LMFDB - Embedded newform 345.2.m.c.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	345.31
Dual form			345.2.m.c.256.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.290073 + 2.01750i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-2.06718 - 0.606979i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-1.95568 + 0.574241i) q^{6} +(3.11544 + 2.00217i) q^{7} +(0.130777 - 0.286362i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.290073 + 2.01750i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-2.06718 - 0.606979i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-1.95568 + 0.574241i) q^{6} +(3.11544 + 2.00217i) q^{7} +(0.130777 - 0.286362i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-1.71468 + 1.10196i) q^{10} +(-0.0961490 - 0.668731i) q^{11} +(-0.306610 - 2.13252i) q^{12} +(2.80919 - 1.80536i) q^{13} +(-4.94309 + 5.70463i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(-3.08508 - 1.98266i) q^{16} +(0.151719 - 0.0445487i) q^{17} +(-1.33477 - 1.54040i) q^{18} +(-0.499595 - 0.146694i) q^{19} +(-0.894992 - 1.95976i) q^{20} +(-0.527039 + 3.66564i) q^{21} +1.37706 q^{22} +(-4.57656 - 1.43355i) q^{23} +0.314810 q^{24} +(-0.142315 + 0.989821i) q^{25} +(2.82744 + 6.19123i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-5.22491 - 6.02986i) q^{28} +(-6.82255 + 2.00328i) q^{29} +(-1.71468 - 1.10196i) q^{30} +(3.12942 - 6.85248i) q^{31} +(5.30723 - 6.12487i) q^{32} +(0.568357 - 0.365261i) q^{33} +(0.0458675 + 0.319015i) q^{34} +(0.527039 + 3.66564i) q^{35} +(1.81244 - 1.16478i) q^{36} +(3.49100 - 4.02883i) q^{37} +(0.440875 - 0.965382i) q^{38} +(2.80919 + 1.80536i) q^{39} +(0.302058 - 0.0886923i) q^{40} +(2.98853 + 3.44894i) q^{41} +(-7.24255 - 2.12660i) q^{42} +(-2.97144 - 6.50654i) q^{43} +(-0.207148 + 1.44075i) q^{44} -1.00000 q^{45} +(4.21972 - 8.81739i) q^{46} +7.39440 q^{47} +(0.521903 - 3.62991i) q^{48} +(2.78938 + 6.10789i) q^{49} +(-1.95568 - 0.574241i) q^{50} +(0.103549 + 0.119502i) q^{51} +(-6.90292 + 2.02688i) q^{52} +(-0.416554 - 0.267703i) q^{53} +(0.846718 - 1.85405i) q^{54} +(0.442429 - 0.510590i) q^{55} +(0.980774 - 0.630305i) q^{56} +(-0.0741015 - 0.515387i) q^{57} +(-2.06259 - 14.3456i) q^{58} +(10.0860 - 6.48185i) q^{59} +(1.41087 - 1.62823i) q^{60} +(-3.44310 + 7.53935i) q^{61} +(12.9171 + 8.30134i) q^{62} +(-3.55332 + 1.04335i) q^{63} +(6.01438 + 6.94097i) q^{64} +(3.20403 + 0.940787i) q^{65} +(0.572049 + 1.25261i) q^{66} +(-2.03327 + 14.1417i) q^{67} -0.340670 q^{68} +(-0.597171 - 4.75851i) q^{69} -7.54831 q^{70} +(-1.48341 + 10.3174i) q^{71} +(0.130777 + 0.286362i) q^{72} +(3.69562 + 1.08513i) q^{73} +(7.11552 + 8.21175i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(0.943714 + 0.606488i) q^{76} +(1.03937 - 2.27590i) q^{77} +(-4.45718 + 5.14386i) q^{78} +(-5.93982 + 3.81729i) q^{79} +(-0.521903 - 3.62991i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-7.82514 + 5.02891i) q^{82} +(1.22007 - 1.40804i) q^{83} +(3.31445 - 7.25764i) q^{84} +(0.133022 + 0.0854882i) q^{85} +(13.9889 - 4.10751i) q^{86} +(-4.65644 - 5.37382i) q^{87} +(-0.204073 - 0.0599212i) q^{88} +(-2.68905 - 5.88819i) q^{89} +(0.290073 - 2.01750i) q^{90} +12.3665 q^{91} +(8.59045 + 5.74128i) q^{92} +7.53325 q^{93} +(-2.14491 + 14.9182i) q^{94} +(-0.216301 - 0.473633i) q^{95} +(7.77608 + 2.28326i) q^{96} +(3.02173 + 3.48726i) q^{97} +(-13.1318 + 3.85584i) q^{98} +(0.568357 + 0.365261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) $ 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.290073	+	2.01750i	−0.205112	+	1.42659i	0.583707	+	0.811964i	$0.301602\pi$
$2$	−0.290073	+	2.01750i	−0.205112	+	1.42659i	−0.788820	+	0.614624i	$0.789308\pi$
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$	−2.06718	−	0.606979i	−1.03359	−	0.303490i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	−1.95568	+	0.574241i	−0.798405	+	0.234433i
$7$	3.11544	+	2.00217i	1.17753	+	0.756750i	0.974930	−	0.222512i	$-0.0714256\pi$
$7$	3.11544	+	2.00217i	1.17753	+	0.756750i	0.202597	+	0.979262i	$0.435062\pi$
$8$	0.130777	−	0.286362i	0.0462366	−	0.101244i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−1.71468	+	1.10196i	−0.542230	+	0.348470i
$11$	−0.0961490	−	0.668731i	−0.0289900	−	0.201630i	0.970179	−	0.242390i	$-0.0779313\pi$
$11$	−0.0961490	−	0.668731i	−0.0289900	−	0.201630i	−0.999169	+	0.0407598i	$0.987022\pi$
$12$	−0.306610	−	2.13252i	−0.0885108	−	0.615606i
$13$	2.80919	−	1.80536i	0.779129	−	0.500716i	−0.0896154	−	0.995976i	$-0.528564\pi$
$13$	2.80919	−	1.80536i	0.779129	−	0.500716i	0.868744	+	0.495261i	$0.164927\pi$
$14$	−4.94309	+	5.70463i	−1.32110	+	1.52463i
$15$	−0.415415	+	0.909632i	−0.107260	+	0.234866i
$16$	−3.08508	−	1.98266i	−0.771270	−	0.495665i
$17$	0.151719	−	0.0445487i	0.0367972	−	0.0108046i	−0.263282	−	0.964719i	$-0.584805\pi$
$17$	0.151719	−	0.0445487i	0.0367972	−	0.0108046i	0.300079	+	0.953914i	$0.402987\pi$
$18$	−1.33477	−	1.54040i	−0.314608	−	0.363077i
$19$	−0.499595	−	0.146694i	−0.114615	−	0.0336540i	0.223922	−	0.974607i	$-0.428114\pi$
$19$	−0.499595	−	0.146694i	−0.114615	−	0.0336540i	−0.338537	+	0.940953i	$0.609932\pi$
$20$	−0.894992	−	1.95976i	−0.200126	−	0.438215i
$21$	−0.527039	+	3.66564i	−0.115009	+	0.799908i
$22$	1.37706			0.293589
$23$	−4.57656	−	1.43355i	−0.954280	−	0.298916i
$23$	−4.57656	−	1.43355i	−0.954280	−	0.298916i
$24$	0.314810			0.0642604
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	2.82744	+	6.19123i	0.554506	+	1.21420i
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$	−5.22491	−	6.02986i	−0.987415	−	1.13954i
$29$	−6.82255	+	2.00328i	−1.26692	+	0.372000i	−0.845064	−	0.534665i	$-0.820438\pi$
$29$	−6.82255	+	2.00328i	−1.26692	+	0.372000i	−0.421852	+	0.906665i	$0.638620\pi$
$30$	−1.71468	−	1.10196i	−0.313057	−	0.201189i
$31$	3.12942	−	6.85248i	0.562061	−	1.23074i	−0.388856	−	0.921298i	$-0.627130\pi$
$31$	3.12942	−	6.85248i	0.562061	−	1.23074i	0.950918	−	0.309444i	$-0.100143\pi$
$32$	5.30723	−	6.12487i	0.938195	−	1.08273i
$33$	0.568357	−	0.365261i	0.0989383	−	0.0635838i
$34$	0.0458675	+	0.319015i	0.00786620	+	0.0547106i
$35$	0.527039	+	3.66564i	0.0890859	+	0.619606i
$36$	1.81244	−	1.16478i	0.302073	−	0.194131i
$37$	3.49100	−	4.02883i	0.573917	−	0.662335i	−0.392369	−	0.919808i	$-0.628344\pi$
$37$	3.49100	−	4.02883i	0.573917	−	0.662335i	0.966286	+	0.257473i	$0.0828897\pi$
$38$	0.440875	−	0.965382i	0.0715194	−	0.156606i
$39$	2.80919	+	1.80536i	0.449830	+	0.289088i
$40$	0.302058	−	0.0886923i	0.0477596	−	0.0140235i
$41$	2.98853	+	3.44894i	0.466729	+	0.538634i	0.939499	−	0.342552i	$-0.111291\pi$
$41$	2.98853	+	3.44894i	0.466729	+	0.538634i	−0.472770	+	0.881186i	$0.656746\pi$
$42$	−7.24255	−	2.12660i	−1.11755	−	0.328142i
$43$	−2.97144	−	6.50654i	−0.453140	−	0.992239i	−0.988998	−	0.147930i	$-0.952739\pi$
$43$	−2.97144	−	6.50654i	−0.453140	−	0.992239i	0.535857	−	0.844308i	$-0.319988\pi$
$44$	−0.207148	+	1.44075i	−0.0312288	+	0.217201i
$45$	−1.00000			−0.149071
$46$	4.21972	−	8.81739i	0.622164	−	1.30005i
$47$	7.39440			1.07858			0.539292	−	0.842119i	$-0.318692\pi$
$47$	7.39440			1.07858			0.539292	+	0.842119i	$0.318692\pi$
$48$	0.521903	−	3.62991i	0.0753302	−	0.523933i
$49$	2.78938	+	6.10789i	0.398483	+	0.872556i
$50$	−1.95568	−	0.574241i	−0.276575	−	0.0812099i
$51$	0.103549	+	0.119502i	0.0144998	+	0.0167336i
$52$	−6.90292	+	2.02688i	−0.957262	+	0.281078i
$53$	−0.416554	−	0.267703i	−0.0572181	−	0.0367719i	0.511719	−	0.859153i	$-0.329009\pi$
$53$	−0.416554	−	0.267703i	−0.0572181	−	0.0367719i	−0.568937	+	0.822381i	$0.692645\pi$
$54$	0.846718	−	1.85405i	0.115224	−	0.252305i
$55$	0.442429	−	0.510590i	0.0596571	−	0.0688480i
$56$	0.980774	−	0.630305i	0.131061	−	0.0842281i
$57$	−0.0741015	−	0.515387i	−0.00981498	−	0.0682647i
$58$	−2.06259	−	14.3456i	−0.270831	−	1.88367i
$59$	10.0860	−	6.48185i	1.31308	−	0.843865i	0.318508	−	0.947920i	$-0.396818\pi$
$59$	10.0860	−	6.48185i	1.31308	−	0.843865i	0.994572	+	0.104055i	$0.0331819\pi$
$60$	1.41087	−	1.62823i	0.182142	−	0.210203i
$61$	−3.44310	+	7.53935i	−0.440844	+	0.965314i	0.550598	+	0.834770i	$0.314400\pi$
$61$	−3.44310	+	7.53935i	−0.440844	+	0.965314i	−0.991443	+	0.130544i	$0.958328\pi$
$62$	12.9171	+	8.30134i	1.64048	+	1.05427i
$63$	−3.55332	+	1.04335i	−0.447677	+	0.131450i
$64$	6.01438	+	6.94097i	0.751798	+	0.867621i
$65$	3.20403	+	0.940787i	0.397410	+	0.116690i
$66$	0.572049	+	1.25261i	0.0704144	+	0.154186i
$67$	−2.03327	+	14.1417i	−0.248404	+	1.72769i	0.359039	+	0.933322i	$0.383104\pi$
$67$	−2.03327	+	14.1417i	−0.248404	+	1.72769i	−0.607443	+	0.794363i	$0.707805\pi$
$68$	−0.340670			−0.0413123
$69$	−0.597171	−	4.75851i	−0.0718910	−	0.572857i
$70$	−7.54831			−0.902196
$71$	−1.48341	+	10.3174i	−0.176049	+	1.22445i	0.689747	+	0.724050i	$0.257722\pi$
$71$	−1.48341	+	10.3174i	−0.176049	+	1.22445i	−0.865796	+	0.500397i	$0.833187\pi$
$72$	0.130777	+	0.286362i	0.0154122	+	0.0337480i
$73$	3.69562	+	1.08513i	0.432539	+	0.127005i	0.490752	−	0.871299i	$-0.336722\pi$
$73$	3.69562	+	1.08513i	0.432539	+	0.127005i	−0.0582130	+	0.998304i	$0.518540\pi$
$74$	7.11552	+	8.21175i	0.827162	+	0.954596i
$75$	−0.959493	+	0.281733i	−0.110793	+	0.0325317i
$76$	0.943714	+	0.606488i	0.108251	+	0.0695689i
$77$	1.03937	−	2.27590i	0.118447	−	0.259363i
$78$	−4.45718	+	5.14386i	−0.504676	+	0.582427i
$79$	−5.93982	+	3.81729i	−0.668282	+	0.429479i	−0.830306	−	0.557308i	$-0.811834\pi$
$79$	−5.93982	+	3.81729i	−0.668282	+	0.429479i	0.162024	+	0.986787i	$0.448198\pi$
$80$	−0.521903	−	3.62991i	−0.0583505	−	0.405837i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−7.82514	+	5.02891i	−0.864142	+	0.555350i
$83$	1.22007	−	1.40804i	0.133921	−	0.154553i	−0.684828	−	0.728705i	$-0.740123\pi$
$83$	1.22007	−	1.40804i	0.133921	−	0.154553i	0.818749	+	0.574152i	$0.194668\pi$
$84$	3.31445	−	7.25764i	0.361636	−	0.791873i
$85$	0.133022	+	0.0854882i	0.0144283	+	0.00927250i
$86$	13.9889	−	4.10751i	1.50846	−	0.442924i
$87$	−4.65644	−	5.37382i	−0.499223	−	0.576134i
$88$	−0.204073	−	0.0599212i	−0.0217542	−	0.00638762i
$89$	−2.68905	−	5.88819i	−0.285038	−	0.624147i	0.711905	−	0.702276i	$-0.247833\pi$
$89$	−2.68905	−	5.88819i	−0.285038	−	0.624147i	−0.996943	+	0.0781288i	$0.975105\pi$
$90$	0.290073	−	2.01750i	0.0305764	−	0.212663i
$91$	12.3665			1.29636
$92$	8.59045	+	5.74128i	0.895617	+	0.598570i
$93$	7.53325			0.781161
$94$	−2.14491	+	14.9182i	−0.221231	+	1.53870i
$95$	−0.216301	−	0.473633i	−0.0221920	−	0.0485938i
$96$	7.77608	+	2.28326i	0.793643	+	0.233035i
$97$	3.02173	+	3.48726i	0.306810	+	0.354078i	0.888126	−	0.459600i	$-0.152007\pi$
$97$	3.02173	+	3.48726i	0.306810	+	0.354078i	−0.581316	+	0.813678i	$0.697462\pi$
$98$	−13.1318	+	3.85584i	−1.32651	+	0.389499i
$99$	0.568357	+	0.365261i	0.0571221	+	0.0367101i
$100$	0.894992	−	1.95976i	0.0894992	−	0.195976i
$101$	−6.81846	+	7.86893i	−0.678462	+	0.782987i	−0.985675	−	0.168653i	$-0.946058\pi$
$101$	−6.81846	+	7.86893i	−0.678462	+	0.782987i	0.307213	+	0.951641i	$0.400604\pi$
$102$	−0.271132	+	0.174246i	−0.0268461	+	0.0172529i
$103$	−2.11927	−	14.7399i	−0.208818	−	1.45236i	−0.777022	−	0.629474i	$-0.783270\pi$
$103$	−2.11927	−	14.7399i	−0.208818	−	1.45236i	0.568204	−	0.822888i	$-0.307639\pi$
$104$	−0.149608	−	1.04054i	−0.0146702	−	0.102034i
$105$	−3.11544	+	2.00217i	−0.304036	+	0.195392i
$106$	0.660922	−	0.762745i	0.0641945	−	0.0740843i
$107$	2.45613	−	5.37817i	0.237443	−	0.519928i	−0.752972	−	0.658053i	$-0.771380\pi$
$107$	2.45613	−	5.37817i	0.237443	−	0.519928i	0.990415	+	0.138125i	$0.0441076\pi$
$108$	1.81244	+	1.16478i	0.174402	+	0.112081i
$109$	17.9535	−	5.27164i	1.71964	−	0.504931i	0.734781	−	0.678304i	$-0.237285\pi$
$109$	17.9535	−	5.27164i	1.71964	−	0.504931i	0.984856	+	0.173373i	$0.0554667\pi$
$110$	0.901779	+	1.04071i	0.0859813	+	0.0992277i
$111$	5.11496	+	1.50189i	0.485491	+	0.142553i
$112$	−5.64176	−	12.3537i	−0.533096	−	1.16732i
$113$	0.0847073	−	0.589152i	0.00796859	−	0.0554228i	−0.985449	−	0.169970i	$-0.945633\pi$
$113$	0.0847073	−	0.589152i	0.00796859	−	0.0554228i	0.993418	+	0.114548i	$0.0365419\pi$
$114$	1.06129			0.0993988
$115$	−1.91361	−	4.39751i	−0.178445	−	0.410070i
$116$	15.3194			1.42237
$117$	−0.475231	+	3.30530i	−0.0439351	+	0.305575i
$118$	10.1515	+	22.2286i	0.934519	+	2.04631i
$119$	0.561865	+	0.164979i	0.0515061	+	0.0151236i
$120$	0.206157	+	0.237918i	0.0188195	+	0.0217188i
$121$	10.1165	−	2.97046i	0.919679	−	0.270042i
$122$	−14.2119	−	9.13342i	−1.28668	−	0.826901i
$123$	−1.89579	+	4.15120i	−0.170938	+	0.374301i
$124$	−10.6284	+	12.2658i	−0.954459	+	1.10150i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	−1.07424	−	7.47148i	−0.0957006	−	0.665612i
$127$	−0.984897	−	6.85011i	−0.0873955	−	0.607849i	−0.985704	−	0.168484i	$-0.946113\pi$
$127$	−0.984897	−	6.85011i	−0.0873955	−	0.607849i	0.898309	−	0.439365i	$-0.144796\pi$
$128$	−2.11237	+	1.35753i	−0.186708	+	0.119990i
$129$	4.68418	−	5.40583i	0.412419	−	0.475957i
$130$	−2.82744	+	6.19123i	−0.247983	+	0.543007i
$131$	−14.4995	−	9.31826i	−1.26683	−	0.814140i	−0.277623	−	0.960690i	$-0.589547\pi$
$131$	−14.4995	−	9.31826i	−1.26683	−	0.814140i	−0.989203	+	0.146550i	$0.953183\pi$
$132$	−1.39660	+	0.410080i	−0.121559	+	0.0356929i
$133$	−1.26275	−	1.45729i	−0.109495	−	0.126363i
$134$	−27.9411	−	8.20426i	−2.41375	−	0.708740i
$135$	−0.415415	−	0.909632i	−0.0357532	−	0.0782887i
$136$	0.00708430	−	0.0492724i	0.000607474	−	0.00422507i
$137$	14.5404			1.24227			0.621136	−	0.783703i	$-0.286671\pi$
$137$	14.5404			1.24227			0.621136	+	0.783703i	$0.286671\pi$
$138$	9.77351	+	0.175520i	0.831977	+	0.0149412i
$139$	−1.54443			−0.130997			−0.0654985	−	0.997853i	$-0.520864\pi$
$139$	−1.54443			−0.130997			−0.0654985	+	0.997853i	$0.520864\pi$
$140$	1.13548	−	7.89744i	0.0959656	−	0.667456i
$141$	3.07174	+	6.72618i	0.258688	+	0.566447i
$142$	−20.3850	−	5.98558i	−1.71067	−	0.502299i
$143$	−1.47740	−	1.70501i	−0.123546	−	0.142580i
$144$	3.51869	−	1.03318i	0.293224	−	0.0860984i
$145$	−5.98180	−	3.84427i	−0.496761	−	0.319249i
$146$	−3.26125	+	7.14114i	−0.269903	+	0.591005i
$147$	−4.39718	+	5.07462i	−0.362673	+	0.418547i
$148$	−9.66194	+	6.20935i	−0.794207	+	0.510406i
$149$	−3.00235	−	20.8818i	−0.245962	−	1.71071i	−0.621095	−	0.783735i	$-0.713312\pi$
$149$	−3.00235	−	20.8818i	−0.245962	−	1.71071i	0.375133	−	0.926971i	$-0.377597\pi$
$150$	−0.290073	−	2.01750i	−0.0236843	−	0.164728i
$151$	−16.9147	+	10.8704i	−1.37650	+	0.884621i	−0.999141	−	0.0414466i	$-0.986803\pi$
$151$	−16.9147	+	10.8704i	−1.37650	+	0.884621i	−0.377357	+	0.926068i	$0.623167\pi$
$152$	−0.107343	+	0.123881i	−0.00870669	+	0.0100481i
$153$	−0.0656871	+	0.143835i	−0.00531048	+	0.0116283i
$154$	4.29014	+	2.75710i	0.345709	+	0.222174i
$155$	7.22810	−	2.12236i	0.580575	−	0.170472i
$156$	−4.71129	−	5.43712i	−0.377205	−	0.435318i
$157$	3.44007	+	1.01010i	0.274547	+	0.0806144i	0.416108	−	0.909315i	$-0.363394\pi$
$157$	3.44007	+	1.01010i	0.274547	+	0.0806144i	−0.141561	+	0.989930i	$0.545212\pi$
$158$	−5.97841	−	13.0909i	−0.475616	−	1.04145i
$159$	0.0704685	−	0.490119i	0.00558851	−	0.0388690i
$160$	8.10437			0.640706
$161$	−11.3878	−	13.6292i	−0.897485	−	1.07413i
$162$	2.03825			0.160140
$163$	−1.08480	+	7.54498i	−0.0849684	+	0.590968i	0.902204	+	0.431310i	$0.141948\pi$
$163$	−1.08480	+	7.54498i	−0.0849684	+	0.590968i	−0.987172	+	0.159659i	$0.948961\pi$
$164$	−4.08439	−	8.94356i	−0.318937	−	0.698375i
$165$	0.648241	+	0.190341i	0.0504655	+	0.0148180i
$166$	2.48681	+	2.86994i	0.193014	+	0.222750i
$167$	−3.30876	+	0.971539i	−0.256039	+	0.0751799i	−0.407233	−	0.913324i	$-0.633506\pi$
$167$	−3.30876	+	0.971539i	−0.256039	+	0.0751799i	0.151194	+	0.988504i	$0.451688\pi$
$168$	0.980774	+	0.630305i	0.0756683	+	0.0486291i
$169$	−0.768161	+	1.68204i	−0.0590893	+	0.129388i
$170$	−0.211059	+	0.243575i	−0.0161875	+	0.0186813i
$171$	0.438030	−	0.281505i	0.0334970	−	0.0215272i
$172$	2.19317	+	15.2538i	0.167227	+	1.16309i
$173$	2.50289	+	17.4080i	0.190291	+	1.32351i	0.831236	+	0.555919i	$0.187634\pi$
$173$	2.50289	+	17.4080i	0.190291	+	1.32351i	−0.640945	+	0.767587i	$0.721457\pi$
$174$	12.1924	−	7.83557i	0.924302	−	0.594013i
$175$	−2.42517	+	2.79879i	−0.183325	+	0.211569i
$176$	−1.02924	+	2.25372i	−0.0775818	+	0.169880i
$177$	10.0860	+	6.48185i	0.758107	+	0.487206i
$178$	12.6595	−	3.71715i	0.948866	−	0.278612i
$179$	−13.0081	−	15.0122i	−0.972274	−	1.12206i	−0.992497	−	0.122269i	$-0.960983\pi$
$179$	−13.0081	−	15.0122i	−0.972274	−	1.12206i	0.0202229	−	0.999795i	$-0.493562\pi$
$180$	2.06718	+	0.606979i	0.154079	+	0.0452416i
$181$	1.87042	+	4.09566i	0.139027	+	0.304428i	0.966320	−	0.257344i	$-0.0828473\pi$
$181$	1.87042	+	4.09566i	0.139027	+	0.304428i	−0.827292	+	0.561772i	$0.810120\pi$
$182$	−3.58719	+	24.9494i	−0.265900	+	1.84938i
$183$	−8.28835			−0.612692
$184$	−1.00902	+	1.12308i	−0.0743861	+	0.0827943i
$185$	5.33090			0.391936
$186$	−2.18519	+	15.1983i	−0.160226	+	1.11440i
$187$	−0.0443787	−	0.0971757i	−0.00324529	−	0.00710619i
$188$	−15.2856	−	4.48825i	−1.11481	−	0.327339i
$189$	−2.42517	−	2.79879i	−0.176405	−	0.203582i
$190$	1.01830	−	0.298999i	0.0738752	−	0.0216917i
$191$	−11.6327	−	7.47585i	−0.841709	−	0.540934i	0.0472696	−	0.998882i	$-0.484948\pi$
$191$	−11.6327	−	7.47585i	−0.841709	−	0.540934i	−0.888979	+	0.457949i	$0.848584\pi$
$192$	−3.81526	+	8.35426i	−0.275343	+	0.602917i
$193$	−2.53148	+	2.92148i	−0.182220	+	0.210293i	−0.839509	−	0.543345i	$-0.817157\pi$
$193$	−2.53148	+	2.92148i	−0.182220	+	0.210293i	0.657290	+	0.753638i	$0.271703\pi$
$194$	−7.91207	+	5.08478i	−0.568054	+	0.365066i
$195$	0.475231	+	3.30530i	0.0340320	+	0.236698i
$196$	−2.05879	−	14.3192i	−0.147057	−	1.02280i
$197$	0.262793	−	0.168887i	0.0187232	−	0.0120327i	−0.531246	−	0.847218i	$-0.678276\pi$
$197$	0.262793	−	0.168887i	0.0187232	−	0.0120327i	0.549969	+	0.835185i	$0.314640\pi$
$198$	−0.901779	+	1.04071i	−0.0640867	+	0.0739600i
$199$	6.49159	−	14.2146i	0.460177	−	1.00765i	−0.527270	−	0.849698i	$-0.676785\pi$
$199$	6.49159	−	14.2146i	0.460177	−	1.00765i	0.987447	−	0.157949i	$-0.0504882\pi$
$200$	0.264835	+	0.170199i	0.0187267	+	0.0120349i
$201$	−13.7084	+	4.02515i	−0.966917	+	0.283912i
$202$	−13.8977	−	16.0388i	−0.977840	−	1.12849i
$203$	−25.2662	−	7.41882i	−1.77334	−	0.520699i
$204$	−0.141520	−	0.309885i	−0.00990835	−	0.0216963i
$205$	−0.649469	+	4.51715i	−0.0453609	+	0.315492i
$206$	30.3524			2.11475
$207$	4.08042	−	2.51996i	0.283609	−	0.175149i
$208$	−12.2460			−0.849106
$209$	−0.0500635	+	0.348199i	−0.00346297	+	0.0240855i
$210$	−3.13568	−	6.86618i	−0.216383	−	0.473812i
$211$	−21.8410	−	6.41309i	−1.50360	−	0.441496i	−0.576745	−	0.816924i	$-0.695677\pi$
$211$	−21.8410	−	6.41309i	−1.50360	−	0.441496i	−0.926851	+	0.375429i	$0.877495\pi$
$212$	0.698603	+	0.806231i	0.0479802	+	0.0553721i
$213$	−10.0012	+	2.93663i	−0.685274	+	0.201215i
$214$	10.1380	+	6.51530i	0.693020	+	0.445377i
$215$	2.97144	−	6.50654i	0.202650	−	0.443743i
$216$	−0.206157	+	0.237918i	−0.0140272	+	0.0161883i
$217$	23.4694	−	15.0829i	1.59321	−	1.02389i
$218$	5.42769	+	37.7504i	0.367610	+	2.55678i
$219$	0.548145	+	3.81243i	0.0370402	+	0.257620i
$220$	−1.22450	+	0.786937i	−0.0825557	+	0.0530553i
$221$	0.345781	−	0.399052i	0.0232597	−	0.0268432i
$222$	−4.51377	+	9.88379i	−0.302945	+	0.663356i
$223$	−9.10566	−	5.85185i	−0.609760	−	0.391869i	0.199007	−	0.979998i	$-0.436228\pi$
$223$	−9.10566	−	5.85185i	−0.609760	−	0.391869i	−0.808767	+	0.588129i	$0.799865\pi$
$224$	28.7974	−	8.45569i	1.92411	−	0.564969i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	1.16404	+	0.341794i	0.0774311	+	0.0227358i
$227$	−7.23438	−	15.8411i	−0.480163	−	1.05141i	−0.982419	−	0.186690i	$-0.940224\pi$
$227$	−7.23438	−	15.8411i	−0.480163	−	1.05141i	0.502256	−	0.864719i	$-0.332503\pi$
$228$	−0.159648	+	1.11038i	−0.0105729	+	0.0735365i
$229$	−11.1307			−0.735535			−0.367768	−	0.929918i	$-0.619878\pi$
$229$	−11.1307			−0.735535			−0.367768	+	0.929918i	$0.619878\pi$
$230$	9.42707	−	2.58511i	0.621602	−	0.170457i
$231$	2.50200			0.164620
$232$	−0.318570	+	2.21570i	−0.0209151	+	0.145468i
$233$	8.57574	+	18.7782i	0.561815	+	1.23020i	0.951042	+	0.309062i	$0.100015\pi$
$233$	8.57574	+	18.7782i	0.561815	+	1.23020i	−0.389227	+	0.921142i	$0.627258\pi$
$234$	−6.53060	−	1.91756i	−0.426918	−	0.125355i
$235$	4.84230	+	5.58832i	0.315877	+	0.364541i
$236$	−24.7838	+	7.27719i	−1.61329	+	0.473705i
$237$	−5.93982	−	3.81729i	−0.385833	−	0.247960i
$238$	−0.495826	+	1.08571i	−0.0321396	+	0.0703760i
$239$	−6.84901	+	7.90418i	−0.443026	+	0.511279i	−0.932713	−	0.360619i	$-0.882565\pi$
$239$	−6.84901	+	7.90418i	−0.443026	+	0.511279i	0.489687	+	0.871898i	$0.337111\pi$
$240$	3.08508	−	1.98266i	0.199141	−	0.127980i
$241$	1.98772	+	13.8249i	0.128040	+	0.890538i	0.948035	+	0.318167i	$0.103067\pi$
$241$	1.98772	+	13.8249i	0.128040	+	0.890538i	−0.819995	+	0.572371i	$0.806024\pi$
$242$	3.05840	+	21.2716i	0.196601	+	1.36739i
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$	11.6937	−	13.4953i	0.748615	−	0.863948i
$245$	−2.78938	+	6.10789i	−0.178207	+	0.390219i
$246$	−7.82514	−	5.02891i	−0.498912	−	0.320632i
$247$	−1.66829	+	0.489855i	−0.106151	+	0.0311687i
$248$	−1.55303	−	1.79229i	−0.0986176	−	0.113811i
$249$	1.78764	+	0.524897i	0.113287	+	0.0332640i
$250$	−0.846718	−	1.85405i	−0.0535512	−	0.117261i
$251$	−2.08012	+	14.4675i	−0.131296	+	0.913182i	0.812572	+	0.582860i	$0.198066\pi$
$251$	−2.08012	+	14.4675i	−0.131296	+	0.913182i	−0.943868	+	0.330322i	$0.892843\pi$
$252$	7.97865			0.502608
$253$	−0.518626	+	3.19832i	−0.0326058	+	0.201077i
$254$	14.1058			0.885076
$255$	−0.0225034	+	0.156514i	−0.00140922	+	0.00980132i
$256$	5.50444	+	12.0530i	0.344027	+	0.753315i
$257$	21.9288	+	6.43887i	1.36788	+	0.401646i	0.881534	−	0.472121i	$-0.156511\pi$
$257$	21.9288	+	6.43887i	1.36788	+	0.401646i	0.486346	+	0.873766i	$0.338330\pi$
$258$	9.54752	+	11.0184i	0.594403	+	0.685977i
$259$	18.9424	−	5.56200i	1.17702	−	0.345606i
$260$	−6.05226	−	3.88955i	−0.375345	−	0.241220i
$261$	2.95384	−	6.46801i	0.182838	−	0.400360i
$262$	23.0055	−	26.5498i	1.42128	−	1.64025i
$263$	17.8959	−	11.5010i	1.10351	−	0.709181i	0.143639	−	0.989630i	$-0.454120\pi$
$263$	17.8959	−	11.5010i	1.10351	−	0.709181i	0.959869	+	0.280449i	$0.0904834\pi$
$264$	−0.0302687	−	0.210523i	−0.00186291	−	0.0129568i
$265$	−0.0704685	−	0.490119i	−0.00432884	−	0.0301078i
$266$	3.30638	−	2.12488i	0.202727	−	0.130285i
$267$	4.23902	−	4.89209i	0.259424	−	0.299391i
$268$	12.7869	−	27.9993i	0.781082	−	1.71033i
$269$	−9.05864	−	5.82164i	−0.552315	−	0.354951i	0.234523	−	0.972111i	$-0.424647\pi$
$269$	−9.05864	−	5.82164i	−0.552315	−	0.354951i	−0.786838	+	0.617159i	$0.788283\pi$
$270$	1.95568	−	0.574241i	0.119019	−	0.0349472i
$271$	19.2886	+	22.2603i	1.17170	+	1.35222i	0.923542	+	0.383496i	$0.125280\pi$
$271$	19.2886	+	22.2603i	1.17170	+	1.35222i	0.248159	+	0.968719i	$0.420175\pi$
$272$	−0.556389	−	0.163371i	−0.0337361	−	0.00990580i
$273$	5.13723	+	11.2490i	0.310919	+	0.680819i
$274$	−4.21778	+	29.3353i	−0.254805	+	1.77221i
$275$	0.675608			0.0407407
$276$	−1.65385	+	10.1992i	−0.0995502	+	0.613918i
$277$	10.8939			0.654548			0.327274	−	0.944929i	$-0.393870\pi$
$277$	10.8939			0.654548			0.327274	+	0.944929i	$0.393870\pi$
$278$	0.447998	−	3.11589i	0.0268691	−	0.186879i
$279$	3.12942	+	6.85248i	0.187354	+	0.410247i
$280$	1.11862	+	0.328457i	0.0668505	+	0.0196291i
$281$	−15.5493	−	17.9448i	−0.927592	−	1.07050i	−0.997337	−	0.0729336i	$-0.976764\pi$
$281$	−15.5493	−	17.9448i	−0.927592	−	1.07050i	0.0697446	−	0.997565i	$-0.477782\pi$
$282$	−14.4611	+	4.24616i	−0.861147	+	0.252855i
$283$	−10.6811	−	6.86432i	−0.634925	−	0.408042i	0.183205	−	0.983075i	$-0.441353\pi$
$283$	−10.6811	−	6.86432i	−0.634925	−	0.408042i	−0.818130	+	0.575033i	$0.804989\pi$
$284$	9.32892	−	20.4275i	0.553570	−	1.21215i
$285$	0.340977	−	0.393509i	0.0201978	−	0.0233095i
$286$	3.86841	−	2.48608i	0.228744	−	0.147005i
$287$	2.40520	+	16.7285i	0.141974	+	0.987454i
$288$	1.15337	+	8.02187i	0.0679631	+	0.472694i
$289$	−14.2803	+	9.17738i	−0.840016	+	0.539846i
$290$	9.49097	−	10.9532i	0.557329	−	0.643192i
$291$	−1.91685	+	4.19732i	−0.112368	+	0.246051i
$292$	−6.98086	−	4.48632i	−0.408524	−	0.262542i
$293$	8.26043	−	2.42548i	0.482580	−	0.141698i	−0.0313889	−	0.999507i	$-0.509993\pi$
$293$	8.26043	−	2.42548i	0.482580	−	0.141698i	0.513968	+	0.857809i	$0.328175\pi$
$294$	−8.96254	−	10.3433i	−0.522706	−	0.603235i
$295$	11.5036	+	3.37775i	0.669763	+	0.196660i
$296$	−0.697159	−	1.52657i	−0.0405216	−	0.0887299i
$297$	−0.0961490	+	0.668731i	−0.00557913	+	0.0388037i
$298$	43.0000			2.49092
$299$	−15.4445	+	4.23522i	−0.893179	+	0.244929i
$300$	2.15445			0.124387
$301$	3.76988	−	26.2201i	0.217292	−	1.51130i
$302$	−17.0246	−	37.2786i	−0.979654	−	2.14514i
$303$	−9.99032	−	2.93342i	−0.573929	−	0.168521i
$304$	1.25045	+	1.44309i	0.0717180	+	0.0827670i
$305$	−7.95261	+	2.33510i	−0.455365	+	0.133707i
$306$	−0.271132	−	0.174246i	−0.0154996	−	0.00996099i
$307$	−10.7514	+	23.5422i	−0.613613	+	1.34362i	0.306462	+	0.951883i	$0.400855\pi$
$307$	−10.7514	+	23.5422i	−0.613613	+	1.34362i	−0.920075	+	0.391742i	$0.871873\pi$
$308$	−3.52999	+	4.07382i	−0.201140	+	0.232128i
$309$	12.5275	−	8.05092i	0.712663	−	0.458001i
$310$	2.18519	+	15.1983i	0.124110	+	0.863207i
$311$	−0.389750	−	2.71077i	−0.0221007	−	0.153714i	0.975783	−	0.218742i	$-0.0701953\pi$
$311$	−0.389750	−	2.71077i	−0.0221007	−	0.153714i	−0.997883	+	0.0650282i	$0.979286\pi$
$312$	0.884362	−	0.568345i	0.0500671	−	0.0321762i
$313$	4.87107	−	5.62151i	0.275329	−	0.317746i	−0.601197	−	0.799101i	$-0.705309\pi$
$313$	4.87107	−	5.62151i	0.275329	−	0.317746i	0.876526	+	0.481354i	$0.159855\pi$
$314$	−3.03574	+	6.64734i	−0.171317	+	0.375131i
$315$	−3.11544	−	2.00217i	−0.175535	−	0.112810i
$316$	14.5957	−	4.28568i	0.821072	−	0.241089i
$317$	−10.7215	−	12.3733i	−0.602179	−	0.694951i	0.370043	−	0.929015i	$-0.379343\pi$
$317$	−10.7215	−	12.3733i	−0.602179	−	0.694951i	−0.972221	+	0.234064i	$0.924798\pi$
$318$	0.968374	+	0.284340i	0.0543037	+	0.0159450i
$319$	1.99564	+	4.36984i	0.111734	+	0.244664i
$320$	−1.30705	+	9.09074i	−0.0730663	+	0.508188i
$321$	5.91247			0.330002
$322$	30.8002	−	19.0214i	1.71643	−	1.06002i
$323$	−0.0823330			−0.00458113
$324$	−0.306610	+	2.13252i	−0.0170339	+	0.118473i
$325$	1.38719	+	3.03753i	0.0769475	+	0.168492i
$326$	−14.9073	−	4.37719i	−0.825641	−	0.242430i
$327$	12.2534	+	14.1412i	0.677616	+	0.782010i
$328$	1.37848	−	0.404757i	0.0761136	−	0.0223490i
$329$	23.0368	+	14.8049i	1.27006	+	0.816219i
$330$	−0.572049	+	1.25261i	−0.0314903	+	0.0689541i
$331$	1.97541	−	2.27974i	0.108578	−	0.125306i	−0.698859	−	0.715260i	$-0.746308\pi$
$331$	1.97541	−	2.27974i	0.108578	−	0.125306i	0.807437	+	0.589954i	$0.200854\pi$
$332$	−3.37677	+	2.17012i	−0.185324	+	0.119101i
$333$	0.758667	+	5.27664i	0.0415747	+	0.289158i
$334$	−1.00030	−	6.95724i	−0.0547340	−	0.380683i
$335$	−12.0191	+	7.72421i	−0.656674	+	0.422019i
$336$	8.89368	−	10.2639i	0.485190	−	0.559939i
$337$	−11.2357	+	24.6026i	−0.612045	+	1.34019i	0.309122	+	0.951023i	$0.399965\pi$
$337$	−11.2357	+	24.6026i	−0.612045	+	1.34019i	−0.921166	+	0.389169i	$0.872762\pi$
$338$	−3.17069	−	2.03768i	−0.172463	−	0.110835i
$339$	0.571101	−	0.167690i	0.0310179	−	0.00910768i
$340$	−0.223092	−	0.257461i	−0.0120988	−	0.0139628i
$341$	−4.88336	−	1.43388i	−0.264449	−	0.0776491i
$342$	0.440875	+	0.965382i	0.0238398	+	0.0522019i
$343$	0.150374	−	1.04588i	0.00811944	−	0.0564720i
$344$	−2.25182			−0.121410
$345$	3.20518	−	3.56747i	0.172561	−	0.192066i
$346$	−35.8467			−1.92713
$347$	3.34086	−	23.2362i	0.179347	−	1.24738i	−0.678933	−	0.734200i	$-0.737557\pi$
$347$	3.34086	−	23.2362i	0.179347	−	1.24738i	0.858280	−	0.513182i	$-0.171534\pi$
$348$	6.36391	+	13.9350i	0.341141	+	0.746995i
$349$	−8.63405	−	2.53519i	−0.462170	−	0.135705i	0.0423545	−	0.999103i	$-0.486514\pi$
$349$	−8.63405	−	2.53519i	−0.462170	−	0.135705i	−0.504525	+	0.863397i	$0.668332\pi$
$350$	−4.94309	−	5.70463i	−0.264219	−	0.304925i
$351$	−3.20403	+	0.940787i	−0.171018	+	0.0502155i
$352$	−4.60618	−	2.96021i	−0.245510	−	0.157780i
$353$	2.72365	−	5.96396i	0.144965	−	0.317429i	−0.823196	−	0.567757i	$-0.807811\pi$
$353$	2.72365	−	5.96396i	0.144965	−	0.317429i	0.968161	+	0.250328i	$0.0805385\pi$
$354$	−16.0028	+	18.4682i	−0.850539	+	0.981574i
$355$	−8.76878	+	5.63535i	−0.465399	+	0.299094i
$356$	1.98474	+	13.8042i	0.105191	+	0.731619i
$357$	0.0833375	+	0.579625i	0.00441069	+	0.0306770i
$358$	34.0604	−	21.8893i	1.80015	−	1.15689i
$359$	−8.77183	+	10.1232i	−0.462960	+	0.534284i	−0.938440	−	0.345443i	$-0.887729\pi$
$359$	−8.77183	+	10.1232i	−0.462960	+	0.534284i	0.475480	+	0.879726i	$0.342274\pi$
$360$	−0.130777	+	0.286362i	−0.00689255	+	0.0150926i
$361$	−15.7557	−	10.1256i	−0.829250	−	0.532926i
$362$	−8.80555	+	2.58554i	−0.462809	+	0.135893i
$363$	6.90456	+	7.96829i	0.362395	+	0.418227i
$364$	−25.5638	−	7.50621i	−1.33991	−	0.393432i
$365$	1.60003	+	3.50357i	0.0837492	+	0.183385i
$366$	2.40422	−	16.7217i	0.125671	−	0.874060i
$367$	−22.9145			−1.19613			−0.598063	−	0.801449i	$-0.704063\pi$
$367$	−22.9145			−1.19613			−0.598063	+	0.801449i	$0.704063\pi$
$368$	11.2768	+	13.4964i	0.587845	+	0.703548i
$369$	−4.56361			−0.237572
$370$	−1.54635	+	10.7551i	−0.0803909	+	0.559131i
$371$	−0.761763	−	1.66803i	−0.0395487	−	0.0865997i
$372$	−15.5726	−	4.57252i	−0.807401	−	0.237074i
$373$	14.7022	+	16.9672i	0.761250	+	0.878530i	0.995608	−	0.0936208i	$-0.0298441\pi$
$373$	14.7022	+	16.9672i	0.761250	+	0.878530i	−0.234358	+	0.972150i	$0.575299\pi$
$374$	0.208925	−	0.0613460i	0.0108033	−	0.00317212i
$375$	−0.841254	−	0.540641i	−0.0434421	−	0.0279186i
$376$	0.967017	−	2.11747i	0.0498701	−	0.109200i
$377$	−15.5492	+	17.9447i	−0.800825	+	0.924201i
$378$	6.35004	−	4.08092i	0.326611	−	0.209900i
$379$	−0.526619	−	3.66271i	−0.0270506	−	0.188141i	0.971816	−	0.235741i	$-0.0757518\pi$
$379$	−0.526619	−	3.66271i	−0.0270506	−	0.188141i	−0.998866	+	0.0476002i	$0.984843\pi$
$380$	0.159648	+	1.11038i	0.00818977	+	0.0569611i
$381$	5.82194	−	3.74153i	0.298267	−	0.191685i
$382$	18.4568	−	21.3003i	0.944335	−	1.08982i
$383$	6.21261	−	13.6037i	0.317449	−	0.695117i	−0.681890	−	0.731455i	$-0.738842\pi$
$383$	6.21261	−	13.6037i	0.317449	−	0.695117i	0.999340	+	0.0363372i	$0.0115691\pi$
$384$	−2.11237	−	1.35753i	−0.107796	−	0.0692764i
$385$	2.40065	−	0.704895i	0.122349	−	0.0359248i
$386$	−5.15977	−	5.95470i	−0.262626	−	0.303086i
$387$	6.86320	+	2.01522i	0.348876	+	0.102439i
$388$	−4.12976	−	9.04292i	−0.209657	−	0.459085i
$389$	1.90570	−	13.2545i	0.0966231	−	0.672028i	−0.882731	−	0.469878i	$-0.844298\pi$
$389$	1.90570	−	13.2545i	0.0966231	−	0.672028i	0.979355	−	0.202150i	$-0.0647930\pi$
$390$	−6.80630			−0.344650
$391$	−0.758213	−	0.0136165i	−0.0383445	−	0.000688618i
$392$	2.11385			0.106766
$393$	2.45288	−	17.0601i	0.123731	−	0.860570i
$394$	0.264500	+	0.579174i	0.0133253	+	0.0291784i
$395$	−6.77467	−	1.98922i	−0.340871	−	0.100089i
$396$	−0.953192	−	1.10004i	−0.0478997	−	0.0552792i
$397$	0.149192	−	0.0438068i	0.00748774	−	0.00219860i	−0.277987	−	0.960585i	$-0.589667\pi$
$397$	0.149192	−	0.0438068i	0.00748774	−	0.00219860i	0.285474	+	0.958386i	$0.407849\pi$
$398$	26.7949	+	17.2201i	1.34311	+	0.863164i
$399$	0.801035	−	1.75402i	0.0401019	−	0.0878110i
$400$	2.40153	−	2.77152i	0.120077	−	0.138576i
$401$	−24.6021	+	15.8108i	−1.22857	+	0.789555i	−0.983668	−	0.179992i	$-0.942393\pi$
$401$	−24.6021	+	15.8108i	−1.22857	+	0.789555i	−0.244904	+	0.969547i	$0.578756\pi$
$402$	−4.14431	−	28.8243i	−0.206699	−	1.43763i
$403$	−3.58003	−	24.8997i	−0.178334	−	1.24034i
$404$	18.8713	−	12.1278i	0.938881	−	0.603382i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	22.2965	−	48.8225i	1.10656	−	2.42302i
$407$	−3.02986	−	1.94717i	−0.150184	−	0.0965177i
$408$	0.0477627	−	0.0140244i	0.00236460	−	0.000694310i
$409$	−7.59681	−	8.76719i	−0.375638	−	0.433510i	0.536180	−	0.844104i	$-0.319867\pi$
$409$	−7.59681	−	8.76719i	−0.375638	−	0.433510i	−0.911818	+	0.410594i	$0.865321\pi$
$410$	−8.92497	−	2.62061i	−0.440773	−	0.129423i
$411$	6.04031	+	13.2264i	0.297946	+	0.652412i
$412$	−4.56587	+	31.7563i	−0.224944	+	1.56452i
$413$	44.4000			2.18478
$414$	3.90041	+	8.96321i	0.191695	+	0.440518i
$415$	1.86311			0.0914563
$416$	3.85144	−	26.7874i	0.188832	−	1.31336i
$417$	−0.641580	−	1.40486i	−0.0314183	−	0.0687965i
$418$	−0.687970	−	0.202006i	−0.0336497	−	0.00988045i
$419$	−16.5128	−	19.0568i	−0.806703	−	0.930985i	0.192025	−	0.981390i	$-0.438494\pi$
$419$	−16.5128	−	19.0568i	−0.806703	−	0.930985i	−0.998729	+	0.0504046i	$0.983949\pi$
$420$	7.65546	−	2.24785i	0.373548	−	0.109684i
$421$	18.0561	+	11.6039i	0.879999	+	0.565541i	0.900796	−	0.434243i	$-0.142984\pi$
$421$	18.0561	+	11.6039i	0.879999	+	0.565541i	−0.0207971	+	0.999784i	$0.506620\pi$
$422$	19.2739	−	42.2040i	0.938239	−	2.05446i
$423$	−4.84230	+	5.58832i	−0.235441	+	0.271713i
$424$	−0.131136	+	0.0842757i	−0.00636851	+	0.00409279i
$425$	0.0225034	+	0.156514i	0.00109157	+	0.00759207i
$426$	−3.02357	−	21.0294i	−0.146492	−	1.01888i
$427$	−25.8219	+	16.5947i	−1.24961	+	0.803074i
$428$	−8.34170	+	9.62684i	−0.403211	+	0.465331i
$429$	0.937197	−	2.05218i	0.0452483	−	0.0990799i
$430$	12.2650	+	7.88225i	0.591472	+	0.380116i
$431$	15.2559	−	4.47953i	0.734850	−	0.215772i	0.107168	−	0.994241i	$-0.465822\pi$
$431$	15.2559	−	4.47953i	0.734850	−	0.215772i	0.627683	+	0.778469i	$0.284004\pi$
$432$	2.40153	+	2.77152i	0.115544	+	0.133345i
$433$	−17.5946	−	5.16625i	−0.845544	−	0.248274i	−0.169863	−	0.985468i	$-0.554332\pi$
$433$	−17.5946	−	5.16625i	−0.845544	−	0.248274i	−0.675682	+	0.737193i	$0.736151\pi$
$434$	23.6219	+	51.7247i	1.13389	+	2.48286i
$435$	1.01194	−	7.03820i	0.0485189	−	0.337456i
$436$	−40.3130			−1.93064
$437$	2.07614	+	1.38755i	0.0993151	+	0.0663756i
$438$	−7.85058			−0.375115
$439$	−5.83650	+	40.5938i	−0.278561	+	1.93743i	0.0640247	+	0.997948i	$0.479606\pi$
$439$	−5.83650	+	40.5938i	−0.278561	+	1.93743i	−0.342586	+	0.939487i	$0.611303\pi$
$440$	−0.0883539	−	0.193468i	−0.00421211	−	0.00922323i
$441$	−6.44269	−	1.89174i	−0.306795	−	0.0900831i
$442$	0.704786	+	0.813367i	0.0335233	+	0.0386879i
$443$	14.2845	−	4.19431i	0.678677	−	0.199278i	0.0758138	−	0.997122i	$-0.475845\pi$
$443$	14.2845	−	4.19431i	0.678677	−	0.199278i	0.602864	+	0.797844i	$0.294026\pi$
$444$	−9.66194	−	6.20935i	−0.458536	−	0.294683i
$445$	2.68905	−	5.88819i	0.127473	−	0.279127i
$446$	14.4474	−	16.6732i	0.684105	−	0.789499i
$447$	17.7476	−	11.4057i	0.839431	−	0.539469i
$448$	4.84044	+	33.6660i	0.228689	+	1.59057i
$449$	3.00921	+	20.9295i	0.142013	+	0.987724i	0.928822	+	0.370527i	$0.120823\pi$
$449$	3.00921	+	20.9295i	0.142013	+	0.987724i	−0.786808	+	0.617197i	$0.788268\pi$
$450$	1.71468	−	1.10196i	0.0808309	−	0.0519469i
$451$	2.01907	−	2.33013i	0.0950743	−	0.109722i
$452$	−0.532709	+	1.16647i	−0.0250565	+	0.0548661i
$453$	−16.9147	−	10.8704i	−0.794721	−	0.510736i
$454$	34.0579	−	10.0003i	1.59842	−	0.469337i
$455$	8.09834	+	9.34598i	0.379656	+	0.438146i
$456$	−0.157278	−	0.0461809i	−0.00736521	−	0.00216262i
$457$	−12.1609	−	26.6287i	−0.568864	−	1.24564i	−0.947400	−	0.320052i	$-0.896300\pi$
$457$	−12.1609	−	26.6287i	−0.568864	−	1.24564i	0.378536	−	0.925587i	$-0.376428\pi$
$458$	3.22870	−	22.4561i	0.150867	−	1.04931i
$459$	−0.158124			−0.00738059
$460$	1.28658	+	10.2520i	0.0599870	+	0.478001i
$461$	37.8376			1.76227			0.881136	−	0.472862i	$-0.156779\pi$
$461$	37.8376			1.76227			0.881136	+	0.472862i	$0.156779\pi$
$462$	−0.725762	+	5.04779i	−0.0337655	+	0.234844i
$463$	9.87492	+	21.6231i	0.458926	+	1.00491i	0.987731	+	0.156165i	$0.0499132\pi$
$463$	9.87492	+	21.6231i	0.458926	+	1.00491i	−0.528805	+	0.848744i	$0.677360\pi$
$464$	25.0199	+	7.34652i	1.16152	+	0.341054i
$465$	4.93323	+	5.69325i	0.228773	+	0.264018i
$466$	−40.3727	+	11.8545i	−1.87023	+	0.549149i
$467$	−25.0762	−	16.1155i	−1.16039	−	0.745736i	−0.188707	−	0.982033i	$-0.560430\pi$
$467$	−25.0762	−	16.1155i	−1.16039	−	0.745736i	−0.971681	+	0.236298i	$0.924066\pi$
$468$	2.98864	−	6.54420i	0.138150	−	0.302506i
$469$	−34.6487	+	39.9867i	−1.59993	+	1.84642i
$470$	−12.6791	+	8.14833i	−0.584841	+	0.375854i
$471$	0.510241	+	3.54881i	0.0235107	+	0.163520i
$472$	−0.537142	−	3.73591i	−0.0247240	−	0.171959i
$473$	−4.06543	+	2.61269i	−0.186929	+	0.120132i
$474$	9.42437	−	10.8763i	0.432875	−	0.499565i
$475$	0.216301	−	0.473633i	0.00992458	−	0.0217318i
$476$	−1.06134	−	0.682081i	−0.0486464	−	0.0312631i
$477$	0.475102	−	0.139502i	0.0217534	−	0.00638738i
$478$	−13.9600	−	16.1107i	−0.638515	−	0.736885i
$479$	−1.12046	−	0.328998i	−0.0511953	−	0.0150323i	0.256035	−	0.966668i	$-0.417584\pi$
$479$	−1.12046	−	0.328998i	−0.0511953	−	0.0150323i	−0.307230	+	0.951635i	$0.599402\pi$
$480$	3.36668	+	7.37199i	0.153667	+	0.336484i
$481$	2.53341	−	17.6202i	0.115513	−	0.803414i
$482$	−28.4683			−1.29669
$483$	7.66690	−	16.0205i	0.348856	−	0.728958i
$484$	−22.7156			−1.03253
$485$	−0.656684	+	4.56734i	−0.0298185	+	0.207392i
$486$	0.846718	+	1.85405i	0.0384079	+	0.0841016i
$487$	24.4126	+	7.16818i	1.10624	+	0.324821i	0.783328	−	0.621608i	$-0.213520\pi$
$487$	24.4126	+	7.16818i	1.10624	+	0.324821i	0.322911	+	0.946429i	$0.395339\pi$
$488$	1.70870	+	1.97195i	0.0773493	+	0.0892658i
$489$	−7.31380	+	2.14752i	−0.330741	+	0.0971144i
$490$	−11.5135	−	7.39931i	−0.520129	−	0.334267i
$491$	0.464006	−	1.01603i	0.0209403	−	0.0458529i	−0.898873	−	0.438209i	$-0.855613\pi$
$491$	0.464006	−	1.01603i	0.0209403	−	0.0458529i	0.919813	+	0.392357i	$0.128340\pi$
$492$	6.43863	−	7.43058i	0.290276	−	0.334996i
$493$	−0.945866	+	0.607871i	−0.0425997	+	0.0273771i
$494$	−0.504357	−	3.50788i	−0.0226921	−	0.157827i
$495$	0.0961490	+	0.668731i	0.00432158	+	0.0300572i
$496$	−23.2407	+	14.9359i	−1.04354	+	0.670641i
$497$	−25.2787	+	29.1731i	−1.13390	+	1.30859i
$498$	−1.57753	+	3.45430i	−0.0706906	+	0.154791i
$499$	−35.6793	−	22.9297i	−1.59722	−	1.02647i	−0.968554	−	0.248802i	$-0.919963\pi$
$499$	−35.6793	−	22.9297i	−1.59722	−	1.02647i	−0.628671	−	0.777672i	$-0.716401\pi$
$500$	2.06718	−	0.606979i	0.0924472	−	0.0271449i
$501$	−2.25825	−	2.60616i	−0.100891	−	0.116435i
$502$	−28.5849	−	8.39327i	−1.27581	−	0.374610i
$503$	11.8265	+	25.8964i	0.527318	+	1.15467i	0.966594	+	0.256313i	$0.0825078\pi$
$503$	11.8265	+	25.8964i	0.527318	+	1.15467i	−0.439276	+	0.898352i	$0.644765\pi$
$504$	−0.165917	+	1.15398i	−0.00739055	+	0.0514024i
$505$	−10.4121			−0.463331
$506$	−6.30218	−	1.97408i	−0.280166	−	0.0877584i
$507$	−1.84914			−0.0821233
$508$	−2.12191	+	14.7582i	−0.0941447	+	0.654791i
$509$	1.14187	+	2.50034i	0.0506123	+	0.110826i	0.933249	−	0.359231i	$-0.116961\pi$
$509$	1.14187	+	2.50034i	0.0506123	+	0.110826i	−0.882636	+	0.470056i	$0.844234\pi$
$510$	−0.309240	−	0.0908012i	−0.0136934	−	0.00402074i
$511$	9.34086	+	10.7799i	0.413215	+	0.476876i
$512$	−30.7322	+	9.02379i	−1.35818	+	0.398799i
$513$	0.438030	+	0.281505i	0.0193395	+	0.0124287i
$514$	−19.3514	+	42.3736i	−0.853552	+	1.86902i
$515$	9.75182	−	11.2542i	0.429716	−	0.495919i
$516$	−12.9643	+	8.33164i	−0.570721	+	0.366780i
$517$	−0.710964	−	4.94486i	−0.0312682	−	0.217475i
$518$	5.72665	+	39.8297i	0.251615	+	1.75002i
$519$	−14.7951	+	9.50826i	−0.649434	+	0.417366i
$520$	0.688418	−	0.794477i	0.0301891	−	0.0348401i
$521$	−8.67248	+	18.9901i	−0.379948	+	0.831971i	0.618967	+	0.785417i	$0.287551\pi$
$521$	−8.67248	+	18.9901i	−0.379948	+	0.831971i	−0.998916	+	0.0465541i	$0.985176\pi$
$522$	12.1924	+	7.83557i	0.533646	+	0.342954i
$523$	−22.5132	+	6.61048i	−0.984434	+	0.289056i	−0.734054	−	0.679092i	$-0.762374\pi$
$523$	−22.5132	+	6.61048i	−0.984434	+	0.289056i	−0.250381	+	0.968147i	$0.580556\pi$
$524$	24.3171	+	28.0634i	1.06230	+	1.22596i
$525$	−3.55332	−	1.04335i	−0.155080	−	0.0455355i
$526$	18.0121	+	39.4411i	0.785367	+	1.71971i
$527$	0.169524	−	1.17906i	0.00738456	−	0.0513608i
$528$	−2.47762			−0.107824
$529$	18.8899	+	13.1215i	0.821299	+	0.570498i
$530$	1.00926			0.0438393
$531$	−1.70624	+	11.8672i	−0.0740445	+	0.514991i
$532$	1.72579	+	3.77896i	0.0748226	+	0.163839i
$533$	14.6219	+	4.29338i	0.633345	+	0.185967i
$534$	8.64017	+	9.97128i	0.373897	+	0.431500i
$535$	5.67297	−	1.66574i	0.245264	−	0.0720160i
$536$	3.78374	+	2.43166i	0.163433	+	0.105032i
$537$	8.25180	−	18.0689i	0.356091	−	0.779731i
$538$	14.3728	−	16.5871i	0.619656	−	0.715121i
$539$	3.81634	−	2.45261i	0.164381	−	0.105641i
$540$	0.306610	+	2.13252i	0.0131944	+	0.0917691i
$541$	−4.22111	−	29.3585i	−0.181480	−	1.26222i	−0.853266	−	0.521475i	$-0.825382\pi$
$541$	−4.22111	−	29.3585i	−0.181480	−	1.26222i	0.671787	−	0.740745i	$-0.265527\pi$
$542$	−50.5052	+	32.4577i	−2.16939	+	1.39418i
$543$	−2.94854	+	3.40279i	−0.126534	+	0.146028i
$544$	0.532352	−	1.16569i	0.0228244	−	0.0499785i
$545$	15.7411	+	10.1162i	0.674275	+	0.433330i
$546$	−24.1850	+	7.10135i	−1.03502	+	0.303910i
$547$	28.2275	+	32.5763i	1.20692	+	1.39286i	0.896960	+	0.442112i	$0.145771\pi$
$547$	28.2275	+	32.5763i	1.20692	+	1.39286i	0.309961	+	0.950749i	$0.399684\pi$
$548$	−30.0577	−	8.82573i	−1.28400	−	0.377017i
$549$	−3.44310	−	7.53935i	−0.146948	−	0.321771i
$550$	−0.195975	+	1.36304i	−0.00835642	+	0.0581202i
$551$	3.70238			0.157727
$552$	−1.44075	−	0.451296i	−0.0613224	−	0.0192084i
$553$	−26.1480			−1.11193
$554$	−3.16001	+	21.9784i	−0.134256	+	0.933771i
$555$	2.21454	+	4.84916i	0.0940019	+	0.205835i
$556$	3.19262	+	0.937438i	0.135397	+	0.0397562i
$557$	9.23553	+	10.6584i	0.391322	+	0.451609i	0.916889	−	0.399143i	$-0.130692\pi$
$557$	9.23553	+	10.6584i	0.391322	+	0.451609i	−0.525567	+	0.850752i	$0.676147\pi$
$558$	−14.7327	+	4.32590i	−0.623683	+	0.183130i
$559$	−20.0940	−	12.9136i	−0.849884	−	0.546188i
$560$	5.64176	−	12.3537i	0.238408	−	0.522040i
$561$	0.0699586	−	0.0807365i	0.00295365	−	0.00340870i
$562$	40.7141	−	26.1654i	1.71742	−	1.10372i
$563$	−5.19638	−	36.1416i	−0.219001	−	1.52319i	−0.741736	−	0.670692i	$-0.765997\pi$
$563$	−5.19638	−	36.1416i	−0.219001	−	1.52319i	0.522734	−	0.852496i	$-0.324912\pi$
$564$	−2.26720	−	15.7687i	−0.0954664	−	0.663983i
$565$	0.500723	−	0.321795i	0.0210656	−	0.0135380i
$566$	16.9471	−	19.5580i	0.712339	−	0.822083i
$567$	1.53842	−	3.36867i	0.0646076	−	0.141471i
$568$	2.76050	+	1.77407i	0.115828	+	0.0744383i
$569$	29.7332	−	8.73044i	1.24648	−	0.365999i	0.409033	−	0.912520i	$-0.365866\pi$
$569$	29.7332	−	8.73044i	1.24648	−	0.365999i	0.837446	+	0.546520i	$0.184048\pi$
$570$	0.694996	+	0.802068i	0.0291102	+	0.0335949i
$571$	−0.314606	−	0.0923766i	−0.0131658	−	0.00386584i	0.275143	−	0.961403i	$-0.411275\pi$
$571$	−0.314606	−	0.0923766i	−0.0131658	−	0.00386584i	−0.288309	+	0.957537i	$0.593093\pi$
$572$	2.01915	+	4.42131i	0.0844247	+	0.184864i
$573$	1.96790	−	13.6870i	0.0822100	−	0.571783i
$574$	−34.4475			−1.43781
$575$	2.07027	−	4.32597i	0.0863362	−	0.180405i
$576$	−9.18422			−0.382676
$577$	−0.665161	+	4.62630i	−0.0276910	+	0.192595i	−0.998972	−	0.0453421i	$-0.985562\pi$
$577$	−0.665161	+	4.62630i	−0.0276910	+	0.192595i	0.971281	+	0.237937i	$0.0764713\pi$
$578$	−14.3730	−	31.4726i	−0.597840	−	1.30909i
$579$	−3.70908	−	1.08909i	−0.154144	−	0.0452609i
$580$	10.0321	+	11.5776i	0.416559	+	0.480735i
$581$	6.62022	−	1.94387i	0.274653	−	0.0806453i
$582$	−7.91207	−	5.08478i	−0.327966	−	0.210771i
$583$	−0.138970	+	0.304302i	−0.00575555	+	0.0126029i
$584$	0.794041	−	0.916372i	0.0328577	−	0.0379198i
$585$	−2.80919	+	1.80536i	−0.116146	+	0.0746423i
$586$	2.49728	+	17.3690i	0.103162	+	0.717507i
$587$	1.82694	+	12.7067i	0.0754060	+	0.524460i	0.992157	+	0.125000i	$0.0398932\pi$
$587$	1.82694	+	12.7067i	0.0754060	+	0.524460i	−0.916751	+	0.399460i	$0.869198\pi$
$588$	12.1700	−	7.82116i	0.501881	−	0.322539i
$589$	−2.56867	+	2.96440i	−0.105840	+	0.122146i
$590$	−10.1515	+	22.2286i	−0.417930	+	0.915138i
$591$	0.262793	+	0.168887i	0.0108099	+	0.00694707i
$592$	−18.7578	+	5.50779i	−0.770941	+	0.226369i
$593$	20.2370	+	23.3548i	0.831035	+	0.959066i	0.999646	−	0.0266168i	$-0.00847338\pi$
$593$	20.2370	+	23.3548i	0.831035	+	0.959066i	−0.168610	+	0.985683i	$0.553928\pi$
$594$	−1.32127	−	0.387961i	−0.0542126	−	0.0159182i
$595$	0.243261	+	0.532667i	0.00997273	+	0.0218372i
$596$	−6.46843	+	44.9889i	−0.264957	+	1.84282i
$597$	15.6268			0.639561
$598$	−4.06453	−	32.3878i	−0.166211	−	1.32444i
$599$	3.93424			0.160749			0.0803744	−	0.996765i	$-0.474388\pi$
$599$	3.93424			0.160749			0.0803744	+	0.996765i	$0.474388\pi$
$600$	−0.0448022	+	0.311606i	−0.00182904	+	0.0127213i
$601$	−19.4784	−	42.6517i	−0.794539	−	1.73980i	−0.663175	−	0.748464i	$-0.730791\pi$
$601$	−19.4784	−	42.6517i	−0.794539	−	1.73980i	−0.131364	−	0.991334i	$-0.541936\pi$
$602$	51.8055	+	15.2115i	2.11144	+	0.619974i
$603$	−9.35609	−	10.7975i	−0.381009	−	0.439708i
$604$	41.5638	−	12.2042i	1.69121	−	0.496584i
$605$	8.86980	+	5.70028i	0.360609	+	0.231749i
$606$	8.81610	−	19.3046i	0.358130	−	0.784194i
$607$	−17.7042	+	20.4317i	−0.718590	+	0.829297i	−0.991137	−	0.132845i	$-0.957589\pi$
$607$	−17.7042	+	20.4317i	−0.718590	+	0.829297i	0.272546	+	0.962143i	$0.412134\pi$
$608$	−3.54995	+	2.28142i	−0.143970	+	0.0925236i
$609$	−3.74756	−	26.0648i	−0.151859	−	1.05620i
$610$	−2.40422	−	16.7217i	−0.0973442	−	0.677044i
$611$	20.7723	−	13.3495i	0.840356	−	0.540064i
$612$	0.223092	−	0.257461i	0.00901794	−	0.0104073i
$613$	−3.68805	+	8.07571i	−0.148959	+	0.326175i	−0.969372	−	0.245596i	$-0.921016\pi$
$613$	−3.68805	+	8.07571i	−0.148959	+	0.326175i	0.820413	+	0.571771i	$0.193744\pi$
$614$	−44.3777	−	28.5198i	−1.79094	−	1.15097i
$615$	−4.37875	+	1.28572i	−0.176568	+	0.0518451i
$616$	−0.515805	−	0.595271i	−0.0207824	−	0.0239841i
$617$	−1.44806	−	0.425189i	−0.0582967	−	0.0171175i	0.252454	−	0.967609i	$-0.418762\pi$
$617$	−1.44806	−	0.425189i	−0.0582967	−	0.0171175i	−0.310751	+	0.950491i	$0.600580\pi$
$618$	12.6089	+	27.6095i	0.507203	+	1.11062i
$619$	5.91513	−	41.1406i	0.237749	−	1.65358i	−0.425334	−	0.905036i	$-0.639843\pi$
$619$	5.91513	−	41.1406i	0.237749	−	1.65358i	0.663083	−	0.748546i	$-0.269248\pi$
$620$	−16.2300			−0.651813
$621$	3.98730	+	2.66485i	0.160005	+	0.106937i
$622$	5.58204			0.223820
$623$	3.41161	−	23.7283i	0.136683	−	0.950653i
$624$	−5.08717	−	11.1393i	−0.203650	−	0.445930i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	9.92844	+	11.4580i	0.396820	+	0.457955i
$627$	−0.337530	+	0.0991079i	−0.0134797	+	0.00395799i
$628$	−6.49814	−	4.17610i	−0.259304	−	0.166645i
$629$	0.350171	−	0.766768i	0.0139622	−	0.0305731i
$630$	4.94309	−	5.70463i	0.196937	−	0.227278i
$631$	39.1991	−	25.1917i	1.56049	−	1.00287i	0.578112	−	0.815957i	$-0.303790\pi$
$631$	39.1991	−	25.1917i	1.56049	−	1.00287i	0.982377	−	0.186909i	$-0.0598468\pi$
$632$	0.316334	+	2.20015i	0.0125831	+	0.0875173i
$633$	−3.23952	−	22.5314i	−0.128759	−	0.895541i
$634$	28.0731	−	18.0415i	1.11492	−	0.716518i
$635$	4.53200	−	5.23021i	0.179847	−	0.207554i
$636$	−0.443163	+	0.970392i	−0.0175726	+	0.0384785i
$637$	18.8628	+	12.1224i	0.747372	+	0.480307i
$638$	−9.39503	+	2.75863i	−0.371953	+	0.109215i
$639$	−6.82592	−	7.87753i	−0.270029	−	0.311630i
$640$	−2.40926	−	0.707423i	−0.0952344	−	0.0279633i
$641$	−11.1088	−	24.3248i	−0.438769	−	0.960771i	−0.991823	−	0.127625i	$-0.959265\pi$
$641$	−11.1088	−	24.3248i	−0.438769	−	0.960771i	0.553053	−	0.833146i	$-0.313463\pi$
$642$	−1.71505	+	11.9284i	−0.0676875	+	0.470777i
$643$	−33.8003			−1.33295			−0.666476	−	0.745527i	$-0.732198\pi$
$643$	−33.8003			−1.33295			−0.666476	+	0.745527i	$0.732198\pi$
$644$	15.2680	+	35.0862i	0.601644	+	1.38259i
$645$	7.15294			0.281647
$646$	0.0238826	−	0.166107i	0.000939647	−	0.00653539i
$647$	1.67041	+	3.65768i	0.0656705	+	0.143798i	0.939621	−	0.342216i	$-0.111178\pi$
$647$	1.67041	+	3.65768i	0.0656705	+	0.143798i	−0.873951	+	0.486014i	$0.838450\pi$
$648$	−0.302058	−	0.0886923i	−0.0118660	−	0.00348416i
$649$	−5.30437	−	6.12157i	−0.208215	−	0.240292i
$650$	−6.53060	+	1.91756i	−0.256151	+	0.0752127i
$651$	23.4694	+	15.0829i	0.919838	+	0.591144i
$652$	6.82213	−	14.9384i	0.267175	−	0.585032i
$653$	10.8629	−	12.5365i	0.425099	−	0.490590i	−0.502285	−	0.864702i	$-0.667507\pi$
$653$	10.8629	−	12.5365i	0.425099	−	0.490590i	0.927384	+	0.374112i	$0.122052\pi$
$654$	−32.0843	+	20.6193i	−1.25459	+	0.806279i
$655$	−2.45288	−	17.0601i	−0.0958419	−	0.666595i
$656$	−2.38176	−	16.5655i	−0.0929921	−	0.646774i
$657$	−3.24020	+	2.08235i	−0.126412	+	0.0812402i
$658$	−36.5512	+	42.1823i	−1.42491	+	1.64444i
$659$	7.31943	−	16.0273i	0.285125	−	0.624336i	−0.711827	−	0.702355i	$-0.752132\pi$
$659$	7.31943	−	16.0273i	0.285125	−	0.624336i	0.996952	+	0.0780187i	$0.0248594\pi$
$660$	−1.22450	−	0.786937i	−0.0476635	−	0.0306315i
$661$	18.7059	−	5.49254i	0.727574	−	0.213635i	0.103089	−	0.994672i	$-0.467127\pi$
$661$	18.7059	−	5.49254i	0.727574	−	0.213635i	0.624484	+	0.781037i	$0.285309\pi$
$662$	4.02637	+	4.64668i	0.156489	+	0.180598i
$663$	0.506633	+	0.148761i	0.0196760	+	0.00577739i
$664$	−0.243651	−	0.533522i	−0.00945550	−	0.0207047i
$665$	0.274422	−	1.90865i	0.0106416	−	0.0740143i
$666$	−10.8657			−0.421037
$667$	34.0956	+	0.612314i	1.32019	+	0.0237089i
$668$	7.42950			0.287456
$669$	1.54040	−	10.7137i	0.0595554	−	0.414217i
$670$	−12.0972	−	26.4891i	−0.467355	−	1.02336i
$671$	5.37284	+	1.57761i	0.207416	+	0.0609029i
$672$	19.6544	+	22.6824i	0.758187	+	0.874994i
$673$	23.9089	−	7.02029i	0.921621	−	0.270612i	0.213696	−	0.976900i	$-0.431450\pi$
$673$	23.9089	−	7.02029i	0.921621	−	0.270612i	0.707925	+	0.706288i	$0.249632\pi$
$674$	−46.3767	−	29.8045i	−1.78636	−	1.14803i
$675$	0.415415	−	0.909632i	0.0159893	−	0.0350118i
$676$	2.60889	−	3.01082i	0.100342	−	0.115801i
$677$	16.4292	−	10.5584i	0.631425	−	0.405792i	−0.185412	−	0.982661i	$-0.559362\pi$
$677$	16.4292	−	10.5584i	0.631425	−	0.405792i	0.816837	+	0.576869i	$0.195726\pi$
$678$	0.172654	+	1.20084i	0.00663075	+	0.0461179i
$679$	2.43192	+	16.9144i	0.0933286	+	0.649114i
$680$	0.0418768	−	0.0269126i	0.00160590	−	0.00103205i
$681$	11.4043	−	13.1612i	0.437013	−	0.504340i
$682$	4.30939	−	9.43625i	0.165015	−	0.361333i
$683$	−30.7013	−	19.7305i	−1.17475	−	0.754968i	−0.200338	−	0.979727i	$-0.564204\pi$
$683$	−30.7013	−	19.7305i	−1.17475	−	0.754968i	−0.974414	+	0.224759i	$0.927840\pi$
$684$	−1.07635	+	0.316046i	−0.0411554	+	0.0120843i
$685$	9.52195	+	10.9889i	0.363815	+	0.419865i
$686$	2.06643	+	0.606760i	0.0788968	+	0.0231662i
$687$	−4.62385	−	10.1248i	−0.176411	−	0.386286i
$688$	−3.73314	+	25.9646i	−0.142325	+	0.989890i
$689$	−1.65348			−0.0629925
$690$	6.26764	+	7.50127i	0.238605	+	0.285568i
$691$	−33.3189			−1.26751			−0.633755	−	0.773533i	$-0.718487\pi$
$691$	−33.3189			−1.26751			−0.633755	+	0.773533i	$0.718487\pi$
$692$	5.39236	−	37.5047i	0.204987	−	1.42571i
$693$	1.03937	+	2.27590i	0.0394823	+	0.0864543i
$694$	45.9099	+	13.4804i	1.74272	+	0.511707i
$695$	−1.01139	−	1.16720i	−0.0383641	−	0.0442746i
$696$	−2.14781	+	0.630654i	−0.0814125	+	0.0239049i
$697$	0.607061	+	0.390135i	0.0229941	+	0.0147774i
$698$	7.61924	−	16.6838i	0.288393	−	0.631492i
$699$	−13.5188	+	15.6015i	−0.511328	+	0.590104i
$700$	6.71207	−	4.31359i	0.253692	−	0.163038i
$701$	6.90764	+	48.0437i	0.260898	+	1.81459i	0.526133	+	0.850402i	$0.323641\pi$
$701$	6.90764	+	48.0437i	0.260898	+	1.81459i	−0.265235	+	0.964184i	$0.585449\pi$
$702$	−0.968637	−	6.73702i	−0.0365589	−	0.254272i
$703$	−2.33509	+	1.50067i	−0.0880697	+	0.0565990i
$704$	4.06336	−	4.68937i	0.153144	−	0.176737i
$705$	−3.07174	+	6.72618i	−0.115689	+	0.253323i
$706$	11.2422	+	7.22494i	0.423107	+	0.271914i
$707$	−36.9975	+	10.8634i	−1.39143	+	0.408562i
$708$	−16.9151	−	19.5211i	−0.635710	−	0.733649i
$709$	−5.78022	−	1.69723i	−0.217081	−	0.0637406i	0.171384	−	0.985204i	$-0.445176\pi$
$709$	−5.78022	−	1.69723i	−0.217081	−	0.0637406i	−0.388464	+	0.921464i	$0.626994\pi$
$710$	−8.82575	−	19.3257i	−0.331224	−	0.725280i
$711$	1.00484	−	6.98881i	0.0376844	−	0.262101i
$712$	−2.03782			−0.0763705
$713$	−24.1454	+	26.8746i	−0.904252	+	1.00646i
$714$	−1.19357			−0.0446682
$715$	0.321069	−	2.23309i	0.0120073	−	0.0835127i
$716$	17.7781	+	38.9286i	0.664399	+	1.45483i
$717$	−10.0351	−	2.94656i	−0.374767	−	0.110041i
$718$	−17.8792	−	20.6336i	−0.667244	−	0.770041i
$719$	16.2533	−	4.77239i	0.606145	−	0.177980i	0.0357637	−	0.999360i	$-0.488614\pi$
$719$	16.2533	−	4.77239i	0.606145	−	0.177980i	0.570381	+	0.821380i	$0.306795\pi$
$720$	3.08508	+	1.98266i	0.114974	+	0.0738894i
$721$	22.9093	−	50.1643i	0.853187	−	1.86822i
$722$	24.9987	−	28.8501i	0.930356	−	1.07369i
$723$	−11.7498	+	7.55115i	−0.436980	+	0.280830i
$724$	−1.38053	−	9.60177i	−0.0513069	−	0.356847i
$725$	−1.01194	−	7.03820i	−0.0375825	−	0.261392i
$726$	−18.0788	+	11.6186i	−0.670969	+	0.431206i
$727$	−21.9285	+	25.3068i	−0.813282	+	0.938577i	−0.999031	−	0.0440200i	$-0.985983\pi$
$727$	−21.9285	+	25.3068i	−0.813282	+	0.938577i	0.185749	+	0.982597i	$0.440529\pi$
$728$	1.61725	−	3.54129i	0.0599394	−	0.131249i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−7.53258	+	2.21176i	−0.278793	+	0.0818611i
$731$	−0.740681	−	0.854792i	−0.0273951	−	0.0316156i
$732$	17.1335	+	5.03085i	0.633273	+	0.185946i
$733$	−2.52739	−	5.53420i	−0.0933511	−	0.204410i	0.857196	−	0.514990i	$-0.172204\pi$
$733$	−2.52739	−	5.53420i	−0.0933511	−	0.204410i	−0.950547	+	0.310579i	$0.899477\pi$
$734$	6.64687	−	46.2300i	0.245340	−	1.70638i
$735$	−6.71468			−0.247675
$736$	−33.0692	+	20.4227i	−1.21895	+	0.752790i
$737$	9.65250			0.355554
$738$	1.32378	−	9.20708i	0.0487289	−	0.338917i
$739$	9.19234	+	20.1284i	0.338146	+	0.740436i	0.999957	−	0.00923436i	$-0.00293943\pi$
$739$	9.19234	+	20.1284i	0.338146	+	0.740436i	−0.661812	+	0.749670i	$0.730212\pi$
$740$	−11.0199	−	3.23575i	−0.405101	−	0.118948i
$741$	−1.13862	−	1.31404i	−0.0418283	−	0.0482725i
$742$	3.58621	−	1.05301i	0.131654	−	0.0386571i
$743$	21.2982	+	13.6875i	0.781354	+	0.502146i	0.869483	−	0.493963i	$-0.164452\pi$
$743$	21.2982	+	13.6875i	0.781354	+	0.502146i	−0.0881288	+	0.996109i	$0.528089\pi$
$744$	0.985175	−	2.15723i	0.0361183	−	0.0790880i
$745$	13.8153	−	15.9437i	0.506154	−	0.584133i
$746$	−38.4961	+	24.7399i	−1.40944	+	0.905794i
$747$	0.265148	+	1.84414i	0.00970124	+	0.0674736i
$748$	0.0327551	+	0.227817i	0.00119765	+	0.00832981i
$749$	18.4200	−	11.8378i	0.673051	−	0.432543i
$750$	1.33477	−	1.54040i	0.0487388	−	0.0562476i
$751$	16.6443	−	36.4460i	0.607361	−	1.32993i	−0.317004	−	0.948424i	$-0.602677\pi$
$751$	16.6443	−	36.4460i	0.607361	−	1.32993i	0.924365	−	0.381510i	$-0.124596\pi$
$752$	−22.8123	−	14.6606i	−0.831880	−	0.534617i
$753$	−14.0242	+	4.11789i	−0.511072	+	0.150064i
$754$	−31.6931	−	36.5758i	−1.15420	−	1.33201i
$755$	−19.2921	−	5.66466i	−0.702110	−	0.206158i
$756$	3.31445	+	7.25764i	0.120545	+	0.263958i
$757$	6.37004	−	44.3046i	0.231523	−	1.61028i	−0.459996	−	0.887921i	$-0.652149\pi$
$757$	6.37004	−	44.3046i	0.231523	−	1.61028i	0.691519	−	0.722358i	$-0.256942\pi$
$758$	7.54229			0.273948
$759$	−3.12474	+	0.856873i	−0.113421	+	0.0311025i
$760$	−0.163918			−0.00594592
$761$	−4.95599	+	34.4696i	−0.179654	+	1.24952i	0.677909	+	0.735146i	$0.262886\pi$
$761$	−4.95599	+	34.4696i	−0.179654	+	1.24952i	−0.857564	+	0.514378i	$0.828023\pi$
$762$	5.85976	+	12.8311i	0.212277	+	0.464821i
$763$	66.4880	+	19.5226i	2.40703	+	0.706766i
$764$	19.5091	+	22.5147i	0.705815	+	0.814554i
$765$	−0.151719	+	0.0445487i	−0.00548540	+	0.00161066i
$766$	25.6434	+	16.4800i	0.926534	+	0.595447i
$767$	16.6313	−	36.4175i	0.600522	−	1.31496i
$768$	−8.67720	+	10.0140i	−0.313111	+	0.361350i
$769$	9.08470	−	5.83838i	0.327603	−	0.210537i	−0.366492	−	0.930421i	$-0.619441\pi$
$769$	9.08470	−	5.83838i	0.327603	−	0.210537i	0.694095	+	0.719884i	$0.255805\pi$
$770$	0.725762	+	5.04779i	0.0261547	+	0.181910i
$771$	3.25254	+	22.6219i	0.117137	+	0.814709i
$772$	7.00630	−	4.50267i	0.252162	−	0.162055i
$773$	−13.1087	+	15.1282i	−0.471486	+	0.544124i	−0.940824	−	0.338895i	$-0.889947\pi$
$773$	−13.1087	+	15.1282i	−0.471486	+	0.544124i	0.469338	+	0.883018i	$0.344492\pi$
$774$	−6.05653	+	13.2619i	−0.217697	+	0.476691i
$775$	6.33737	+	4.07278i	0.227645	+	0.146299i
$776$	1.39379	−	0.409254i	0.0500341	−	0.0146913i
$777$	12.9283	+	14.9201i	0.463802	+	0.535255i
$778$	26.1881	+	7.68952i	0.938889	+	0.275683i
$779$	−0.987113	−	2.16148i	−0.0353670	−	0.0774429i
$780$	1.02386	−	7.12111i	0.0366601	−	0.254977i
$781$	7.04218			0.251989
$782$	0.247408	−	1.52575i	0.00884731	−	0.0545606i
$783$	7.11058			0.254111
$784$	3.50441	−	24.3737i	0.125158	−	0.870490i
$785$	1.48939	+	3.26130i	0.0531585	+	0.116401i
$786$	33.7073	+	9.89737i	1.20230	+	0.353027i
$787$	−1.88795	−	2.17881i	−0.0672981	−	0.0776661i	0.721102	−	0.692829i	$-0.243636\pi$
$787$	−1.88795	−	2.17881i	−0.0672981	−	0.0776661i	−0.788400	+	0.615163i	$0.789090\pi$
$788$	−0.645751	+	0.189610i	−0.0230039	+	0.00675456i
$789$	17.8959	+	11.5010i	0.637110	+	0.409446i
$790$	5.97841	−	13.0909i	0.212702	−	0.465753i
$791$	1.44349	−	1.66587i	0.0513245	−	0.0592316i
$792$	0.178925	−	0.114988i	0.00635782	−	0.00408592i
$793$	3.93888	+	27.3955i	0.139874	+	0.972842i
$794$	0.0451036	+	0.313702i	0.00160067	+	0.0111329i
$795$	0.416554	−	0.267703i	0.0147737	−	0.00949445i
$796$	−22.0473	+	25.4439i	−0.781445	+	0.901835i
$797$	−16.9607	+	37.1387i	−0.600778	+	1.31552i	0.327927	+	0.944703i	$0.393650\pi$
$797$	−16.9607	+	37.1387i	−0.600778	+	1.31552i	−0.928705	+	0.370818i	$0.879077\pi$
$798$	3.30638	+	2.12488i	0.117045	+	0.0752201i
$799$	1.12187	−	0.329411i	0.0396889	−	0.0116537i
$800$	5.30723	+	6.12487i	0.187639	+	0.216547i
$801$	6.21095	+	1.82370i	0.219453	+	0.0644373i
$802$	−24.7620	−	54.2211i	−0.874375	−	1.91461i
$803$	0.370331	−	2.57571i	0.0130687	−	0.0908947i
$804$	30.7810			1.08556
$805$	2.84284	−	17.5316i	0.100197	−	0.617907i
$806$	51.2735			1.80603
$807$	1.53245	−	10.6584i	0.0539448	−	0.375194i
$808$	1.36166	+	2.98162i	0.0479030	+	0.104893i
$809$	18.9816	+	5.57350i	0.667358	+	0.195954i	0.597826	−	0.801626i	$-0.296031\pi$
$809$	18.9816	+	5.57350i	0.667358	+	0.195954i	0.0695316	+	0.997580i	$0.477850\pi$
$810$	1.33477	+	1.54040i	0.0468990	+	0.0541243i
$811$	22.3016	−	6.54835i	0.783117	−	0.229944i	0.134353	−	0.990934i	$-0.457104\pi$
$811$	22.3016	−	6.54835i	0.783117	−	0.229944i	0.648764	+	0.760990i	$0.275286\pi$
$812$	47.7267	+	30.6721i	1.67488	+	1.07638i
$813$	−12.2359	+	26.7928i	−0.429131	+	0.939665i
$814$	4.80730	−	5.54792i	0.168496	−	0.194454i
$815$	−6.41251	+	4.12107i	−0.224620	+	0.144355i
$816$	−0.0825253	−	0.573976i	−0.00288896	−	0.0200932i
$817$	0.530043	+	3.68653i	0.0185439	+	0.128975i
$818$	19.8914	−	12.7834i	0.695488	−	0.446963i
$819$	−8.09834	+	9.34598i	−0.282979	+	0.326575i
$820$	4.08439	−	8.94356i	0.142633	−	0.312323i
$821$	−44.9160	−	28.8658i	−1.56758	−	1.00742i	−0.980176	−	0.198127i	$-0.936514\pi$
$821$	−44.9160	−	28.8658i	−1.56758	−	1.00742i	−0.587402	−	0.809295i	$-0.699849\pi$
$822$	−28.4365	+	8.34970i	−0.991836	+	0.291229i
$823$	−2.08620	−	2.40760i	−0.0727203	−	0.0839237i	0.718224	−	0.695812i	$-0.244956\pi$
$823$	−2.08620	−	2.40760i	−0.0727203	−	0.0839237i	−0.790944	+	0.611889i	$0.790410\pi$
$824$	−4.49808	−	1.32076i	−0.156698	−	0.0460107i
$825$	0.280658	+	0.614554i	0.00977124	+	0.0213960i
$826$	−12.8792	+	89.5770i	−0.448126	+	3.11678i
$827$	−7.66506			−0.266540			−0.133270	−	0.991080i	$-0.542548\pi$
$827$	−7.66506			−0.266540			−0.133270	+	0.991080i	$0.542548\pi$
$828$	−9.96452	+	2.73249i	−0.346291	+	0.0949606i
$829$	−29.2882			−1.01722			−0.508610	−	0.860997i	$-0.669840\pi$
$829$	−29.2882			−1.01722			−0.508610	+	0.860997i	$0.669840\pi$
$830$	−0.540436	+	3.75882i	−0.0187588	+	0.130470i
$831$	4.52547	+	9.90940i	0.156987	+	0.343753i
$832$	29.4265	+	8.64039i	1.02018	+	0.299552i
$833$	0.695300	+	0.802418i	0.0240907	+	0.0278022i
$834$	3.02042	−	0.886876i	0.104589	−	0.0307100i
$835$	−2.90101	−	1.86437i	−0.100394	−	0.0645192i
$836$	0.314840	−	0.689404i	0.0108890	−	0.0238435i
$837$	−4.93323	+	5.69325i	−0.170517	+	0.196787i
$838$	43.2370	−	27.7867i	1.49360	−	0.959877i
$839$	−1.37230	−	9.54457i	−0.0473771	−	0.329515i	−0.999702	−	0.0244280i	$-0.992224\pi$
$839$	−1.37230	−	9.54457i	−0.0473771	−	0.329515i	0.952324	−	0.305087i	$-0.0986855\pi$
$840$	0.165917	+	1.15398i	0.00572470	+	0.0398161i
$841$	18.1377	−	11.6564i	0.625438	−	0.401945i
$842$	−28.6485	+	33.0621i	−0.987293	+	1.13940i
$843$	9.86378	−	21.5987i	0.339727	−	0.743898i
$844$	41.2567	+	26.5141i	1.42011	+	0.912651i
$845$	−1.77424	+	0.520963i	−0.0610357	+	0.0179217i
$846$	−9.86981	−	11.3904i	−0.339331	−	0.391609i
$847$	37.4647	+	11.0006i	1.28730	+	0.377986i
$848$	0.754339	+	1.65177i	0.0259041	+	0.0567221i
$849$	1.80692	−	12.5674i	0.0620134	−	0.431312i
$850$	−0.322296			−0.0110546
$851$	−21.7523	+	13.4337i	−0.745659	+	0.460500i
$852$	22.4569			0.769360
$853$	0.364778	−	2.53709i	0.0124898	−	0.0868682i	−0.982623	−	0.185612i	$-0.940573\pi$
$853$	0.364778	−	2.53709i	0.0124898	−	0.0868682i	0.995113	+	0.0987437i	$0.0314824\pi$
$854$	−25.9896	−	56.9093i	−0.889346	−	1.94740i
$855$	0.499595	+	0.146694i	0.0170858	+	0.00501684i
$856$	−1.21890	−	1.40668i	−0.0416610	−	0.0480794i
$857$	−17.9082	+	5.25832i	−0.611732	+	0.179621i	−0.572900	−	0.819625i	$-0.694182\pi$
$857$	−17.9082	+	5.25832i	−0.611732	+	0.179621i	−0.0388318	+	0.999246i	$0.512364\pi$
$858$	3.86841	+	2.48608i	0.132065	+	0.0848732i
$859$	9.64206	−	21.1132i	0.328983	−	0.720372i	−0.670791	−	0.741646i	$-0.734045\pi$
$859$	9.64206	−	21.1132i	0.328983	−	0.720372i	0.999774	+	0.0212748i	$0.00677249\pi$
$860$	−10.0918	+	11.6466i	−0.344129	+	0.397146i
$861$	−14.2177	+	9.13713i	−0.484536	+	0.311393i
$862$	4.61214	+	32.0782i	0.157090	+	1.09259i
$863$	4.92719	+	34.2693i	0.167723	+	1.16654i	0.883575	+	0.468289i	$0.155130\pi$
$863$	4.92719	+	34.2693i	0.167723	+	1.16654i	−0.715852	+	0.698252i	$0.753961\pi$
$864$	−6.81783	+	4.38155i	−0.231947	+	0.149063i
$865$	−11.5170	+	13.2914i	−0.391591	+	0.451920i
$866$	15.5266	−	33.9986i	0.527617	−	1.15532i
$867$	−14.2803	−	9.17738i	−0.484984	−	0.311680i
$868$	−57.6705	+	16.9336i	−1.95746	+	0.574763i
$869$	3.12385	+	3.60511i	0.105969	+	0.122295i
$870$	13.9060	+	4.08318i	0.471459	+	0.138433i
$871$	19.8190	+	43.3975i	0.671541	+	1.47047i
$872$	0.838316	−	5.83061i	0.0283890	−	0.197450i
$873$	−4.61431			−0.156171
$874$	−3.40162	+	3.78612i	−0.115061	+	0.128067i
$875$	−3.70333			−0.125196
$876$	1.18095	−	8.21370i	0.0399006	−	0.277515i
$877$	−0.574320	−	1.25758i	−0.0193934	−	0.0424656i	0.899687	−	0.436535i	$-0.143794\pi$
$877$	−0.574320	−	1.25758i	−0.0193934	−	0.0424656i	−0.919081	+	0.394069i	$0.871067\pi$
$878$	−80.2049	−	23.5503i	−2.70679	−	0.794784i
$879$	5.63780	+	6.50637i	0.190158	+	0.219454i
$880$	−2.37726	+	0.698025i	−0.0801373	+	0.0235304i
$881$	−16.9143	−	10.8701i	−0.569856	−	0.366224i	0.223759	−	0.974644i	$-0.428167\pi$
$881$	−16.9143	−	10.8701i	−0.569856	−	0.366224i	−0.793615	+	0.608420i	$0.791803\pi$
$882$	5.68544	−	12.4494i	0.191439	−	0.419193i
$883$	−15.6559	+	18.0678i	−0.526861	+	0.608030i	−0.955335	−	0.295524i	$-0.904506\pi$
$883$	−15.6559	+	18.0678i	−0.526861	+	0.608030i	0.428474	+	0.903554i	$0.359051\pi$
$884$	−0.957008	+	0.615031i	−0.0321876	+	0.0206857i
$885$	1.70624	+	11.8672i	0.0573547	+	0.398910i
$886$	4.31848	+	30.0357i	0.145082	+	1.00907i
$887$	1.70383	−	1.09498i	0.0572089	−	0.0367659i	−0.511724	−	0.859150i	$-0.670993\pi$
$887$	1.70383	−	1.09498i	0.0572089	−	0.0367659i	0.568933	+	0.822384i	$0.307356\pi$
$888$	1.09900	−	1.26832i	0.0368801	−	0.0425619i
$889$	10.6467	−	23.3131i	0.357080	−	0.781895i
$890$	11.0994	+	7.13316i	0.372053	+	0.239104i
$891$	−0.648241	+	0.190341i	−0.0217169	+	0.00637665i
$892$	15.2711	+	17.6238i	0.511314	+	0.590088i
$893$	−3.69421	−	1.08472i	−0.123622	−	0.0362987i
$894$	17.8628	+	39.1142i	0.597423	+	1.30817i
$895$	2.82694	−	19.6618i	0.0944942	−	0.657221i
$896$	−9.29897			−0.310657
$897$	−10.2684	−	12.2894i	−0.342851	−	0.410332i
$898$	−43.0982			−1.43820
$899$	−7.62320	+	53.0205i	−0.254248	+	1.76833i
$900$	0.894992	+	1.95976i	0.0298331	+	0.0653253i
$901$	−0.0751249	−	0.0220587i	−0.00250277	−	0.000734881i
$902$	4.11537	+	4.74939i	0.137027	+	0.158137i
$903$	25.4167	−	7.46302i	0.845815	−	0.248354i
$904$	−0.157633	−	0.101304i	−0.00524279	−	0.00336934i
$905$	−1.87042	+	4.09566i	−0.0621750	+	0.136144i
$906$	26.8375	−	30.9722i	0.891618	−	1.02898i
$907$	−8.22048	+	5.28298i	−0.272956	+	0.175418i	−0.669957	−	0.742400i	$-0.733687\pi$
$907$	−8.22048	+	5.28298i	−0.272956	+	0.175418i	0.397001	+	0.917818i	$0.370051\pi$
$908$	5.33957	+	37.1375i	0.177200	+	1.23245i
$909$	−1.48179	−	10.3061i	−0.0491480	−	0.341832i
$910$	−21.2046	+	13.6274i	−0.702927	+	0.451744i
$911$	0.133940	−	0.154576i	0.00443765	−	0.00512132i	−0.753526	−	0.657418i	$-0.771649\pi$
$911$	0.133940	−	0.154576i	0.00443765	−	0.00512132i	0.757964	+	0.652296i	$0.226194\pi$
$912$	−0.793228	+	1.73693i	−0.0262664	+	0.0575154i
$913$	−1.05891	−	0.680520i	−0.0350448	−	0.0225219i
$914$	57.2510	−	16.8104i	1.89370	−	0.556039i
$915$	−5.42771	−	6.26392i	−0.179435	−	0.207079i
$916$	23.0091	+	6.75608i	0.760242	+	0.223227i
$917$	−26.5156	−	58.0610i	−0.875621	−	1.91734i
$918$	0.0458675	−	0.319015i	0.00151385	−	0.0105291i
$919$	52.8913			1.74472			0.872362	−	0.488860i	$-0.162587\pi$
$919$	52.8913			1.74472			0.872362	+	0.488860i	$0.162587\pi$
$920$	−1.50953	−	0.0271093i	−0.0497679	−	0.000893767i
$921$	−25.8810			−0.852809
$922$	−10.9757	+	76.3374i	−0.361464	+	2.51404i
$923$	14.4593	+	31.6616i	0.475935	+	1.04215i
$924$	−5.17209	−	1.51866i	−0.170149	−	0.0499603i
$925$	3.49100	+	4.02883i	0.114783	+	0.132467i
$926$	−46.4890	+	13.6504i	−1.52772	+	0.448580i
$927$	12.5275	+	8.05092i	0.411456	+	0.264427i
$928$	−23.9390	+	52.4191i	−0.785837	+	1.72074i
$929$	17.1689	−	19.8140i	0.563293	−	0.650075i	−0.400635	−	0.916238i	$-0.631210\pi$
$929$	17.1689	−	19.8140i	0.563293	−	0.650075i	0.963928	+	0.266163i	$0.0857559\pi$
$930$	−12.9171	+	8.30134i	−0.423569	+	0.272212i
$931$	−0.497568	−	3.46066i	−0.0163071	−	0.113419i
$932$	−6.32960	−	44.0233i	−0.207333	−	1.44203i
$933$	2.30390	−	1.48063i	0.0754262	−	0.0484735i
$934$	39.7869	−	45.9166i	1.30187	−	1.50244i
$935$	0.0443787	−	0.0971757i	0.00145134	−	0.00317799i
$936$	0.884362	+	0.568345i	0.0289063	+	0.0185769i
$937$	−39.1271	+	11.4888i	−1.27823	+	0.375322i	−0.849249	−	0.527993i	$-0.822945\pi$
$937$	−39.1271	+	11.4888i	−1.27823	+	0.375322i	−0.428979	+	0.903314i	$0.641127\pi$
$938$	−70.6226	−	81.5029i	−2.30591	−	2.66116i
$939$	7.13702	+	2.09562i	0.232908	+	0.0683879i
$940$	−6.61793	−	14.4912i	−0.215853	−	0.472652i
$941$	2.96621	−	20.6305i	0.0966958	−	0.672534i	−0.882604	−	0.470118i	$-0.844211\pi$
$941$	2.96621	−	20.6305i	0.0966958	−	0.672534i	0.979300	−	0.202417i	$-0.0648795\pi$
$942$	−7.30773			−0.238099
$943$	−8.73295	−	20.0685i	−0.284384	−	0.653521i
$944$	−43.9673			−1.43101
$945$	0.527039	−	3.66564i	0.0171446	−	0.119243i
$946$	−4.09184	−	8.95987i	−0.133037	−	0.291311i
$947$	37.9881	+	11.1543i	1.23445	+	0.362467i	0.832927	−	0.553383i	$-0.186663\pi$
$947$	37.9881	+	11.1543i	1.23445	+	0.362467i	0.401521	+	0.915850i	$0.368482\pi$
$948$	9.96167	+	11.4964i	0.323540	+	0.373385i
$949$	12.3407	−	3.62357i	0.400597	−	0.117626i
$950$	0.892813	+	0.573776i	0.0289667	+	0.0186157i
$951$	6.80124	−	14.8926i	0.220545	−	0.482927i
$952$	0.120723	−	0.139321i	0.00391264	−	0.00451543i
$953$	−14.8551	+	9.54678i	−0.481203	+	0.309251i	−0.758659	−	0.651488i	$-0.774145\pi$
$953$	−14.8551	+	9.54678i	−0.481203	+	0.309251i	0.277456	+	0.960738i	$0.410509\pi$
$954$	0.143632	+	0.998984i	0.00465026	+	0.0323433i
$955$	−1.96790	−	13.6870i	−0.0636796	−	0.442901i
$956$	18.9558	−	12.1822i	0.613075	−	0.393999i
$957$	−3.14593	+	3.63059i	−0.101693	+	0.117360i
$958$	0.988769	−	2.16510i	0.0319457	−	0.0699513i
$959$	45.2998	+	29.1124i	1.46281	+	0.940090i
$960$	−8.81219	+	2.58749i	−0.284412	+	0.0835110i
$961$	−16.8625	−	19.4604i	−0.543953	−	0.627755i
$962$	34.8140	+	10.2223i	1.12245	+	0.329580i
$963$	2.45613	+	5.37817i	0.0791477	+	0.173309i
$964$	4.28244	−	29.7850i	0.137928	−	0.959310i
$965$	−3.86567			−0.124440
$966$	30.0974	+	20.1151i	0.968368	+	0.647192i
$967$	2.16743			0.0696999			0.0348500	−	0.999393i	$-0.488905\pi$
$967$	2.16743			0.0696999			0.0348500	+	0.999393i	$0.488905\pi$
$968$	0.472374	−	3.28544i	0.0151827	−	0.105598i
$969$	−0.0342024	−	0.0748928i	−0.00109874	−	0.00240590i
$970$	−9.02412	−	2.64972i	−0.289747	−	0.0850774i
$971$	5.99614	+	6.91991i	0.192425	+	0.222070i	0.843761	−	0.536719i	$-0.180337\pi$
$971$	5.99614	+	6.91991i	0.192425	+	0.222070i	−0.651336	+	0.758790i	$0.725791\pi$
$972$	−2.06718	+	0.606979i	−0.0663049	+	0.0194689i
$973$	−4.81159	−	3.09222i	−0.154252	−	0.0991320i
$974$	−21.5432	+	47.1731i	−0.690289	+	1.51152i
$975$	−2.18677	+	2.52367i	−0.0700327	+	0.0808220i
$976$	25.5702	−	16.4330i	0.818483	−	0.526007i
$977$	4.47262	+	31.1078i	0.143092	+	0.995226i	0.927191	+	0.374590i	$0.122216\pi$
$977$	4.47262	+	31.1078i	0.143092	+	0.995226i	−0.784099	+	0.620636i	$0.786874\pi$
$978$	−2.21110	−	15.3785i	−0.0707032	−	0.491751i
$979$	−3.67907	+	2.36439i	−0.117584	+	0.0755663i
$980$	9.47351	−	10.9330i	0.302620	−	0.349242i
$981$	−7.77303	+	17.0206i	−0.248174	+	0.543425i
$982$	1.91525	+	1.23086i	0.0611181	+	0.0392782i
$983$	−32.5046	+	9.54421i	−1.03674	+	0.304413i	−0.755447	−	0.655210i	$-0.772580\pi$
$983$	−32.5046	+	9.54421i	−1.03674	+	0.304413i	−0.281289	+	0.959623i	$0.590762\pi$
$984$	0.940819	+	1.08576i	0.0299922	+	0.0346129i
$985$	0.299729	+	0.0880083i	0.00955015	+	0.00280418i
$986$	−0.952010	−	2.08461i	−0.0303182	−	0.0663876i
$987$	−3.89714	+	27.1052i	−0.124047	+	0.862768i
$988$	3.74600			0.119176
$989$	4.27153	+	34.0373i	0.135827	+	1.08232i
$990$	−1.37706			−0.0437657
$991$	−6.21426	+	43.2211i	−0.197402	+	1.37296i	0.614383	+	0.789008i	$0.289405\pi$
$991$	−6.21426	+	43.2211i	−0.197402	+	1.37296i	−0.811786	+	0.583956i	$0.801504\pi$
$992$	−25.3620	−	55.5350i	−0.805244	−	1.76324i
$993$	2.89434	+	0.849855i	0.0918492	+	0.0269693i
$994$	−51.5242	−	59.4621i	−1.63425	−	1.88602i
$995$	14.9938	−	4.40257i	0.475335	−	0.139571i
$996$	−3.37677	−	2.17012i	−0.106997	−	0.0687628i
$997$	4.61575	−	10.1071i	0.146182	−	0.320094i	−0.822350	−	0.568982i	$-0.807338\pi$
$997$	4.61575	−	10.1071i	0.146182	−	0.320094i	0.968532	+	0.248887i	$0.0800648\pi$
$998$	56.6103	−	65.3317i	1.79197	−	2.06804i
$999$	−4.48464	+	2.88210i	−0.141888	+	0.0911857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.c.31.2	✓	50
23.3	even	11	inner	345.2.m.c.256.2	yes	50
23.7	odd	22		7935.2.a.bw.1.20		25
23.16	even	11		7935.2.a.bv.1.20		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.31.2	✓	50	1.1	even	1	trivial
345.2.m.c.256.2	yes	50	23.3	even	11	inner
7935.2.a.bv.1.20		25	23.16	even	11
7935.2.a.bw.1.20		25	23.7	odd	22

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.290073 + 2.01750i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-2.06718 - 0.606979i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-1.95568 + 0.574241i) q^{6} +(3.11544 + 2.00217i) q^{7} +(0.130777 - 0.286362i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.290073 + 2.01750i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-2.06718 - 0.606979i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-1.95568 + 0.574241i) q^{6} +(3.11544 + 2.00217i) q^{7} +(0.130777 - 0.286362i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-1.71468 + 1.10196i) q^{10} +(-0.0961490 - 0.668731i) q^{11} +(-0.306610 - 2.13252i) q^{12} +(2.80919 - 1.80536i) q^{13} +(-4.94309 + 5.70463i) q^{14} +(-0.415415 + 0.909632i) q^{15} +(-3.08508 - 1.98266i) q^{16} +(0.151719 - 0.0445487i) q^{17} +(-1.33477 - 1.54040i) q^{18} +(-0.499595 - 0.146694i) q^{19} +(-0.894992 - 1.95976i) q^{20} +(-0.527039 + 3.66564i) q^{21} +1.37706 q^{22} +(-4.57656 - 1.43355i) q^{23} +0.314810 q^{24} +(-0.142315 + 0.989821i) q^{25} +(2.82744 + 6.19123i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-5.22491 - 6.02986i) q^{28} +(-6.82255 + 2.00328i) q^{29} +(-1.71468 - 1.10196i) q^{30} +(3.12942 - 6.85248i) q^{31} +(5.30723 - 6.12487i) q^{32} +(0.568357 - 0.365261i) q^{33} +(0.0458675 + 0.319015i) q^{34} +(0.527039 + 3.66564i) q^{35} +(1.81244 - 1.16478i) q^{36} +(3.49100 - 4.02883i) q^{37} +(0.440875 - 0.965382i) q^{38} +(2.80919 + 1.80536i) q^{39} +(0.302058 - 0.0886923i) q^{40} +(2.98853 + 3.44894i) q^{41} +(-7.24255 - 2.12660i) q^{42} +(-2.97144 - 6.50654i) q^{43} +(-0.207148 + 1.44075i) q^{44} -1.00000 q^{45} +(4.21972 - 8.81739i) q^{46} +7.39440 q^{47} +(0.521903 - 3.62991i) q^{48} +(2.78938 + 6.10789i) q^{49} +(-1.95568 - 0.574241i) q^{50} +(0.103549 + 0.119502i) q^{51} +(-6.90292 + 2.02688i) q^{52} +(-0.416554 - 0.267703i) q^{53} +(0.846718 - 1.85405i) q^{54} +(0.442429 - 0.510590i) q^{55} +(0.980774 - 0.630305i) q^{56} +(-0.0741015 - 0.515387i) q^{57} +(-2.06259 - 14.3456i) q^{58} +(10.0860 - 6.48185i) q^{59} +(1.41087 - 1.62823i) q^{60} +(-3.44310 + 7.53935i) q^{61} +(12.9171 + 8.30134i) q^{62} +(-3.55332 + 1.04335i) q^{63} +(6.01438 + 6.94097i) q^{64} +(3.20403 + 0.940787i) q^{65} +(0.572049 + 1.25261i) q^{66} +(-2.03327 + 14.1417i) q^{67} -0.340670 q^{68} +(-0.597171 - 4.75851i) q^{69} -7.54831 q^{70} +(-1.48341 + 10.3174i) q^{71} +(0.130777 + 0.286362i) q^{72} +(3.69562 + 1.08513i) q^{73} +(7.11552 + 8.21175i) q^{74} +(-0.959493 + 0.281733i) q^{75} +(0.943714 + 0.606488i) q^{76} +(1.03937 - 2.27590i) q^{77} +(-4.45718 + 5.14386i) q^{78} +(-5.93982 + 3.81729i) q^{79} +(-0.521903 - 3.62991i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-7.82514 + 5.02891i) q^{82} +(1.22007 - 1.40804i) q^{83} +(3.31445 - 7.25764i) q^{84} +(0.133022 + 0.0854882i) q^{85} +(13.9889 - 4.10751i) q^{86} +(-4.65644 - 5.37382i) q^{87} +(-0.204073 - 0.0599212i) q^{88} +(-2.68905 - 5.88819i) q^{89} +(0.290073 - 2.01750i) q^{90} +12.3665 q^{91} +(8.59045 + 5.74128i) q^{92} +7.53325 q^{93} +(-2.14491 + 14.9182i) q^{94} +(-0.216301 - 0.473633i) q^{95} +(7.77608 + 2.28326i) q^{96} +(3.02173 + 3.48726i) q^{97} +(-13.1318 + 3.85584i) q^{98} +(0.568357 + 0.365261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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