0380634i
$435$	−39.1185	+	46.6642i	−0.0899275	+	0.107274i
$436$	22.4704	−	38.9199i	0.0515376	−	0.0892657i
$437$	−81.5549	+	21.8526i	−0.186624	+	0.0500059i
$438$	−169.899	+	30.6216i	−0.387897	+	0.0699123i
$439$	−376.432	+	217.333i	−0.857476	+	0.495064i	−0.863166	−	0.504920i	$-0.831522\pi$
$439$	−376.432	+	217.333i	−0.857476	+	0.495064i	0.00569024	+	0.999984i	$0.498189\pi$
$440$	−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
$443$	−9.43446	−	2.52796i	−0.0212967	−	0.00570644i	0.248155	−	0.968720i	$-0.420176\pi$
$443$	−9.43446	−	2.52796i	−0.0212967	−	0.00570644i	−0.269452	+	0.963014i	$0.586842\pi$
$444$	28.6713	+	2.39905i	0.0645750	+	0.00540326i
$445$	−131.500	+	109.601i	−0.295506	+	0.246294i
$446$	230.347	−	398.972i	0.516472	−	0.894556i
$447$	−33.2114	+	28.0827i	−0.0742984	+	0.0628247i
$448$	−206.533	−	55.3404i	−0.461012	−	0.123528i
$449$			529.226i			1.17868i	0.807886	+	0.589339i	$0.200612\pi$
$449$			529.226i			1.17868i	−0.807886	+	0.589339i	$0.799388\pi$
$450$	182.304	+	389.993i	0.405119	+	0.866651i
$451$	301.339			0.668158
$452$	6.36964	−	23.7718i	0.0140921	−	0.0525925i
$453$	611.714	−	110.252i	1.35036	−	0.243381i
$454$	127.217	+	73.4488i	0.280214	+	0.161781i
$455$	−176.225	−	211.437i	−0.387307	−	0.464696i
$456$	−363.829	+	171.336i	−0.797871	+	0.375738i
$457$	−84.5200	+	315.433i	−0.184945	+	0.690225i	0.809697	+	0.586848i	$0.199632\pi$
$457$	−84.5200	+	315.433i	−0.184945	+	0.690225i	−0.994642	+	0.103377i	$0.967035\pi$
$458$	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	$0.746760\pi$
$462$	111.965	+	40.2723i	0.242348	+	0.0871695i
$463$	104.255	+	389.085i	0.225173	+	0.840356i	0.982335	+	0.187129i	$0.0599183\pi$
$463$	104.255	+	389.085i	0.225173	+	0.840356i	−0.757163	+	0.653226i	$0.773415\pi$
$464$	51.0753	+	29.4883i	0.110076	+	0.0635525i
$465$	14.3640	−	81.6872i	0.0308904	−	0.175671i
$466$	−357.844	−	619.804i	−0.767906	−	1.33005i
$467$	−74.7515	−	74.7515i	−0.160067	−	0.160067i	0.622529	−	0.782597i	$-0.286105\pi$
$467$	−74.7515	−	74.7515i	−0.160067	−	0.160067i	−0.782597	+	0.622529i	$0.786105\pi$
$468$	−43.8430	+	31.1967i	−0.0936816	+	0.0666595i
$469$			87.9609i			0.187550i
$470$	23.0840	+	133.503i	0.0491149	+	0.284049i
$471$	−4.20832	+	50.2940i	−0.00893486	+	0.106781i
$472$	42.6327	−	11.4234i	0.0903236	−	0.0242021i
$473$	138.232	+	515.889i	0.292245	+	1.09067i
$474$	−672.818	−	56.2975i	−1.41945	−	0.118771i
$475$	−397.053	−	72.7296i	−0.835900	−	0.153115i
$476$	−29.5837			−0.0621507
$477$	624.882	−	59.4419i	1.31002	−	0.124616i
$478$	137.441	−	137.441i	0.287534	−	0.287534i
$479$	607.427	−	350.698i	1.26811	−	0.732146i	0.293483	−	0.955964i	$-0.405186\pi$
$479$	607.427	−	350.698i	1.26811	−	0.732146i	0.974631	+	0.223818i	$0.0718522\pi$
$480$	−66.4737	+	46.5920i	−0.138487	+	0.0970667i
$481$	249.216	−	431.655i	0.518121	−	0.897411i
$482$	−291.644	+	78.1457i	−0.605070	+	0.162128i
$483$	16.5814	−	46.0995i	0.0343301	−	0.0954440i
$484$	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	0.930460	−	0.366395i	$-0.119408\pi$
$487$	274.700	+	274.700i	0.564065	+	0.564065i	−0.366395	+	0.930460i	$0.619408\pi$
$488$	400.014	+	107.183i	0.819700	+	0.219638i
$489$	−191.252	−	406.119i	−0.391108	−	0.830509i
$490$	−373.926	−	33.9641i	−0.763114	−	0.0693145i
$491$	−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	$0.975589\pi$
$492$	−8.19350	−	45.4604i	−0.0166535	−	0.0923991i
$493$	109.516	+	29.3447i	0.222142	+	0.0595226i
$494$			544.570i			1.10237i
$495$	258.046	−	150.451i	0.521306	−	0.303942i
$496$	−80.3321			−0.161960
$497$	44.7346	−	166.952i	0.0900092	−	0.335919i
$498$	336.402	+	397.839i	0.675506	+	0.798873i
$499$	367.132	+	211.964i	0.735736	+	0.424778i	0.820517	−	0.571622i	$-0.193686\pi$
$499$	367.132	+	211.964i	0.735736	+	0.424778i	−0.0847806	+	0.996400i	$0.527019\pi$
$500$	−42.3949	−	0.421784i	−0.0847897	−	0.000843568i
$501$	−4.16810	+	49.8134i	−0.00831956	+	0.0994279i
$502$	−111.824	+	417.333i	−0.222757	+	0.831340i
$503$	−307.613	+	307.613i	−0.611557	+	0.611557i	−0.943352	−	0.331795i	$-0.892346\pi$
$503$	−307.613	+	307.613i	−0.611557	+	0.611557i	0.331795	+	0.943352i	$0.392346\pi$
$504$	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
$507$	75.4173	+	418.441i	0.148752	+	0.825327i
$508$	−15.2663	−	56.9745i	−0.0300517	−	0.112155i
$509$	−697.404	−	402.646i	−1.37014	−	0.791053i	−0.379199	−	0.925315i	$-0.623800\pi$
$509$	−697.404	−	402.646i	−1.37014	−	0.791053i	−0.990946	+	0.134262i	$0.957134\pi$
$510$	514.957	−	614.288i	1.00972	−	1.20449i
$511$	46.9628	+	81.3419i	0.0919037	+	0.159182i
$512$	396.753	+	396.753i	0.774908	+	0.774908i
$513$	−222.250	−	375.044i	−0.433237	−	0.731081i
$514$			743.150i			1.44582i
$515$	−397.899	+	564.267i	−0.772619	+	1.09566i
$516$	74.0689	−	34.8810i	0.143544	−	0.0675988i
$517$	90.8030	−	24.3306i	0.175635	−	0.0470611i
$518$	43.7284	+	163.197i	0.0844178	+	0.315051i
$519$	−67.9984	+	97.8987i	−0.131018	+	0.188630i
$520$	124.675	+	721.040i	0.239759	+	1.38662i
$521$	752.815			1.44494			0.722471	−	0.691401i	$-0.243006\pi$
$521$	752.815			1.44494			0.722471	+	0.691401i	$0.243006\pi$
$522$	−29.0618	+	63.5760i	−0.0556740	+	0.121793i
$523$	637.569	−	637.569i	1.21906	−	1.21906i	0.251100	−	0.967961i	$-0.419208\pi$
$523$	637.569	−	637.569i	1.21906	−	1.21906i	0.967961	−	0.251100i	$-0.0807924\pi$
$524$	36.0380	−	20.8066i	0.0687748	−	0.0397072i
$525$	166.089	−	165.146i	0.316360	−	0.314564i
$526$	−61.3832	+	106.319i	−0.116698	+	0.202127i
$527$	−149.171	+	39.9703i	−0.283058	+	0.0758450i
$528$	−186.802	−	220.918i	−0.353792	−	0.418405i
$529$	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
$533$	−772.969	−	207.117i	−1.45022	−	0.388586i
$534$	−112.109	+	161.406i	−0.209943	+	0.302259i
$535$	9.97721	−	109.843i	0.0186490	−	0.205315i
$536$	116.922	−	202.514i	0.218137	−	0.377825i
$537$	−753.948	−	271.186i	−1.40400	−	0.505002i
$538$	478.154	+	128.121i	0.888763	+	0.238143i
$539$			260.518i			0.483335i
$540$	−29.7136	−	34.8383i	−0.0550252	−	0.0645154i
$541$	−771.736			−1.42650			−0.713250	−	0.700910i	$-0.752778\pi$
$541$	−771.736			−1.42650			−0.713250	+	0.700910i	$0.752778\pi$
$542$	208.130	−	776.751i	0.384004	−	1.43312i
$543$	−74.2951	+	206.554i	−0.136823	+	0.380395i
$544$	130.898	+	75.5742i	0.240622	+	0.138923i
$545$	508.914	−	424.161i	0.933787	−	0.778278i
$546$	−259.522	−	180.259i	−0.475315	−	0.330144i
$547$	42.4522	−	158.434i	0.0776092	−	0.289642i	−0.916203	−	0.400714i	$-0.868762\pi$
$547$	42.4522	−	158.434i	0.0776092	−	0.289642i	0.993812	+	0.111073i	$0.0354287\pi$
$548$	−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
$552$	−99.4532	+	84.0949i	−0.180169	+	0.152346i
$553$	95.0736	+	354.819i	0.171923	+	0.641626i
$554$	66.3482	+	38.3061i	0.119762	+	0.0691447i
$555$	384.484	+	179.068i	0.692764	+	0.322644i
$556$	14.3793	+	24.9057i	0.0258621	+	0.0447945i
$557$	−63.7862	−	63.7862i	−0.114517	−	0.114517i	0.647526	−	0.762043i	$-0.275804\pi$
$557$	−63.7862	−	63.7862i	−0.114517	−	0.114517i	−0.762043	+	0.647526i	$0.775804\pi$
$558$	−9.01667	−	94.7876i	−0.0161589	−	0.169870i
$559$		−	1418.32i		−	2.53725i
$560$	−185.395	−	130.733i	−0.331062	−	0.233452i
$561$	−456.800	−	317.284i	−0.814260	−	0.565568i
$562$	876.905	−	234.966i	1.56033	−	0.418089i
$563$	176.762	+	659.684i	0.313964	+	1.17173i	0.924950	+	0.380089i	$0.124107\pi$
$563$	176.762	+	659.684i	0.313964	+	1.17173i	−0.610986	+	0.791641i	$0.709227\pi$
$564$	−6.13950	−	13.0371i	−0.0108856	−	0.0231154i
$565$	209.076	−	296.494i	0.370046	−	0.524768i
$566$	−49.7083			−0.0878238
$567$	252.300	+	18.2275i	0.444973	+	0.0321472i
$568$	−324.913	+	324.913i	−0.572029	+	0.572029i
$569$	11.9524	−	6.90074i	0.0210060	−	0.0121278i	−0.489460	−	0.872026i	$-0.662806\pi$
$569$	11.9524	−	6.90074i	0.0210060	−	0.0121278i	0.510466	+	0.859898i	$0.329473\pi$
$570$	−461.616	+	40.6050i	−0.809853	+	0.0712369i
$571$	−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	$0.873751\pi$
$572$	38.3342	−	10.2716i	0.0670178	−	0.0179574i
$573$	−105.188	+	18.9584i	−0.183573	+	0.0330862i
$574$	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	0.999887	+	0.0150252i	$0.00478284\pi$
$577$	585.604	+	585.604i	1.01491	+	1.01491i	0.0150252	+	0.999887i	$0.495217\pi$
$578$	−907.558	−	243.179i	−1.57017	−	0.420726i
$579$	−866.392	−	72.4948i	−1.49636	−	0.125207i
$580$	−4.40765	−	5.28835i	−0.00759939	−	0.00911784i
$581$	141.729	−	245.482i	0.243940	−	0.422517i
$582$	77.4262	−	65.4695i	0.133035	−	0.112491i
$583$	−447.180	−	119.822i	−0.767033	−	0.205526i
$584$		−	249.700i		−	0.427569i
$585$	−765.326	+	208.565i	−1.30825	+	0.356521i
$586$	111.144			0.189665
$587$	−102.904	+	384.041i	−0.175304	+	0.654244i	0.821195	+	0.570647i	$0.193308\pi$
$587$	−102.904	+	384.041i	−0.175304	+	0.654244i	−0.996500	+	0.0835973i	$0.973359\pi$
$588$	39.3020	−	7.08355i	0.0668401	−	0.0120469i
$589$	77.3179	+	44.6395i	0.131270	+	0.0757887i
$590$	50.6498	+	4.60059i	0.0858472	+	0.00779760i
$591$	42.2549	−	19.8989i	0.0714973	−	0.0336699i
$592$	106.323	−	396.802i	0.179599	−	0.670273i
$593$	211.922	−	211.922i	0.357372	−	0.357372i	−0.505471	−	0.862843i	$-0.668681\pi$
$593$	211.922	−	211.922i	0.357372	−	0.357372i	0.862843	+	0.505471i	$0.168681\pi$
$594$	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
$597$	461.194	+	165.886i	0.772520	+	0.277866i
$598$	45.6465	+	170.355i	0.0763319	+	0.284875i
$599$	−889.994	−	513.838i	−1.48580	−	0.857827i	−0.485930	−	0.873998i	$-0.661519\pi$
$599$	−889.994	−	513.838i	−1.48580	−	0.857827i	−0.999869	+	0.0161711i	$0.994852\pi$
$600$	−601.909	+	159.447i	−1.00318	+	0.265744i
$601$	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
$603$	230.550	+	105.389i	0.382338	+	0.174774i
$604$			70.2738i			0.116347i
$605$	379.070	−	65.5448i	0.626562	−	0.108339i
$606$	25.6779	−	306.880i	0.0423728	−	0.506402i
$607$	−605.663	+	162.287i	−0.997798	+	0.267359i	−0.720523	−	0.693431i	$-0.756098\pi$
$607$	−605.663	+	162.287i	−0.997798	+	0.267359i	−0.277275	+	0.960790i	$0.589431\pi$
$608$	−22.6156	−	84.4025i	−0.0371967	−	0.138820i
$609$	37.8996	+	3.17123i	0.0622326	+	0.00520727i
$610$	389.984	+	275.001i	0.639317	+	0.450822i
$611$	−249.643			−0.408581
$612$	−35.4452	+	77.5403i	−0.0579170	+	0.126700i
$613$	−176.801	+	176.801i	−0.288419	+	0.288419i	−0.836455	−	0.548036i	$-0.815376\pi$
$613$	−176.801	+	176.801i	−0.288419	+	0.288419i	0.548036	+	0.836455i	$0.315376\pi$
$614$	336.434	−	194.240i	0.547938	−	0.316352i
$615$	117.931	−	670.667i	0.191759	−	1.09052i
$616$	−86.0510	+	149.045i	−0.139693	+	0.241956i
$617$	246.879	−	66.1511i	0.400128	−	0.107214i	−0.0531425	−	0.998587i	$-0.516924\pi$
$617$	246.879	−	66.1511i	0.400128	−	0.107214i	0.453271	+	0.891373i	$0.350257\pi$
$618$	−268.274	+	745.853i	−0.434101	+	1.20688i
$619$	−635.172	+	366.717i	−1.02613	+	0.592434i	−0.915873	−	0.401469i	$-0.868500\pi$
$619$	−635.172	+	366.717i	−1.02613	+	0.592434i	−0.110254	+	0.993903i	$0.535166\pi$
$620$	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
$623$	103.277	+	27.6730i	0.165774	+	0.0444189i
$624$	327.327	+	695.072i	0.524563	+	1.11390i
$625$	−584.421	−	221.534i	−0.935073	−	0.354455i
$626$	60.8247	−	105.351i	0.0971640	−	0.168293i
$627$	57.0319	+	316.433i	0.0909600	+	0.504677i
$628$	−5.51161	−	1.47683i	−0.00877646	−	0.00235164i
$629$		−	789.736i		−	1.25554i
$630$	133.449	−	233.430i	0.211824	−	0.370524i
$631$	476.284			0.754808			0.377404	−	0.926049i	$-0.376817\pi$
$631$	476.284			0.754808			0.377404	+	0.926049i	$0.376817\pi$
$632$	252.752	−	943.283i	0.399924	−	1.49254i
$633$	347.049	+	410.431i	0.548261	+	0.648390i
$634$	301.893	+	174.298i	0.476171	+	0.274918i
$635$	78.6563	−	865.960i	0.123868	−	1.36372i
$636$	−5.91745	+	70.7200i	−0.00930416	+	0.111195i
$637$	179.059	−	668.257i	0.281097	−	1.04907i
$638$	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	$0.496465\pi$
$642$	−22.4592	−	124.611i	−0.0349831	−	0.194098i
$643$	−300.742	−	1122.39i	−0.467717	−	1.74555i	−0.647719	−	0.761879i	$-0.724277\pi$
$643$	−300.742	−	1122.39i	−0.467717	−	1.74555i	0.180002	−	0.983666i	$-0.442390\pi$
$644$	4.79677	+	2.76942i	0.00744841	+	0.00430034i
$645$	1202.27	−	105.755i	1.86399	−	0.163961i
$646$	431.420	+	747.241i	0.667832	+	1.15672i
$647$	−172.070	−	172.070i	−0.265951	−	0.265951i	0.561516	−	0.827466i	$-0.310218\pi$
$647$	−172.070	−	172.070i	−0.265951	−	0.265951i	−0.827466	+	0.561516i	$0.810218\pi$
$648$	−556.645	−	377.333i	−0.859020	−	0.582304i
$649$		−	35.2882i		−	0.0543733i
$650$	−151.920	+	829.379i	−0.233724	+	1.27597i
$651$	−46.8666	+	22.0707i	−0.0719918	+	0.0339028i
$652$	49.0225	−	13.1355i	0.0751879	−	0.0201465i
$653$	−189.333	−	706.599i	−0.289943	−	1.08208i	−0.945151	−	0.326633i	$-0.894086\pi$
$653$	−189.333	−	706.599i	−0.289943	−	1.08208i	0.655208	−	0.755448i	$-0.272581\pi$
$654$	433.870	−	624.652i	0.663410	−	0.955125i
$655$	604.475	−	104.520i	0.922863	−	0.159572i
$656$	−659.541			−1.00540
$657$	269.469	−	25.6332i	0.410150	−	0.0390156i
$658$	59.8364	−	59.8364i	0.0909368	−	0.0909368i
$659$	−288.199	+	166.392i	−0.437328	+	0.252491i	−0.702463	−	0.711720i	$-0.747917\pi$
$659$	−288.199	+	166.392i	−0.437328	+	0.252491i	0.265136	+	0.964211i	$0.414583\pi$
$660$	11.5653	+	31.7289i	0.0175231	+	0.0480741i
$661$	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	$0.123337\pi$
$662$	−245.924	+	65.8950i	−0.371486	+	0.0995393i
$663$	953.668	+	1127.84i	1.43841	+	1.70111i
$664$	−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
$668$	−5.45894	−	1.46272i	−0.00817207	−	0.00218970i
$669$	−412.075	+	593.273i	−0.615957	+	0.886806i
$670$	206.988	−	172.517i	0.308938	−	0.257488i
$671$	165.551	−	286.743i	0.246723	−	0.427336i
$672$	47.7091	+	17.1604i	0.0709957	+	0.0255363i
$673$	447.097	+	119.799i	0.664334	+	0.178008i	0.575201	−	0.818012i	$-0.304924\pi$
$673$	447.097	+	119.799i	0.664334	+	0.178008i	0.0891327	+	0.996020i	$0.471590\pi$
$674$		−	610.406i		−	0.905646i
$675$	−233.860	−	633.194i	−0.346459	−	0.938065i
$676$	−48.0706			−0.0711104
$677$	−209.919	+	783.429i	−0.310073	+	1.15721i	0.618417	+	0.785850i	$0.287774\pi$
$677$	−209.919	+	783.429i	−0.310073	+	1.15721i	−0.928490	+	0.371357i	$0.878892\pi$
$678$	140.965	−	391.909i	0.207913	−	0.578037i
$679$	−47.7751	−	27.5829i	−0.0703609	−	0.0406229i
$680$	742.298	+	890.617i	1.09161	+	1.30973i
$681$	−189.172	−	131.395i	−0.277786	−	0.192944i
$682$	−18.1756	+	67.8322i	−0.0266504	+	0.0994607i
$683$	312.857	−	312.857i	0.458064	−	0.458064i	−0.439956	−	0.898019i	$-0.645006\pi$
$683$	312.857	−	312.857i	0.458064	−	0.458064i	0.898019	+	0.439956i	$0.145006\pi$
$684$	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
$687$	−72.0032	+	60.8840i	−0.104808	+	0.0886230i
$688$	−302.548	−	1129.13i	−0.439750	−	1.64117i
$689$	1064.71	+	614.712i	1.54530	+	0.892179i
$690$	−141.002	+	51.3955i	−0.204350	+	0.0744862i
$691$	−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
$693$	−169.678	−	77.5633i	−0.244846	−	0.111924i
$694$			858.875i			1.23757i
$695$	72.2330	+	417.750i	0.103932	+	0.601079i
$696$	−83.0417	−	57.6790i	−0.119313	−	0.0828722i
$697$	−1224.72	+	328.164i	−1.75714	+	0.470823i
$698$	151.124	+	564.001i	0.216509	+	0.808024i
$699$	478.094	+	1015.22i	0.683969	+	1.45239i
$700$	15.0444	+	21.7918i	0.0214920	+	0.0311312i
$701$	−502.118			−0.716289			−0.358144	−	0.933666i	$-0.616590\pi$
$701$	−502.118			−0.716289			−0.358144	+	0.933666i	$0.616590\pi$
$702$	−783.408	+	464.245i	−1.11597	+	0.661318i
$703$	−322.831	+	322.831i	−0.459219	+	0.459219i
$704$	393.588	−	227.238i	0.559074	−	0.322782i
$705$	−18.6142	−	211.615i	−0.0264032	−	0.300163i
$706$	8.40567	−	14.5590i	0.0119060	−	0.0206219i
$707$	−161.837	+	43.3641i	−0.228907	+	0.0613354i
$708$	−5.32362	+	0.959497i	−0.00751924	+	0.00135522i
$709$	494.504	−	285.502i	0.697468	−	0.402683i	−0.108936	−	0.994049i	$-0.534744\pi$
$709$	494.504	−	285.502i	0.697468	−	0.402683i	0.806403	+	0.591366i	$0.201411\pi$
$710$	−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
$713$	27.9287	+	7.48348i	0.0391707	+	0.0104958i
$714$	−498.912	−	41.7461i	−0.698756	−	0.0584679i
$715$	582.644	+	52.9223i	0.814886	+	0.0740171i
$716$	45.2933	−	78.4503i	0.0632588	−	0.109567i
$717$	−232.719	+	196.781i	−0.324574	+	0.274451i
$718$	−518.403	−	138.906i	−0.722009	−	0.193462i
$719$			1063.07i			1.47854i	0.673410	+	0.739269i	$0.264829\pi$
$719$			1063.07i			1.47854i	−0.673410	+	0.739269i	$0.735171\pi$
$720$	−564.786	+	329.293i	−0.784425	+	0.457351i
$721$	431.245			0.598120
$722$	−49.6669	+	185.359i	−0.0687907	+	0.256731i
$723$	465.906	−	83.9722i	0.644407	−	0.116144i
$724$	−21.4925	−	12.4087i	−0.0296858	−	0.0171391i
$725$	−34.0770	−	95.5939i	−0.0470028	−	0.131854i
$726$	399.542	−	188.155i	0.550333	−	0.259166i
$727$	306.415	−	1143.56i	0.421479	−	1.57298i	−0.350014	−	0.936744i	$-0.613823\pi$
$727$	306.415	−	1143.56i	0.421479	−	1.57298i	0.771493	−	0.636238i	$-0.219510\pi$
$728$	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
$732$	−47.7597	−	17.1786i	−0.0652454	−	0.0234680i
$733$	204.894	+	764.676i	0.279529	+	1.04321i	0.952745	+	0.303770i	$0.0982453\pi$
$733$	204.894	+	764.676i	0.279529	+	1.04321i	−0.673217	+	0.739445i	$0.735088\pi$
$734$	−475.718	−	274.656i	−0.648117	−	0.374190i
$735$	579.814	+	101.956i	0.788863	+	0.138715i
$736$	−14.1494	−	24.5075i	−0.0192248	−	0.0332983i
$737$	−132.203	−	132.203i	−0.179379	−	0.179379i
$738$	−74.0286	−	778.224i	−0.100310	−	1.05450i
$739$			286.434i			0.387597i	0.981041	+	0.193798i	$0.0620808\pi$
$739$			286.434i			0.387597i	−0.981041	+	0.193798i	$0.937919\pi$
$740$	−27.6345	+	39.1889i	−0.0373439	+	0.0529580i
$741$	71.1971	−	850.884i	0.0960825	−	1.14829i
$742$	−402.538	+	107.860i	−0.542504	+	0.145363i
$743$	330.963	+	1235.17i	0.445442	+	1.66241i	0.714768	+	0.699362i	$0.246532\pi$
$743$	330.963	+	1235.17i	0.445442	+	1.66241i	−0.269326	+	0.963049i	$0.586801\pi$
$744$	137.239	+	11.4834i	0.184461	+	0.0154347i
$745$	−12.3506	−	71.4282i	−0.0165780	−	0.0958768i
$746$	−430.635			−0.577259
$747$	−473.610	−	665.600i	−0.634017	−	0.891031i
$748$	44.4635	−	44.4635i	0.0594431	−	0.0594431i
$749$	−59.6597	+	34.4445i	−0.0796524	+	0.0459874i
$750$	−714.369	−	66.9372i	−0.952492	−	0.0892497i
$751$	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	$0.108960\pi$
$752$	−198.741	+	53.2524i	−0.264283	+	0.0708143i
$753$	229.286	−	637.458i	0.304497	−	0.846558i
$754$	−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	0.405799	−	0.913962i	$-0.366993\pi$
$757$	−384.680	−	384.680i	−0.508163	−	0.508163i	−0.913962	+	0.405799i	$0.866993\pi$
$758$	126.775	+	33.9693i	0.167250	+	0.0448144i
$759$	44.3648	+	94.2075i	0.0584516	+	0.124121i
$760$	60.6306	−	667.508i	0.0797771	−	0.878301i
$761$	−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	$0.966048\pi$
$762$	−177.059	−	982.384i	−0.232361	−	1.28922i
$763$	−399.688	−	107.096i	−0.523838	−	0.140362i
$764$		−	12.0840i		−	0.0158167i
$765$	−884.926	+	892.492i	−1.15677	+	1.16666i
$766$	−236.312			−0.308501
$767$	−24.2543	+	90.5183i	−0.0316223	+	0.118016i
$768$	−125.212	−	148.079i	−0.163036	−	0.192811i
$769$	−427.597	−	246.873i	−0.556042	−	0.321031i	0.195513	−	0.980701i	$-0.437363\pi$
$769$	−427.597	−	246.873i	−0.556042	−	0.321031i	−0.751555	+	0.659670i	$0.770696\pi$
$770$	−152.338	+	126.968i	−0.197841	+	0.164893i
$771$	97.1595	−	1161.16i	0.126018	−	1.50605i
$772$	25.4407	−	94.9460i	0.0329543	−	0.122987i
$773$	753.113	−	753.113i	0.974273	−	0.974273i	−0.0254041	−	0.999677i	$-0.508087\pi$
$773$	753.113	−	753.113i	0.974273	−	0.974273i	0.999677	+	0.0254041i	$0.00808725\pi$
$774$	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
$777$	−46.9888	−	260.710i	−0.0604746	−	0.335534i
$778$	−80.4272	−	300.158i	−0.103377	−	0.385808i
$779$	634.795	+	366.499i	0.814884	+	0.470474i
$780$	−7.85834	−	89.3372i	−0.0100748	−	0.114535i
$781$	183.689	+	318.158i	0.235197	+	0.407373i
$782$	197.593	+	197.593i	0.252677	+	0.252677i
$783$	53.7207	−	95.5372i	0.0686088	−	0.122014i
$784$		−	570.195i		−	0.727290i
$785$	−68.7437	−	48.4754i	−0.0875716	−	0.0617521i
$786$	637.120	−	300.036i	0.810585	−	0.381726i
$787$	1496.20	−	400.905i	1.90114	−	0.509409i	0.904602	−	0.426257i	$-0.140168\pi$
$787$	1496.20	−	400.905i	1.90114	−	0.509409i	0.996537	−	0.0831516i	$-0.0264986\pi$
$788$	1.36669	+	5.10057i	0.00173438	+	0.00647281i
$789$	109.811	−	158.097i	0.139177	−	0.200376i
$790$	648.488	−	919.631i	0.820871	−	1.16409i
$791$	−226.598			−0.286470
$792$	287.553	+	404.119i	0.363072	+	0.510251i
$793$	−621.741	+	621.741i	−0.784036	+	0.784036i
$794$	−143.173	+	82.6608i	−0.180318	+	0.104107i
$795$	−441.685	+	948.361i	−0.555578	+	1.19291i
$796$	−27.7062	+	47.9885i	−0.0348068	+	0.0602871i
$797$	−1007.34	+	269.915i	−1.26391	+	0.338663i	−0.827694	−	0.561179i	$-0.810348\pi$
$797$	−1007.34	+	269.915i	−1.26391	+	0.338663i	−0.436215	+	0.899843i	$0.643681\pi$
$798$	186.882	+	221.012i	0.234188	+	0.276957i
$799$	−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
$803$	−192.838	−	51.6708i	−0.240147	−	0.0643472i
$804$	−16.3496	+	23.5388i	−0.0203353	+	0.0292772i
$805$	52.2768	+	62.7223i	0.0649402	+	0.0779159i
$806$	93.2449	−	161.505i	0.115688	−	0.200378i
$807$	−730.360	−	262.702i	−0.905031	−	0.325529i
$808$	430.242	+	115.283i	0.532478	+	0.142677i
$809$			467.191i			0.577492i	0.957406	+	0.288746i	$0.0932383\pi$
$809$			467.191i			0.577492i	−0.957406	+	0.288746i	$0.906762\pi$
$810$	−451.941	−	629.457i	−0.557952	−	0.777107i
$811$	645.976			0.796518			0.398259	−	0.917273i	$-0.369615\pi$
$811$	645.976			0.796518			0.398259	+	0.917273i	$0.369615\pi$
$812$	−1.11288	+	4.15334i	−0.00137055	+	0.00511495i
$813$	−426.753	+	1186.45i	−0.524912	+	1.45935i
$814$	−311.002	−	179.557i	−0.382067	−	0.220586i
$815$	745.097	+	67.6781i	0.914230	+	0.0830406i
$816$	999.798	+	694.439i	1.22524	+	0.851028i
$817$	−336.245	+	1254.88i	−0.411560	+	1.53596i
$818$	−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	$0.642410\pi$
$822$	−1004.95	+	849.756i	−1.22256	+	1.03377i
$823$	−135.657	−	506.278i	−0.164832	−	0.615162i	−0.998062	−	0.0622344i	$-0.980177\pi$
$823$	−135.657	−	506.278i	−0.164832	−	0.615162i	0.833229	−	0.552927i	$-0.186489\pi$
$824$	−992.862	−	573.229i	−1.20493	−	0.695667i
$825$	−1.41674	+	497.837i	−0.00171726	+	0.603438i
$826$	−15.8827	−	27.5096i	−0.0192284	−	0.0333046i
$827$	524.578	+	524.578i	0.634314	+	0.634314i	0.949147	−	0.314833i	$-0.101948\pi$
$827$	524.578	+	524.578i	0.634314	+	0.634314i	−0.314833	+	0.949147i	$0.601948\pi$
$828$	13.0060	−	9.25444i	0.0157077	−	0.0111769i
$829$			800.305i			0.965386i	0.875790	+	0.482693i	$0.160341\pi$
$829$			800.305i			0.965386i	−0.875790	+	0.482693i	$0.839659\pi$
$830$	−855.638	+	147.948i	−1.03089	+	0.178251i
$831$	−98.6601	−	68.5273i	−0.118725	−	0.0824636i
$832$	−1165.78	+	312.371i	−1.40118	+	0.375446i
$833$	−283.708	−	1058.81i	−0.340586	−	1.27109i
$834$	207.354	+	440.311i	0.248626	+	0.527951i
$835$	−68.0867	−	48.0121i	−0.0815410	−	0.0574995i
$836$	−36.3518			−0.0434831
$837$	1.69591	+	149.283i	0.00202618	+	0.178355i
$838$	−268.832	+	268.832i	−0.320801	+	0.320801i
$839$	1135.49	−	655.573i	1.35338	−	0.781374i	0.364658	−	0.931141i	$-0.381186\pi$
$839$	1135.49	−	655.573i	1.35338	−	0.781374i	0.988721	+	0.149767i	$0.0478525\pi$
$840$	298.040	+	249.847i	0.354810	+	0.297437i
$841$	−412.260	+	714.056i	−0.490203	+	0.849056i
$842$	1543.05	−	413.460i	1.83260	−	0.491045i
$843$	−1400.87	+	252.485i	−1.66177	+	0.299508i
$844$	−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
$848$	978.743	+	262.253i	1.15418	+	0.309261i
$849$	77.6686	+	6.49887i	0.0914825	+	0.00765473i
$850$	448.591	+	1258.40i	0.527754	+	1.48047i
$851$	−73.9295	+	128.050i	−0.0868737	+	0.150470i
$852$	43.0031	−	36.3623i	0.0504731	−	0.0426787i
$853$	951.879	+	255.055i	1.11592	+	0.299010i	0.769231	−	0.638971i	$-0.220640\pi$
$853$	951.879	+	255.055i	1.11592	+	0.299010i	0.346688	+	0.937980i	$0.387306\pi$
$854$		−	298.048i		−	0.349002i
$855$	726.579	−	3.09309i	0.849800	−	0.00361765i
$856$	183.141			0.213949
$857$	304.985	−	1138.22i	0.355875	−	1.32815i	−0.523504	−	0.852023i	$-0.675375\pi$
$857$	304.985	−	1138.22i	0.355875	−	1.32815i	0.879379	−	0.476122i	$-0.157958\pi$
$858$	660.977	−	119.130i	0.770369	−	0.138847i
$859$	−937.566	−	541.304i	−1.09146	−	0.630156i	−0.157497	−	0.987519i	$-0.550342\pi$
$859$	−937.566	−	541.304i	−1.09146	−	0.630156i	−0.933965	+	0.357363i	$0.883676\pi$
$860$	−12.3433	+	135.892i	−0.0143527	+	0.158014i
$861$	−384.784	+	181.205i	−0.446903	+	0.210458i
$862$	148.591	−	554.550i	0.172380	−	0.643329i
$863$	854.886	−	854.886i	0.990598	−	0.990598i	−0.00935826	−	0.999956i	$-0.502979\pi$
$863$	854.886	−	854.886i	0.990598	−	0.990598i	0.999956	+	0.00935826i	$0.00297887\pi$
$864$	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
$867$	1386.26	+	498.619i	1.59891	+	0.575109i
$868$	−1.51586	−	5.65726i	−0.00174638	−	0.00651758i
$869$	−676.176	−	390.390i	−0.778108	−	0.449241i
$870$	−66.8699	−	95.4045i	−0.0768619	−	0.109660i
$871$	248.249	+	429.980i	0.285016	+	0.493663i
$872$	777.853	+	777.853i	0.892033	+	0.892033i
$873$	−129.537	+	92.1726i	−0.148381	+	0.105581i
$874$		−	161.546i		−	0.184835i
$875$	97.2779	+	378.051i	0.111175	+	0.432058i
$876$	−2.55179	+	30.4967i	−0.00291300	+	0.0348136i
$877$	366.323	−	98.1561i	0.417701	−	0.111923i	−0.0438464	−	0.999038i	$-0.513961\pi$
$877$	366.323	−	98.1561i	0.417701	−	0.111923i	0.461547	+	0.887116i	$0.347295\pi$
$878$	−215.249	−	803.321i	−0.245159	−	0.914944i
$879$	−173.661	−	14.5310i	−0.197567	−	0.0165313i
$880$	475.131	−	82.1548i	0.539922	−	0.0933578i
$881$	570.971			0.648094			0.324047	−	0.946041i	$-0.394956\pi$
$881$	570.971			0.648094			0.324047	+	0.946041i	$0.394956\pi$
$882$	672.800	−	64.0001i	0.762812	−	0.0725625i
$883$	−119.737	+	119.737i	−0.135603	+	0.135603i	−0.771650	−	0.636047i	$-0.780568\pi$
$883$	−119.737	+	119.737i	−0.135603	+	0.135603i	0.636047	+	0.771650i	$0.280568\pi$
$884$	−144.614	+	83.4932i	−0.163591	+	0.0944493i
$885$	−78.5383	−	13.8103i	−0.0887438	−	0.0156049i
$886$	9.34399	−	16.1843i	0.0105463	−	0.0182667i
$887$	−938.896	+	251.576i	−1.05851	+	0.283626i	−0.745763	−	0.666211i	$-0.767915\pi$
$887$	−938.896	+	251.576i	−1.05851	+	0.283626i	−0.312744	+	0.949837i	$0.601248\pi$
$888$	−238.364	+	662.697i	−0.268428	+	0.746280i
$889$	−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
$893$	220.875	+	59.1834i	0.247341	+	0.0662748i
$894$	−35.4540	−	75.2858i	−0.0396577	−	0.0842123i
$895$	1025.81	−	854.977i	1.14616	−	0.955282i
$896$	170.752	−	295.751i	0.190571	−	0.330079i
$897$	−49.0499	−	272.146i	−0.0546821	−	0.303395i
$898$	−978.080	−	262.076i	−1.08918	−	0.291844i
$899$			22.4462i			0.0249679i
$900$	75.1427	−	13.3226i	0.0834918	−	0.0148029i
$901$	1947.95			2.16198
$902$	−149.225	+	556.915i	−0.165438	+	0.617423i
$903$	−486.730	−	575.621i	−0.539014	−	0.637454i
$904$	521.700	+	301.204i	0.577102	+	0.333190i
$905$	−234.233	−	281.035i	−0.258821	−	0.310536i
$906$	−99.1646	+	1185.13i	−0.109453	+	1.30809i
$907$	−228.474	+	852.678i	−0.251901	+	0.940108i	0.717887	+	0.696160i	$0.245109\pi$
$907$	−228.474	+	852.678i	−0.251901	+	0.940108i	−0.969788	+	0.243948i	$0.921557\pi$
$908$	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	$0.968162\pi$
$912$	−124.826	−	692.576i	−0.136870	−	0.759403i
$913$	155.938	+	581.968i	0.170797	+	0.637424i
$914$	−541.107	−	312.409i	−0.592021	−	0.341804i
$915$	−573.391	−	480.673i	−0.626657	−	0.525325i
$916$	−5.33036	−	9.23246i	−0.00581917	−	0.0100791i
$917$	−270.927	−	270.927i	−0.295449	−	0.295449i
$918$	−707.181	+	1257.65i	−0.770350	+	1.36999i
$919$		−	1476.26i		−	1.60638i	−0.595724	−	0.803189i	$-0.703135\pi$
$919$		−	1476.26i		−	1.60638i	0.595724	−	0.803189i	$-0.296865\pi$
$920$	−36.9846	−	213.895i	−0.0402006	−	0.232495i
$921$	−551.069	+	259.512i	−0.598337	+	0.281772i
$922$	−457.753	+	122.655i	−0.496479	+	0.133031i
$923$	−252.506	−	942.364i	−0.273571	−	1.02098i
$924$	12.0329	−	17.3239i	0.0130226	−	0.0187489i
$925$	−581.732	+	401.610i	−0.628900	+	0.434173i
$926$	−770.708			−0.832298
$927$	516.688	−	1130.31i	0.557377	−	1.21932i
$928$	15.5342	−	15.5342i	0.0167395	−	0.0167395i
$929$	−104.797	+	60.5047i	−0.112807	+	0.0651289i	−0.555342	−	0.831622i	$-0.687413\pi$
$929$	−104.797	+	60.5047i	−0.112807	+	0.0651289i	0.442535	+	0.896751i	$0.354079\pi$
$930$	143.856	+	66.9986i	0.154684	+	0.0720416i
$931$	−316.850	+	548.801i	−0.340333	+	0.589475i
$932$	−122.547	+	32.8364i	−0.131488	+	0.0352322i
$933$	−612.660	−	724.550i	−0.656656	−	0.776581i
$934$	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	0.695444	−	0.718581i	$-0.255208\pi$
$937$	−21.6794	−	21.6794i	−0.0231370	−	0.0231370i	−0.718581	+	0.695444i	$0.755208\pi$
$938$	−162.563	−	43.5588i	−0.173309	−	0.0464379i
$939$	−108.811	+	156.658i	−0.115880	+	0.166835i
$940$	23.9188	+	2.17258i	0.0254456	+	0.00231125i
$941$	−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	$0.297774\pi$
$942$	−90.8661	−	32.6834i	−0.0964608	−	0.0346958i
$943$	229.300	+	61.4408i	0.243160	+	0.0651546i
$944$			77.2354i			0.0818171i
$945$	−239.031	+	347.285i	−0.252943	+	0.367497i
$946$	−1021.88			−1.08022
$947$	−74.0806	+	276.473i	−0.0782266	+	0.291946i	−0.993946	−	0.109874i	$-0.964955\pi$
$947$	−74.0806	+	276.473i	−0.0782266	+	0.291946i	0.915719	+	0.401819i	$0.131622\pi$
$948$	−40.5093	+	112.623i	−0.0427313	+	0.118801i
$949$	459.137	+	265.083i	0.483812	+	0.279329i
$950$	331.037	−	697.790i	0.348460	−	0.734516i
$951$	−448.916	−	311.808i	−0.472046	−	0.327874i
$952$	187.422	−	699.469i	0.196872	−	0.734736i
$953$	−124.868	+	124.868i	−0.131026	+	0.131026i	−0.769578	−	0.638552i	$-0.779534\pi$
$953$	−124.868	+	124.868i	−0.131026	+	0.131026i	0.638552	+	0.769578i	$0.279534\pi$
$954$	−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
$957$	−61.7283	+	52.1958i	−0.0645019	+	0.0545410i
$958$	347.335	+	1296.27i	0.362563	+	1.35310i
$959$	620.092	+	358.010i	0.646603	+	0.373316i
$960$	−351.713	−	964.910i	−0.366367	−	1.00511i
$961$	465.213	+	805.773i	0.484093	+	0.838473i
$962$	674.342	+	674.342i	0.700980	+	0.700980i
$963$	18.8005	+	197.640i	0.0195229	+	0.205234i
$964$			53.5234i			0.0555222i
$965$	835.063	−	1184.22i	0.865350	−	1.22717i
$966$	76.9867	+	53.4734i	0.0796964	+	0.0553555i
$967$	1226.52	−	328.646i	1.26838	−	0.339861i	0.438970	−	0.898502i	$-0.355344\pi$
$967$	1226.52	−	328.646i	1.26838	−	0.339861i	0.829410	+	0.558641i	$0.188677\pi$
$968$	165.325	+	617.002i	0.170791	+	0.637399i
$969$	−576.394	−	1223.96i	−0.594833	−	1.26312i
$970$	28.7932	+	166.522i	0.0296837	+	0.171672i
$971$	−1494.20			−1.53883			−0.769413	−	0.638752i	$-0.779451\pi$
$971$	−1494.20			−1.53883			−0.769413	+	0.638752i	$0.779451\pi$
$972$	64.1288	+	51.7736i	0.0659762	+	0.0532650i
$973$	187.237	−	187.237i	0.192432	−	0.192432i
$974$	−643.714	+	371.649i	−0.660898	+	0.381569i
$975$	345.807	−	1276.03i	0.354674	−	1.30875i
$976$	−362.341	+	627.593i	−0.371251	+	0.643026i
$977$	1636.69	−	438.550i	1.67522	−	0.448874i	0.708709	−	0.705501i	$-0.249278\pi$
$977$	1636.69	−	438.550i	1.67522	−	0.448874i	0.966510	+	0.256628i	$0.0826114\pi$
$978$	845.271	−	152.347i	0.864286	−	0.155774i
$979$	−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
$983$	−1490.60	−	399.405i	−1.51638	−	0.406312i	−0.597829	−	0.801623i	$-0.703970\pi$
$983$	−1490.60	−	399.405i	−1.51638	−	0.406312i	−0.918547	+	0.395311i	$0.870637\pi$
$984$	1126.76	+	94.2809i	1.14508	+	0.0958139i
$985$	−7.04160	+	77.5240i	−0.00714884	+	0.0787046i
$986$	−108.466	+	187.868i	−0.110006	+	0.190536i
$987$	−101.317	+	85.6707i	−0.102651	+	0.0867991i
$988$	93.2466	+	24.9853i	0.0943791	+	0.0252888i
$989$			420.743i			0.425422i
$990$	150.268	+	551.409i	0.151786	+	0.556978i
$991$	−1790.72			−1.80698			−0.903491	−	0.428607i	$-0.859004\pi$
$991$	−1790.72			−1.80698			−0.903491	+	0.428607i	$0.859004\pi$
$992$	−7.74478	+	28.9039i	−0.00780724	+	0.0291370i
$993$	392.868	−	70.8081i	0.395637	−	0.0713073i
$994$	286.396	+	165.351i	0.288125	+	0.166349i
$995$	−627.495	+	522.995i	−0.630648	+	0.525623i
$996$	83.5563	−	39.3488i	0.0838918	−	0.0395068i
$997$	385.948	−	1440.38i	0.387110	−	1.44471i	−0.447705	−	0.894181i	$-0.647758\pi$
$997$	385.948	−	1440.38i	0.387110	−	1.44471i	0.834814	−	0.550532i	$-0.185575\pi$
$998$	−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.22.3	yes	40
3.2	odd	2		135.3.l.a.37.8		40
5.2	odd	4		225.3.o.b.193.3		40
5.3	odd	4	inner	45.3.k.a.13.8	yes	40
5.4	even	2		225.3.o.b.157.8		40
9.2	odd	6		135.3.l.a.127.3		40
9.4	even	3		405.3.g.h.82.3		20
9.5	odd	6		405.3.g.g.82.8		20
9.7	even	3	inner	45.3.k.a.7.8	✓	40
15.8	even	4		135.3.l.a.118.3		40
45.7	odd	12		225.3.o.b.43.8		40
45.13	odd	12		405.3.g.h.163.3		20
45.23	even	12		405.3.g.g.163.8		20
45.34	even	6		225.3.o.b.7.3		40
45.38	even	12		135.3.l.a.73.8		40
45.43	odd	12	inner	45.3.k.a.43.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.8	✓	40	9.7	even	3	inner
45.3.k.a.13.8	yes	40	5.3	odd	4	inner
45.3.k.a.22.3	yes	40	1.1	even	1	trivial
45.3.k.a.43.3	yes	40	45.43	odd	12	inner
135.3.l.a.37.8		40	3.2	odd	2
135.3.l.a.73.8		40	45.38	even	12
135.3.l.a.118.3		40	15.8	even	4
135.3.l.a.127.3		40	9.2	odd	6
225.3.o.b.7.3		40	45.34	even	6
225.3.o.b.43.8		40	45.7	odd	12
225.3.o.b.157.8		40	5.4	even	2
225.3.o.b.193.3		40	5.2	odd	4
405.3.g.g.82.8		20	9.5	odd	6
405.3.g.g.163.8		20	45.23	even	12
405.3.g.h.82.3		20	9.4	even	3
405.3.g.h.163.3		20	45.13	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-0.495206 + 1.84813i) q^{2} +(1.01538 - 2.82294i) q^{3} +(0.293735 + 0.169588i) q^{4} +(3.20122 + 3.84086i) q^{5} +(4.71435 + 3.27449i) q^{6} +(0.808273 - 3.01652i) q^{7} +(-5.87059 + 5.87059i) q^{8} +(-6.93801 - 5.73271i) q^{9} +O(q^{10})\)	\(q+(-0.495206 + 1.84813i) q^{2} +(1.01538 - 2.82294i) q^{3} +(0.293735 + 0.169588i) q^{4} +(3.20122 + 3.84086i) q^{5} +(4.71435 + 3.27449i) q^{6} +(0.808273 - 3.01652i) 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} +(0.776989 - 0.657001i) q^{12} +(-4.56232 - 17.0268i) q^{13} +(5.17466 + 2.98759i) q^{14} +(14.0930 - 5.13693i) q^{15} +(-7.26413 - 12.5818i) q^{16} +(-19.7493 - 19.7493i) q^{17} +(14.0306 - 9.98350i) q^{18} +16.1463i q^{19} +(0.288946 + 1.67108i) q^{20} +(-7.69475 - 5.34462i) q^{21} +(-12.2676 + 3.28710i) q^{22} +(1.35341 + 5.05098i) q^{23} +(10.6115 + 22.5332i) q^{24} +(-4.50440 + 24.5909i) q^{25} +33.7271 q^{26} +(-23.2278 + 13.7647i) q^{27} +(0.748983 - 0.748983i) q^{28} +(-3.51558 + 2.02972i) q^{29} +(2.51481 + 28.5895i) q^{30} +(2.76468 - 4.78857i) q^{31} +(-5.22734 + 1.40066i) q^{32} +(19.5978 - 3.53219i) 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} +(-29.8406 - 7.99576i) q^{38} +(-52.6983 - 4.40949i) q^{39} +(-41.3411 - 3.75507i) q^{40} +(22.6986 - 39.3151i) q^{41} +(13.6880 - 11.5742i) q^{42} +(77.7192 + 20.8248i) q^{43} +2.25140i q^{44} +(-0.191566 - 44.9996i) q^{45} -10.0051 q^{46} +(3.66543 - 13.6796i) q^{47} +(-42.8937 + 7.73089i) q^{48} +(33.9892 + 19.6237i) q^{49} +(-43.2166 - 20.5023i) q^{50} +(-75.8041 + 35.6981i) q^{51} +(1.54743 - 5.77509i) 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} +(45.5802 + 16.3946i) q^{57} +(-2.01026 - 7.50240i) q^{58} +(-4.60398 - 2.65811i) q^{59} +(5.01076 + 0.881102i) q^{60} +(-24.9404 - 43.1981i) q^{61} +(7.48083 + 7.48083i) q^{62} +(-22.9006 + 16.2950i) q^{63} -68.4675i q^{64} +(50.7927 - 72.0298i) q^{65} +(-3.17698 + 37.9685i) q^{66} +(-27.2064 + 7.28994i) q^{67} +(-2.45181 - 9.15029i) q^{68} +(15.6328 + 1.30807i) q^{69} +(5.09030 + 29.4391i) q^{70} +55.3458 q^{71} +(74.3846 - 7.07584i) q^{72} +(-21.2670 + 21.2670i) q^{73} +(-46.8529 + 27.0505i) q^{74} +(64.8449 + 37.6847i) q^{75} +(-2.73822 + 4.74274i) q^{76} +(20.0232 - 5.36520i) q^{77} +(34.2458 - 95.2098i) 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} +(87.6742 + 23.4922i) q^{83} +(-1.35383 - 2.87484i) q^{84} +(12.6324 - 139.076i) q^{85} +(-76.9740 + 133.323i) q^{86} +(2.16015 + 11.9852i) q^{87} +(-53.2314 - 14.2633i) q^{88} +34.2372i q^{89} +(83.2601 + 21.9300i) q^{90} -55.0493 q^{91} +(-0.459043 + 1.71317i) q^{92} +(-10.7107 - 12.6668i) q^{93} +(23.4666 + 13.5484i) q^{94} +(-62.0158 + 51.6880i) q^{95} +(-1.35374 + 16.1787i) q^{96} +(4.57199 - 17.0629i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more